Novel Bioinspired Actuator Designs for Robotics (Studies in Computational Intelligence, 888) 303040885X, 9783030408855

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Studies in Computational Intelligence 888

Philipp Beckerle ·  Maziar Ahmad Sharbafi ·  Tom Verstraten · Peter P. Pott ·  André Seyfarth   Editors

Novel Bioinspired Actuator Designs for Robotics

Studies in Computational Intelligence Volume 888

Series Editor Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland

The series “Studies in Computational Intelligence” (SCI) publishes new developments and advances in the various areas of computational intelligence—quickly and with a high quality. The intent is to cover the theory, applications, and design methods of computational intelligence, as embedded in the fields of engineering, computer science, physics and life sciences, as well as the methodologies behind them. The series contains monographs, lecture notes and edited volumes in computational intelligence spanning the areas of neural networks, connectionist systems, genetic algorithms, evolutionary computation, artificial intelligence, cellular automata, self-organizing systems, soft computing, fuzzy systems, and hybrid intelligent systems. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution, which enable both wide and rapid dissemination of research output. Indexed by SCOPUS, DBLP, WTI Frankfurt eG, zbMATH, SCImago. All books published in the series are submitted for consideration in Web of Science.

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Philipp Beckerle · Maziar Ahmad Sharbafi · Tom Verstraten · Peter P. Pott · André Seyfarth Editors

Novel Bioinspired Actuator Designs for Robotics

Editors Philipp Beckerle Chair of Autonomous Systems and Mechatronics Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen, Germany Tom Verstraten Dienst Werktuigkunde (MECH) Vrije Universiteit Brussel and Flanders Make Brussels, Belgium

Maziar Ahmad Sharbafi Electrical and Computer Engineering Department University of Tehran School of Engineering Tehran, Iran Peter P. Pott Institute of Medical Device Technology University of Stuttgart Stuttgart, Germany

André Seyfarth Technische Universität Darmstadt Darmstadt, Germany

ISSN 1860-949X ISSN 1860-9503 (electronic) Studies in Computational Intelligence ISBN 978-3-030-40885-5 ISBN 978-3-030-40886-2 (eBook) https://doi.org/10.1007/978-3-030-40886-2 © Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

While robotic technologies have the potential to change our future lives, their research is a very challenging endeavor. This book gives an overview of approaches to endow robots with biologically inspired actuators that provide not only the performance, but also the efficiency and versatility of muscles. It provides a cutting-edge research perspective and, besides addressing researchers, aims at introducing Ph.D. students and advanced graduate students to the field. Therefore, we gathered input from leading authorities and promising young researchers who contributed their diverse points of view on the topic, covering the full spectrum from biomechanics to engineering. Looking back at this extensive project, I want to thank all contributors for their highly valuable input, their dedication, and all their efforts. Special thanks go to my fellow editors who coordinated the development of the parts and chapters. Finally, I want to admit that we are not yet there: bioinspired actuation for robotics seems to remain a research topic for quite some more decades. Dortmund, Germany

Philipp Beckerle

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Introduction

Abstract This book aims at providing an accessible introduction to the field of bioinspired actuators, which also enriches contemporary scientific discussion. After motivating the topic, we outline the structure and contents. Through evolution, muscles have been optimized to generate and fine-tune motions. They provide highly versatile force sources, i.e., they have an extremely low impedance (perfectly back-drivable), provide functional damping and low stiction. Although their bandwidth is limited, it is sufficient for even highly dynamic human/animal locomotion. Learning from biological actuators could be a shortcut to apply the advantageous principles to robotic devices, e.g., the addition of compliance to traditional rigid actuators. Elastic actuators can increase safety in human-robot interaction, improve energy efficiency, reduce impacts, and augment performance in dynamic tasks. While such actuators have been researched extensively over the past quarter century, there are still various open questions. These relate not only to the fundamental properties mentioned above, but also to their implementation and control as well as the integration of their hardware and software. Elastic actuators have been applied in wearable robotic devices, rehabilitation robots, and humanoid robots. In the last years, bioinspired approaches have brought the capabilities of elastic actuators closer to those of the human muscle, e.g., by introducing redundancy to mimic the muscle fiber recruitment. Another level of redundancy can be achieved by employing monoand bi-articular actuators to achieve designs with increased efficiency, robustness, and simplified control. This book is based on the outcomes of the IEEE BioRob 2018 Workshop “Novel bioinspired actuator designs for robotics (BioAct)”, which was held in Enschede, The Netherlands, on August 28, 2018. Moreover, it is supported by contributors of the IEEE AIM 2017 Workshop “Promoting Elastic Actuators for Robotics (PEAR): novel approaches and biomedical applications”, which was held in Munich, Germany, on July 3, 2017. In both workshops, leading authorities and promising young researchers from different fields of science, e.g., robotics, controls, biomechanics, and neuromechanics, discussed current developments and future directions of bioinspired actuators. vii

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Introduction

The book aims at providing an accessible introduction to the field of bioinspired actuators, which also enriches the contemporary scientific discussion. Part I reviews and analyzes research on biological actuation, its control, and redundancies, highlighting the concepts that can be borrowed from biology. Regarding biological actuation as a role model, dynamical muscle behaviors are described in depth. Moreover, human muscle neuromechanics and human motor control are considered as sources of bioinspiration. Part II gives a technical perspective on the important class of variable impedance actuators including detailed views on serial and parallel compliances. Elastic and variable impedance actuators are one solution to achieve efficient and versatile robot actuation. Design approaches, control methods, and system integration techniques are presented and discussed, considering electromechanical and pneumatic actuation approaches as well as single and multiple degrees of freedom. The state of the art of engineered actuators approaching the behaviors of biological muscles is reported and discussed in Part III. Beyond classic designs, cellular and redundant concepts are considered. Even biological muscles are investigated as an attempt to developing artificial muscles. To understand which robots and assistive devices do already and could potentially benefit from bioinspired actuators, Part IV presents recent applications of compliant actuators in wearable robots, i.e., exoskeletons and prostheses. Thereby, bioinspired implementations are discussed regarding their potential benefits and feasibility. Finally, the back matter concludes the book and gives an outlook on future works and potential perspectives of how bioinspired actuator research and application may develop. Philipp Beckerle Maziar Ahmad Sharbafi Tom Verstraten Peter P. Pott André Seyfarth

Contents

Recent Research on Biological Actuation—What can we Learn from Biology? Dynamic Muscle Behaviours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Christian Rode

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Modelling and Simulating Human Movement Neuromechanics . . . . . . . . Massimo Sartori

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Template-Based Approach to Resolve Redundancies in Motor Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . André Seyfarth

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Variable Impedance Actuators and their Relation to Biology Design and Hardware Integration of Elastic Actuators for HMI . . . . . . . . Peter Paul Pott, Philipp Beckerle, and Kent W. Stewart

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Compliant Multi-DOF Actuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. Vallery and M. Plooij

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Hybrid Electric-Pneumatic Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maziar Ahmad Sharbafi and Aida Mohammadi Nejad Rashty

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State of the Art of Engineered Actuators Approaching Muscle Behaviors Muscle-Like Actuators and Their System Dynamics . . . . . . . . . . . . . . . . . . Joshua Schultz

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Energy-Efficient Kinematically Redundant Actuation . . . . . . . . . . . . . . . . . Tom Verstraten

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Attempts to Develop Artificial Muscles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Koh Hosoda and Masahiro Shimizu

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Contents

Applying Compliant Actuators in Wearable Robots Compliant Actuation for Wearable Robotics . . . . . . . . . . . . . . . . . . . . . . . . . Tom Verstraten and Dirk Lefeber Compliant Actuation for Transfemoral Prostheses: The CYBERLEGS Prosthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Louis Flynn

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Parallel-Elastic Actuation of a Back-Support Exoskeleton . . . . . . . . . . . . . 107 Stefano Toxiri and Andrea Calanca Considerations and conclusions Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Philipp Beckerle, Maziar Ahmad Sharbafi, Peter P. Pott, André Seyfarth, and Tom Verstraten Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Philipp Beckerle, Maziar Ahmad Sharbafi, Peter P. Pott, André Seyfarth, and Tom Verstraten

Recent Research on Biological Actuation—What can we Learn from Biology?

Abstract Biological actuators are different from their technical counterparts in the way they are designed and controlled. We summarize some recent findings on muscle function and on the organization of the neural control system, which enables the execution of versatile movement tasks with different body configurations and in varying environments.

Dynamic Muscle Behaviours Christian Rode

Abstract This chapter provides a brief biological overview of fundamental skeletal muscle mechanics and current muscle contraction theories, focusing own previous work. The overview includes dynamical 1D behavior and models of muscle fibers or whole muscles as well as some results on 3D behavior and models of muscles. One of the impressive current results is that in isometric contractions followed by a stretch, the muscle fiber acts like a linear spring with adjustable rest length. While this may suggest simpler 1D models of muscle fiber force development, effects on the level of the 3D muscle might again hamper simple descriptions. More detailed introductions to dynamical muscle behaviours can be found, e.g., in Rode and Siebert (2017).

1 Structural Background Typically, skeletal muscles connect bones across joints. Induced by neural stimulation, muscles contract and move the segmented body. A skeletal muscle is a massively cascaded actuator with parallel and serial motors (Fig. 1). Muscle is characterized by parallel arranged muscle fiber bundles (fascicles, visible with the naked eye). The fascicles contain parallel muscle fibers, and muscle fibers, in turn, contain parallel myofibrils. The myofibrils are made of hundreds to thousands of half-sarcomeres in series, the smallest force-producing units of muscle. Within half-sarcomeres, actin and myosin filaments are arranged in parallel. Actin filaments are anchored at the Zdisc and myosin filaments at the M-line. Anchoring myosin filaments to the Z-disc, titin filaments connect the two sets of myofilaments, which guarantees structural integrity when the muscle is pulled to long lengths. Here, titin delivers a considerable fraction of the passive muscle force (that includes forces by connective tissue surrounding the fibers, the fascicles, and the whole muscle belly). Moreover, it seems to play a crucial force-producing role in active contractions (see Sect. 1.4). C. Rode (B) Motion and Exercise Science, University of Stuttgart, Allmandring 28, 70569 Stuttgart, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2021 P. Beckerle et al. (eds.), Novel Bioinspired Actuator Designs for Robotics, Studies in Computational Intelligence 888, https://doi.org/10.1007/978-3-030-40886-2_1

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Fig. 1 Muscle structure. For explanations see text

2 Fundamental Muscle Mechanics When the muscle is electrically stimulated and subsequently activated by influx of calcium ions into the sarcoplasm (Ebashi and Endo 1968), myosin heads projecting from the myosin filaments form temporary cross-bridges with actin filaments at binding sites (crossbridge theory; Huxley 1957) that pull the sets of filaments together (sliding filament theory; Huxley and Hanson 1954); Huxley and Niedergerke 1954) (Fig. 1, bottom left). Thereby, the cross-bridges turn chemical energy into mechanical energy and heat. The sliding filament and crossbridge theories (including later refinements; Huxley 1969; Huxley and Simmons 1971) explain (parts of) the fundamental mechanical muscle properties, the force-length and the force-velocity relationships (Fig. 2) as well as the liberated heat and the constant maximal contraction velocity vmax of muscle fibers within a specific length range (Edman 1979). Each point of the force-length relationship is obtained with isometric (constant length) measurements (Gordon et al. 1966), and each point on the force-velocity relationship with isokinetic (constant contraction velocity) experiments (Hill 1938; Till et al. 2008). The dependencies of muscle force on length and contraction speed are both highly nonlinear (Fig. 2). For very short lengths and very long lengths, the muscle can produce no active force (Fig. 2a). At its optimal length lopt , the muscle produces maximum isometric force F im . The slope of the force-length relationship changes distinctly in different working ranges. Because the length of the myosin filament is relatively constant in vertebrates (1.6 µm, thus 0.8 µm in the half-sarcomere, Walker and Schrodt 1974) while the actin filament varies in length between species (around 1.1 µm, Burkholder and Lieber 2001) and fiber types (shorter for fast-twitch fibers, Granzier et al. 1991) the shape of the fiber’s force-length relationship varies characteristically (cf. caption Fig. 2a). Force decreases to zero if the muscle contracts with

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Fig. 2 Fundamental muscle properties. a Force-length relationship f l of frog fiber. Classical f l (Gordon et al. 1966) (black lines), f l accounting for myosin filament sliding through the Z-disc (Rode et al. 2016) (grey lines), and experimental data (Ramsey and Street 1940). f l is normalized to maximum isometric force F im and optimal length l opt chosen to coincide with the beginning of the plateau region. The width of the ascending part within the grey range increases with actin filament length. Taken with a grain of salt, the ‘typical muscle’ operates in the range of l opt ± 15% (Burkholder and Lieber 2001). Passive forces (dashed line) depend strongly on the muscle (Baratta and Solomonow 1992) and are lower in fibers compared with muscles (due to missing connective tissue layers). b Force-velocity relationship f v of cat gastrocnemius medialis (Till et al. 2008) normalized to F im and maximal contraction velocity vmax . Note that f v is invertible

maximal velocity (Fig. 2b). The curvature and thus damping is stronger for slowtwitch fibered muscles (e.g., cat or human soleus muscles). The force produced in eccentric (lengthening) contractions is higher than in concentric (shortening) contractions. It is easy for us to jump 1 m down and land in a controlled way; it is less easy to jump 1 m up. This is a direct consequence of the force-velocity relationship. Classically, the steep ascending part of the force-length relationship is explained with myosin filament compression or folding. However, the muscle does not produce sufficient force to achieve myosin filament buckling, let alone myosin filament compression (Rode et al. 2016). Moreover, fibers produce force (shown with triangles and squares in Fig. 2a) at unphysiologically short lengths after prolonged stimulation (Ramsey and Street 1940; Rode et al. 2016) and other strange behavior (Ramsey and Street 1940). This motivated us to suggest that the myosin filaments slide through the Z-disc (when the muscle gets shorter than indicated with the circle in Fig. 2a). Including this mechanism in a simple model and postulating that the second myosin head generates swiveled cross-bridges (Toyoshima et al. 1989; Reedy et al. 1989) in vivo that dampen muscle contraction predicted the whole force-length relationship (Fig. 2a, grey lines). The mechanism explains how the Z-disc becomes an integral part of muscle contraction and how the muscle can work at short lengths without destroying itself.

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3 Classic Hill-Type Muscle Models Active forces. Classic Hill-type models describe the active force F of the muscle, fiber, or myofibril in a product approach combining all active force-producing units into one contractile component (CC):  F Fim = Act (Stim) · · · f 1 · · · f v .

(1.1)

The muscle activation Act scales the force from multiplied normalized forcelength (fl) and force-velocity relationships (fv). Act can be thought to represent the average calcium ion concentration in the sarcoplasm normalized to the maximum calcium concentration. It depends on the fraction of electrically stimulated muscle fibers Stim (hence Act, Stim ∈ [0, 1]). In a simple version, the dependency of the activation on stimulation can be modeled by the following differential equation (Otten 1987):   d AC T dt = 1 τ ∗ (Sim(t) − Act).

(1.2)

The time constant τ governs the influx of Calcium ions from the sarcoplasmic reticulum (where they are stored) into the sarcoplasm. Passive forces. In a simplifying view, muscle fibers are embedded within parallelly and serially arranged passive, viscoelastic tissues. These tissues play a key role in muscle function and locomotion (Alexander 1990). For example, it has been shown that, while the whole muscle tendon unit undergoes a stretch-shortening cycle, the fiber lengths can remain relatively constant, and all length changes can be taken up by series elastic structures, thereby minimizing fiber work (Roberts et al. 1997). In simple Hill-type models, all sources of elasticity in series with the fibers like those of collagen fibers (aponeurosis and tendon), actin filaments, or the Z-disc are lumped in a series elastic component (SEC), while; parallel sources of elasticity like those of connective tissue and proteins like titin are lumped in a parallel elastic component (PEC). If they are arranged in a physiologically plausible way (as in Fig. 3, in contrast to an arrangement of PEC in parallel to both, the serially arranged CC and SEC) when calculating the active muscle force from total and passive muscle force, the forcelength relationship of the half-sarcomere is reflected in whole muscles with low fiber angles (Rode et al. 2009a). If deemed necessary, viscous damping elements can be easily added to this basic muscle model structure. The inclusion of the SEC introduces a degree of freedom in the muscle model. The force in the SEC equals the sum of the forces in the PEC and the CC. The muscle force F (equalling F SEC ) can favorably be obtained from integrating the velocity of the contractile component vCC :   FS EC − FP EC dvCC = f v−1 dt Act · f Fl · Fim

(1.3)

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Fig. 3 Muscle model and parameter determination. a Active forces (black) calculated from experimental total and passive muscle forces (using the model shown in c, top) approximate the sarcomere force-length relationship (grey, derived from cat myofilament lengths). Adapted from (Rode et al. 2009a). b Comparison of experimental forces (black) from isometric contractions followed by concentric isokinetic ramps with model (shown in c, top) forces. c Model parameters from fitting the model force output to the data shown in (b) compared with parameters determined in isolated experiments (symbols) Adapted from (Siebert et al. 2008). Note that the CC velocity is not constant during experiments

Adapting all Hill-type muscle model (Fig. 3c) parameters by fitting model forces to muscle forces obtained in a set of ramp experiments, we obtained accurate model parameters that were verified with isolated experiments (Siebert et al. 2008). Only the force-length relationship was underestimated, which was interpreted to be related to neglected titin effects (see Sect. 1.4).

4 1D Hill-Model Limitations The cross-bridge theory’s parameters were tuned to describe the force-velocity relationship point-wise with equilibrated cross-bridge distributions (Huxley 1957). The dynamics of changing cross-bridge distributions might lead to deviations of force predictions with Hill-type models from muscle forces in contractions with changing velocity. For example, short-range stiffness (Rack and Westbury 1974) determines

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the muscle’s initial response to stretch due to attached cross-bridges which is essential when modeling neural control. Further limitations arise from the often neglected shift of l opt to longer lengths in submaximally stimulated fibers (Huijing 1996), i.e., in typical conditions in daily use. Accounting for this effect is when, e.g., using EMG-driven muscle models to predict joint torques (Lloyd and Besier 2003; Sartori et al. 2015). Moreover, the muscle force depends not only on the fiber state (Abbott and Aubert 1952; Herzog and Leonard 2000). Steady-state forces after stretch can vastly exceed isometric forces at the corresponding length, especially on the active force-length relationship’s descending limb, while forces after shortening are lower than predicted with Hill-type models. Some purely mathematical descriptions exist to describe aspects of these effects (Ettema and Meijer 2000; Meijer et al. 1998; Till et al. 2008); however, these approaches have not been extensively validated and have thus not been included in standard muscle-skeletal simulation software. During extensive eccentric contractions, non-linear non-crossbridge forces and non-linear cross-bridge forces result in linear muscle fiber behavior (Tomalka et al. 2017). From a technical perspective, the behavior of the muscle in isometric followed by eccentric contractions can be described by a series elastic actuator with adjustable resting length. Its stiffness would scale with activation. Evidence accumulates that titin–actin interactions are responsible for the non-cross-bridge forces in the activated muscle. Some similar biophysical models have been devised to elucidate the contribution of titin to muscle force generation (e.g., Rode et al. 2009; Nishikawa et al. 2011).

5 3D Muscle Effects Fiber thickening and fiber rotation. Due to the constant volume of the fiber, it radially thickens when shortening. This leads to complex mechanical behavior of the aponeurosis, a sheet of collagen fibers that increases in thickness until all collagen fibers merge into the tendon. While the tendon can be considered purely in series with the muscle, the aponeurosis is not. The aponeurosis is not only loaded in the longitudinal direction but increases in width when the fibers shorten. It has been shown that the longitudinal stiffness can increase by a factor of two or three when comparing the muscle at the same force in the passive versus the active state (Azizi and Roberts 2009). Further, applying different activation levels at different whole muscle lengths changed the slope of the aponeurosis force-length relationship and shifted it to longer lengths (Raiteri 2018). Thus, aponeuroses may represent tunable springs (Arellano et al. 2019). Fiber rotation during shortening of fibers contributes to muscle shortening. Interestingly, the amount of rotation depends on the force. Fiber rotation supports muscle speed in fast contractions and muscle force in slow contractions (Eng et al. 2018).

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Muscle force decrease through transversal loading. Muscles are embedded within other muscles and bones that lead to transverse forces on the muscle. Unidirectional lateral loading decreases muscle force (Siebert et al. 2014) and is independent of the local pressure (Siebert et al. 2016). The force decrease and the muscle’s associated deformation can be described for loads up to 15%F im by a simple Hill-model expansion (Siebert et al. 2018).

6 Conclusion Enhancing 1D half-sarcomere models to account for the effects of titin and shortrange stiffness seems essential for (I) developing 1D and 3D models useful in fundamental muscle research and (II) for approximating muscle function in applied research. Further, depending on the specific muscle and its in vivo use, a 1D muscle model should capture the specific muscle (e.g., accounting for effects of fiber thickening and rotation or lateral compression). Determining the relevance of these effects for specific muscles is an ongoing research topic. First 3D continuum mechanical models have been formulated that include titin effects (Heidlauf et al. 2016, 2017), and comprehensive datasets have been collected for the rabbit hindlimb (Siebert et al. 2015) that can be used for model validation.

References Abbott, B. C., & Aubert, X. M. (1952). The force exerted by active striated muscle during and after change of length. The Journal of Physiology, 117(1), 77. Arellano, C. J., Konow, N., Gidmark, N. J., & Roberts, T. J. (2019). Evidence of a tunable biological spring: Elastic energy storage in aponeuroses varies with transverse strain in vivo. Proceedings of the Royal Society B, 286(1900), 20182764. Alexander, R. (1990). Three uses for springs in legged locomotion. International Journal of Robotics Research, 9(2), 53–61. Azizi, E., & Roberts, T. J. (2009). Biaxial strain and variable stiffness in aponeuroses. The Journal of Physiology, 587(17), 4309–4318. Baratta, R. V., & Solomonow, M. (1992). The dynamic performance model of skeletal muscle. Critical Reviews in Biomedical Engineering, 19(6), 419–454. Burkholder, T. J., & Lieber, R. L. (2001). Sarcomere length operating range of vertebrate muscles during movement. Journal of Experimental Biology, 204(9), 1529–1536. Ebashi, S., & Endo, M. (1968). Calcium ion and muscle contraction. Progress in Biophysics and Molecular Biology, 18, 123–183. Edman, K. A. (1979). The velocity of unloaded shortening and its relation to sarcomere length and isometric force in vertebrate muscle fibres. The Journal of Physiology, 219, 143–159. https://doi. org/10.1113/jphysiol.1979.sp012804. Eng, C. M., Azizi, E., & Roberts, T. J. (2018). Structural determinants of muscle gearing during dynamic contractions. Integrative and Comparative Biology, 58(2), 207–218. Ettema, G. J., & Meijer, K. (2000). Muscle contraction history: Modified Hill versus an exponential decay model. Biological Cybernetics, 83(6), 491–500.

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Gordon, A. M., Huxley, A. F., & Julian, F. J. (1966). The variation in isometric tension with sarcomere length in vertebrate muscle fibres. The Journal of Physiology, 184(1), 170–192. Granzier, H. L., Akster, H. A., & Ter Keurs, H. E. (1991). Effect of thin filament length on the forcesarcomere length relation of skeletal muscle. American Journal of Physiology-Cell Physiology, 260(5), C1060–C1070. Heidlauf, T., Klotz, T., Rode, C., Altan, E., Bleiler, C., Siebert, T., et al. (2016). A multi-scale continuum model of skeletal muscle mechanics predicting force enhancement based on actin–titin interaction. Biomechanics and Modeling in Mechanobiology, 15(6), 1423–1437. Heidlauf, T., Klotz, T., Rode, C., Siebert, T., & Röhrle, O. (2017). A continuum-mechanical skeletal muscle model including actin-titin interaction predicts stable contractions on the descending limb of the force-length relation. PLoS Computational Biology, 13(10), e1005773. Herzog, W., & Leonard, T. R. (2000). The history dependence of force production in mammalian skeletal muscle following stretch-shortening and shortening-stretch cycles. Journal of Biomechanics, 33(5), 531–542. Hill, A. V. (1938). The heat of shortening and the dynamic constants of muscle. Proceedings of the Royal Society of London. Series B-Biological Sciences, 126(843), 136–195. Huijing, P. A. (1996). Important experimental factors for skeletal muscle modelling: non-linear changes of muscle length force characteristics as a function of degree of activity. European Journal of Morphology, 34(1), 47–54. Huxley, H., & Hanson, J. (1954). Changes in the cross-striations of muscle during contraction and stretch and their structural interpretation. Nature, 173(4412), 973–976. Huxley, A. F., & Niedergerke, R. (1954). Structural changes in muscle during contraction; interference microscopy of living muscle fibres. Nature, 173(4412), 971–973. Huxley, A. F. (1957). Muscle structure and theories of contraction. Progress in Biophysics and Biophysical Chemistry, 7, 255–318. Huxley, H. E. (1969). The mechanismof muscular contraction. Science, 164(886), 1356–1365. Huxley, A. F., & Simmons, R. M. (1971). Proposed mechanismof force generation in striated muscle. Nature, 233, 533–538. Lloyd, D. G., & Besier, T. F. (2003). An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo. Journal of Biomechanics, 36, 765–776. https://doi.org/ 10.1016/S0021-9290(03)00010-1. Meijer, K., Grootenboer, H. J., Koopman, H. F., van Der Linden, B. J. J. J., & Huijing, P. A. (1998). A Hill type model of rat medial gastrocnemius muscle that accounts for shortening history effects. Journal of Biomechanics, 31(6), 555–563. Nishikawa, K. C., Monroy, J. A., Uyeno, T. E., Yeo, S. H., Pai, D. K., & Lindstedt, S. L. (2011). Is titin a ‘winding filament’? A new twist on muscle contraction. Proceedings of the royal society B: Biological Sciences, 279(1730), 981–990. Otten, E. (1987). A myocybernetic model of the jaw system of the rat. Journal of Neuroscience Methods, 21(2–4), 287–302. Rack, P. M., & Westbury, D. R. (1974). The short range stiffness of active mammalian muscle and its effect on mechanical properties. The Journal of Physiology, 240(2), 331–350. Raiteri, B. J. (2018). Aponeurosis behaviour during muscular contraction: A narrative review. European Journal of Sport Science, 18(8), 1128–1138. Ramsey, R. W., & Street, S. F. (1940). The isometric length-tension diagram of isolated skeletal muscle fibers of the frog. Journal of Cellular and Comparative Physiology, 15(1), 11–34. Reedy, M. C., Beall, C., & Fyrberg, E. (1989). Formation of reverse rigor chevrons by myosin heads. Nature, 339(6224), 481. Roberts, T. J., Marsh, R. L., Weyand, P. G., & Taylor, C. R. (1997). Muscular force in running turkeys: The economy of minimizing work. Science, 275(5303), 1113–1115. Rode, C., Siebert, T., & Blickhan, R. (2009). Titin-induced force enhancement and force depression: a ‘sticky-spring’mechanism in muscle contractions? Journal of Theoretical Biology, 259(2), 350– 360.

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Rode, C., Siebert, T., Tomalka, A., & Blickhan, R. (2016). Myosin filament sliding through thez-disc relates striated muscle fibre structure to function. Proceedings of the Royal Society of London B: BiologicalSciences, 283(1826), 20153030. Rode, C., & Siebert, T. (2017). Muscle-like actuation for locomotion. In M. Sharbafi, & A. Seyfarth (Eds.), Bioinspired Legged Locomotion: Models, Concepts, Control and Applications, pp. 564– 591. Butterworth-Heinemann, 1st edition. Sartori, M., Maculan, M., Pizzolato, C., et al. (2015). Modeling and Simulating the Neuromuscular Mechanisms regulating Ankle and Knee Joint Stiffness during Human Locomotion. Journal of Neurophysiology, 114, 2509–2527. https://doi.org/10.1152/jn.00989.2014. Siebert, T., Leichsenring, K., Rode, C., Wick, C., Stutzig, N., Schubert, H.,… & Böl, M. (2015). Three-dimensional muscle architecture and comprehensive dynamic properties of rabbit gastrocnemius, plantaris and soleus: input for simulation studies. PLoS One, 10(6), e0130985. Siebert, T., Rode, C., Herzog, W., Till, O., & Blickhan, R. (2008). Nonlinearities make a difference: comparison of two common Hill-type models with real muscle. Biological Cybernetics, 98(2), 133–143. Siebert, T., Rode, C., Till, O., Stutzig, N., & Blickhan, R. (2016). Force reduction induced by unidirectional transversal muscle loading is independent of local pressure. Journal of Biomechanics, 49(7), 1156–1161. Siebert, T., Stutzig, N., & Rode, C. (2018). A hill-type muscle model expansion accounting for effects of varying transverse muscle load. Journal of Biomechanics, 66, 57–62. Siebert, T., Till, O., Stutzig, N., Günther, M., & Blickhan, R. (2014). Muscle force depends on the amount of transversal muscle loading. Journal of Biomechanics, 47(8), 1822–1828. Till, O., Siebert, T., Rode, C., & Blickhan, R. (2008). Characterization of isovelocity extension of activated muscle: a Hill-type model for eccentric contractions and a method for parameter determination. Journal of Theoretical Biology, 255(2), 176–187. Tomalka, A., Rode, C., Schumacher, J., & Siebert, T. (2017). The active force–length relationship is invisible during extensive eccentric contractions in skinned skeletal muscle fibres. Proceedings of the Royal Society B: Biological Sciences, 284(1854), 20162497. Toyoshima, Y. Y., Toyoshima, C., & Spudich, J. A. (1989). Bidirectional movement of actin filaments along tracks of myosin heads. Nature, 341(6238), 154. Walker, S. M., & Schrodt, G. R. (1974). I segment lengths and thin filament periods in skeletal muscle fibers of the Rhesus monkey and the human. The Anatomical Record, 178(1), 63–81.

Modelling and Simulating Human Movement Neuromechanics Massimo Sartori

Abstract Biological actuators are different from their mechatronic counterparts in terms of form and function. In this chapter, we discuss a data-driven neuromechanical model-based approach to estimate how muscles are neurally recruited as well as how they contribute to actuate multiple biological joints.

Human movement emerges from the coordinated interaction between the neuromuscular and the musculoskeletal systems (Enoka 2008). Despite knowledge of the mechanisms underlying movement neuromuscular and musculoskeletal functions, there currently is no relevant understanding of the neuro-mechanical interplay in the composite neuro-musculo-skeletal system. This represents a major challenge to the understanding of human movement, where the characterisation of mechanisms at one level, i.e., skeletal level, requires knowledge of mechanisms at the other levels, i.e., neuro-muscular (Enoka 2008; Sartori et al. 2017b). This chapter proposes a neuromechanical modelling approach developed by the author and colleagues in the past years for the study of human movement neuromechanics. This is based on solving for how muscles are neurally recruited and for how they transfer mechanical forces to skeletal structures (Fig. 1).

1 Sampling α-Motor Neuron Discharges in Vivo The motor unit is the actual biological interface between neural and musculoskeletal functions in humans and animals (Enoka and Pearson 2013). The ‘α-motor neuron side’ of the motor unit is the final common pathway of synaptic inputs produced in

M. Sartori (B) Department of Biomechanical Engineering, University of Twente, De Horst 2, Enschede 7522LW, NL, Netherlands e-mail: [email protected] © Springer Nature Switzerland AG 2021 P. Beckerle et al. (eds.), Novel Bioinspired Actuator Designs for Robotics, Studies in Computational Intelligence 888, https://doi.org/10.1007/978-3-030-40886-2_2

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Fig. 1 High-density electromyograms (HD-EMGs) are recorded and decomposed into constituent motor unit discharges. This enables inferring spinal cord neural activity in vivo and non-invasively. Decoded discharges are used to drive forward neuro-musculo-skeletal models that can estimate a larger spectrum of neuromuscular mechanisms than is possible via signal-based techniques alone (a). Example spike trains decoded for 19 active motor units in the soleus muscle during isometric plantar flexion. The graph also shows the ankle plantar flexion torque generated during the task (b)

different areas of the nervous system and represents the optimal level for bridging the neuro-muscular ‘knowledge gap’ in movement. In this context, advances in electromyography (EMG) are enabling discerning the activity of motor units from interferent EMGs data. This is helping understand how α-motor neurons receive synaptic input from spinal and supraspinal levels and regulate muscle activation (Bizzi et al. 2008; Farina and Negro 2015). The α-motor neurons can be recorded from the intact moving human in vivo using soft-electronic skins; highly dense (HD) grids of electrodes that can be placed on the skin surface for recording HD-EMGs from a large number of muscle fibers simultaneously (Fig. 1a). This is possible because of the safe synaptic connection between a motor neuron and the innervated muscle fibers. As a result, there is a one to one relationship between action potential produced by an α-motor neuron and that generated by the innervated fibers. That is, each motor neuron action potential is transduced into a compound muscle fiber action potential that carries the same neural information. HD-EMGs carry this information in the form of an interferent signal, from which the underlying α-motor neuron discharges can be unmixed via deconvolution-based blind source separation (Farina et al. 2017). This provides the same feature that direct nerve interfacing extracts via implanted electrodes, i.e., nerve intrafascicular or epimysial electrodes. That is, it provides access to the time series of discharge events of populations of motor neurons, i.e., > 30 neurons per controlled muscle.

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Fig. 2 Neural discharge-driven modelling. In vivo motor neuron cellular cumulative spike trains are decoded for muscles including tibialis anterior (tibant), peroneus tertius (pertert), brevis (perbrev), longus (perlong), gastricnemius medialis (gasmed), lateralis (gaslat), and soleus (sol). These drive forward musculoskeletal models enabling prediction of isometric ankle moment (a). Reference and predicted ankle joint stiffness via electromyography-driven modelling during locomotion. This datamodel fusion framework shows how agonist–antagonist co-activation ratio varies from dominant dorsi flexors (+1; initial stance) to plantar flexors(−1; late stance) and regulates joint-equivalent stiffness (b)

We recently showed how multi-muscle spatial sampling and deconvolution of high-density fiber electrical activity could be used to decode accurate alpha-motor neuron discharges across five lumbosacral segments in the human spinal cord (Sartori et al. 2017a, b). This was achieved by recording HD-EMG from five ankle muscles using more than 250 recording sites (Fig. 2b). This provides a window into α-motor neuron pool activity and its distribution across the rostrocaudal axis of the spinal cord (Sartori et al. 2017a, b). This information can be used to estimate motor unit anatomical properties including fiber diameter and fatiguability (Del Vecchio et al. 2017). This enables building motor unit-specific twitch models that can convert decoded α-motor neuron discharges into muscle activation profiles. Moreover, complete motor neuron decoding potentially provides a window into the synaptic inputs converging onto these pools (Negro et al. 2016), thus enabling understanding the organization and connections in higher spinal neural networks (Fig. 2). Coherence analysis can be employed to determine the proportion of common and independent synaptic input converging to α-motor neuron pools (Farina and Negro 2015, Gogeascoechea et al. 2020). Dimensionality reduction techniques (Lee and Seung 1999), can be used to extract estimates of muscle modularity and synergies (Sartori et al. 2013b; Gonzalez-Vargas et al. 2015).

2 From α-Motor Neurons Discharges to Muscle–Tendon Force Common neurophysiological analyses typically focus on the ‘motor neuron side’ with less emphasis on the ‘muscle fiber side’ and how its contractile dynamics contributes to motor control and function (Herzog 2014). However, human movement must be

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understood with a linked perspective to motor neurons and muscle contractile properties simultaneously. It was shown that the difference between muscle isometric force to microstimulation and dynamic force during movement produced by the same microstimulation can be one order of magnitude different (Barbeau et al. 1999). Studies established that central nervous system (CNS) control strategies change across contraction types, i.e., lengthening, shortening or isometric (Duchateau and Enoka 2016). Furthermore, muscle contraction history dependence (not regulated by the CNS) can directly affect muscle excitation–contraction couplings, i.e., force enhancement following stretch can reach values of almost 50% of the corresponding isometric reference force (Herzog et al. 2015). These differences need to be accounted for via mechanistic models of the contribution of fiber contractile properties. A possible way of doing this is via neural data-driven musculoskeletal modelling formulations (Sartori et al. 2016). Previous research demonstrated that this can effectively translate motor neuron discharges into multi-muscle coordinated force patterns resulting into net ankle joint moment (Sartori et al. 2017b). This is a “predictive formulation” where cumulative spike trains (CSTs) decoded from all motor neurons active in the control of a specific muscle directly drive muscle fibers and series elastic tendons, i.e., muscle–tendon units (MTUs, Fig. 2). This modelling formulation comprises six main components (Sartori et al. 2012a, b, c, 2013a). The neural activation component converts incoming CSTs into the resulting twitch response triggered in the innervated muscle fibers using a critically damped, linear, second-order, differential system (Milner-Brown et al. 1973). This can be expressed in a discrete form using a time history-dependent, infinite impulsive response filter (Lloyd and Besier 2003): u(t) = α · x(t − d) − β1 · u(t − 1) − β2 · u(t − 2)

(1)

where x(t) is the motor neuron spike train at time sample t, u(t) is the innervated fiber twitch response whereas α, β1 , β2 are the recursive filtering coefficients. These are constrained to obtain a filter positive stable solution and unit gain: β1 = C1 + C2 , β2 = C1 · C2 , α−β1 −β2 = 1, with −1 < C1 , C2 < 0. The term d is the electromechanical delay. The resulting u(t) is further processed via a nonlinear transfer function to compute the resulting neural activation: a(t) =

e Au(t) − 1 , eA − 1

(2)

where −3 < A < 0 is the non-linear shape factor, with 0 being a linear relationship. Neural activation a(t) reflects the ensemble dynamics of all electro-chemical transformations triggered at the muscle fiber level by the motor neuron discharges (Sartori et al. 2016). The musculotendon kinematics component synthetizes subject-specific musculoskeletal geometry (e.g., MTU length and moment arms) into a set of MTU-specific

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multidimensional cubic B-splines (Sartori et al. 2012c). Each B-spline computes MTU kinematics (i.e., MTU length and moment arms) as a function of input joint knee and ankle angles (Sartori et al. 2012c). The musculotendon dynamics component uses neural activation and MTU length mt and velocity vmt to control a Hill-type muscle model and estimate instantaneous length, contraction velocity, and force in the muscle fibers, as well as strain and force in the series-elastic tendon within each MTU (Sartori et al. 2012a, 2013a). The static of muscle fibers aremodelled using parallel force–length  mproperties   l and activation-dependent f A  l m curves (Lloyd and Besier 2003). passive f P  The dynamic properties of fibers are modelled using an activation-dependent force– velocity f ( vm ) curve. These curves are normalized to maximum isometric muscle max vm represent fiber length and velocity normalized to l m and  force (F ), while  m optimal fiber length l O and maximum muscle contraction velocity respectively (Zajac 1989). The tendon properties are modelled using a force-strain function f (ε) with non-linear toe region normalized to F max (Zajac 1989). The total MTU force F M T U is calculated as a function of a(t), normalized fiber length  l m and contraction velocity m  v :         m  m  m  max cos φ l m l f  v + fP  l F F M T U = F t = F m cos φ l m = a(t) f  (3)

2.1 From α-Motor Neurons Discharges to Muscle–Tendon Stiffness The total stiffness K iM T U in each MTU can be modelled as muscle fiber stiffness K m in series with tendon stiffness K t (Sartori et al. 2015):  K

MTU

=

1 1 + t m K K

−1 (4)

Tendon stiffness K t can be estimated from the slope of the non-linear forcestrain relationship f (ε) in the correspondence of the instantaneous tendon strain value E. The tendon strain can be calculated at each simulation frame by solving for equilibrium between tendon and fiber force in the MTU dynamics equation (Eq. 3). Muscle fiber stiffness K m is calculated as the partial derivative of fiber force F m (Eq. 3) with respect to the normalized fiber length  lm: K

m

 m m  l ,V ∂ F m a, = m ∂ l

(5)

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The partial derivative in Eq. 4 is calculated by creating a multi-dimensional cubic B-spline function per muscle (Sartori et al. 2015).

2.2 α-Motor Neurons Regulation of Joint Torque and Stiffness Net joint moments are directly computed as the product of each MTU force (Eq. 3) and their associated moment arms from the MTU kinematics block. The net stiffness about a joint DOF, K DOF , is determined as: K DO F =

#M TU i=1

K iM T U · ri2 +

∂ri · FiM T U ∂θ D O F

(6)

where K iM T U and r i respectively represent the stiffness and moment arm of the ith MTU spanning the specific DOF, whereas θ DOF is the joint angle about the specific DOF, as previously described (Sartori et al. 2015). Previous research showed that the proposed neural data-driven modelling method could translate motor neuron spike trains into accurate joint moments in an openloop way (Sartori et al. 2017a, b). This demonstrated the ability of establishing subject-specific modelling formulations that could convert neural activity from highdimensional sets of motor neurons (on average 56.7 ± 10.2 for all muscles) into multimuscle coordinated force profiles that well reconstruct experimental joint moments over all subjects and conditions (Fig. 2a). These studies showed that that the effective part of the cumulative spike train responsible for force modulation was in the low frequency band (Negro and Farina 2011; Dideriksen et al. 2012; Sartori et al. 2017b). This was represented via slow neural activation profiles i.e., motor neuron spike trains filtered via a second-order twitch model. The direct association found between neural activation and joint moment is explained by the fact that the musculoskeletal system acts as a natural low pass filter of the spinal segments neural output. The neural drive high frequency band is filtered out by the slow twitch response of muscle fibers triggering electrochemical transformations (i.e., calcium dynamic) and inducing limits in fiber action potential propagation velocity as well as by intrinsic viscoelasticity properties of muscle–tendon units (Enoka 2004). Recent research proposed musculoskeletal models for estimating dynamic kneeankle stiffness from muscle forces (Sartori et al. 2015). These studies suggested that the ankle joint modulates stiffness for accelerating or decelerating the body with co-contraction transitioning from dominant dorsi-flexors to dominant plantar-flexors throughout the stance phase of walking and running. On the other hand, knee joint stiffness appeared to be modulated for optimizing body weight acceptance and joint stability with more distributed co-contraction between flexor and extensor muscles

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in the correspondence of the stiffness peaks produced during walking and running (Fig. 2b).

3 Conclusion This chapter proposed the use of multi-muscle high-density EMG sampling and decomposition in combination with subject-specific neuromechanical modelling. This enables opening up a window into spinal motor neuron behavior and resulting mechanical function in vivo in the intact moving human.

References Barbeau, H., McCrea, D. A., & O’Donovan, M. J., et al. (1999). Tapping into spinal circuits to restore motor function. Bizzi, E., Cheung, V. C. K., & d’Avella et al. (2008). Combining modules for movement. Brain Research Reviews, 57, 125–133. https://doi.org/10.1016/j.brainresrev.2007.08.004. Del Vecchio, A., Negro, F., Felici, F., & Farina, D. (2017). Distribution of muscle fiber conduction velocity for representative samples of motor units in the full recruitment range of the tibialis anterior muscle. Acta Physiologica. https://doi.org/10.1111/apha.12930. Dideriksen, J. L., Negro, F., Enoka, R. M., & Farina, D. (2012). Motor unit recruitment strategies and muscle properties determine the influence of synaptic noise on force steadiness. Journal of Neurophysiology, 107, 3357–3369. https://doi.org/10.1152/jn.00938.2011. Duchateau, J., & Enoka, R. M. (2016). Neural control of lengthening contractions. Journal of Experimental Biology, 219, 197–204. https://doi.org/10.1242/jeb.123158. Enoka, R. M. (2008). Neuromechanics of human movement, 4th edn. Human KineticsPublishers, Inc. Enoka, R. M. (2004). Biomechanics and neuroscience: A failure to communicate. Exercise and Sport Sciences Reviews, 32, 1–3. https://doi.org/10.1097/00003677-200401000-00001. Enoka, R. M., & Pearson, K. G. (2013). The motor unit and muscle action. Princ neural Sci 768–789. Farina, D., & Negro, F. (2015). Common synaptic input to motor neurons, motor unit synchronization, and force control. Exercise and Sport Sciences Reviews,, 43. https://doi.org/10.1249/JES. 0000000000000032. Farina, D., Vujaklija, I., Sartori, M., et al. (2017). Man/machine interface based on the discharge timings of spinal motor neurons after targeted muscle reinnervation. Nature Biomedical Engineering 1, 0025. https://doi.org/10.1038/s41551-016-0025. Gogeascoechea, A., Kuck, A., Van Asseldonk, E., Negro, F., Buitenweg, J. R., Yavuz, U. S., Sartori M. (2020). Interfacing with alpha motor neurons in spinal cord injury patients receiving transspinal electrical stimulation. Frontiers in neurology. https://doi.org/10.3389/fneur.2020.00493. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7296155/ Gonzalez-Vargas, J., Sartori, M., Dosen, S., et al. (2015). A predictive model of muscle excitations based on muscle modularity for a large repertoire of human locomotion conditions. Frontiers in Computational Neuroscience, 9, 1–14. https://doi.org/10.3389/fncom.2015.00114. Herzog, W. (2014). Mechanisms of enhanced force production in lengthening (eccentric) muscle contractions. Journal of Applied Physiology, 116, 1407–1417. https://doi.org/10.1152/japplphys iol.00069.2013.

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Herzog, W., Powers, K., Johnston, K., & Duvall, M. (2015). A new paradigm for muscle contraction. Front Physiol, 6, 1–11. https://doi.org/10.3389/fphys.2015.00174. Lee, D. D., & Seung, H. S. (1999). Learning the parts of objects by non-negative matrix factorization. Nature, 401, 788–791. https://doi.org/10.1038/44565. Lloyd, D. G., & Besier, T. F. (2003). An EMG-driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo. Journal of Biomechanics, 36, 765–776. https://doi.org/ 10.1016/S0021-9290(03)00010-1. Milner-Brown, H. S., Stein, R. B., & Yemm, R. (1973). Changes in firing rate of human motor units during linearly changing voluntary contractions. Journal of Physiology, 230, 371–390. Negro, F., & Farina, D. (2011). Linear transmission of cortical oscillations to the neural drive to muscles is mediated by common projections to populations of motoneurons in humans. Journal of Physiology, 589, 629–637. https://doi.org/10.1113/jphysiol.2010.202473. Negro, F., Sükrü ¸ Yavuz, U., & Farina, D (2016). The human motor neuron pools receive a dominant slow-varying common synaptic input. The Journal of Physiology, 1–45. https://doi.org/10.1113/ JP271748. Sartori, M., Fernandez, J. W., & Modenese, L. et al. (2017a). Toward modeling locomotion using electromyography-informed 3D models: application to cerebral palsy. WIREs System Biology Medicine, e1368. https://doi.org/10.1002/wsbm.1368. Sartori, M., Gizzi, L., Lloyd, D. G., & Farina, D. (2013a). A musculoskeletal model of human locomotion driven by a low dimensional set of impulsive excitation primitives. Frontiers in Computational Neuroscience, 7. Sartori, M., Gizzi, L., Lloyd, D. G. D. G., & Farina, D. (2013b). A musculoskeletal model of human locomotion driven by a low dimensional set of impulsive excitation primitives. Frontiers in Computational Neuroscience, 7, 79. https://doi.org/10.3389/fncom.2013.00079. Sartori, M., Llyod, D. G., & Farina, D. (2016). Neural Data-driven Musculoskeletal Modeling for Personalized Neurorehabilitation Technologies. IEEE Transactions on Biomedical Engineering, 63, 879–893. https://doi.org/10.1109/TBME.2016.2538296. Sartori, M., Maculan, M., Pizzolato, C., et al. (2015). Modeling and Simulating the Neuromuscular Mechanisms regulating Ankle and Knee Joint Stiffness during Human Locomotion. Journal of Neurophysiology, 114, 2509–2527. https://doi.org/10.1152/jn.00989.2014. Sartori, M., Reggiani, M., Farina, D., & Lloyd, D. G. (2012a). EMG-driven forward-dynamic estimation of muscle force and joint moment about multiple degrees of freedom in the human lower extremity. PLoS One, 7, 1–11. https://doi.org/10.1371/journal.pone.0052618. Sartori, M., Reggiani, M., Pagello, E., & Lloyd, D. G. (2012). Modeling the human knee for assistive technologies. IEEE Transactions on Biomedical Engineering, 59, 2642–2649. https://doi.org/10. 1109/TBME.2012.2208746. Sartori, M., Reggiani, M., van den Bogert, A. J., & Lloyd, D. G. (2012). Estimation of musculotendon kinematics in large musculoskeletal models using multidimensional B-splines. Journal of Biomechanics, 45, 595–601. https://doi.org/10.1016/j.jbiomech.2011.10.040. Sartori, M., Yavuz, U. S., & Farina, D. (2017). In Vivo Neuromechanics: Decoding Causal Motor Neuron Behavior with Resulting Musculoskeletal Function. Scientific Reports, 7, 13465. https:// doi.org/10.1038/s41598-017-13766-6. Zajac, F. E. (1989). Muscle and tendon: Properties, models, scaling, and application to biomechanics and motor control. Critical Reviews in Biomedical Engineering, 17, 359–411.

Template-Based Approach to Resolve Redundancies in Motor Control André Seyfarth

Abstract Biological actuators can be recruited to match the requirements of different motor tasks and conditions. In this chapter, we discuss how redundancies in motor control could be resolved following a template-based approach. We explore the recruitment of sensory pathways using the concepts of graphical sensor motor maps and locomotor subfunctions.

Redundancy is a key design principle in biological movement systems. It occurs at the different levels of the organization of the movement system ranging from multisegment kinematics, kinetics and control. This redundancy enables animal and humans to adapt to different tasks, environments and body conditions, e.g., in the case of motor impairments or challenging environments. At the kinematic level, the segmented body enables to achieve the same hand or foot placement (position in space) with different joint configurations. In human hopping for instance, different knee and ankle configurations can result in the same leg length, defined by the leg axis from the contacting point of the foot (e.g., the ball of the foot) to the hip (Seyfarth et al. 2001). The same holds for adjusting leg angle, i.e., the orientation of leg axis in space. Hence, within the physiological and anatomical limits, the leg is able to adapt to changed joint function e.g., due to fatigue or injuries while maintaining the general leg function. At the kinetic (motor redundancy) level, different muscle are contributing to generating a specific joint torque. Again, the individual contributions of the muscles may change without changing the resulting joint torque. This enables the motor control system to adapt muscle coordination while maintaining the joint kinetics (Bernstein 1935). At the muscle recruitment level, the force generated by a muscle can be achieved by different combinations of contributing motor units (Henneman 1957). In general, A. Seyfarth (B) Lauflabor Locomotion Laboratory, Institute of Sport Science and Centre for Cognitive Science, Technische Universität Darmstadt, Darmstadt, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2021 P. Beckerle et al. (eds.), Novel Bioinspired Actuator Designs for Robotics, Studies in Computational Intelligence 888, https://doi.org/10.1007/978-3-030-40886-2_3

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this motor unit recruitment is organized in a specific order, starting with smaller motor units at low muscles force and with subsequentially activating additional larger motor units at higher force outputs. This recruitment strategy may differ depending on the condition of the muscle (e.g., fatigue) or changed loading conditions (e.g., eccentric vs. concentric muscle function, see Chap. 2). At the neural level, different control circuits can be involved in creating and stabilizing a desired movement task (e.g., walking, running, jumping). Among the simplest control structures are proprioceptive feedback loops (Geyer and Herr 2010) and central pattern generators (CPG; Ijspeert 2008). These elementary control circuits can be complemented and potentially replaced by higher-control centers, e.g., in the brain stem and the motor cortex. The blending a highly decentralized spinal mechanisms and more central control commands provides an additional redundancy to the control of biological movement. So far, the basic mechanisms of adaptation of these four redundancy levels are not well understood. And it is even still challenging to understand, how these different redundancy levels are organized as an integrative system. A better understanding could be achieved by connecting the research in human biomechanics and neural control more closely. In this chapter we will take an alternative perspective compared to the previous chapter 3 by asking, how the mechanics of a motor task will shape the execution of the task at the different levels of the motor control system.

1 How Mechanics Shapes to Way We Move Biological movements such as walking or running are characterized by movementspecific features (Blickhan and Full 1993), e.g., typical patterns of the joint kinematics, joint torques, or (ground) reaction forces. When analyzing these movements with the help of biomechanical models, clear dependencies between—in principle independent—system states (e.g., COM position, leg forces) become apparent. For instance, in different gaits, characteristic patterns of the experimentally observed ground reaction force can be explained by describing leg force as a linear relationship of leg compression, i.e., the change in leg length during stance phase in walking or running (Geyer et al. 2006). These dependencies can be conveniently modeled using low-dimensional templates models such as the spring-mass model (Blickhan 1989), commonly called SLIP (spring-loaded inverted pendulum). Here a spring-like leg function is assumed to predict the generation of stable gait patterns for walking and running. Low-dimensional mechanical models can be found to describe different features of locomotor systems, such as axial stance leg dynamics (SLIP model), swing leg dynamics (Sharbafi et al. 2017) and postural balance (Maus et al. 2010). In these models, pendulum and spring-mass dynamics are found at different levels of the locomotor system, which can be coordinated using using sensory feedback between the different locomotor subfunctions (stance, swing and balance function; Sharbafi

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and Seyfarth 2017). However, it is still not well understood, how these mechanical systems are coordinated at the level of the sensor-motor-control.

2 Matching Dimensionality Between Mechanics and Sensor-Motor Control? The equations of motions for the human locomotor systems are very complex and difficult to understand. The architecture of the skeletal systems allows a high diversity of motor performances as it can be observed in sports and performing arts, e.g., in dance. Still, once learned many of the tasks can be performed with ease despite of the complexity of the sensor-motor system with hundreds of muscles and degrees of freedom. The insights gained from the biomechanical template models suggest that we might learn a low dimensional movement representation (Maus et al. 2015) for achieving stable movements. If the neural system would take full advantage of the dimension reduction observed on the mechanical level, a matching low-dimensional representation of movement on the sensor-motor level would be an adequate solution. Here, we ask whether we can translate a mechanical template (e.g., the spring-like stance leg function) into a neuromuscular template (i.e., a mapping between sensory states and motor commands to the muscles). Let us consider the representation of the spring-like leg function in the SLIP model: Fleg = k(l − l0 )

(1)

Here, k describes the leg stiffness, l the leg length (distance from contact point at the ground to the center of mass, COM), l0 represents the rest length of the leg (nominal leg length corresponding to slack length of the leg spring) and F leg is the resulting stance leg force. If we ask for a matching low-dimensional representation of this leg-spring model on the neuromuscular level we can consider the representation of a reflex pathway contributing to muscle stimulation STIM: STIM(t) = G ∗ (P(t − δt) − P0 )

(2)

Here, G describes the reflex gain, P(t-δt) the proprioceptive signal (e.g., muscle force) delayed by δt and P0 is the offset value of the proprioceptive signal P. In both cases (Eqs. 1 and 2), a linear relationship describes the dependency between two system states (leg force vs. leg length and muscle stimulation vs. proprioceptive signal).

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Can the mechanical description of the axial stance leg function during locomotion (leg spring function) be translated into a neuromuscular control template of similar level of complexity? We will approach this question using a simulation model.

3 Sensor-Motor Map for Axial Leg Function in Hopping In a recent study (Schumacher and Seyfarth 2017) we investigated how proprioceptive signals can be recruited to generate required muscle stimulation patterns for stable hopping. Hopping on place was selected as a motor task to focus on the axial leg function which is fundamental in legged locomotion (e.g., in running). We asked whether a specific set of sensory pathways as described in Eq. (2) would be required to obtain hopping movements. In a previous study (Häufle et al. 2010) we additionally asked, which intrinsic muscle properties (see Chap. 2) would be most important to achieve stable hopping. With the Hill-type muscle properties including force–length and force–velocity relationship it is possible to achieve stable hopping in a segmented neuromuscular leg model comprising a leg extensor muscle with different proprioceptive pathways, namely with positive force feedback, positive length feedback and different combinations (superpositions) of these feedback pathways. Interestingly, hopping movements were disabled with velocity feedback. For maximum performance, pure positive force feedback was predicted to be close to optimal. This was previously found in a simulation study of Geyer et al. (2003). In contrast, for maximum metabolic efficiency, length feedback was predicted to be of advantage. Hence, depending on the desired characteristics of the selected task (performance vs. endurance), individual sensor-motor pathways may provide adequate neuromuscular ‘programs’. In order to enable such elementary motor programs to achieve the required axial leg function for hopping, the force–velocity function of the muscle was found to essential (Häufle et al. 2010).

References Bernstein, N. A. (1935). The problem of the interrelation of coordination and localization. Archives of Biological SciencesArchives of Biological Sciences, 38, 15–59. Blickhan, R. (1989). The spring-mass model for running and hopping. Journal of Biomechanics, 22(11–12), 1217–1227. Blickhan, R., & Full, R. J. (1993). Similarity in multilegged locomotion: Bouncing like a monopode. Journal of Comparative Physiology A, 173(5), 509–517. Geyer, H., & Herr, H. (2010). A muscle-reflex model that encodes principles of legged mechanics produces human walking dynamics and muscle activities. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 18(3), 263–273. Geyer, H., Seyfarth, A., & Blickhan, R. (2006). Compliant leg behaviour explains basic dynamics of walking and running. Proceedings of the Royal Society B: Biological Sciences, 273(1603), 2861–2867.

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Haeufle, D. F. B., Grimmer, S., & Seyfarth, A. (2010). The role of intrinsic muscle properties for stable hopping—stability is achieved by the force–velocity relation. Bioinspiration & Biomimetics, 5(1), 016004. Henneman, E. (1957). Relation between size of neurons and their susceptibility to discharge. Science, 126(3287), 1345–1347. Ijspeert, A. J. (2008). Central pattern generators for locomotion control in animals and robots: A review. Neural Networks, 21(4), 642–653. Geyer et al. (2003). XXXX. Maus, H. M., Lipfert, S. W., Gross, M., Rummel, J., & Seyfarth, A. (2010). Upright human gait did not provide a major mechanical challenge for our ancestors. Nature Communications, 1, 70. Maus, H. M., Revzen, S., Guckenheimer, J., Ludwig, C., Reger, J., & Seyfarth, A. (2015). Constructing predictive models of human running. Journal of the Royal Society Interface, 12(103), 20140899. Schumacher, C., & Seyfarth, A. (2017). Sensor-motor maps for describing linear reflex composition in hopping. Frontiers in Computational Neuroscience, 11, 108. Seyfarth, A., Günther, M., & Blickhan, R. (2001). Stable operation of an elastic three-segment leg. Biological Cybernetics, 84(5), 365–382. Sharbafi, M. A., & Seyfarth, A. (2017). How locomotion sub-functions can control walking at different speeds? Journal of Biomechanics, 53, 163–170. Sharbafi, M. A., Rashty, A. M. N., Rode, C., & Seyfarth, A. (2017). Reconstruction of human swing leg motion with passive biarticular muscle models. Human Movement Science, 52, 96–107.

Variable Impedance Actuators and their Relation to Biology

Abstract Their impedance makes elastic actuators promising for the use in mechanical human support systems. To achieve this, all parts of an elastic actuation system need to be addressed. In this part of the book, we first discuss the mechanaical setup and especially the design of elastic elements, joints, and the specific properties of electromechanical transducers . Secondly, the control of elastic actuators is explained and also under-actuated elastic systems are considered. Finally, exemplary applications and the integration of pneumatic actuators are presented.

Design and Hardware Integration of Elastic Actuators for HMI Peter Paul Pott, Philipp Beckerle, and Kent W. Stewart

Abstract In this chapter, the basic mechanical setup is described and its potential for human-machine interaction and how it can be leveraged by design and hardware integration is discussed.

1 Motivation and Background Elastic actuators of various configurations are commonly used for human-machine interaction. In most cases for the support or replacement of joint functions in the form of orthoses, prostheses, and exoskeletons for the upper (Gopura et al. 2016) and lower extremities (Young and Ferris 2017; Veneman et al. 2017; Windrich et al. 2016). In addition, elastic actuators can also be used in human-machine interfaces, providing haptic feedback. Overall, elastic actuators have been shown to be beneficial for many human-machine interaction applications. Depending on the design of an elastic actuator, it is able to achieve a certain torque, stroke, and stiffness for any given application. In unstructured environments, where adaptation to changing boundary conditions is required, the use of variableimpedance elastic actuators have been shown to be beneficial (Ham et al. 2009; Wolf et al. 2016; Vanderborght et al. 2013). In addition, in comparison to rigid actuators, P. P. Pott (B) · K. W. Stewart Institute of Medical Device Technology, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany e-mail: [email protected] K. W. Stewart e-mail: [email protected] P. Beckerle Friedrich-Alexander-Universität Erlangen-Nürnberg, Department Electrical Engineering, Faculty of Engineering, Chair of Autonomous Systems and Mechatronics, Paul-Gordan-Straße 3/5, 91052 Erlangen, Germany e-mail: [email protected]

© Springer Nature Switzerland AG 2021 P. Beckerle et al. (eds.), Novel Bioinspired Actuator Designs for Robotics, Studies in Computational Intelligence 888, https://doi.org/10.1007/978-3-030-40886-2_4

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only elastic actuators are able to feasibly (in relation to control) imitate a zeroimpedance environment (tracking zero force), ensuring the actuator is not felt by the user (Grün 2012). This chapter is designed to give an overview of the design considerations for an elastic actuator for a given application. The actuator configuration and component selection will be discussed. Note, only rotating actuators will be looked at, however, all findings apply to linear configurations in the same way. In addition, methods of system integration and specific considerations for human-machine interaction are addressed.

2 Elastic Actuator Design Considerations When implementing an elastic actuator, several practical and usually applicationspecific considerations need to be considered. The most important consideration is the desired output impedance magnitude and frequency, as this is influenced by many factors. The following section will describe important factors to consider when building an elastic actuator.

2.1 Arrangement The first consideration in the development of an elastic actuator system is determining the appropriate, serial or parallel, system arrangement. In parallel elastic systems (Fig. 1c), the elastic element is present primarily to compensate for static loads (Beckerle et al. 2017; Arakelian 2016), so that the actual actuator has to provide only the torque or force required to conduct dynamic motions. However, the elasticity of both configurations makes it possible to store energy temporarily, such as to transfer energy from one part of the gait cycle to another (Wiggin et al. 2011; Hitt et al. 2009). Serial elasticities (Fig. 1a, b) are used for various reasons and, accordingly, take over different tasks. In the case of the spring being located between the motor and the system chassis (Fig. 1b), the spring is not rotating but only deflecting. This setup leads to rather high effort of integration due to the additional bearing being needed to allow the motor shaft to move or rotate with the spring, but not to bend. Lastly, combinations of both configurations exist, such that the positive properties of the static force/torque transfer of parallel elasticity can be combined with the advantageous control properties of serial elasticity (Mathijssen et al. 2015).

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Fig. 1 General representation of elastic drives and possible configurations. a, b show possible serial arrangements, c shows a parallel arrangement in which the load path is divided into an active and a passive branch

2.2 Elastic Element Stiffness Regardless of the configuration and design, elastic actuators add an energy-storing capability to the overall system and thus influence its dynamics and oscillating properties. Therefore, the stiffness of the spring is commonly a trade-off between compliance and output bandwidth requirements (Altes et al. 2014; Roozing et al. 2017), due to the lower natural frequency dynamics potentially overlapping with the desired operating frequencies. As a result, this elastic compliance boundary condition has to be taken into account when designing an elastic actuation system, especially with regard to the drive unit and any gearing present. If ignored, the required performance will not be achieved in transient movements or the system will exhibit undesirable oscillations. Conversely, vibration characteristics can also be used to deploy elastic drives in resonance or anti-resonance with the load, if the load shows cyclic behaviour. This is particularly the case with gear support. Large energy savings during assistive movements are possible if the resonant frequency of the elastic drive is tuned to the current resonant frequency of the system to be supported, such as with the aid of variable spring stiffness (Beckerle et al. 2017; Verstraten et al. 2016). A low-stiffness spring absorbs small perturbations and motor tracking errors, and may reduce potential damage to the surrounding environment and/or harm to users at the cost of reduced force bandwidth (Zinn et al. 2004). Moreover, they enable storing mechanical energy temporarily (Wiggin et al. 2011; Hitt et al. 2009), which reduces the overall energy requirements, e.g., of walking (Grimmer and Seyfarth 2011). While a high stiffness spring will allow a higher force/torque bandwidth (Roozing et al. 2017), however, higher controller gains will be required and the influence of

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P. P. Pott et al. ϕ2 τ 2

ϕ2 τ 2

τ1 ϕ1

τ1 ϕ1

b)

ϕ2

τ2 ϕ2

τ ϕ11 τ1

a)

τ2

ϕ2 τ 2

c)

ϕ1 d)

τ1

ϕ1 e)

Fig. 2 Overview of possible spring types in elastic rotary actuators ϕ1 , ω1 refer to the input, ϕ2 , ω2 to the output accordingly. a spiral spring (bending beam), b circular arrangement of tension/compression springs), c monolithic structured bending spring elements (bending beam), d torsion bar with arbitrary cross-section, e classical coil spring (bending beam under torsion load). In linear systems leaf springs an coil springs are commonly used.scal

disturbance loads will be significantly higher. If a rather stiff spring is chosen, the elasticity is primarily used to measure the momentary force or torque by evaluating the difference in angle. In state-space, such a system allows direct access to the otherwise unknown acting output torque magnitude. Note, an elastic actuator is not able to render a stiffness higher than that of the selected spring. Therefore, the spring stiffness should be equivalent to or more than the stiffest environment to be rendered. Robinson and Pratt define a rough guide on how to choose the appropriate spring constant for a SEA (Robinson and Pratt 2000). However, the spring stiffness is ultimately dependent on the intended application of an elastic actuator. The stiffness of SEAs made for human exoskeletons reported in literature varies anywhere from 1 (Ates et al. 2014) to 280 (Accoto et al. 2013) Nm/rad, with stiffness generally increasing with the expected load side disturbance torque. However, considerable variation can be seen, likely due to different magnitude and bandwidth of output torques being required.

2.3 Elastic Element Design The central component of an elastic actuator is the spring or, more generally, the elastic element. The state of the art comprises numerous forms of springs (Fig. 2), some of which were developed empirically, some within optimization processes (Sahoo et al. 2018; Stuhlenmiller et al. 2018). In design, integration-specific boundary conditions such as diameter, width, or scalability (Pott et al. 2013) often play a major role. Additionally, energy density is limited, so that each optimization method—at given forces or moments—must come to the same minimum volume. Most spring designs aim at achieving linear spring behaviour. The elastic element absorbs mechanical energy and stores it through deformation in the form of material stresses. These stresses must not exceed a material-specific value in order to prevent plastic deformation or permanent damage to this element.

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However, the permissible stresses do not only depend on the material, but also on the geometry of the spring. For this reason, multi-axial stress states or strong notch effects should be considered and avoided during design. In addition, when selecting the spring material, the hysteresis of material should be kept in mind. Moreover, spring geometry should also be further considered. Long and thin slender springs (Fig. 2d, e) require more axial space, have a low rotational inertia, and are more prone to buckling from potential axial misalignments. Conversely, short springs of a large diameter (Fig. 2a–c) require more radial space, have a high rotational inertia, and are less prone to buckling. The most of important factors for this design choice should be inertia, as this will directly reduce system bandwidth and energy density as this affects mass (Saerens et al. 2019).

2.4 Actuator and Gearing The torque-velocity characteristics of actuator and gearing are important as they directly influence the frequency and magnitude response of the SEA (Altes et al. 2014). Commonly, electric actuators in the form of DC or BLDC motors are used, where BLDC motors have the advantage of increased actuator lifetime and reduced rotational friction. These usually exhibit speeds in the range of 3000 to 6000 rpm, which is unsuitable for human-machine interaction actuators, where in extreme cases, such as the knee joint velocity in the sit-to-stand movement, only 200◦ /s (33.3 rpm) are achieved (Pott et al. 2017). Conversely, the high torques required (e.g., approx. 1 Nm per kg of body weight in the knee required when standing up) exceed the capabilities of DC motors. Therefore, reduction gears are necessary to meet the design requirements. Depending on the task, the desired output characteristics, and the kind of movement (rotation or linear) a variety of gearing can be used. Simple spur gearing, planetary gearing, and strain wave gears (SWG, also known as Harmonic Drive™ gearing are commonly used in rotating systems. Lead screws, rack and pinion drives, or winches that coil up a thread are used in linear systems that use rotating actuators. The introduction of gearing, however, introduces friction and gear backlash, creating ’dead times’ that have to be considered in control design, especially for cyclical movements. In addition, the gear reduction reduces the output angular velocity, therefore limiting the frequency bandwidth of the actuation system. Furthermore, the manufacturers of such gear units usually design these for a specific service life under a continuous nominal load in one direction, which is far from matching the load profile in human-robot interaction. As a result, standard gearboxes are often larger and heavier than necessary for the specific case when chosen for the maximum torque expected during interaction. Close consultation with the manufacturer is therefore advisable to ensure the best actuator and gearbox is selected. In addition, the efficiency characteristics of off-the-shelf gear boxes should be taken into account and modelled (Verstraten et al. 2015), which supports the optimization of component selection and actuator design (Stuhlenmiller et al. 2019).

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Note, if a high bandwidth and/or torque output may be required, a larger and more powerful motor might be selected. However, when attempting to use a higher power motor the accompanying increase of inertia and coil inductance and resistance that leads to a slower torque response of the motor should be considered. Equation 1 presents a simplified relationship of the motor circuit dynamics Im =

Vm , (L m · s + Rm )

(1)

while Eq. 2 shows the mechanical behaviour θ=

1 · Tm J · s2

(2)

where Im = Motor Current, Vm = Voltage applied to the motor, L m = Motor coil inductance, Rm = Motor coil resistance, J = Inertia of motor and drive train, and Tm = Motor torque. To avoid this issue and increase the response of the motor, previous systems have applied a voltage significantly higher than what the motor is designed for, e.g., 60 V on a 24 V-rated DC motor. This is feasible as long as the duration of the over-current is kept low when compared to the motor coil’s thermal time constant to reduce the heat build-up in the coil itself. This duration can be estimated using the thermal mass of the coil and the upper temperature limit of the windings’ insulation. Heat dissipation by thermal conduction has to be considered for longer overload and is based on the motor’s thermal time constant. Furthermore, if the device is designed for interaction with humans it can be expected that there will be considerable load-side disturbances. Thus for lowimpedance interaction, back drivability of the motor should be possible and the motor controller and power supply should be protected against any potentially large back electromotive force created from these disturbances in this case. Given active compliance (compliance by control), Finally, elastic drives are not limited to electrical actuation. Hydraulic and pneumatic drives are also conceivable and already applied (Toedtheide et al. 2016). Especially in the case of pneumatic systems, the compliance of the air has to be considered when designing the control system.

2.5 Bearing Arrangement Bearings are needed in most SEA arrangements to avoid deforming the elastic element (Fig. 2) in an undesired way direction or DoF. However, bearings are a source of friction and noise and thus have to be carefully aligned—also under load. Thus, a rather stiff construction is usually necessary. It has to be kept in mind, that some

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spring designs, e.g., coil springs and torsion bars (Fig. 2e) yield a considerable axial force when deformed. A similar consideration applies to the bearings in the motor and gearbox. Spring designs such as coil springs (Fig. 2a) generate potentially relevant axial forces under torsional load, which are absorbed by the gear box output shaft (see Fig. 1a) and transmitted to the bearings. Such internal loads must also be taken into account when configuring the actuators to avoid early defects, such as bearings and failure of the structure. In general, torsion springs cannot transmit significant transverse forces, so that additional bearings, intermediate shafts, and couplings may be required.

2.6 Measuring Spring Deflection The spring deflection can be measured by two different methods. The first and most common method is to measure the motor displacement, e.g., with a rear optical encoder, and the load side displacement with another encoder. The second method is to integrate the spring deflection sensor into the spring itself, i.e., locating one part of the encoder on the motor side and the other part on the load side. This has the advantage of less parts and direct measurement of the spring deflection, but requires robust alignment of the two parts of the encoder, accounting for any axial and radial deformation that may occur in the torsional spring and the fact that both parts rotate with the spring. The resolution and accuracy of the method used to measure the spring deflection determines the resolution and accuracy of the torque measured and thus, used for control. Therefore, it is very important that measurement spring deflection is accurate enough for the given spring constant and the desired output accuracy. Spring deflection is commonly measured using rotational optical encoders or a magnetic ring with GMR (giant magnetoresistive effect) or hall effect sensors due to these methods being contactless and having low inertia.

3 System Integration 3.1 Mechanical Design To build a serial elastic actuator (SEA), the spring has to be integrated in the rotating flux of torque. Thus, rigid and robust couplings are needed. Also, the angle of rotation before and after the elastic element have to be measured. To protect the spring from excessive strain, limit stops are useful. In addition, in many cases the axes of rotation of the physiological joint and the motor cannot be congruent or parallel due to space limitations, which results in the need for a transmission, such as a bevel gear or linkage.

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Figure 3 shows an example of a highly integrated serial-elastic drive unit for a knee orthosis designed to generate a peak torque of 30 Nm (Pott et al. 2013). The stiffness of the spiral spring is also designed such that it can be easily matched to a specific application by only changing its length. Sensors and limit stops are also integrated (Fig. 4). The prototype also has two ball bearings that support the bending moment created by the bevel gear and avoid a lateral deflection of the spiral spring.

Fig. 3 Example of a fully integrated SEA prototype (Pott et al. 2013). Chassis and lever arm are excluded for better visibility. Here, the spring is printed from PA6 using a selective laser melting process. For the final application it was intended to be manufactured from spring steel

Fig. 4 CAD model of the spring structure shown in Fig. 3

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3.2 Electronics and Software Design Beyond geometrical integration of hardware components, the interplay of software and hardware can be exploited to create additional functions via controls and algorithms. Moreover, software monitoring based on available sensor data can help to improve the performance and reliability of elastic actuators. An important task of high- and low-level controllers is to allocate the control input to achieve desired impedance characteristics (Calanca et al. 2015; Pott et al. 2013). Furthermore, data from the existing motion sensors on the elastic element can be used to determine the elastic torque, which might also be used for control reasons (Pratt and Williamson 1995; Veneman et al. 2006; Vallery et al. 2007). A very promising aspect is the implementation of mechanical damping through energy recuperation via the actual actuator (Beckerle 2014). Through avoiding the use of brakes or similar dissipative components, such “software damping” can reduce the system dimensions, weight, and electrical power consumption of elastic actuators. As mentioned above, an additional increase of energy efficiency might be achieved through exploiting the system’s thermal capabilities. High-level control algorithms could include models to predict the thermal behaviour of the system and overload the actuator in thermally uncritical situations. For an even more granular adaptation and thermal exploitation of the system, the thermal behaviour might be compared to data of the usage history and user intent detection algorithms, which are required for control reasons anyway. According to the expert study reported in (Beckerle 2016), technical faults are a relevant issue of elastic actuators and diagnosis methods as well as tolerance measures are subject to ongoing research. As a means for diagnosis and fault-tolerant control, monitoring the state of the actuation system and its components is promising, e.g., estimating the actual stiffness (Stuhlenmiller et al. 2019). With this information, the compliant controller can be adapted to compensate for fault-induced stiffness deviations (Stuhlenmiller et al. 2019b). While such algorithms increase the functionality of the actuation system, they need to be considered in the risk analysis and quality management process, e.g., through a Failure Modes and Effects Analysis (FMEA) (Beckerle 2017).

4 Factors for Human-Machine Interaction Particular attention should be paid to the weight of an elastic actuation system when it is used in human-machine interaction. Its overall weight comprises the weights of the electromechanical converter (motor), speed/torque adjustment (gear box), elastic element (spring), and energy storage (battery). All four components must be designed for their intended purpose and should not be over-dimensioned. Accordingly, the thermal management of the motor in particular should be considered: very high torques, e.g., when climbing stairs, mostly occur for rather short periods of time and

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thus result in peak loads that might be much higher than the constant loads during normal operation, e.g., level walking. The thermal time constant of the motor and the thermal resistance when dissipating the heat are the crucial features here. Considering them in design, it might prove applicable to overload a smaller actuator to cover the load peaks while keeping it within in its thermal constraints. Gear units must be carefully matched to the load level and the desired service life. A well-designed spring is already almost weight-optimal. Therefore, the energy accumulator should be considered in the overall system. In the long run, a short-term high current drawn by the motor can mean less energy consumption than the continuous demand of the control electronics. This should be designed for low electrical power consumption right from the start of development (Pott et al. 2017; Verstraten et al. 2015). When an elastic actuator is integrated into a wearable robotic system, force or torque generated by the drive needs to be transmitted to the human body. This is accomplished by normal and shear forces on the skin. Maximum allowable surface pressures on the skin can be determined by the duration of the period of application, body area, and individual factors like age, for instance (Zhang et al. 1994; Zinn et al. 2004). Torque and acceptable forces then define the minimum lever arm of the device and size and stiffness of the force transmitting cushion. The alignment of the technical axis of rotation of the orthotic device and the biological axis of rotation of the human joint has to be achieved as close as possible to avoid excess shear forces on the skin. The knee joint, for example, is only a hinge joint with a fixed axis of rotation in its first approximation. Rather, the axis of rotation of the knee tumbles during the flexion-extension movement. Depending on the load, that cartilage surfaces deform dynamically. This can be remedied by carefully designing the static determination of the joints by inserting additional degrees of freedom and integrating them into the design of the actual drive (Fig. 5) (Pott et al. 2017).

5 Discussion and Future Developments Elastic actuator design aims at miniaturization to reduce size, weight, and cost of the devices. Thus, maximum utilization of components (motor, gear-box, and material (spring)) is strived for. Concluding the analysis in this chapter, directions for future integration are proposed.

5.1 Potential Bandwidth Extensions Particularly applications in haptics, such as the representation of kinesthetic (Oblak and Matjaˇci´c 2011) or – above all – tactile stimuli, require frequencies in the range of 200 to 500 Hz, which cannot be generated with conventional elastic actuation systems (Hatzfeld and Kern 2016). The reduction of mechanical bandwidth is one of the most significant drawbacks of elastic actuators (Hurst et al. 2004). As a result,

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some groups have proposed the method of combining both low- and high- frequency actuators in parallel to extend the overall elastic actuator system bandwidth. Morrell et al. first proposed this parallel structure combining a 4 Hz elastic macro-actuator and a 60 Hz rigid micro-actuator, achieving 56 Hz elastic actuation (Morrell et al. 1998). This concept was again further developed later by Zinn et al. 2004 (Zinn et al. 2004), combining 20 and 200 Hz actuators reducing 5 Hz tracking error by greater than 10 times. However, the major drawback of this method is the increased actuator impedance (Morrell et al. 1998). Another potential method could be implementing the second actuator in series, with equivalent torque output but a higher frequency response and lower stroke. This would have the advantage of reduce impedance seen by the load, while maintaining the frequency bandwidth. Figure 6 shows a possible schematic design for a serialelastic drive with an additional highly dynamic drive on the output side, e.g., a piezo actuator.

Fig. 5 Different joints of an active knee orthosis (described in Pott.2017). a 1 DOF hinge joint, b hinge joint combined with a passive horizontal prismatic joint (2 DOF), c hinge joint combined with a spring-loaded vertical prismatic joint (2 DOF), d four-bar linkage matched to the movement of the knee axis

Fig. 6 Possible configuration of a highly integrated elastic drive with several actuators of different dynamics and stroke

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5.2 Thermal Management Following the goal of small and lightweight systems and considering the more or less constant power-to-weight ratio of DC motors, controlled overload of the motor is a very promising strategy. This requires careful thermal modelling of the affected parts (motor, chassis, gearing). Moreover, assessing the actual load profile, e.g., the gait cycle, is necessary to provide a valid basis for simulation. Finally, the back coupling of the weight of the device on the actual movement and thus torque requirements make an iterative approach necessary.

5.3 Conclusion Actuators with serial, parallel or both elastic elements provide many advantages for human-machine interaction in the field of robotics, collaborative work, wearable robotic systems, and medical systems. Dedicated development to reach the goals of small lightweight and powerful systems is necessary.

References Accoto, D., Carpino, G., Sergi, F., Tagliamonte, N. L., Zollo, L., & Guglielmelli, E. (2013). Design and characterization of a novel high-power series elastic actuator for a lower limb robotic orthosis. International Journal of Advanced Robotic Systems, 10(10), 359. Altes, S., Sluiter, V. I., Lammertse, P., & Stienen, A. H. A. (2014). Servosea concept: Cheap, miniature series-elastic actuators for orthotic, prosthetic and robotic hands. In 5th IEEE RAS/EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob), pp. 752–757. Arakelian, V. (2016). Gravity compensation in robotics. Advanced Robotics, 30(2), 79–96. Ates, S., Sluiter, V. I., Lammertse, P., & Stienen, A. H. A. (2014). Servosea concept: Cheap, miniature series-elastic actuators for orthotic, prosthetic and robotic hands. 5th IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics, 2014 (pp. 752– 757). IEEE: Piscataway, NJ. Beckerle, P. (2014). Human-machine-centered design and actuation of lower limb prosthetic systems: Dissertation. Beckerle, P., Perner, G., Stuhlenmiller, F., & Rinderknecht, S. (2017). Technische fehler in robotern mit elastischen aktoren-experteneinschätzungen und methodische analysen. atp edition, vol. 06, no. 59, pp. 36–45. Beckerle, P. (2016). Practical relevance of faults, diagnosis, and tolerance in elastically actuated robots. Control Engineering Practice, 50, 95–100. Beckerle, P., Verstraten, T., Mathijssen, G., Furnémont, R., Vander-borght, B., & Lefeber, D. (2017). Series and parallel elastic actuation: Influence of operating positions on design and control. IEEE/ASME Transactions on Mechatronics, 22(1), 521–529. Calanca, A., Muradore, R., & Fiorini, P. (2015). A review of algorithms for compliant control of stiff and fixed-compliance robots. IEEE/ASME Transactions on Mechatronics, 21(2), 613–624. Dominici, N., Keller, U., Vallery, H., Friedli, L., van den Brand, R., Starkey, M. L., et al. (2012). Versatile robotic interface to evaluate, enable and train locomotion and balance after neuro-motor disorders. Nature Medicine, 18(7), 1142–1147.

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Geyer, H., Seyfarth, A., & Blickhan, R. (2003). Positive force feedback in bouncing gaits? Proceedings of the Royal Society of London. Series B: Biological Sciences, 270(1529), 2173–2183. Gopura, R., Bandara, D., Kiguchi, K., & Mann, G. (2016). Developments in hardware systems of active upper-limb exoskeleton robots: A review. Robotics and Autonomous Systems, 75, 203–220. Grimmer, M., & Seyfarth, A. (2011). Stiffness adjustment of a series elastic actuator in a knee prosthesis for walking and running: The trade-off between energy and peak power optimization. In 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, I. Staff, Ed., [Place of publication not identified]: IEEE, 2011, pp. 1811–1816. Grimmer, M., Eslamy, M., Gliech, S., & Seyfarth, A. (2012). A comparison of parallel-and series elastic elements in an actuator for mimicking human ankle joint in walking and running. In Robotics and Automation (ICRA), 2012 IEEE International Conference on, IEEE, pp. 2463– 2470. Grün, P., Müller, R., & Konigorski, U. (2012). Model based control of series elastic actuators. In 4th IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob 2012), pp. 538–543. Ham, R., Sugar, T., Vanderborght, B., Hollander, K., & Lefeber, D. (2009). Compliant actuator designs. IEEE Robotics and Automation Magazine, 16(3), 81–94. Hatzfeld, C., & Kern T., Engineering haptic devices: Hatzfeld C, Kern T. (2016). Springer and London. Hitt, J., Sugar, T., Holgate, M., Bellman, R., & Hollander, K. (2009). Robotic transtibial prosthesis with biomechanical energy regeneration. Industrial Robot: An International Journal, 36(5), 441– 447. Hosoda, K., Rode, C., Siebert, T., Vanderborght, B., Weckx, M., & Lefeber, M. (2017). Actuation in legged locomotion. in Bioinspired Legged Loco-motion, Elsevier, pp. 563–622. Hosoda, K., Takuma, T., Nakamoto, A., & Hayashi, S. (2008). Biped robot design powered by antagonistic pneumatic actuators for multi-modal loco- motion. Robotics and Autonomous Systems, 56(1), 46–53. Hurst, J., Rizzi, A., & Hobbelen, D. (2004). Series elastic actuation: Potential and pitfalls. In International Conference on Climbing and Walking Robots. Hurst, J. (2019). Walk this way: To be useful around people, robots need to learn how to move like we do. IEEE Spectrum, 56(3), 30–51. Klute, G. K., Czerniecki, J. M., & Hannaford, B. (1999). McKibben artificial muscles: pneumatic actuators with biomechanical intelligence. In Advanced Intelligent Mechatronics, 1999 Proceedings. 1999 IEEE/ASME International Conference on, IEEE, pp. 221–226. Komi, P. V. (2008). Stretch-shortening cycle. Strength and power in sport, 3, 184–202. Mathijssen, G., Lefeber, D., & Vanderborght, B. (2015). Variable recruitment of parallel elastic elements: Series-parallel elastic actuators (spea) with dephased mutilated gears. IEEE/ASME Transactions on Mechatronics, 20(2), 594–602. Morrell, J. B., & Salisbury, J. K. (1998). Parallel-coupled micro-macro actuators. The International Journal of Robotics Research, 17(7), 773–791. Nelson, G., Saunders, A., Neville, N., Swilling, B., Bondaryk, J., Billings, D., et al. (2012). Petman: A humanoid robot for testing chemical protective clothing. Journal of the Robotics Society of Japan, 30(4), 372–377. Oblak, J., & Matjaˇci´c, Z. (2011). Design of a series visco-elastic actuator for multi-purpose rehabilitation haptic device. Journal of neuroengineering and rehabilitation, 8, 3. Okunaka, R., Ikemoto, S., & Hosoda, K. (2018). A new concept of pneumatic tactile sensor using pressure wave propagation in a soft chamber. In 2018 IEEE International Conference on Robotics and Biomimetics (ROBIO), IEEE, 2018, pp. 1809–1813. Papageorgiou, M. (1991). Optimierung. Statische, dynamische, stochastische Ver- fahren f"ur die Anwendung. Oldenbourg-Verlag. Plooij, M., Wisse, M., & Vallery, H. (2016). Reducing the energy consumption of robots using the bidirectional clutched parallel elastic actuator. IEEE Transactions on Robotics, 32(6), 1512–1523.

42

P. P. Pott et al.

Plooij, M., Keller, U., Sterke, B., Komi, S., Vallery, H., & von Zitzewitz, J. (2018). Design of rysen: An intrinsically safe and low-power three-dimensional overground body weight support. IEEE Robotics and Automation Letters, 3(3), 2253–2260. Pott, P. P., Graefenstein, H., Fischer, J., Müller, R., Schlaak, H. F., & Abele, E. (2013). Series elastic actuators for man-machine cooperation. In 9. ETG/GMM-Fachtagung Innovative Kleinund Mikroantriebstechnik, 19.20.09.2013, Nürnberg. Pott, P. P., Müller, R., Grün, M., Konigorski, U., & Schlaak, H. F. (2013). Seriell-elastische aktoren als antrieb für aktive orthesen. at-Automatisierungstechnik, vol. 61, no. 9, pp. 638–644. Pott, P. P., Wolf, S. I., Block, J., van Drongelen, S., Grün, M., Heitz-mann, D. W., Hielscher, J., Horn, A., Müller, R., Rettig, O., Konigorski, U., Werthschützky, R., Schlaak, H. F., & Meiß, T. (2017). Knee-ankle-foot orthosis with powered knee for support in the elderly. Proceedings of the Institution of Mechanical Engineers. Part H, Journal of Engineering in Medicine, 231(8), 715–727. Pratt, J. E., & Krupp, B. T. (2004). Series elastic actuators for legged robots. In Defense and Security. International Society for Optics and Photonics, 135–144. Pratt, G. A., & Williamson, M. M. (1995). Series elastic actuators. 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems (pp. 399–406). Los Alamitos: Calif. IEEE Computer Society Press. Raibert, M., Blankespoor, K., Nelson, G., Playter, R., & Team, T. B. (2008). Bigdog, the roughterrain quadruped robot. In Proceedings of the 17th World Congress, Proceedings Seoul, Korea, pp. 10,822–10,825. Robinson, D. W., & Pratt, G. A. (2000). Force controllable hydro-elastic actuator. In IEEE Int. Conf. Robot. Autom. Symp (ICRA 2000), vol. 2, 2000, pp. 1321–1327. Roozing, W., Malzahn, J., Kashiri, N., Caldwell, D. G., & Tsagarakis, N. G. (2017). On the stiffness selection for torque-controlled series-elastic actuators. IEEE Robotics and Automation Letters, 2(4), 2255–2262. Saerens, E., Furnémont, R., Verstraten, T., García, P. L., Crispel, S., Ducastel, V., et al. (2019). Scaling laws of compliant elements for high energy storage capacity in robotics. Mechanism and Machine Theory, 139, 482–505. Sahoo, S., Jain, A., & Pratihar, D. K. (2019). Reduction of jerk through optimization of a knee assistive device designed using four-bar controlled compliance actuator. In ASME (Hg.) 2019— Proceedings of the IMECE, 2018, V04AT06A022. Sakagami, Y., Watanabe, R., Aoyama, C., Matsunaga, S., Higaki, N., & Fujimura, K. (2002). The intelligent ASIMO: System overview and integration. in Intelligent Robots and Systems, 2002. IEEE/RSJ International Conference on, IEEE, 2002, pp. 2478–2483. Semini, C., Tsagarakis, N. G., Guglielmino, E., Focchi, M., Cannella, F., & Caldwell, D. G. (2011). Design of HyQ-a hydraulically and electrically actuated quadruped robot. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, p. 0 959 651 811 402 275. Sharbafi, M. A., Rode, C., Kurowski, S., Scholz, D., Möckel, R., Radkhah, K., Zhao, G., Rashty, A. M., von Stryk, O., & Seyfarth, A. (2016). A new biarticular actuator design facilitates control of leg function in biobiped3. Bioinspiration & Biomimetics, 11(4), p. 046 003. Sharbafi, M. A., & Seyfarth, A. (2017). How locomotion sub-functions can control walking at different speeds? Journal of biomechanics, 53, 163–170. Sharbafi, M., Shin, H., Zhao, G., Hosoda, K., & Seyfarth, A. (2017). Electric- pneumatic actuator: A new muscle for locomotion, in Actuators. Multi- disciplinary Digital Publishing Institute, 6, 30. Sharbafi, M. A., Barazesh, H., Iranikhah, M., & Seyfarth, A. (2018). Leg force control through biarticular muscles for human walking assistance. Fron- tiers in neurorobotics, 12, 39. Stuhlenmiller, F., Perner, G., Rinderknecht, S., & Beckerle, P. (2019). A stiffness- fault-tolerant control strategy for reliable physical human-robot interaction. In F. Ficuciello, F. Ruggiero, and A. Finzi (Eds.), Human friendly robotics, ser. Springer Proceedings in Advanced Robotics, vol. 7, Cham: Springer, 2019, pp. 3–14.

Design and Hardware Integration of Elastic Actuators for HMI

43

Stuhlenmiller, F., Schuy, J., & Beckerle, P. (2018). Probabilistic elastic element design for robust natural dynamics of structure-controlled variable stiffness actuators. Journal of Mechanisms and Robotics, 10(1), 011 009. Stuhlenmiller, F., Clos, D., Rinderknecht, S., Beckerle, P., & Font-Llagunes, J. M. (2019). Impact of friction and gait parameters on the optimization of series elastic actuators for gait assistance. Mechanism and Machine Theory, 133, 737–749. Toedtheide, A., Lilge, T., & Haddadin, S. (2016). Antagonistic impedance control for pneumatically actuated robot joints. IEEE Robotics and Automation Letters, 1(1), 161–168. Vallery, H., Duschau-Wicke, A., & Riener, R. (2010). "Hiding Robot Inertia Using Resonance," in Proceedings of the International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) (pp. 1271–1274). Buenos Aires: Argentina. Vallery, H., Ekkelenkamp, R., van der Kooij, H., & Buss, M. (2007). Passive and accurate torque control of series elastic actuators. IEEE/RSJ Inter- national Conference on Intelligent Robots and Systems, 2007 (pp. 3534–3538). IEEE Service Center: Piscataway, NJ. Vallery, H., Lutz, P., von Zitzewitz, J., Rauter, G., Fritschi, M., Ever-arts, C., et al. (2013). Multidirectional transparent support for overground gait training. Proceedings of the IEEE International Conference on Rehabilitation Robotics (ICORR), 1–7. Van Ham, R., Vanderborght, B., Van Damme, M., Verrelst, B., & Lefeber, D. (2007). MACCEPA, the mechanically adjustable compliance and controllable equilibrium position actuator: Design and implementation in a biped robot. Robotics and Autonomous Systems, 55(10), 761–768. Vanderborght, B., Albu-Schaeffer, A., Bicchi, A., Burdet, E., Cald-well, D. G., Carloni, R., et al. (2013). Variable impedance actuators: A review. Robotics and Autonomous Systems, 61(12), 1601–1614. Veneman, J. F. A., Burdet, N., Etienne, van der Kooji, H., & Lefeber, D. (2017). Emerging directions in lower limb externally wearable robots for gait rehabilitation and augmentation—a review. In M. O. Tokhi & G. S. Virk (eds.) Advances in Cooperative Robotics, New Jersey. World Scientific, 2017, pp. 840–850. Veneman, J. F., Ekkelenkamp, R., Kruidhof, R., van der Helm, F. C., & van der Kooij, H. (2006). A series elastic- and bowden-cable-based actuation system for use as torque actuator in exoskeletontype robots. The International Journal of Robotics Research, 25(3), 261–281. Verrelst, B., Van Ham, R., Vanderborght, B., Daerden, F., Lefeber, D., & Vermeulen, J. (2005). The pneumatic biped “Lucy” actuated with pleated pneumatic artificial muscles. Autonomous Robots, 18(2), 201–213. Verstraten, T., Mathijssen, G., Furnémont, R., Vanderborght, B., & Lefeber, D. (2015). Modeling and design of geared dc motors for energy efficiency: Comparison between theory and experiments. Mechatronics, 30, 198–213. Verstraten, T., Beckerle, P., Furnémont, R., Mathijssen, G., Vander-borght, B., & Lefeber, D. (2016). Series and parallel elastic actuation: Impact of natural dynamics on power and energy consumption. Mechanism and Machine Theory, 102, 232–246. von Zitzewitz, J., Asboth, L., Fumeaux, N., Hasse, A., Baud, L., Vallery, H., & Courtine, G. (2016). A neurorobotic platform for locomotor prosthetic de- velopment in rats and mice. Journal of Neural Engineering, 13(2), p. 026 007. Wiggin, M. B., Sawicki, G. S., & Collins, S. H. (2011). An exoskeleton using controlled energy storage and release to aid ankle propulsion. Proceedings of the IEEE International Conference on Rehabilitation Robotics, 2011, 5 975 342. Windrich, M., Grimmer, M., Christ, O., Rinderknecht, S., & Beckerle, P. (2016). Active lower limb prosthetics: A systematic review of design issues and solutions. Biomedical Engineering Online, 15(Suppl 3), 140. Wisse, M., & Van der Linde, R. Q. (2007). Delft pneumatic bipeds. Springer Science & Business Media, vol. 34. Wolf, S., Grioli, G., Eiberger, O., Friedl, W., Grebenstein, M., Hoppner, H., et al. (2016). Variable stiffness actuators: Review on design and components. IEEE/ASME Transactions on Mechatronics, 21(5), 2418–2430.

44

P. P. Pott et al.

Wyss, D., Pennycott, A., Bartenbach, P., Riener, R., & Vallery, H. (2019). A multidimensional compliant decoupled actuator (mucda) for pelvic support during gait. IEEE Transactions on Mechatronics, 24(1), 164–174. Young, A. J., & Ferris, D. P. (2017). State of the art and future directions for lower limb robotic exoskeletons. IEEE Transactions on Neural Systems and Rehabilitation Engineering : A Publication of the IEEE Engineering in Medicine and Biology Society, 25(2), 171–182. Zhang, M., Turner-Smith, A. R., & Roberts, V. C. (1994). The reaction of skin and soft tissue to shear forces applied externally to the skin surface. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 208(4), 217–222. Zhao, G., Sharbafi, M., Vlutters, M., Van Asseldonk, E., & Seyfarth, A. (2017). Template model inspired leg force feedback based control can assist human walking. In 2017 International Conference on Rehabilitation Robotics (ICORR), IEEE, pp. 473–478. Zinn, M., Khatib, M., Roth, B., & Salisbury, K. (2004). Playing it safe again. IEEE Robotics & Automation Magazine, 12–21.

Compliant Multi-DOF Actuation H. Vallery and M. Plooij

Abstract The basic approach of elastic actuation can be expanded to applications with multiple Degrees of Freedom (DoF). In this chapter, conceptual configurations and examples are described. Control approaches such as linear-quadratic-integral (LQI) and cascaded force-velocity control are presented and discussed, including the equivalence of these schemes for the 1-DoF case. In addition, underactuation and kinematic redundancy are considered with relation to robotic systems with elastic actuation.

1 Motivation for n-DoF Series Elastic Actuators The concept of Series Elastic Actuators (SEAs) can be extended to enable also applications with more than one Degree of Freedom (DoF). In this part, several concepts for possible configurations, as well as examples will be provided. All examples are given for robotic manipulators that are connected to a load only at their end effectors.

2 State-space Representation of n-DoF Series Elastic Actuators In most cases, it is convenient to choose a state vector x that consists of a minimal set of generalized coordinates, subsumed in vector q, and their derivatives q˙ with respect to time. As such generalized coordinates, it is often convenient to choose as q the motor positions s, such that the state vector is H. Vallery (B) TU Delft, Mekelweg 2, 2628 Delft, CD, The Netherlands e-mail: [email protected] M. Plooij Demcon, Delft, The Netherlands © Springer Nature Switzerland AG 2021 P. Beckerle et al. (eds.), Novel Bioinspired Actuator Designs for Robotics, Studies in Computational Intelligence 888, https://doi.org/10.1007/978-3-030-40886-2_5

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x=

  s s˙

(1)

Furthermore, we have an input vector u with motor forces, a disturbance vector v with the position of the end effector and an output vector y. The time derivative of the state is a vector function of the state, the disturbance and the input: x˙ = f (x, v, u).

(2)

We assume that the output is a vector function of the positions and disturbance only: y = g(s, v) (3) Such an output can for instance contain forces, desired positions, or desired relationships between positions. More specifically, because the force in a SEA is a function of positions, y, as a function of states, can directly contain the SEA’s forces. Now we linearize the system as follows: xˆ = x − x ∗ yˆ = y − y ∗

(4) (5)

uˆ = u − u ∗

(6)

where the * denotes a desired vector. In order to make sure that this is a stationary point of the system, the desired vectors have to be such that: f (x ∗ , v, u ∗ ) = 0 g(s ∗ , v) = y ∗

(7) (8)

Equation 7 implies that s˙ ∗ = 0. The linearized system equations are x˙ˆ = Axˆ + Buˆ yˆ = Cx, ˆ

(9) (10)

with A, B and C calculated as:   ∂f 0 I = −M−1 K −M−1 D ∂x   ∂f 0 B= = M−1 ∂u   ∂g = −G 0 C= ∂x

A=

(11) (12) (13)

Compliant Multi-DOF Actuation

47

where M is the mass matrix, I is the identity matrix, K is a stiffness matrix, D is a damping matrix and G defines the outputs.

3 LQI Control of n-DoF SEAs There are many possible controllers that can be applied to systems in the form of (9), (10). Here, we will derive a linear-quadratic-integral (LQI) controller. In the next section, we will demonstrate that LQI control leads to a structure that is identical to conventional cascaded force-velocity control. LQI control optimizes the cost function (Papageorgiou 1991): J= with the definition

1 2

 0

∞

(||x − x ∗ ||2Q + ||χ ||2W + ||u − u ∗ ||2R )dt,

χ˙ := y − y ∗ ,

(14)

(15)

and Q, W and R are positive definite weight matrices. In (14), the notation with a weighting matrix W and a vector χ is shorthand for ||χ||2W = χ T Wχ. The optimal solution has the following structure (Papageorgiou 1991): ∗

u = u − Kp xˆ − Ki

 yˆ dt

(16)

The gain matrices Kp and Ki are obtained as follows:   P˜ P˜ Kp = R−1 BT ˜ 11 ˜ 12 P21 P22   P˜ Ki = R−1 BT ˜ 13 P23

(17) (18)

where the P˜ i j matrices are part of the solution of the Continuous-Time Algebraic Ricatti Equation: ˜ −1 B˜ T P˜ + Q ˜ = 0, with ˜ +A ˜ T P˜ − P˜ BR P˜ A ⎡ ⎤   0 I 0 A 0 ˜ = A = ⎣−M−1 K −M−1 D 0⎦ C0 −G 0 0 ⎤ ⎡   0 B B˜ = = ⎣M−1 ⎦ 0 0

(19) (20)

(21)

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⎡

⎤ Q11 Q12 0 ˜ = ⎣Q21 Q22 0 ⎦ Q 0 0 W ⎤ ⎡ ˜P11 P˜ 12 P˜ 13 P˜ = ⎣P˜ 21 P˜ 22 P˜ 23 ⎦ P˜ 31 P˜ 32 P˜ 33

(22)

(23)

From Eqs. 16, 17 and 18, we derive that: u = u ∗ − R−1 M−1 P˜ 21 sˆ − R−1 M−1 P˜ 22 s˙ˆ − R−1 M−1 P˜ 23

 yˆ dt

(24)

Note that s˙ ∗ = 0 and thus s˙ˆ = s˙ . Furthermore, by taking an inverse of G, we can obtain sˆ as function of ˆy: sˆ = −G−1 ˆy. We now derive our final control law for LQI control:  ∗ −1 −1 ˜ −1 −1 −1 ˜ u = u + R M P21 G yˆ − R M P23 yˆ dt − R−1 M−1 P˜ 22 s˙ (25)  = u ∗ − Kp,y yˆ − Ki,y yˆ dt − ˙s (26) where Kp,y is the proportional gain on y, Ki,y is the integral gain on y, and  is a damping matrix on motor level.

4 1-DoF Example Showing the Equivalence of Cascaded Force-Velocity Control and LQI Control of SEAs For the simple 1-DoF SEA, with s the position variable of the motor, xL the position of the load, k stiffness of the spring, Fm the force applied by the motor, and FL the force applied by the SEA on the load, we have  s s˙ y = FL = k(s − xL ), u = Fm ,

x=

(27) (28) (29)

and the equations of motion are m s¨ = Fm − FL = Fm + k(xL − s).

(30)

Compliant Multi-DOF Actuation

49

This system is linear already. With the definitions y ∗ = FL,ref yˆ = y − y ∗ = FL − FL,ref

(31) (32)

u ∗ = FL,ref ,  FL,ref + xL k , x∗ = 0

(33) (34)

we directly obtain the state-space equations as in (9) and (10), with  A=

B=

C=

0 1 − mk 0



 0 1 m

 k 0

In this scalar case, the LQI control (26) resolves to:  Fm = FL,ref + K p,y (FL,ref − FL ) + K i,y (FL,ref − FL )dt − ˙s

(35)

(36)

(37)

(38)

The solution of the Ricatti equation, which provides gains as function of weights in the cost function, involves solving a fourth-order polynomial. However, in this simple 1-DoF case, the inverse calculation is simpler. In fact, it can be shown that for arbitrary choice of positive feedback gains in this case, equivalent weight matrices exist and a cost function can be reverse-engineered. So, as long as the structure of the feedback law is maintained, tuning can still be done at gain level, while maintaining the desirable stability properties of LQI. In practice, it is often beneficial to implement motor damping at drive level, because then additional delay due to communication is avoided, and one can benefit from the usually higher sampling rates in the motor drives. Without changing the above solution (38), one can re-write it to its cascaded version:  1 (39) s˙ref = [FL,ref + K p,y (FL,ref − FL ) + K i,y (FL,ref − FL )dt]  Fm = (˙sref − s˙ ), (40)

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whereby the latter is the inner (velocity) control loop implemented in the drive, the former is the outer (force) control loop that coordinates the different actuators of the robot. In order not to lose the equivalence with (38), it is important not to implement an integrator in the drive, but to use purely proportional velocity feedback.

5 n-DoF SEAs with Decoupled DoF In robots with serial kinematics, it is in principle possible to configure the robot using multiple individual SEAs for each DoF. However, there are practical limitations to this approach: Mainly, the closer an actuator is to the base of the robot, the more mass it will need to move, such that the benefit of its associated spring regarding impedance reduction reduces considerably. Generally for SEAs, it is advisable to place the compliant elements as close as possible to the end-effector, decoupling all of the robot inertia simultaneously. The concept of multidimensional SEAs with selective compliance (mSEA-SC) remedies this issue for multiple DoF. It employs a serial configuration of an n-DoF rigidly actuated robot and a separate, selectively compliant n-DoF module attached at this stiff robot’s end-effector. The compliant module again consists of two parts: A set of passive elastic elements for the n DoF that are actuated, and a set of linkages that constrain the (6-n) DoF that are not actuated. The mSEA-SC concept was applied to realize a gait rehabilitation robot for rats (Dominici et al. 2012) In that robot, the constrained DoF are rotations about the two horizontal axes. The resulting state-space model is linear, and the matrices A and B are blockdiagonal. So, the mSEA-SC can be interpreted as a set of n individual SEAs, one for each DoF, although they physically share a common elastic module. This property makes the concept particularly simple to control; it is possible to implement separate loops for each individual actuator using (39, 40) or (38). The mSEA-SC can equally be realized by unifying the two separate functions of the selective-compliant module into elements that are intrinsically designed for high compliance in some DoF and high rigidity in others. This eliminates the joints of the linkages and the friction caused in these. As an example, this was realized in a similar robot that was dedicated to rehabilitation of rats and mice (Zitzewitz et al. 2016). In contrast to the earlier rat robot (Dominici et al. 2012), this second version uses flexure joints instead of coil springs in combination with linkages. That makes it suitable for use with mice, which have a much lower body weight and are therefore more disturbed by the range of friction forces generated in linkages.

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6 Under-actuated n-DoF SEAs In practically relevant mechanical systems, (2) can be written more specifically as affine in the input: (41) x˙ = f 1 (x, v) + B(x, v)u. The matrix B may not have rank equal to the number of states. Then, it is not possible to steer the system to an arbitrary desired state vector, and the system is underactuated. Underactuation is trivially detected in case there are less actuators than DoF. However, not in all cases, it is necessary or even beneficial to fully actuate an n-DoF SEA. An extreme example is the MUltidimensional Compliant Decoupled Actuator (MUCDA) (Wyss et al. 2019), which enables six-DoF pelvis motion and actuates only one, namely lateral translation. Another example is the FLOAT (Vallery et al. 2013), a cable robot for gait rehabilitation, which has six DoF while having only four actuators. Yet, it realizes force control at its endeffector in the three relevant Cartesian DoF in task space, in order to provide support to a human user suspended in a harness. Underactuation does not necessarily imply that it is not possible to control a desired output vector y. It can be a choice to introduce additional DoF in the hardware if these bring other benefits to the system. In case of the FLOAT, such additional DoF are introduced in the form of positions of passive trolleys that displace along rails. The trolleys contain pulleys that deflect the cables and thereby extend the workspace of the system, while adding only little inertia. Although the dynamics of these trolleys can be influenced only partially, the remaining dynamics are self-stabilizing. The desired output of the system, the forces acting on a human user in three directions, remain unaffected and can still be controlled to any desired values within the gemoetric limitations of the system. So, the additional states remain hidden. To control such underactuated systems, choosing motor positions as generalized coordinates is not sufficient to describe the system, and further states need to be introduced. In the FLOAT robot, the vector of generalized coordinates was chosen as q = (s, x T )T , with motor (winch) positions s and trolley positions x T . Also for that robot, cascaded control was used with an outer PI force control loop, and an inner P velocity loop in the drives (Vallery et al. 2013). As such, the control structure is also identical to one that would be derived via LQI control, but gains are tuned manually.

7 Kinematic Redundancy In systems like the FLOAT (Vallery et al. 2013), where there are more DoF (motor and trolley positions) than outputs (Cartesian forces acting on the human) to be controlled, a nullspace remains regarding desired internal states. Another example is the RYSEN (Plooij et al. 2018), also a recently introduced cable robot for gait reha-

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bilitation. The RYSEN also contains trolleys with pulleys deflecting cables. In both systems, the two trolleys could displace with respect to each other without affecting the output force vector. The RYSEN features another kinematic redundancy, because lateral forces can be rendered either by moving two main motors antagonistically, or by rotating a dedicated variable-radius (VR) winch (Plooij et al. 2018). This winch compensates the intrinsic nonlinearity introduced by the geometry of the cable robot, thereby rendering almost any configuration of the system a static equilibrium, and improving lateral force tracking. However, even though locally there are infinitely many possible configurations all leading to the same output force vector, some can be far more desirable than others. Sometimes, this is due to nonlinearities in the system, which dominate the long-term behavior of the system. In the linearized model, this long-term behavior may not be visible, such that it will not be considered by the LQI controller. For example, in the RYSEN it is not desirable to perform an excessive amount of lateral motion by the VR winch, because the winch’s range is limited. Neither is it desirable to perform all lateral motion by the main BWS motors, because they are severely limited in their bandwidth. In order to deal with kinematic redundancy, additional functions of the generalized coordinates can be added to the output vector y to explicitly control hidden states, in congruence also with specific desired states x ∗ . These desired states can e.g., be found by solving the nonlinear equations for static equilibrium given the current reference and disturbance, and by providing additional expert knowledge. In the example of the FLOAT and the RYSEN, expert knowledge could be the desire to keep both trolleys at the same location, which is achieved by adding the difference of the two trolley positions to the output vector and commanding this to zero. It is worth noting that in the RYSEN, even though there is no 1-1 association of a single motor with a particular DoF, its mechanical concept does allow for nearlydecoupled actuation: While two low-bandwidth actuators, with springs in series, are mainly responsible for support of body weight, safety against falling, and slow adjustment of lateral position, three further high-bandwidth actuators are responsible for fast, low-amplitude force control in both horizontal directions.

8 Dual use of Compliant Elements in Different DoF In a standard 1-DoF situation, a spring combined with a motor is either configured in series or parallel. In an n-DoF SEA, the same spring can be configured in series with one motor, and in parallel with another in a different DoF. In case one of the motors is not present but replaced by a ground, the special case of the spring being just a passive element for one of the DoF emerges. Passive springs can be used to manipulate the passive dynamics of a system, for example to create resonance at a particular frequency, which for example be used to reduce energy consumption (Plooij et al. 2016) or to obscure inertia in haptic interaction (Vallery et al. 2010). More conventionally, they are used to compensate for offset forces such as gravity.

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The MUltidimensional Compliant DecoupledActuator (MUCDA) (Wyss et al. 2019) makes use of a compliant element that provides passive-elastic forces in 5 DoF, while simultaneously serving as series element in one single actuated DoF. Thereby, in its application as a pelvic manipulator, it guides lateral balance actively, while providing passive support in all other directions. The concept could easily be modified to include more actuators.

9 Practical Considerations of n-DoF SEAs One practical consideration with n-DoF SEAs is the physical location of the compliant elements. Especially in high-force applications, springs can be heavy and bulky. The FLOAT assembles all springs physically at the endeffector location. The issue of weight and mass is partially mitigated by combining metal coil springs with rubber insets, which are lighter. It is sometimes also possible to locate the springs at a different physical location within the system, such as in the RYSEN (Plooij et al. 2018), as long as their net effect is that of a series element close to the endeffector. The advantage is that, besides from deflection, they do not need to move with the system. Cascaded velocity loops, as in (39, 40) require separate implementation per actuator if they are realized at drive level. While this is easily done in 1-DoF or decoupled SEAs, it does not readily emerge from the LQI concept. In those cases, weighting matrices need to be chosen such that the matrix  will be diagonal, because otherwise all off-diagonal terms will be ignored.

References Dominici, N., Keller, U., Vallery, H., Friedli, L., van den Brand, R., Starkey, M. L., et al. (2012). Versatile robotic interface to evaluate, enable and train locomotion and balance after neuro-motor disorders. Nature Medicine, 18(7), 1142–1147. Papageorgiou, M. (1991). Optimierung. Statische, dynamische, stochastische Ver- fahren f"ur die Anwendung. Oldenbourg-Verlag. Plooij, M., Wisse, M., & Vallery, H. (2016). Reducing the energy consumption of robots using the bidirectional clutched parallel elastic actuator. IEEE Transactions on Robotics, 32(6), 1512–1523. Plooij, M., Keller, U., Sterke, B., Komi, S., Vallery, H., & von Zitzewitz, J. (2018). Design of rysen: An intrinsically safe and low-power three-dimensional overground body weight support. IEEE Robotics and Automation Letters, 3(3), 2253–2260. Vallery, H., Duschau-Wicke, A., & Riener, R. (2010). Hiding robot inertia using resonance. In Proceedings of the International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 1271–1274. Buenos Aires: Argentina. Vallery, H., Lutz, P., von Zitzewitz, J., Rauter, G., Fritschi, M., Everarts, C., Ronsse, R., Curt, A., & Bolliger, M. (2013). Multidirectional transparent support for overground gait training. In: Proceedings of the IEEE International Conference on Rehabilitation Robotics (ICORR) pp. 1–7.

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von Zitzewitz, J., Asboth, L., Fumeaux, N., Hasse, A., Baud, L., Vallery, H., & Courtine, G. (2016). A neurorobotic platform for locomotor prosthetic development in rats and mice. Journal of Neural Engineering, 13(2), 026 007. Wyss, D., Pennycott, A., Bartenbach, P., Riener, R., & Vallery, H. (2019). A multidimensional compliant decoupled actuator (mucda) for pelvic support during gait. IEEE Transactions on Mechatronics, 24(1), 164–174.

Hybrid Electric-Pneumatic Actuator Maziar Ahmad Sharbafi and Aida Mohammadi Nejad Rashty

Abstract Compared to biological muscles, current technical actuators are limited in their performance and versatility to realize human-like locomotion. In order to overcome the actuator limitations for locomotion, we introduce the hybrid EPA actuator as a combination of electric and pneumatic actuators in this chapter. As a new variable impedance actuator, the EPA design provides direct access to the control and morphological properties. We demonstrate that with the EPA, the actuator limitations could be clearly reduced in vertical hopping.

Biological muscles with extremely low impedance (backdrivable) and stiction, providing a perfect force source, could be considered as templates to design performant actuators (Pratt and Krupp 2004). Evolution in millions of years decided that moderate bandwidth is sufficient for controlled movement while the compromise among precision, versatility and efficiency is optimized for a large range of tasks e.g., locomotion. Indeed, a limited bandwidth is sufficient for even highly dynamic human/animal locomotion. Useful properties of biological actuators missing in artificial ones relate not only to their differences in fundamental characteristics, but also to the implementation and control methods of engineered actuators. Since our actuators differ from biological muscles, the combination of different actuators can be helpful for mimicking muscle behaviors. This bioinspired approach could result in either hybrid actuators (similar to what is observed in muscle tendon interactions) or redundancy (similar to muscle fiber recruitment). Another level of redundancy can be achieved by employing mono- and bi-articular actuators to achieve designs with M. Ahmad Sharbafi (B) College of Engineering, School of ECE, University of Tehran, P.O. Box 14395/515, Tehran, Iran e-mail: [email protected] A. Mohammadi Nejad Rashty Institut für Sportwissenschaft, Centre for Cognitive Science, Technische Universität Darmstadt, Alexanderstr. 10, D-64289, Darmstadt, Germany e-mail: [email protected]

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increased robustness and simplified control. Here, we explain a new hybrid design comprising electric motors (EM) and pneumatic artificial muscles (PAM) which can be used in different complementary arrangements. In this architecture, PAMs can be utilized as either adjustable compliance or actuators to inject energy.

1 The Need for a New Variable Impedance Actuator Actuation mechanism which supports different functions of locomotion could improve design and development of robotic legged systems such as powered assistive devices (Hosoda et al. 2017). Basically, actuators are responsible for moving the passive parts of the robots such as links, in a coordinated manner. Electric motors (EM) or Hydraulic actuators (HA) are widely utilized in legged robots (e.g., EM in Asimo (Sakagami et al. 2002), Cassie (Hurst et al. 2019), Spot robot series and HRP-4 or HA in ATLAS, PetMan (Nelson et al. 2012), BigDog (Raibert et al. 2008) or HyQ (Semini et al. 2011). Although with these actuators either position or torque control is achievable with high precision, there are issues hindering them from being perfect actuators for locomotion. For example, the EM’s torque-velocity range with the highest power output is not sufficient for the range required for locomotion tasks. Unlike non-optimal weight/power ratios of EMs for human-size robots HAs are often used in large legged robots. Nevertheless, their high price, low efficiency, nonbackdrivability are some of issues for such applications and their high impedance make them also different from biological actuators. In addition, HAs could be hazardous while interacting with human bodies (e.g., in exoskeletons). Adding elasticity to these rigid actuators (mainly EMs) like in series elastic actuators (SEA, Pratt and Williamson 1995) resolved issues such as reducing fragility to impacts. Lower impedance in SEA can also improve the efficiency of the actuator by recycling energy during the loading/unloading cycle. This similarity to the stretchshortening cycles in biological muscles, (Komi 2008) is increased with stiffness adjustment in variable impedance actuators (VIA). In (Vanderborght et al. 2013), different types of VIAs, which utilize more than one actuator such as Maccepa (Ham et al. 2007) with two EMs, are compared. If they are back-drivable (e.g., as in the humanoid robot Veronica Ham et al. 2007), both actuators with different bandwidths need to continuously consume power during joint movements which is not an efficient design. This indicates that, VIAs with serial compliance can reduce the required power, but not the torque (Mathijssen et al. 2015). Adding parallel stiffness to the SEA (called SPEA) (See Figure 5.1 for more details) could reduce peak power and energy consumption of the actuator (Mathijssen et al. 2015; Grimmer 2012). Tuning parallel stiffness needs more active mechanisms. Therefore, developing a hybrid actuator with serial and parallel compliance which can be simply adjusted could result in an efficient, robust and (biological) muscle-like actuation mechanism. This missing actuation system is required for achieving optimal bioinspired movement tasks such as locomotion. Investigating the functionality and neuromechanical con-

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trol of biological muscles, also demonstrates the need for a new actuation system with a novel control approach to enhance locomotor functions. Another type of actuators applied for legged robots are pneumatic artificial muscles (PAM, e.g., in Wisse and Linde 2007; Verrelst et al. 2005) which are introduced as the most similar actuators to biological muscles (Klute et al. 1999). Although PAMs are compliant, cheap and lightweight, their low bandwidth and low control precision make them imperfect for legged robots. However, this actuator can be considered as adjustable compliance with ability to inject and absorb energy. As a result, using PAMs, some sorts of stable gaits could be achieved with simple control methods (Hosoda et al. 2008; Okunaka et al. 2018).

2 EPA Design The importance of having easily adjustable compliance for legged locomotion was confirmed in our experimental studies on humans walking (Sharbafi and Seyfarth 2017), gait assistance with exoskeleton (Zhao et al. 2017) or exosuits (Sharbafi et al. 2018), robot experiments (Sharbafi et al. 2016). In the previous section, a hybrid actuator with combination of parallel and serial adjustable compliant elements was suggested to address the issues of the existing actuation systems and also to benefit from advantageous properties of the biological muscles. One of these characteristics is having similar functionality of the muscles while they are different in contraction properties (e.g., maximum contraction speed, maximum isometric force). In artificial muscles (engineered actuators), we could implement this feature using combination of different actuator types e.g., electric motors and pneumatic actuators. On one hand, electric motors (EM) are appropriate for continuous operation at constant speeds. On the other hand, pneumatic artificial muscles could be employed as variable compliance (Vanderborght et al. 2013). It was shown that combining EM and PAM result in improved robustness, efficiency and simpler control in legged locomotion (Sharbafi et al. 2017). In this design, PAMs can be integrated in the actuation system of segmented mechanism beside the EMs in a serial or parallel arrangement. Figure 1 demonstrates a bioinspired robot design (BioBiped3) and the adapted version using PAMs instead of springs. The original idea of developing BioBiped robot series was mimicking human musculoskeletal system using passive springs or SEAs. Because of different issues emerged from the fixed compliance in the experiments with the robot such as energy inefficiency and sensitivity of the control parameters for achieving stable gait at different conditions (e.g., hopping frequency) (Sharbafi et al. 2016), we came up with a new design of employing variable compliance. Here, PAMs are suggested to be used as adjustable compliance (e.g., for different gaits), or energy injector in the EPA (Electric-Pneumatic Actuator) design (see Fig. 1 right). The preliminary experimental results of implementing this idea on a simpler robot with one leg which support the claims are presented in the following.

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Fig. 1 Schematic design of (left) BioBiped3 (Sharbafi et al. 2016) and (right) the concept for an EPA-instrumented BioBiped (Sharbafi et al. 2017) by replacing SEAs (serial elastic actuator) with EPAs (electric-pneumatic actuator) and passive springs with PAMs (pneumatic artificial muscle)

3 Experimental Evidence In this section, we briefly describe the EPA-Hopper robot experiments and the effects of the PAM pressure on performance and efficiency of the hopping motion. The EPA-Hopper robot series (called EPAH hereafter) are designed based on the hybrid actuation concept. EPAH1 includes two-segment leg (thigh and shank) which is extended by a human-like foot in EPAH2, as shown in Fig. 2. Both of these hopper robots include two EMs (electric motors) for controlling hip and knee joints (both placed at hip) and three PAMs (pneumatic artificial muscle). Two PAMs work as antagonistic parallel variable compliant elements for the knee joint. The third PAM is used as serial compliance to the EM at knee and the ankle extensor, in EPAH1 and EPAH2, respectively (see Fig. 2). The robot hip is constrained by a vertical guide which avoids its horizontal motion. Most of the body mass is concentrated at the hip joint where the two motors are placed. In these robots, different arrangements of EM and PAM are utilized; (1) EM for hip, (2) PAM for the ankle, and (3) EPA with combination of EM and PAM in series and parallel for the knee joint. Position control is used for knee and hip joint in the flight phase, while the ankle joint use passive compliant PAM (with closed valves). For the knee joint in the stance phase,

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(a)

Ankle-extensor PAM

Antagonistic Parallel PAMS

Serial PAM

Antagonistic Parallel PAMS

2 EMs for hip & knee joints

(b)

Fig. 2 The EPA-Hopper robot series (a) with two segmented legs and EPA (electric-pneumatic actuator) for knee joint (b) with three segments, two antagonistic PAMs at knee and one PAM (pneumatic artificial muscle) for ankle extensor

the reflex control with positive force feedback from (Geyer et al. 2003) is employed. Surprisingly, after tuning the control parameters for EPAH1 to reach stable hopping, the same controller (without changing control parameters) could stabilize EPAH2. This means that a neuromuscular controller besides the bioinspired body design could yield stable locomotion for a wide range of locomotor systems. Roughly speaking, bioinspiration through control and mechanical embodiment could result in increasing robustness and reducing sensitivity to significant changes such as adding a new segment. For this, the EPA as a bioinspired actuation system has an important role in providing robustness against variations in mechanical design of the robot. This is confirmed when the stabilizing controller for the EPAH1 robot without PAMs cannot generate stable hopping in EPAH2 (without PAMs at knee) unless after control parameter modification. Here, we briefly explain the outcomes of experiments on EPAH1. It is observed that tuning the actuator compliance (impedance) with the PAMs results in increasing the efficiency and robustness of the movement. We performed several experiments to examine the role of parallel and serial PAMs and their corresponding compliance

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(tuned by the pressure). Three different pressures (4, 5 and 6 bar) for the serial PAM and the flexor parallel PAM are examined besides the case of removing each PAM (No-PAM). For the parallel extensor PAM, we considered two options which were a fixed sinusoidal pressure and No-PAM. With fixed pressure for this PAM, no stable hopping can be achieved. Stability is measured by performing 15 continuous hops (including stance and flight phases) without deviating more than 20% from the average hopping height. With this definition, the variation in hopping height could be considered as stability index. It means that in some cases, there is no asymptotically stable limit cycle, but the states are bounded in an acceptable neighborhood of a limit cycle. The results showed that with PAMs having appropriate pressures, the performance (hopping height), energy efficiency (measured by integrating the electric power) and stability can be significantly improved. It is worth to mention that for all cases, the same controllers are used for the EMs.

References Geyer, H., Seyfarth, A., & Blickhan, R. (2003). Positive force feedback in bouncing gaits?. Proceedings of the Royal Society of London. Series B: Biological Sciences, vol. 270, no. 1529, pp. 2173–2183. Grimmer, M., Eslamy, M., Gliech,S., & Seyfarth, A. (2012). A comparison of parallel-and serieselastic elements in an actuator for mimicking human ankle joint inwalking and running. In Robotics and Automation (ICRA), 2012IEEE International Conference on, IEEE, pp. 2463–2470. Hosoda, K., Rode, C., Siebert, B., Vanderborght, T., Weckx, M., & Lefeber, D. (2017). Actuation in legged locomotion, in Bioinspired Legged Locomotion, Elsevier, pp. 563–622. Hosoda, K., Takuma, T., Nakamoto, A., & Hayashi, S. (2008). Biped robot design powered by antagonistic pneumatic actuators for multi-modal loco-motion. Robotics and Autonomous Systems, 56(1), 46–53. Hurst, J. (2019). Walk this way: To be useful around people, robots need to learn how to move like we do. IEEE Spectrum, 56(3), 30–51. Klute, G. K., Czerniecki, J. M., & Hannaford, B. (1999). McKibben artificial muscles: Pneumatic actuators with biomechanical intelligence. In Advanced Intelligent Mechatronics, 1999. Proceedings. 1999 IEEE/ASME International Conference on, IEEE, pp. 221–226. Komi, P. V. (2008). Stretch-shortening cycle. Strength and Power in Sport, 3, 184–202. Mathijssen, G., Lefeber, D., & Vanderborght, B. (2015). Variable recruitment of parallel elastic elements: Series-parallel elastic actuators (spea) with dephased mutilated gears. IEEE/ASME Transactions on Mechatronics, 20(2), 594–602. Nelson, G., Saunders, A., Neville, N., Swilling, B., Bondaryk, J., Billings, D., et al. (2012). Petman: A humanoid robot for testing chemical protective clothing. Journal of the Robotics Society of Japan, 30(4), 372–377. Okunaka, R., Ikemoto, S., & Hosoda, K. (2018). A new concept of pneumatic tactile sensor using pressure wave propagation in a soft chamber. In 2018 IEEE International Conference on Robotics and Biomimetics (ROBIO), IEEE, 2018, pp. 1809–1813. Pratt, J. E., & Krupp, B. T. (2004). Series elastic actuators for legged robots, in Defense and Security. International Society for Optics and Photonics, 135–144.

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Pratt, G. A., & Williamson, M. M. (1995). Series elastic actuators. In 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems, Los Alamitos, Calif. IEEE Computer Society Press, pp. 399–406. Raibert, M., Blankespoor, K., Nelson, G., Playter, R., & Team, T. B. (2008) Bigdog, the roughterrain quadruped robot, in Proceedings of the 17th World Congress, Proceedings Seoul, Korea, pp. 10,822–10,825. Sakagami, Y., Watanabe, R., Aoyama, C., Matsunaga, S., Higaki, N., & Fujimura, K. (2002). The intelligent ASIMO: System overview and integration, in Intelligent Robots and Systems, 2002. IEEE/RSJ International Conference on, IEEE, 2002, pp. 2478–2483. Semini, C., Tsagarakis, N. G., Guglielmino, E., Focchi, M., Cannella, F., & Caldwell, D. G. (2011). Design of HyQ-a hydraulically and electrically actuated quadruped robot. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, p. 0 959 651 811 402 275. Sharbafi, M. A., Rode, C., Kurowski, S., Scholz, D., Möckel, R., Radkhah, K., Zhao, G., Rashty, A. M., von Stryk, O., & Seyfarth, A. (2016) A new biarticular actuator design facilitates control of leg function in biobiped3. Bioinspiration & Biomimetics, 11(4), 046 003. Sharbafi, M. A., & Seyfarth, A. (2017). How locomotion sub-functions can control walking at different speeds? Journal of Biomechanics, 53, 163–170. Sharbafi, M., Shin, H., Zhao, G., Hosoda, K., & Seyfarth, A. (2017). “Electric- pneumatic actuator: A new muscle for locomotion,” in Actuators. Multi-disciplinary Digital Publishing Institute, 6, 30. Sharbafi, M. A., Barazesh, H., Iranikhah, M., & Seyfarth, A. (2018). Leg force control through biarticular muscles for human walking assistance. Frontiers in Neurorobotics, 12, 39. Van Ham, R., Vanderborght, B., Van Damme, M., Verrelst, B., & Lefeber, D. (2007). MACCEPA, the mechanically adjustable compliance and controllable equilibrium position actuator: Design and implementation in a biped robot. Robotics and Autonomous Systems, 55(10), 761–768. Vanderborght, B., Albu-Schaeffer, A.,Bicchi, A., Burdet, E., Cald- well, D. G., Carloni, R., Catalano,M., Eiberger, O., Friedl, W., Ganesh, G., Garabini, M., Grebenstein,M., Grioli, G., Haddadin, S., Hoppner, H., Jafari, A., Laffranchi,M., Lefeber, D., Petit, F., Stramigioli, S., Tsagarakis, N., vanDamme, M., van Ham, R., Visser, L. C., & Wolf, S. (2013). Variableimpedance actuators: A review. Robotics and AutonomousSystems, 61(12), 1601–1614. Verrelst, B., Van Ham, R., Vanderborght, B., Daerden, F., Lefeber, D., & Vermeulen, J. (2005). The pneumatic biped “Lucy” actuated with pleated pneumatic artificial muscles. Autonomous Robots, 18(2), 201–213. Wisse, M., & Van der Linde, R. Q. (2007). Delft pneumatic bipeds. Springer Science & Business Media, Vol. 34. Zhao, G., Sharbafi, M., Vlutters, M., Van Asseldonk, E., & Seyfarth, A. (2017). Template model inspired leg force feedback based control can assist human walking. In 2017 International Conference on Rehabilitation Robotics (ICORR), IEEE, pp. 473–478.

State of the Art of Engineered Actuators Approaching Muscle Behaviors

Abstract We present three different perspectives. Analyzing muscle dynamics shows the integrative design of the biological actuation system within the motor unit recruitment concept. This contrasts with the traditional design procedure of an engineered actuation system. We describe how the motor unit recruitment concept can be extended for an actuator design in the light of considering each unit as a finite (adjustable) impedance. Then, the implementation of this concept on man-made actuators is explored by introducing the Dual-Motor Actuator (DMA) as another type of redundant actuators. We focus on the potential of kinematically redundant actuation, which fulfills a role similar to that of sarcomeres in the human muscle. Finally, we describe how real biological muscles can be used for driving movement in artificial locomotor systems. Moreover, we explain how pneumatic actuators (as the closest known actuators to the biological muscles in terms of similarity in force-generating mechanism) can benefit from biological muscle-like behaviors to drive legged robots.

Muscle-Like Actuators and Their System Dynamics Joshua Schultz

Abstract Muscle-like actuators can be composed by connecting together individual contractile modules in a variety of configurations. This chapter shows that by including more or fewer modules and varying how they are connected the designer can tailor the configuration to the application in precise ways and produce actuators in a range of form factors. As more of the units are recruited, or brought into the active state, the muscle-like actuator contracts, imparting motion to the robot. New algorithms are needed to determine how best to recruit, and these algorithms must consider the system dynamics of the muscle-like actuator, which will depend on how they are configured, unlike traditional actuators which are easily modeled by linear filters.

1 Muscle-Like Actuators Behave like an Impedance to Accommodate Environmental Uncertainty A couple of decades after the advent of industrial robots, researchers recognized that human muscles have certain benefits with regard to producing explosive motions, as well as coping with uncertainty in the environment. Although traditional servomotors have several notable advantages in a general context (high power density, ease of operation), to capture the specific benefits posed by muscles in the motions taken by humans and animals the search began for actuators that are “muscle-like”. Naturally, what would qualify as “muscle-like” is a matter of interpretation, but there was a loose consensus that a muscle-like actuator is one that responds to an external load in the manner that a muscle does. This brings up the notion of the system dynamics of the actuator; that it is in some way like how a muscle behaves from the standpoint of its impulse response. A muscle is not simply a position or torque source that is proportional to a neural stimulus; how it is loaded and its length directly influence the forces and differential J. Schultz (B) Department of Mechanical Engineering, University of Tulsa, Tulsa, OK 74104, USA e-mail: [email protected] © Springer Nature Switzerland AG 2021 P. Beckerle et al. (eds.), Novel Bioinspired Actuator Designs for Robotics, Studies in Computational Intelligence 888, https://doi.org/10.1007/978-3-030-40886-2_7

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change in length that it will produce. This is important when the robot is in contact with the environment: Hogan (1984) wrote. An important consequence of dynamic interaction between two physical systems such as a manipulator and its environment is that one interaction must physically complement the other: Along any degree of freedom, if one is an impedance, the other must be an admittance and vice versa.

Hogan goes on to say that it may not always be possible to represent the environment as an impedance, but it is always possible to represent it as an admittance (as even an immovable object is well-posed when represented as an admittance). If the designer can make sure that the robot’s force–displacement behavior is that of an impedance, it can accommodate uncertainties in position in a well-posed way. If the actuator contains physical components that behave as an impedance when a force is imposed by the environment (i.e., it has some “give”, rather than being a kinematic constraint), the robot will be an impedance regardless of the control signal applied—even if the robot is “off”. Human muscle can also said to exploit this idea of impedance for successful operation. In another work (Hogan 1984), Hogan used human subject studies to show that humans actively increase the stiffness of a joint (the impedance viewed from the standpoint of the environment) by co-activation of the muscles to offset a gravitational disturbance. So, the human body is not only behaving as an impedance, but it is able to modulate the system dynamics of that impedance to govern the mechanics of the interaction. From this point of view, any muscle-like actuator should have a finite impedance and better yet, the ability to vary this impedance within some range. Because muscles have length-dependent and load-dependent behavior, musclelike actuators may very well need a more involved treatment of their system dynamics than traditional actuators. Consider the control block diagram shown in Fig. 1: typically one begins with a control design and a model of whatever is being driven. Actuator dynamics are often added as an afterthought, by putting a transfer function between the control input and the driven system. This is equivalent to viewing the actuator as a filter or correction factor to make the interaction more realistic. There is a key assumption made that comes along with the block diagram representation, however. One tacitly assumes that each block has high input impedance and low output impedance, or the signal coming from the actuator block and going to the plant is the same as it would be if the plant were not attached.1 Another way of expressing this is that the actuator only interacts with the plant through the actuator’s output equation; the plant cannot affect the actuator states (other than by virtue of the control error in the feedback configuration). When the actuator can store and return energy from the plant, and the plant state affects its force production, the model in Fig. 1 a no longer works. It is more accurate to augment the state model with the actuator physics in a manner that represents the energy exchange between the actuator and the system it drives. 1I

first recall hearing this point in a lecture at Vanderbilt University given by Michael Goldfarb; I do not recall seeing it stated explicitly in an extant work.

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Fig. 1 “Squeezing” an actuator transfer function between the controller and the plant assumes a high input impedance/low output impedance relationship. To truly represent the physics of a muscle-like actuator, you need to include a feedback loop as shown in the lower graphic

The vast majority of work in muscle-like actuators has been on understanding the behavior of the various technological devices that display this type of behavior. Because they are composed of elastomeric materials and the compressibility of air, fiber reinforced bladder actuators (McKibben muscles) were among the earliest types of artificial muscles to be studied. Although there are scholarly works on this technology dating back to the early to mid twentieth century, the work of Chou and Hannaford (1996) can be considered to be the seminal work, proposing the basis of the mathematical model used today, with later improvements and dynamic experiments conducted by Davis et al. (2011). Pneumatic artificial muscles are discussed at length in this chapter. Since the development of McKibben muscles, there have been a variety of active technologies with intrinsic compliance considered for use as artificial muscles. Madden et al. provide a good summary (Madden et al. 2004).

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2 Actuators Composed of Discrete Units The ability of muscles to provide a natural impedance in response to perturbations from the environment is not the only characteristic that is desirable for robotic applications. Muscle is composed of numerous small cells (or fibers) that work together to produce a contraction. It is unlikely that many of these fibers will fail simultaneously. If some fibers fail, the remaining fibers can still carry the load in most scenarios, and instead of losing a degree of freedom, the muscle can still operate; only some performance is lost. These built-in redundancy properties are very attractive to roboticists as they will enable missions of greater persistence to be accomplished. Researchers began examining ways that this property could be captured in an engineering device. One of the earliest examples is the work of Huston (2005, 2002), who proposed an actuator composed of “subactuators”, shape memory alloy contractile elements joined by whiffletree mechanism. Originally developed to allow a pair of oxen to drive a load, whiffletree mechanisms have a branching structure to couple the actions of two force sources to the load while allowing slight variations in displacement between each one. Du et al. (2010) used a high-redundancy system composed of multiple motors with ball-screws that prevented one from backdriving its neighbor. They examined the consequences of different types of failures of individual units on the actuator as a whole. One important point that they made was that failures of individual units alter the system dynamics of the actuator. Bryant et al. (2014) extended the McKibben muscle concept to one with multiple, redundant chambers, and (Kianzad et al. 2015) used pennate nylon fibers which contracted under a thermal stimulus. These and other technologies represent “nifty ideas” on how to make some sort of “muscle cell” that can physically work with its neighbors to produce a contraction while still displaying compliant behavior with respect to the environment. While the proofs of concept are interesting and exciting, from a design perspective there was a need for a systematic approach for how to architect an actuator from its individual “fibers” and determine the corresponding dynamic plant model. New theories are also needed for how to control the actuator in a manner consistent with its embodiment, as the control signal needs to be distributed to all “cells” in the muscle in some way. How the control signal is distributed throughout the muscle will affect its dynamic response in many cases. Much of this decade-long work was conducted in the context of the piezoelectric cellular actuator, which uses piezoelectric stacks that have been “amplified” by a compliant mechanism to increase their stroke at the expense of force. This work, conducted primarily at MIT and Georgia Tech by many collaborators, has been collected in a book by Ueda et al. (2017). Included are methods to compute the natural frequencies based on which “cells” are active (Secord and Asada 2010), approximating the impedance seen from the environment of a complex nested system (Schultz and Ueda 2013), time-shifting boolean inputs to suppress vibration (Schultz and Ueda 2012), stochastically evaluating the consequences of individual unit failure (MacNair and Ueda 2011), and a probabilistic control methodology (Ueda et al. 2007) that allows each “cell” to transition from “off” to “on” without directly managing each one.

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Supposing that we have some suitable technology that, like a muscle cell, produces a mechanical strain in response to a signal, (referred to in the literature as “actuation units”, “subactuators”, etc.), these can be connected together or arranged in some way so that they work together as a team to move a robotic joint. One can imagine many such configurations; arranging them in series or “chains” will increase the stroke length of the actuator, and parallel combinations or “bundles” will increase the total force that can be obtained. As will be seen later, these are by no means the only ways that actuation units can be arranged, and the dynamic properties will depend on the arrangement. In a muscle-like actuator composed of on–off “cells”, an increase in control effort corresponds to some number of these units contracting.2 Inspired by human motor neurons, it is envisioned that there are a certain number of channels, and when any channel is activated (deactivated), all the contractile components connected to that channel attempt to shorten, while those on another channel take no action. These “cells” (or portions of cells) are collectively referred to as a “motor unit”, consistently with biological terminology. At instant t0 , given control input u(t) to the actuator, the number of motor units whose activation (if u(t) > 0, deactivation if otherwise) most closely approximates the value of u(t0 ) will be activated. Drawing an analogy with its biological counterpart, Mathijssen et al. referred to the selection of which units to move to the active state as recruitment (Mathijssen et al. 2015). Understanding how to recruit motor units for these discrete muscle-like actuators composed of individual actuation units is one of the foremost research questions in this area. From a philosophical standpoint this problem is abstract—simply recruit enough motor units to match the controller’s intent and it should work, but the physical reality of the actuator embodiment means that the behavior observed will depend on the concrete details of the implementation. More specifically, the actuator’s dynamic response will depend on where the cells belonging to the motor unit(s) being recruited at that instant are located (with a few exceptions, such as a single chain or a single bundle). In human skeletal muscle, the fibers from different motor units are scattered among one another (Edström and Kugelberg 1968), but in a muscle-like actuator this is up to the designer. It is possible that certain choices of arrangement will have a superior (e.g., smoother, higher bandwidth) dynamic response with certain recruitment algorithms. It is also possible that the way the units are arranged to make up the actuator at design time will greatly affect the dynamic response at run-time. Operating under the notion that “cells” can be configured any number of ways to make up an actuator is an important research frontier to be able to deduce the system dynamics of the actuator from the system dynamics of the individual units and the manner in which they are connected. In practice, it is certainly a reasonable proposition to perform a characterization of a single artificial muscle “cell”, but characterizing each and every way a collection of these cells could conceivably be 2 As

skeletal muscles can only contract in response to a stimulus and not extend, the term “contraction” is commonly used for muscle-like actuators, even though not all underlying technologies necessarily have this limitation. Due to the biological inspiration, many are contractile only in the final implementation and must be used antagonistically.

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combined into a “muscle” would be dauting indeed. The remainder of this chapter will serve as a guide for how to embark on this problem and how to discover strategic recruitment strategies. As far as the authors are aware, this is largely unexplored. Recent work by Schultz et al. (2015), Fuller and Schultz (2018), Mathijssen et al. (2017), Ebrahemi et al. (2018), represent a scant few that approach the question of how to disburse the control effort over the actuator and why one choice is superior to another.

3 Deducing the Actuator Dynamic Model from the Way the Units are Combined and Recruited As motor units are activated, the actions of each of the “cells” that make up that motor unit must propagate through the “muscle” to act on the load. Following biological terminology, we call the end of the actuator that is attached to the most proximal link the origin, and the attachment to the more distal link the insertion.3 Thus, any analysis of a muscle-like actuator must consider position and force changes from the origin, the insertion, and changes internally due to activation/or deactivation of individual units. It therefore follows that the dynamic model of an individual “cell” should accept the same perturbations at either end as well as changes in its own activation. With a good understanding of the underlying physics, it should be possible to propose a mass-spring-damper model of an individual “cell” for a given technological implementation. A unit that is activated in response to recruitment will attempt to contract, but will not behave the way that it would in free space, because it is affixed to neighboring units in some sort of junction. However, it will “pull” in some sort of dynamic way on the junction, and all the other units affixed at that junction will respond consistently with their system dynamics. Since the manner in which junctions are made has great influence on how activation “travels” through the actuator, it is a major contributor to the system dynamics. For example, the configuration in Fig. 2a would be expected to have drastically different system dynamics from the one in Fig. 2b. When discrete muscle-like actuation units (cells) are connected together, they must have some sort of series elastic element included in each one (or be comprised of an elastic active material); this is central to their dynamic properties. To do otherwise would create a hyperstatic situation, which is not well-posed mathematically and practically would create high stresses. The series spring resolves this. To see this, imagine two such units in parallel affixed at each end. If one contracts and the other does not, they are no longer at the same length and either the contraction would fail or the junction would break. However, if the unit is compliant, each of the units can have its length imposed, and the force exerted depends on the stiffness of 3 One advantage of muscle-like actuators composed of discrete units is that “muscles” can be created

containing both mono-articular and poly-articular “heads”, as with human skeletal muscle, but this will not be discussed in this work.

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Fig. 2 a “Staggered strand” of units (each represented as a brown and white “plunger” element with a series spring), four at each junction alternating connections so that the unit-to-unit connections are rich b a “bundle of chains” each junction connects only the two units (except for the “cap” at the ends), so that each “chain” is relatively decoupled from one another

the spring. Because of this compliance, if the individual units have non-negligible mass compared to the driven load, there will be lightly damped poles (for a linear or linearized model), and the actuator will have a tendency to oscillate. With large numbers of units, the number of modes will be considerable. Some of these oscillations could be transmitted to the load itself at the origin and insertion of the actuator. Depending on the physics of the individual units, the resonant frequencies of these modes may change as the activation is varied. This is the case in the piezoelectric cellular actuator of Secord and Asada (2010). Given the complexity inherent in even small configurations, there is a great need for research into methods that are able to suppress the oscillations that result.

4 Conclusion and Future Work We have discussed two key aspects of muscle-like actuators that merit further study: muscle-like actuators behave with a finite impedance, and they have a discrete structure. Preliminary work indicates a connection between the two; the actuator’s

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dynamic model depends on the characteristics of the individual units and how they are affixed to one another in the implementation. For these actuators to be useful in practice, the community needs ways to predict the dynamic behavior that will result from how the units are configured and recruited. Several areas of study will lead to progress in the near term. Model reduction techniques, abstractions of the representation and sensorization of the “muscle” will be needed. It is possible that the recruitment algorithm can be tuned so that it suppresses the oscillation from unit to unit merely by choosing motor units judiciously, and this responsibility will not need to fall to the external controller itself. Building on the various proof of concept platforms already developed, more robust platforms that can accommodate larger numbers of units also need to be developed, characterized, and validated. With any success, we may see robotic devices that resemble our own anatomy and physiology. Both the variable impedance nature and the discrete nature will be instrumental in allowing robots to succeed in uncertain and even hostile environments for long periods of time.

References Bryant, M., Meller, M., & Garcia, E. (2014). Variable recruitment fluidic artificial muscles: Modeling and experiments. Smart Materials and Structures, 23(7), 074009. https://doi.org/10.1088/09641726/23/7/074009. Chou, C.-P., & Hannaford, B. (1996). Measurement and modeling of McKibben pneumatic artificial muscles. IEEE Transactions on Robotics and Automation, 12(1), 90–102. Davis, S., & Caldwell, D. G. (2011). Biologically inspired damage tolerance in braided pneumatic muscle actuators. Journal of Intelligent Material Systems and Structures, 23(3), 313–325. https:// doi.org/10.1177/1045389X11422106. Du, X., Dixon, R., Goodall, R. M. M., Zolotas, A. C., & Zolotas, A. C. (2010). Modelling and control of a high redundancy actuator. Mechatronics, 20(1), 102–112. https://doi.org/10.1016/j. mechatronics.2009.09.009. Ebrahimi, N., Nugroho, S., Taha, A. F., Gatsis, N., Gao, W., & Jafari, A. (2018). Dynamic actuator selection and robust state-feedback control of networked soft actuators. Proceedings of the 2018 International Conference on Robotics and Automation, 2857–2864. Brisbane. Edström, L., & Kugelberg, E. (1968). Histochemical composition, distribution of fibres and fatiguability of single motor units. Anterior tibial muscle of the rat. Journal of Neurology, Neurosurgery, and Psychiatry, 31(5), 424–433. Fuller, C., & Schultz, J. (2018). Characterization of control-dependent variable stiffness behavior in discrete muscle-like actuators. Applied Sciences (Switzerland), 8(3). https://doi.org/10.3390/ app8030346. Hogan, N. (1984). Adaptive control of mechanical impedance by coactivation of antagonist muscles. IEEE Transactions on Automatic Control, 29(8), 681–690. https://doi.org/10.1109/TAC.1984.110 3644. Huston, D., Esser, B., & Werner, M. (2002). Hierarchical actuators. Proceedings of the First World Congress on Biomimetics and Artificial Muscles. Albuquerque. Huston, D., Esser, B., Spencer, G., Burns, D., & Kahn, E. (2005). Hierarchical actuator systems. Proceedings of SPIE, 5762, 311–319. https://doi.org/10.1117/12.607220. Kianzad, S., Pandit, M., Lewis, J. D., Berlingeri, A. R., Haebler, K. J., & Madden, J. D. W. (2015). Variable stiffness structure using nylon actuators arranged in a pennate muscle configuration.

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SPIE Smart Structures and Materials+ Nondestructive Evaluation and Health Monitoring, (604), 94301Z--94301Z. https://doi.org/10.1117/12.2086799. MacNair, D. L., & Ueda, J. (2011). A fingerprint method for variability and robustness analysis of stochastically controlled cellular actuator arrays. the International Journal of Robotics Research, 30(5), 536–555. https://doi.org/10.1177/0278364910397678. Madden, J. D. W. D. W., Vandesteeg, N., & A., Anquetil, P. A., Madden, P. G. A., Takshi, A., Pytel, R. Z. Z., … Hunter, I. W. W. (2004). Artificial muscle technology: Physical principles and naval prospects. IEEE Journal of Oceanic Engineering, 29(3), 706–728. https://doi.org/10.1109/JOE. 2004.833135. Mathijssen, G., Schultz, J., Vanderborght, B., & Bicchi, A. (2015). A muscle-like recruitment actuator with modular redundant actuation units for soft robotics. Robotics and Autonomous Systems, 74 Part A, 40–50. https://doi.org/10.1016/j.robot.2015.06.010. Mathijssen, G., Furnémont, R., Saraens, E., Lefeber, D., & Vanderborght, B. (2017). Discrete binary muscle-inspired actuation with motor unit overpowering and binary control strategy. IEEE /RSJ Intelligent Robots and Systems Conference, 2128–2134. Vancouver, Canada. Schultz, J., & Ueda, J. (2012). Experimental verification of discrete switching vibration suppression. Mechatronics, IEEE/ASME Transactions on, 17(2), 298–308. Schultz, J., & Ueda, J. (2013). Nested piezoelectric cellular actuators for a biologically inspired camera positioning mechanism. IEEE Transactions on Robotics, 29(5), 1125–1138. https://doi. org/10.1109/TRO.2013.2264863. Secord, T. W., & Asada, H. H. (2010). A variable stiffness actuator having tunable resonant frequencies. IEEE Transactions on Robotics, 26(6), 993–1005. Ueda, J., Odhner, L., & Asada, H. H. (2007). Broadcast feedback for stochastic cellular actuator systems consisting of Nonuniform actuator units. Proceedings of 2007 IEEE International Conference on Robotics and Automation (ICRA ’07), 642–647. https://doi.org/10.1109/ROBOT. 2007.363059. Ueda, J., Schultz, J. A., & Asada, H. H. (2017). Cellular actuators: Modularity and variability in muscle-inspired actuation (1st ed.). Cambridge, MA: Elsevier.

Energy-Efficient Kinematically Redundant Actuation Tom Verstraten

Abstract Muscles feature a large number of motor units (sarcomeres), distributed over parallel strands of muscle fibers. Only a selection of these motor units is recruited to generate the required muscle force. This mechanism has inspired researchers to introduce redundancy into engineered actuators. In this chapter, we discuss the potential of kinematically redundant actuation with regards to energy efficiency. The Dual-Motor Actuator is presented as a promising implementation.

1 Kinematic and Static Redundancy As explained in part I, human muscle exhibits redundancy on many levels. This redundancy explains many desirable features of the human muscle, which is why some researchers have become interested in incorporating redundancy into engineered actuators. The EPA presented in Chap. 6, which couples both a pneumatic and electromagnetic actuator to a single joint, is one example of a redundant actuator. Here, we will provide a more general outlook on redundant actuation. Following Müller’s reference work on planetary drivetrains (Müller 1982), we can distinguish between static and kinematic redundancy. In a kinematically redundant actuator, a specific output speed can be produced by an infinite number of input speed combinations. Conversely, in a statically redundant actuator, the output torque can be produced by an infinite number of input torque combinations. Whether an actuator is kinematically or statically redundant depends on its design. In some cases, actuators may exhibit both types of redundancy, or springs may be used which relate the mechanism’s output torque to its kinematics through Hooke’s law. Both types of redundancy are found in the human muscle as well as in engineered actuators. There are several motivations for redundancy in actuation, some of which T. Verstraten (B) Robotics and Multibody Mechanics Research Group (R&MM), Vrije Universiteit Brussel and Flanders Make, Pleinlaan 2, 1050 Elsene, Belgium e-mail: [email protected] © Springer Nature Switzerland AG 2021 P. Beckerle et al. (eds.), Novel Bioinspired Actuator Designs for Robotics, Studies in Computational Intelligence 888, https://doi.org/10.1007/978-3-030-40886-2_8

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have been documented to a lesser or greater extent. These motivations include backlash compensation and seamless gear shifting (Girard and Asada 2015; Ontañón-Ruiz et al. 1998), increased fault-tolerance, the ability to shape the actuator’s operating range to the task requirements (Lee and Choi 2012; Verstraten et al. 2019c) and improved impedance control (Kim et al. 2010). Another important motivation for redundant actuation is energy efficiency. In order to study their energy efficiency, researchers at the University of Brussels have developed two redundant actuators. The first is the statically redundant + SPEA, a series–parallel elastic actuator (SPEA) with multiple motors, springs and locking mechanisms in parallel (Mathijssen et al. 2016). The second is the kinematically redundant Dual-Motor Actuator (DMA). This chapter presents an overview of the research on the latter.

2 The Dual-Motor Actuator (DMA): Energy Efficient Kinematically Redundant Actuation The Dual-Motor Actuator (DMA), as presented in (Verstraten et al. 2018) and illustrated in Fig. 1, features two geared DC motors coupled to a single output through a planetary differential. As such, the output speed becomes a weighted sum of the two motor speeds, which makes the actuator kinematically redundant. The actuator’s redundancy creates three important mechanisms through which the actuator can lower its energy consumption: (1) tunable working points of the motors, (2) single-motor operation through controllable brakes, and (3) the ability to minimize the influence of motor inertia. These three mechanisms are discussed briefly below.

2.1 Optimizing the Working Points of the Motors Electric motors are often used as actuation units because of their high maximum efficiency. However, the efficiency of an electric motor depends strongly on its working point, i.e., its speed and torque. Typically, electric motors exhibit extremely low efficiencies at low speeds and low torques (Verstraten et al. 2015). For non-redundant actuators such as regular servomotors, the operating points are fully determined by the imposed motion and the external torques or forces applied to the load. This is particularly relevant for dynamic applications where, unlike in typical steady-state applications such as fans, pumps, the operating point constantly changes in time. Therefore, in most cases, there will be instants when the motor is used at a low efficiency, leading to a surprisingly high overall energy consumption. This is an inevitable consequence of the use of non-redundant actuators. Conversely, kinematically redundant actuators can reach a desired output speed with different combinations of input speeds. In other words, the operating points of

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(b) Fig. 1 a Prototype of the kinematically redundant Dual-Motor Actuator. b Schematic of the actuator

the actuator’s individual motors can be optimized to yield the lowest possible energy consumption. In some cases, this can bring down the energy consumption below that of a single, non-redundant motor. Still there are cases in which it may be more beneficial to use only one single, wellsized motor at a time instead of two in concert. This is where the next energy-saving mechanism applies.

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2.2 Single-motor Operation Through Controllable Brakes A disadvantage of the DMA architecture is the fact that the maximum achievable output torque is limited by the weakest motor (Verstraten et al. 2018). This can be resolved by equipping the motors with controllable holding brakes which take over whenever the motor is forced to provide a torque beyond its capabilities (Fig. 1). Brakes also enable the design of an actuator with an L-shaped operating range in the torque-speed plane, which is favourable in many robotic applications (Girard and Asada 2015; Lee and Choi 2012; Verstraten et al. 2019a). The brakes can, however, also be exploited for energy efficiency. The idea is to create one branch which provides high torques at low speeds, while the other provides low torques at high speeds. Whenever a single motor is sufficient to drive the load, the brakes will be operated such that only one motor contributes to the output. The selected motor will be the one that provides a better fit with the output requirements. A study at various steady-state operating points (Verstraten et al. 2018) and one on an active ankle prosthesis (Verstraten et al. 2019b) have indicated that, in terms of energy-efficiency, single-motor operation is to be preferred over using both motors, which entails more friction and gearbox losses. In highly dynamic applications, however, dual-motor operation presents an additional advantage, which is discussed in the following paragraph.

2.3 Optimizing Speed Ratio to Minimize the Influence of Motor Inertia In highly dynamic applications, the use of controllable brakes may not be feasible because rapid switching would be required. Still, a dual-motor actuator can provide an extended operating range—albeit not as large as with brakes—and increased energy efficiency. A brief explanation is given below; for an extended analysis we refer to (Verstraten et al. 2019c). In many robots, e.g., pick-and-place and walking robots, actuators operate in two distinct modes. During one part of the motion they are lightly loaded but move quickly, while during another part they move a high load at a lower speed. The size of the motor and its gearbox is typically defined by the highest load; consequently, the motor is effectively oversized for the lightly loaded part of the motion. Practically, this means that high torques would be required to accelerate the high reflected inertia of the motor, limiting the maximum acceleration of the motor in this phase. Kinematically redundant actuators such as the DMA have the unique ability to distribute the output speed over their input motors. It is evident that this statement also holds for its accelerations. This is the key to the energetic advantage of the DMA: the speed ratio, which characterizes the speed distribution, can be tuned to minimize the impact of the reflected inertia. Results in (Verstraten et al. 2019c). have shown

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that this strategy allows the actuator to be more efficient than a regular servomotor for a wide range of highly dynamic motions with various output accelerations and torques.

3 Series Elastic Dual-Motor Actuation As explained in part II, elastic elements provide several benefits, one of which being improved energy efficiency. Motivated by this knowledge, the DMA was combined with a series spring, forming the so-called Series-Elastic Dual-Motor Actuator (SEDMA). In (Verstraten et al. 2019b), we simulated an active ankle prosthesis driven by a SEDMA specifically designed for the task. The actuator was shown to reduce the energy consumption by 16% compared to an optimized SEA. While the SEDMA was larger than the SEA, it could provide a higher power output, making it more suitable for tasks such as walking up slopes and stair climbing. To further test the concept, a hopping robot with SEDMA-actuated knee was presented and studied in (Verstraten et al. 2019a, 2020). These works demonstrate and discuss the difficulties in terms of control and design associated with redundant actuators. Indeed: the additional motor makes the actuator much more complex. Dealing with this complexity in control, especially in dynamic applications, is a prominent challenge. In conclusion, while redundant actuation shows great promise in many ways, much research and development is still needed in order to unlock its full potential.

References Girard, A., & Asada, H. H. (2015). A two-speed actuator for robotics with fast seamless gear shifting. IEEE International Conference on Intelligent Robots and Systems. https://doi.org/10. 1109/IROS.2015.7354047. Kim, B. S., Song, J. B., & Park, J. J. (2010). A serial-type dual actuator unit with planetary gear train: Basic design and applications. IEEE/ASME Transactions on Mechatronics. https://doi.org/ 10.1109/TMECH.2009.2019639. Lee, H., & Choi, Y. (2012). A new actuator system using dual-motors and a planetary gear. IEEE/ASME Transactions on Mechatronics. https://doi.org/10.1109/TMECH.2011.2165221. Mathijssen, G., Furnémont, R., Verstraten, T., Brackx, B., Premec, J., Jiménez, R., … Vanderborght, B. (2016). +SPEA introduction: Drastic actuator energy requirement reduction by symbiosis of parallel motors, springs and locking mechanisms. Proceedings—IEEE International Conference on Robotics and Automation. https://doi.org/10.1109/ICRA.2016.7487193. Müller, H. W. (1982). Epicyclic drive trains: Analysis, synthesis, and applications. Detroit: Wayne State University Press. ˇ Ontañón-Ruiz, J., Daniel, R. W., & McAree, P. R. (1998). On the use of differential drives for overcoming transmission nonlinearities. Journal of Robotic Systems. https://doi.org/10.1002/(SIC I)1097-4563(199811)15:11%3c641::AID-ROB3%3e3.3.CO;2-M.

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Verstraten, T., Mathijssen, G., Furnémont, R., Vanderborght, B., & Lefeber, D. (2015). Modeling and design of geared DC motors for energy efficiency: Comparison between theory and experiments. Mechatronics. https://doi.org/10.1016/j.mechatronics.2015.07.004. Verstraten, T., Furnemont, R., Beckerle, P., Vanderborght, B., & Lefeber, D. (2019a). A Hopping Robot Driven by a Series Elastic Dual-Motor Actuator. IEEE Robotics and Automation Letters. https://doi.org/10.1109/LRA.2019.2902071. Verstraten, T., Furnémont, R., López-García, P., Crispel, S., Vanderborght, B., & Lefeber, D. (2019b). A series elastic dual-motor actuator concept for wearable robotics. Biosystems and Biorobotics. https://doi.org/10.1007/978-3-030-01887-0_32. Verstraten, T., Furnémont, R., López-García, P., Rodriguez-Cianca, D., Vanderborght, B., & Lefeber, D. (2019c). Kinematically redundant actuators, a solution for conflicting torque–speed requirements. International Journal of Robotics Research. https://doi.org/10.1177/027836491 9826382. Verstraten, T., Furnémont, R., López-García, P., Rodriguez-Cianca, D., Cao, H. L., Vanderborght, B., & Lefeber, D. (2018). Modeling and design of an energy-efficient dual-motor actuation unit with a planetary differential and holding brakes. Mechatronics. https://doi.org/10.1016/j.mechat ronics.2017.12.005. Verstraten, T., Schumacher, C., Furnémont, R., Seyfarth, A., & Beckerle, P. (2020). Redundancy in Biology and Robotics: Potential of kinematic redundancy and its interplay with elasticity. Journal of Bionic Engineering, 17(4), 695–707. https://doi.org/10.1007/s42235-020-0062-z

Attempts to Develop Artificial Muscles Koh Hosoda and Masahiro Shimizu

Abstract This chapter firstly demonstrates that the compliance of the pneumatic artificial muscles plays important role to modulate some robot behaviors. Then, it discusses our attempt to realize Xenopus-noid, a robot constructed by a 3D printer driven by real muscles. We demonstrate that the robot can swim and jump by using the living muscles. It finally mentions our attempt to develop artificial muscles from living cells, which will be very important technique to realize mech-bio hybrid robot.

1 Which Property of the Muscle is Important for Adaptive Behavior? Why are we trying to build bionic/biomimetic actuators? Biological muscles are energy efficient and have high power-weight ratios that can produce high power with less weight. However, their structure is complicated because it is evolved biologically and created by reaction–diffusion processes. It is difficult to control it precisely, and furthermore, the control principle is not yet known. Just reproducing biomimetic actuators does not make sense; what we can do is to consider the functions of the muscles in the context of intelligent behavior. Biological muscles, as stated above, are too complicated that we cannot simply reproduce them with the current technology. Understanding their function by analyzing the detailed mechanism of the muscles is so difficult and the functions are not really revealed yet. For understanding the function, we have to take another research methodology, called a constructive approach. By constructing real entities, dynamic models and/or real muscles, equipping them to the biomimetic structure, and realizing some behavior, we can understand their function. It is extremely important to use the models/muscles in the realistic context of structure and of behavior. K. Hosoda (B) · M. Shimizu Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, Osaka 560-8531, Japan e-mail: [email protected] © Springer Nature Switzerland AG 2021 P. Beckerle et al. (eds.), Novel Bioinspired Actuator Designs for Robotics, Studies in Computational Intelligence 888, https://doi.org/10.1007/978-3-030-40886-2_9

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walking cycle [ms]

We are researching intelligent control of our body. We believe that morphological computation plays a great role for realizing intelligent behavior. Morphological computation is a term that indicates that the body serves as a substitute for the computation normally performed by the brain/computers. To take this approach, we should be aware to what extent our model imitates biological counterpart. Typical features, and therefore maybe advantages for intelligent behavior, of the biological muscles are (1) their compliance, (2) energy conservation/release behavior, and (3) structural compliance provided by the muscular-skeletal structure. We have to look into these points one by one. Compliance is one of the most important features of biological muscles. Because our muscles are compliant, they can be an antagonistic pair driving one joint that realizes variable compliance of the joint. Figure 1 shows a biped robot driven by antagonistic pairs of artificial muscles (Takuma and Hosoda 2006). We supplied air over a certain period of time after the touchdown signal of one leg (duration of air supply). We tested two cases, one in which the hip joint is free after the air supplement and another where it is antagonistically driven. Since the former case cannot control joint compliance, it cannot change the walking cycle. In contrast, the latter case can change the compliance of the hip joint, and it can affect the walking cycle (Fig. 1b) (Takuma and Hosoda 2016). An interesting point about this robot is that its walking cycle can be controlled by the compliance (body tonus, so to say) whereas the cycle of the normal conventional robots can be controlled by changing desired trajectory given from a higher level of intelligence. By introducing compliance of the artificial muscles, we can construct a biologically plausible control system: tonus and gait.

duration of air supply [ms] (a) The planar biped robot

(b) Relation between duration of air supply and waking cycle.

Fig. 1 A biped robot driven by antagonistic pairs of pneumatic muscles: a the planar biped robot used for the experiment, b experimental result: relation between duration of air supply and walking cycle in two cases, the case hip joint is free (passive joint) and the case hip joint is antagonistically driven (compliant)

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Fig. 2 A monopod driven by antagonistic pairs of pneumatic muscles: It has a so called “5 pairs 9 muscles” structure. The robot has 3 joints, each of which is driven by a pair of muscles antagonistically. In addition, the robot has 3 bi-articular muscles; the Rectus femoris, Hamstrings, and Gastrocnemious. This redundancy provides structural compliance for the robot

The compliance of biological muscles also provides energy conservation and release. Pneumatic artificial muscle has compliance and it can contribute to energy conservation. Figure 2 shows a monopod driven by 5 pairs of pneumatic artificial muscles (Hosoda et al. 2010). Again, since the robot is driven by antagonistic pairs of compliant pneumatic muscles, it can conserve energy when the robot hits the ground, and it can release the stored energy so that it can be used to jump up again. Last but not least, structural compliance provided by the muscular-skeletal system is very important. The aforementioned monopod, for instance, can jump up almost in the same direction when it drops on the ground without any attitude control. If the total compliance of the body is not appropriately designed, it cannot reproduce the same attitude without control on the subsequent jump. This “stability” is provided by the muscular-skeletal structure of the body, not from the control. This is a good example of morphological computation.

2 Constructive Approach to Study the Living Muscles Previously, we introduced two robots driven by artificial muscles, and demonstrate that the pneumatic artificial muscle can realize some desirable functions, adaptability from compliance, energy conservation/release for continuous movement, and

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stability from structural compliance. We found these functions important through the constructive approach, but still, we may miss some functions that exist in the biological muscles not realized by the artificial muscles. Studying real muscles, therefore, is still important, bringing us ideas for building a new type of bioinspired robot. Biologists are also analyzing and observing real muscles to discover new functions. Robotics researchers have their own manner of studying the real muscle; again, by the constructive approach. We study real muscles, putting into context of their realistic behavior so that we can find real functions, hiding behind when the muscles are studied separately and individually. We developed a robot called “Xenopus-noid” shown in Fig. 3 (Ishii et al. 2018). The Plantaris Longus muscle is taken from a frog and is packed in a silicone tube with physiological ringer solution (Fig. 4a). The muscle contracts when we apply a

CR

SM PL PL

Fig. 3 Xenopus-noid equipped with real biological muscle. Plantaris Longus muscle (PL) is dissected and attached to the robot. SM and CR are supposed to form a parallel link mechanism. The trunk has a micro-controller and battery inside, as a result, the robot is controlled by wireless, which is important for investigating its fluid dynamics

(a) Plantaris Longus muscle (PL) is packed in a silicone tube. It is filled with ringer solution.

(b) Packed muscle contract when it is stimulated (below).

Fig. 4 Packaged Plantaris Longus muscle (PL) inside a silicon tube

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certain pattern of pulses (Fig. 4b). The generated force is transmitted by the threads attached to the both ends of the muscle package. Since it is fully covered by the silicon tube, it will not be exposed to water even if the robot swims in the water nor dried even if it moves on the land. This packaging enables us to reveal some functions of the living muscles through realizing several locomotion modes in/out of the water. Firstly, we realized swimming locomotion of the robot. The reaction of the muscle can be observed under the control of the electro-stimuli in the swimming condition. Since the robot has webbed feet that can generate unidirectional flow for propulsion, we can expect that the reaction force from the environment (water dynamics) can be emulated in the context of swimming. We expect to observe the total reaction of the living muscle in the context of swimming in the water, which cannot be observed by only using artificial muscles. Since the muscle is packaged, we can conduct experiments in the water, but on the other hand, available energy is only stocked in the tube as ATP. Thus, we can conduct experiment for a limited period of time. Some basic measurement has been done, but still it is on-going research. Secondly, we realized jumping locomotion of the robot frog. Just applying stimulation to the muscles could not make the robot jump, so, we put a ratchet mechanism by an electric magnet so that the robot can store the energy to jump up (Fig. 5). We still need some technique to estimate the energy conservation during this behavior.

3 Attempt to Develop Artificial Muscles from Living Cells Is it possible to develop artificial muscles from living cells? This is one of the ultimate goals to realize bio-inspired robots. Utilizing “real” materials, we can duplicate not only the function of the muscles (which we do this with artificial pneumatic muscles), but also the structure as a function. However, an artificial muscle is different from normal living muscles even if it is constructed from living cells; we can/have to design the structure and function of the muscle because it is “artificial”. The field to develop artificial muscle out of living cells is not well established yet. There are, at least, two points to be considered to design the artificial muscle: how should we place the cells and how should we control the growth of the cells. Here, we would like to explain our attempts to design the artificial muscle by growing living cells. About the first point, we propose to utilize vibration to make a pattern of cells to structure the design (Tashiro et al. 2017), but we suppose this is one method to structure the pattern of cells. Regarding how we can control the growth of the cells, we investigate chemical conditions (Mori et al. 2015) and physical interaction with the cells (Seki et al. 2016). There has been no method for designing artificial muscles by growing living cells yet.

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(a)

(c)

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Fig. 5 Jumping locomotion of Xenopus-noid robot

The aspects presented here are quite new and have primarily been introduced in the last couple of years. This shows a tremendous potential for future research not only in robotics, but also in related research fields such as gait assistance and rehabilitation.

References Hosoda, K., Sakaguchi, Y., Takayama, H., & Takuma, T. (2010). Pneumatic-driven jumping robot with anthropomorphic muscular skeleton structure. Autonomous Robots. https://doi.org/10.1007/ s10514-009-9171-6. Ishii, D., Shimizu, M., Asanuma, H., & Hosoda, K. (2018). Implementation of long lifetime dissected-muscle actuator for frog cyborg. 2017 IEEE International Conference on Robotics and Biomimetics, ROBIO 2017. https://doi.org/https://doi.org/10.1109/ROBIO.2017.8324387. Mori, K., Shimizu, M., Miyasaka, K., Ogura, T., & Hosoda, K. (2015). Remodeling muscle cells by inducing mechanical stimulus. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). https://doi.org/10.1007/9783-319-22979-9_23.

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Seki, K., Shimizu, M., Miyasaka, K., Ogura, T., & Hosoda, K. (2016). Aligning collagen fibers by cyclic mechanical stretch for efficiently muscle cell actuator. 2016 IEEE International Conference on Robotics and Biomimetics, ROBIO 2016. https://doi.org/10.1109/ROBIO.2016.7866488. Takuma, T., & Hosoda, K. (2006). Controlling the walking period of a pneumatic muscle walker. International Journal of Robotics Research. https://doi.org/10.1177/0278364906069187. Takuma, T., & Hosoda, K. (2016). Terrain negotiation of a compliant biped robot Driven by Antagonistic Artificial Muscles. Journal of Robotics and Mechatronics. https://doi.org/10.20965/jrm. 2007.p0423. Tashiro, I., Shimizu, M., & Hosoda, K. (2017). Cell patterning method by vibratory stimuli. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). https://doi.org/10.1007/978-3-319-63537-8_59.

Applying Compliant Actuators in Wearable Robots

Abstract Governments worldwide are looking for solutions to the problems related to an ageing population. Wearable robotic technologies such as active exoskeletons and prostheses, for one, can play a major role in keeping the elderly active on the job market and improving their quality of life. After decades of research on wearable robots, commercial devices have finally started to spawn, marking the beginning of an era of robot-assisted living. Part of the success of wearable robotics can be attributed to the great advances made in actuation. Rather than traditional servomotors, wearable robots often rely on compliant actuators. Such actuators have, in recent years, been implemented with tremendous success in powered exoskeletons and lower-limb prostheses. We will explore how these compliant actuators can be designed and implemented assistive devices and what benefits they can bring. After a general outlook on compliant actuators and their impact on energy efficiency, we present two recent case studies: the CYBERLEGs transfemoral prosthesis and a back-support exoskeleton actuated by a parallel elastic actuator.

Compliant Actuation for Wearable Robotics Tom Verstraten and Dirk Lefeber

Abstract The requirements of wearable robots such as robotic prostheses and exoskeletons differ considerably from those of traditional robots. These requirements are usually met well by compliant actuators, i.e., actuators which feature an elastic element. In this chapter, we explain how compliant actuators can solve the formidable actuation challenges inherent to wearable robots, with particular attention for their ability to improve energy efficiency.

1 Actuation Challenges for Wearable Robotics Within the wearable robotics community, it is generally accepted that the lack of adequate actuators is one of the main bottlenecks for the development of such devices. Among the challenges involved in the mechanical design of actuators for wearable robots, we highlight the following four aspects: – Intrinsic safety: Traditional robotic drivetrains consisting of an electric motor with transmission are designed to deliver high torques. As a result, they exhibit a high impedance, meaning that they provide strong resistance against being moved by an external force. This entails a risk for the wearer, as he may be hindered by the actuator when rapid movements are needed to correct for, e.g., a fall. The risk is even greater in in rehabilitation robotics, where the strong resistance of the actuator may cause harm to patients who go into a spasm. – Reliability and durability: Taking the high cost of wearable robots into consideration, an appreciable lifespan is essential to make such devices commercially viable. Reliability is an important concern as well, especially for lower-limb devices designed for amputees and paraplegics. Such devices are safety–critical, as a loss of functionality can easily lead to severe injury through falls. Because T. Verstraten (B) · D. Lefeber Robotics and Multibody Mechanics Research Grup (R&MM), Vrije Universiteit Brussel and Flanders Make, Pleinlaan 2, 1050 Elsene, Belgium e-mail: [email protected] © Springer Nature Switzerland AG 2021 P. Beckerle et al. (eds.), Novel Bioinspired Actuator Designs for Robotics, Studies in Computational Intelligence 888, https://doi.org/10.1007/978-3-030-40886-2_10

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the joints of our lower limbs face high shock loads upon touchdown of the foot, guaranteeing reliability and durability is challenging. It is well-known that shock loads decrease the lifetime of mechanical components and may cause unexpected failures. The gearbox, in particular, is very sensitive to shocks and should therefore be protected by the design of the actuator. – Size and weight: Wearable robots, in particular exoskeletons, need to be compact and lightweight so that they do not encumber the wearer. Moreover, the addition of mass to the legs will increase metabolic energy consumption, especially if the mass is placed at more distal locations (Browning et al. 2007; Royer et al. 2005). Actuators with high power-to-mass ratio are the key to meeting these requirements. – Energy efficiency: Untethered wearable robots need to carry their own power supply, typically in the form of batteries. The energy efficiency of the actuators is important for wearable robots since it determines the autonomy of the device, i.e., the number of hours it can be used before it needs to be charged. Additionally, the energy consumption of the device is directly related to the size and weight of the batteries, hence to the size and weight of the overall device and the comfort of wearing it. The effect is further enhanced by the fact that a lighter exoskeleton will require less energy to actuate, creating an avalanche effect which favours energy-efficient designs even more. Compliant actuators, which feature elastic elements such as springs, have two very desirable characteristics which present solutions to the issues mentioned above. First, an elastic element placed in series with the actuator acts as a low-pass filter. High power peaks will be absorbed by the elastic element and then slowly released to the motor (providing shock resistance and protecting the drivetrain) or the wearer (providing intrinsic safety). Second, the elastic element acts as an energy buffer. With a properly chosen spring constant, the power flow through the drivetrain can be reduced considerably. As such, smaller drivetrain components can be used, reducing the overall size and weight of the actuator. Moreover, the losses in the drivetrain components—which are strongly correlated to the power flow—will decrease as well, resulting in a more efficient actuator. In the following, we will provide a brief overview of compliant actuator designs and their effect on kinematics, dynamics, and energy consumption. For more information about the safety aspects and shock absorbance of compliant actuators, we refer to Bicchi et al. (2004).

2 Example: Compliant Actuation for an Ankle Actuator To illustrate the potential of compliant actuators for wearable robots, let us have a look at the requirements for an ankle actuator. Designers of compliant actuators often represent the kinematics and torques of a joint in a single graph which shows torque vs. angle. Such a graph is shown in Fig. 1, which represents the human ankle during

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Fig. 1 Torque–angle plot for the human ankle during a typical gait cycle. Torque is normalized by dividing by body mass. Data from Winter (2009). Gait events marked in the figure are initial contact (IC), foot flat (FF), maximum dorsiflexion (MD) and toe-off (TO)

a walking gait cycle. Although the temporal aspect is lost in this plot, it does capture the dynamics of the leg since gait datasets typically include dynamic effects in the joint torques. For the ankle, however, dynamics are of minor significance due to the small inertia of the foot. It is the torque needed to sustain and propel the body during stance which determines the ankle torque almost entirely. Note that the dynamics of swing do have an important influence for actuator design. We will dive deeper into this aspect in Sect. 3. The main advantage of a torque–angle plot is that it allows for a quick assessment of the potential for an elastic element. Indeed: the torque–angle plot of the human ankle during walking exhibits a strong linear component, indicating that a large part of the ankle torque could be provided by a simple torsion spring. While a motor would still be needed to inject energy to the gait, the spring itself can significantly reduce its power requirements. How this is done, depends on the way the spring is implemented. As mentioned in Chap. 5, the designer has two basic options: series springs and parallel springs. By adding a (unidirectional) parallel spring to a stiff motor, one obtains a Parallel Elastic Actuator (PEA). The parallel spring does not alter the motor speed, as the motor is directly coupled to the output. It does, however, take over a part of the load, leading to a reduction of the motor torque. This is paired with an overall decrease in power flow, as illustrated in Fig. 2. The spring absorbs negative power between foot-flat (FF) and maximum dorsiflexion (MD) and releases it during push-off; as a result, the motor itself delivers less negative power and less positive power overall. Alternatively, a Series Elastic Actuator (SEA) places the spring in between the motor and load, i.e., in a series configuration. Here, the torque seen by the motor is not affected by the spring, but the speed requirements are lowered. Again, this results in a decrease in power flow (Fig. 2). Notice how the SEA spreads out the power peak between 30–50% of the gait cycle to reduce its amplitude. Overall, the result is the same as with the PEA: the motor provides less negative power and less positive power.

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Fig. 2 Torque and mechanical power of a stiff actuator, a PEA and an SEA, the latter two optimized for minimal mechanical power flow. Data from Winter (2009)

The advantages of the smaller power flow in compliant actuators are twofold. Firstly, the actuator will be more energy efficient, as power losses—which roughly correlate to power flow—are reduced (Verstraten et al. 2018). Secondly, the decrease in power and torque enables the use of a smaller electric motor and gearbox, hence decreasing actuator weight and size. Both efficiency and weight/size are crucial aspects of wearable robots. This explains why elastic actuators are the actuators of choice for many state-of-the-art devices.

3 Electrical Energy Consumption of Compliant Actuation The majority of wearable robots are driven by electromagnetic actuators (typically brushless DC motors). In the review paper by Shorter et al. (2013), 72% of the surveyed powered ankle–foot orthosis designs were actuated with this technology. The same ratio of 72% was also found for upper-limb exoskeletons in Gopura et al. (2016). Similar numbers also apply to actuated prostheses: in the review by Windrich et al. (2016), 18 of the 21 surveyed active lower limb prostheses were actuated electromagnetically. Motivated by these numbers, we will dive deeper into the power consumed by wearable robots driven by electric motors.

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Fig. 3 Mechanical (red) and electrical (orange) power flows for an SEA (left) and PEA (right) with springs optimized for minimal mechanical power flow. The biological power requirement (blue), derived from Winter (2009), is shown for reference

Many works discussing the energetic benefits of elastic actuation for active ankle prostheses have focused on the mechanical domain, i.e., on the mechanical power. Recent studies have, however, shown that there are considerable differences between the mechanical power and the electrical power at the motor terminals (Verstraten et al. 2018). This is illustrated in Fig. 3, where the mechanical and electrical power flows are shown for the same SEA and PEA as in Fig. 2. A particular issue with compliant actuators driven by electric motors is their behaviour during swing. While gait data indicates a near-zero torque requirement at the ankle joint, the motors of simple compliant actuator designs will still need to deliver torque and work during this phase. As seen in Fig. 3, this leads to relatively high power peaks during the swing phase, especially for the SEA. The existence of these power peaks has been confirmed by experiments on early prototypes of SEAdriven ankle prostheses (Hitt et al. 2010; Geeroms et al. 2017). A theoretical study on the optimal design of ankle prostheses by Verstraten et al. (2017) confirms that this is inherent to the use of compliant actuators. There are two main reasons behind these power peaks. The first and most important is high reflected inertia, which is typical of actuators for ankle prostheses and exoskeletons. During walking, the ankle delivers high torques at relatively low speeds. Ankle actuators are therefore commonly equipped with a large-reduction gearbox, leading to a large reflected inertia of the drivetrain. Combined with the high accelerations during the swing phase, this inertia results in the demand for high torques from the motor. This problem is particularly relevant for the SEA due to its typically high gear ratio. Unlike the PEA, a SEA does not enjoy the reduction in torque due to the parallel spring. As a result, its gear ratio is generally higher than that of the PEA, and high accelerations are provided at the cost of higher torques. Figure 3 shows that the resulting peak powers of the SEA during late stance and early swing—caused by reflected inertia—can reach values higher than those during stance, which actually contribute to the output. The second reason applies to the PEA alone. In this actuator, the parallel spring— which has a fixed equilibrium angle—counteracts the movement of the swinging

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limb, providing an undesired torque to the limb which needs to be compensated by the motor. To mitigate this problem, the spring’s equilibrium angle and stiffness must be carefully selected. While this approach can be effective—in Figs. 2 and 3, the torque and power of the optimized PEA are relatively low during swing— the selected spring effectively becomes a trade-off between torque reduction in the stance phase and the appearance of undesired torques in the swing phase (Verstraten et al. 2017). In other words, the full potential of the parallel spring is not exploited by a traditional PEA. In both cases, performance can be improved by adding locking mechanisms and clutches (Plooij et al. 2017). This is relatively straightforward for a PEA, where a simple clutch can be used to disengage the parallel spring. Such a design, often called a “clutched parallel elastic actuator” (Haeufle et al. 2012), effectively eliminates the additional torques required during swing. For the SEA, the situation is slightly more complicated. A clutch could be used to disengage the entire actuator during swing, which would effectively eliminate the actuator’s inertia. While this solution would be suitable for performance augmenting exoskeletons, it is probably ill-advised for assistive exoskeletons and prosthetics, where actuation during the swing phase is crucial in order to provide sufficient toe clearance and prevent falls. For these devices, more advanced solutions need to be sought.

4 Advanced Actuation Solutions The SEA and PEA discussed so far are the most basic examples of how springs can be used to boost the performance of actuators for wearable robots. It is obvious that further refinements can be made to these architectures. Some examples are listed below. – Series and parallel elasticity can be combined in a single actuator to combine the benefits of both topologies. The first example of such an actuator is the powered ankle–foot prosthesis by Au et al. (2009), where the parallel spring was designed for torque reduction while the series spring was intended for shock absorption. – Variable Stiffness Actuators (VSAs) are SEAs which enable the user to vary the stiffness of a series elastic element (Vanderborght et al. 2013). Typically, stiffness variation is accomplished by means of a secondary motor. By continuously varying stiffness during a gait cycle, the actuator can achieve higher performance in terms of bandwidth and, possibly, energy efficiency. Control, however, becomes more complicated, as both motors need to work in concert to achieve the desired output. A simpler but effective solution is to change stiffness gradually over a long period of time to accommodate for changes in gait parameters—in particular, gait speed. – Variable transmissions have been proposed as an effective way to deal with the disparity between requirements during the stance and swing phase of gait (Sugar and Holgate 2013). They can be implemented in a multitude of ways,

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e.g., two-speed gearboxes, continuously variable transmissions or smart dedicated mechanisms. – Locking mechanisms can be utilized to release the energy in a single burst and reduce loading on the motor (Explosive Elastic Actuation) (Cherelle et al. 2014). The locking mechanism enables the motor the motor to spread its work over a longer time period (typically 3 times for a prosthetic ankle), thereby reducing its speed and power requirement.

References Au, S. K., Weber, J., & Herr, H. (2009). Powered ankle-foot prosthesis improves walking metabolic economy. IEEE Transactions on Robotics, 25(1), 51–66. Bicchi, A., & Tonietti, G. (2004). Fast and" soft-arm" tactics [robot arm design]. IEEE Robotics & Automation Magazine, 11(2), 22–33. Browning, R. C., Modica, J. R., Kram, R., & Goswami, A. (2007). The effects of adding mass to the legs on the energetics and biomechanics of walking. Medicine and sciencein sports and exercise, 39(3), 515. Cherelle, P., Mathijssen, G., Wang, Q., Vanderborght, B., & Lefeber, D. (2014). Advances in propulsive bionic feet and their actuation principles (p. 6). Eng: Adv. Mech. Geeroms, J., Flynn, L., Jimenez-Fabian, R., Vanderborght, B., & Lefeber, D. (2017). Energetic analysis and optimization of a MACCEPA actuator in an ankle prosthesis. Autonomous Robots, 1–12. Gopura, R. A. R. C., Bandara, D. S. V., Kiguchi, K., & Mann, G. K. (2016). Developments in hardware systems of active upper-limb exoskeleton robots: A review. Robotics and Autonomous Systems, 75, 203–220. Haeufle, D. F. B., Taylor, M. D., Schmitt, S., & Geyer, H. (2012). A clutched parallel elastic actuator concept: Towards energy efficient powered legs in prosthetics and robotics. In: Biomedical Robotics and Biomechatronics (BioRob), 2012 4th IEEE RAS EMBS International Conference on, pp. 1614–1619. Hitt, J. K., Sugar, T. G., Holgate, M., & Bellman, R. (2010). An active foot–ankle prosthesis with biomechanical energy regeneration. Journal of Medical Devices, 4(1), 011003. Plooij, M., Wolfslag, W., & Wisse, M. (2017). Clutched elastic actuators. IEEE/ASME Transactions on Mechatronics, 22(2), 739–750. Royer, T. D., & Martin, P. E. (2005). Manipulations of leg mass and moment of inertia: effects on energy cost of walking. Medicine and science in sports and exercise, 37(4), 649. Shorter, K. A., Xia, J., Hsiao-Wecksler, E. T., Durfee, W. K., & Kogler, G. F. (2013). Technologies for powered ankle-foot orthotic systems: Possibilities and challenges. IEEE/ASME Transactions on mechatronics, 18(1), 337–347. Sugar, T. G., & Holgate, M. (2013). Compliant mechanisms for robotic ankles. In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (pp. V06AT07A002–V06AT07A002). American Society of Mechanical Engineers. Vanderborght, B., Albu-Schäffer, A., Bicchi, A., Burdet, E., Caldwell, D. G., Carloni, R., ... & Garabini, M. (2013). Variable impedance actuators: A review. Robotics and Autonomous Systems, 61(12), 1601–1614. Verstraten, T., Geeroms, J., Mathijssen, G., Convens, B., Vanderborght, B., & Lefeber, D. (2017). Optimizing the power and energy consumption of powered prosthetic ankles with series and parallel elasticity. Mechanism and Machine Theory, 116, 419–432.

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Verstraten, T., Flynn, L., Geeroms, J., Vanderborght, B., & Lefeber, D. (2018). On the electrical energy consumption of active ankle prostheses with series and parallel elastic elements. In: 2018 7th IEEE International Conference on Biomedical Robotics and Biomechatronics (Biorob) (pp. 720–725). Windrich, M., Grimmer, M., Christ, O., Rinderknecht, S., & Beckerle, P. (2016). Active lower limb prosthetics: A systematic review of design issues and solutions. Biomedical Engineering Online, 15(3), 140. Winter, D. A. (2009). Biomechanics and motor control of human movement, 4th ed. Wiley.

Compliant Actuation for Transfemoral Prostheses: The CYBERLEGS Prosthesis Louis Flynn

Abstract In this chapter, we discuss the design of the CYBERLEGs Beta-Prosthesis developed by the Vrije Universiteit Brussel (Belgium). This transfemoral prosthesis consists of compliant actuators which provide full support torques to the ankle and knee during level ground walking. To deliver an energy-efficient and compact system, the springs are combined with locking elements, and a mechanism is introduced to transfer energy from the knee to the ankle during push off. The performance of the prosthesis is evaluated by comparing bench tests to experiments with an amputee.

1 Introduction We present the CYBERLEGs Beta-Prosthesis (Flynn et al. 2018) as a case study in the real-world use of SEA/PEAs in a device. The prosthesis is an active transfemoral prosthesis that can provide the full torque required for reproducing average level ground walking at both the knee and ankle in the sagittal plane. It heavily utilizes the SEA/PEA concepts in order to deliver a relatively efficient and compact powered prosthetic system. The ankle is composed of a combined SEA/PEA setup, similar to the ones discussed in detail previously. The knee consists of a SEA with a lockable PEA. In addition, this prosthesis has a locking mechanism to transfer energy from the knee to the ankle during pushoff. Each of these systems was tested on the bench showing that it was possible to reproduce average torque/angle characteristics of normal walking. Testing on actual amputees showed some of the issues with using highly compliant SEA configurations, as errors in output kinematics had a large influence on the efficiency and capability of the actuation.

L. Flynn (B) Robotics and Multibody Mechanics Research Group (R&MM), Vrije Universiteit Brussel and Flanders Make, Pleinlaan 2, 1050 Elsene, Belgium e-mail: [email protected] © Springer Nature Switzerland AG 2021 P. Beckerle et al. (eds.), Novel Bioinspired Actuator Designs for Robotics, Studies in Computational Intelligence 888, https://doi.org/10.1007/978-3-030-40886-2_11

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2 The Use of SEA/PEA Concepts in CYBERLEGs The design for the CYBERLEGs Beta-Prosthesis began with the study of the torque– angle characteristics for the knee and ankle joint for normal average walking for a 80 kg person (Winter 2009). The intention in most of these designs is to deliver the average torque with passive springs. These springs would naturally follow the quasi-stiffness behavior of the desired gait cycle and in theory would not need to be actuated to provide the desired output behavior. The rationale for specific design decisions for each of the two joints is slightly different due to the different output characteristics required for each joint.

2.1 Ankle Design The ankle actuator is composed of a main motive actuator, a series elastic linkage, and a fixed parallel spring, as seen in Fig. 1. The main motive actuator of the ankle is a Mechanically Adjustable Compliance and Controllable Equilibrium Position Actuator (MACCEPA) series elastic architecture (Van Ham et al. 2007; JimenezFabian et al. 2017). The actuator torque is created by relative displacement of the moment arm a¯c around the ankle axis a from the axis a¯b, a displacement called α. This displacement is caused by a motor that is mounted in the shank of the ankle, which in this schematic is represented by the immobile link a¯g to the left. This behavior is fully outlined in Flynn et al. (2015) and Jimenez-Fabian et al. (2015). A spring acts in parallel with the actuator to reduce required peak torques and can allow for a smaller motor size. One thing of note about this design is the stiffening characteristic of the device. At the rest position, the stiffness is essentially zero due to the singularity of the moment arm with respect to the spring. The stiffness then rises dramatically as the moment arm is displaced. This is how both the quasi-stiffness and real stiffness of the ankle progresses during normal walking, and therefore does not require motor activation to modify this stiffness (Shepherd and Rouse 2017).

Fig. 1 The CYBERLEGs Beta-Prosthesis ankle schematic and CAD representation (Flynn et al. 2018)

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2.2 Knee Design The knee (Fig. 2) is composed of two major parts, the main actuator, which is a standard SEA at the front of the knee, placed in parallel with the Weight Acceptance (WA) actuator, which is an actuated spring that is either allowed to be compressed during knee flexion or moved so that it cannot be compressed by flexion. The stiffness values of the series and parallel spring used in the design are directly derived from the quasi-static characteristics of the average walking cycle for an 80 kg person. Figure 3 shows the torque/angle characteristics of the knee joint and how the different systems are used to generate the required torque during the total cycle. Directly after heel strike the knee enters the WA stage, where the knee behaves like a stiff spring. The green line shows the torque angle characteristics when the WA actuator is in the locked position. For normal walking the WA would be positioned such that the spring is compressed at approximately 8° flexion. The Baseline Spring (BL, blue line in Fig. 3) spring stiffness was chosen such that the knee motor does not have to move to reproduce the desired joint torques during knee extension, but simply provides a holding torque. In this case, the spring carriage is positioned such that the rest position of the BL spring is approximately 60 deg. The result is an economic knee actuator that is capable of reproducing most of the knee characteristics of normal gait with passive springs.

Fig. 2 The CYBERLEGs Beta-Prosthesis knee schematic and CAD representation (Flynn et al. 2018)

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Fig. 3 The knee torque angle characteristics for an average 80 kg normal gait cycle. The choices of knee spring stiffness are determined by the slopes of the curve in the torque–angle diagram, the quasi-stiffness of the task

2.3 Energy Transfer The remaining portion of the gait cycle, during the late stance phase to early swing, is of dissipative nature. The Energy Transfer (ET) mechanism is designed to provide this behavior by directly tying the knee and ankle together when active. This allows negative work that should be dissipated at the knee joint to be delivered to the ankle by plantar flexing the ankle. It achieves this through a cable wrapped around pulleys, creating a 2:1 ratio of knee to ankle joint rotation.

3 Energy Measurements Experiments were conducted on a test bench setup and energy consumption measurements were made on the ankle and knee. During these tests the joint was tested by driving the output side of the system with a large rigidly attached motor through a torque transducer. This allowed a desired output desired trajectory to be applied to the actuator while the actuator applied a desired torque. In the case of the prosthesis this simulated the interaction of the person and the ground. The energy transfer mechanism was also measured in a similar fashion to assess the reduction of the knee torque due to transfer of energy to the ankle (Fig. 4).

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Fig. 4 The Prosthesis behavior using both the WA and ET systems while on the bench. The mainly passive system is able to produce nearly normative torque–angle characteristics. The energy transferred to the ankle was approximately 8.2 J/stride. Total energy consumed was approximately 12 J/stride for the knee joint

3.1 Ankle The ankle use of SEA/PEA systems primarily showed a reduction of the power peaks during testing. Peak power showed a reduction of 40% with the use of the SEA ankle when compared to a direct drive system, although the overall energy consumption of the ankle remained approximately the same (motor power of 33 J/stride) (Geeroms et al. 2017).

3.2 Knee For the system using both the WA and ET systems, the average knee motor energy required to walk at 2 s/stride is about 23 J/stride (Geeroms et al. 2017). This is the result of a combination of the WA actuator requiring about 10 J/stride and the holding torque required for the SEA which was about 3.2 J/stride. The ET motor also takes about 10 J/stride to operate, partially because of the inefficient design. However, note that in this example about 8.2 J is transferred to the ankle, reducing the load on the ankle motor considerably. If the ET is not used, then the energy consumption of the knee motors is about 38 J/stride due to the extra work of handling the dissipation of energy that would originally be handled by the ET system (Geeroms et al. 2017).

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4 Human Interaction and the Effect on SEA/PEA Designs When tested on the bench it can be shown that the device works as desired and that the energy consumption required to produce the desired torque/angle characteristics is lower than a rigidly connected motor drive. These tests were made under the assumption that gait kinematics would remain near normal if the joint torques of the prosthesis remained somewhat normal. The reality was that when tried with a real person the actual human interactions resulted in output kinematics that greatly differed from the average, resulting in less than optimal energy consumption.

4.1 Ankle Adaptations The ankle torque/angle characteristics are discussed in detail in Sect. 2.2, but the choice of parallel spring was decided in part on factors outside actuator energy consumption. Originally a spring with rest position of approximately −10° was used to minimize the peak required torque of the actuator and allow a reduction of the gear ratio to increase motor velocity and reduce reflected inertia, as discussed in Sect. 2.3. This was found not to be suitable because the constant plantar flexion of the ankle due to the parallel spring was found to be very intrusive to the user when used passively and required motor power to remain comfortable for tasks that should be passive, such as standing. Regardless of this, the ankle characteristics (Fig. 5, left) were very similar to average gait, having overall kinematics and torque–angle characteristics that were

Fig. 5 The experimental data was collected while walking down a hall at self-selected speed (~2 km/h). Each individual stride is in light grey, the average of joint torque vs the average of stride angle is plotted in blue. The normal average Winter torque angle curve at 3.2 m/s is in red. Average ankle output is 10.6 J/stride

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nearly normal. The average ankle mechanical output was 10.6 J/stride and motor energy was approximately 23.8 J/stride (SD = 3.32).

4.2 Knee Behavior Walking with the prosthesis in a primarily passive manner with little actuation of the main knee drive was found to lead to kinematics that were far from the desired targets (Fig. 5, right). This led to a number of problems with the knee, primarily the inability to use the ET system. This meant that in order to track the normal gait torque requirements, the knee motor needed to be driven to make up the deficit. The result was a much more inefficient gait than expected, and due to the soft stiffness required for the BL torque–angle characteristics, an actuator with a low torque bandwidth. Note that because the specific modifications in actuator position made to create a stable gait were relative efficient, the overall consumption was still a reasonable 27.5 J/stride (SD = 1.23).

5 Conclusions Although SEA/PEA actuators have the potential for high energy savings and reduced power requirements, the actual use of the devices should be well understood to optimize the actual behavior of the actuator, because assumptions about the output kinematics make large differences in the efficiency of the actuation. This implies that even with active compliant actuators, different operations should require different series and parallel stiffness to remain optimal, particularly in systems where the interaction forces are varied. In the case of the CYBERLEGs Beta-Prosthesis, the passive ankle stiffness was suitable for the tasks that were conducted, although the static parallel stiffness could have been more efficient if not limited by factors other than normal walking. The knee actuator was not able to produce normal gait kinematics as designed, but was able to find a suitable gait cycle with a modified controller. The reasons that the knee kinematics did not turn out as expected is likely a mixture of a number of issues. First is the control, particularly timing within the gait cycle and state machine tuning, which is likely not optimal. Second is training of the subject. The subject is not used to walking with normal gait kinematics on the prosthetic side and in fact forces the active prosthesis to behave much like their passive one, particularly in the WA phase. Third, the quasi- stiffness of the knee actuator might not be close enough to the real stiffness of the knee during walking. This mismatch may explain why the ankle behavior is much better than that of the knee as well, as real ankle stiffness is much closer to the quasi-stiffness than in the knee.

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References Flynn, L., Geeroms, J., Jimenez Fabian, R. E., Vanderborght, B., Vitiello, N., & Lefeber, D. (2015). Ankle-Knee prosthesis with Active ankle and energy transfer: Development of the CYBERLEGs Alpha-prosthesis robotics and autonomous systems, 73, 4–15. Flynn, L., Geeroms, J., Jimenez-Fabian, R., Heins, S., Vanderborght, B., Munih, M., et al. (2018). The challenges and achievements of experimental implementation of an active transfemoral prosthesis based on biological Quasi-Stiffness: The CYBERLEGs Beta-Prosthesis. Frontiers in Neurorobotics, 12, 80. Geeroms, J., Flynn, L., Jimenez-Fabian, R., Vanderborght, B., & Lefeber, D. (2017). Energetic analysis and optimization of a MACCEPA actuator in an ankle prosthesis. Autonomous Robots, 1–12. Jimenez Fabian, R. E., Flynn, L., Geeroms, J., Vitiello, N., Vanderborght, B., & Lefeber, D. (2015). Sliding-bar MACCEPA for a powered ankle prosthesis. Journal of Mechanisms and Robotics (4). Jimenez-Fabian, R., Geeroms, J., Flynn, L., Vanderborght, B., Lefeber, D. (2017). Reduction of the torque requirements of an active ankle prosthesis using a parallel spring. Robotics and Autonomous Systems, 2, 187–196. Shepherd, M. K., & Rouse, E. J. (2017). The VSPA foot: A uasi-passive ankle-foot prosthesis with continuously variable stiffness. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 25, 2375–2386. Van Ham, R., Vanderborght, B., van Damme, M., Verrelst, B., & Lefeber, D. (2007). MACCEPA, the mechanically adjustable compliance and controllable equilibrium position actuator: Design and implementation in a biped robot. Robotics and Autonomous Systems, 55(10), 761–768. Winter, D. A. (2009). Biomechanics and motor control of human movement, 4th ed. Wiley.

Parallel-Elastic Actuation of a Back-Support Exoskeleton Stefano Toxiri and Andrea Calanca

Abstract In this chapter, we discuss the implementation of compliant actuators on a back-support exoskeleton developed at Istituto Italiano di Tecnologia (Italy). The exoskeleton provides physical assistance to the lower back during lifting tasks, reducing the associated loading and, consequently, the risk of injuries. A detailed analysis of the actuation requirements, along with experiments with different physical prototypes, indicate the advantages of parallel elasticity for this specific application.

1 Back-Support Exoskeletons In industrial settings, workers often perform manual handling activities, e.g., moving and carrying objects such as baggage in airports and assembly parts in manufacturing. During these activities, the lumbar spine is subject to substantial biomechanical loading, which is associated with musculoskeletal injuries (Coenen et al. 2014). To mitigate the risk of injury, back-support exoskeletons have been designed to provide physical assistance to the lower back and reduce the associated loading. This chapter illustrates the example of an active device developed at Istituto Italiano di Tecnologia as part of the Robo-Mate EU project (https://www.robo-mate.eu/), and focuses on the choices for its actuators. Several back-support exoskeletons can be found in literature. The interested reader may find more comprehensive overviews of the state of the art in (ExR, WearRA, Toxiri et al. 2019b). The vast majority of them generate forces/torques between the torso and upper legs, thus contributing to back extension moments. Unlike prostheses, in which the robot fully replaces a missing human joint, exoskeletons are worn in parallel to the joint of interest, are secured on the adjacent S. Toxiri (B) Department of Advanced Robotics, Istituto Italiano di Tecnologia, via S. Quirico 19d, 16163 Genoa, Italy e-mail: [email protected] A. Calanca Department of Computer Science, University of Verona, Strada Le Grazie 15, 37134 Verona, Italy © Springer Nature Switzerland AG 2021 P. Beckerle et al. (eds.), Novel Bioinspired Actuator Designs for Robotics, Studies in Computational Intelligence 888, https://doi.org/10.1007/978-3-030-40886-2_12

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limb segments, and contribute to its motion. Moreover, since in industrial applications wearers are able-bodied people, the goal of exoskeletons is typically to provide only a portion of the necessary torque as opposed to fully taking over the specific joint. Concerning actuation principles, there are examples of passive (relying on mechanical elements only) and active (additionally or solely using powered actuators, e.g., geared electromagnetic motors) solutions for back-support exoskeletons. The device which will be described here (Fig. 1) is an active one. It consists of a main rigid frame secured to the torso via backpack-like straps on the shoulders and waist. The two actuators sit on this frame laterally, approximately aligned with the corresponding hip joints. The output of the actuators connects to the corresponding thigh via articulated structures, whose unactuated degrees of freedom promote unrestricted user movements outside the sagittal plane.

Fig. 1 Illustration of the exoskeleton prototype as seen sideways. Bottom-right is a close-up of the custom thigh attachment, consisting of an elastic strap and an aluminium plate

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2 Rationale for Parallel Elasticity The desirable behavior for this exoskeleton can be described as following the user’s movements and generating a portion of the torque required to complete the task. This reduces the required muscular effort (Toxiri et al. 2018a) and correspondingly reduces the biomechanical loading on the lumbar spine (Koopman et al. 2019). To extract actuation requirements for the exoskeleton described above, our approach started by studying the dynamics of the L5S1 joint (connecting the lumbar spine to the pelvis) during the activity of interest. The data shown in Fig. 2 was obtained by recording motion and estimating forces/torques using inverse dynamics on a simplified model of the torso, spinal muscles, and external object being lifted (De Looze 1994; Toxiri et al. 2018a). The torque is positive at almost all times. The “traditional” approach for actuation would be to choose and dimension a powered actuator, e.g., geared motor, that is able to generate the maximum values of torques if required. However, the torque–angle relationship clearly exhibits a linear (or static) component, which motivates the inclusion of an elastic element on this exoskeleton acting in parallel with the actuator. Indeed, a passive elastic element with an approximately linear profile (and stiffness value dimensioned to generate the desired portion of the total torque) would be capable of generating a substantial portion of the joint torque while the remaining torque may be generated by the actuator. Compared to the traditional nonelastic approach, in this solution the actuator’s torque requirements are substantially reduced. The inclusion of a parallel spring may be interpreted as shifting the motor’s operating points to a torque range that betters exploit its entire (symmetric) working area. By including negative values, the torque range becomes lower in magnitude. In such a case, the parallel spring may be selected by considering the two configurations illustrated in Fig. 3. In (a) the spring is at rest, thus the torque capability is

Fig. 2 The dynamics of the lifting task, shown for one of the three subjects for illustration purposes. On the left, the time profiles of joint angle (top) and torque (bottom) are shown. Starting (a) and ending (e) in an upright position, the user bends forward twice to first pick up (b) and secondly to release (d) the external object

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Fig. 3 Two operating points for a PEA, illustrating the torque capacity at different joint configurations as depending on the spring torque-deflection profile and properties of the gear motor

determined by that of the motor. On our device (a) corresponds to the user’s upright position, where the lowest torque output is required (see also (a), (c), and (e) in Fig. 2). Point (b) on the right is where the spring has been loaded and thus generates torque on the joint. This point corresponds to the user being fully bent over, which is where the highest torque contribution is necessary (see also (b) and (d) in Fig. 2). The actuator can then be used to add or subtract torque around that value. Our parallel elastic actuator is based on a bungee cord and a geared brushless DC motor. The elastic element is implemented by routing a bungee cord around metal pins. In this configuration, the angular displacement of the joint determines an elongation of the cord. The design and characteristics of the elastic element are described in greater detail in (Masood et al. 2016; Toxiri 2017). The selected gear motor combination includes a 100 W EC60flat (maxon motor AG, Switzerland) and 100:1 SHD-20–100-2SH reduction gear (Harmonic Drive AG, Germany). The total torque output of spring and motor is measured by a TS110a torque sensor (ME-Meßsysteme GmbH, Germany) and used for control purposes.

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3 Comparative Analysis In this part, we show comparisons between traditional and PEA-based solutions focusing on different aspects. With reference to the back-support exoskeleton described above and its target task of lifting, our results associate the use of parallel elasticity with: – lower required mechanical power output from the electric motor; – improved torque-tracking performance; – reduced electrical energy consumption.

3.1 Torque-Speed Relation: Peak Power The torque–angle plot in Fig. 4 on the left shows the desired torques in red. As mentioned above, torque is positive in almost all cases. The linear dashed profile in blue represents the average static load. A passive elastic element in accordance with this load profile, placed in parallel with the motor, would deliver a substantial portion of the desired torque on the target joint. The remaining part (solid blue line) would then need to be covered by the motor. Of course such a reduction in torque requirements also affects the power demand. The right plot in Fig. 4 shows the desired joint torque output against the measured joint speed. The red lines represent the full joint torque whereas the blue lines represent the portion of the torque required to the geared motor in a PEA configuration. Considering the active mechanical power as the product of motor torque and joint speed, in this illustrative case the required peak active power decreases from 109 to 53 W. This reduction in active power substantially relaxes the technical requirements for the geared motor. Along with reducing active

Fig. 4 Left: torque–angle plot representing the desired performance in solid red. The dashed blue line illustrates the relation between torque and angle, which may be implemented with a parallel elastic element. This leaves the remaining part, in solid blue, to be generated by the electric motor. Right: torque-speed plot shows the lower active power required from a PEA compared to a nonelastic actuator

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power, this enables designs with more advantageous properties including reduced weight, reflected inertia and friction (Toxiri 2018b).

3.2 Effect of Inertia on Torque Bandwidth The design choices enabled by the presence of a parallel spring lead to improvements in dynamic performance. Torque tracking is important on assistive exoskeletons like the Robo-Mate active back-support. It determines biomechanical effectiveness of the device as well as how it is perceived by its users. In (Toxiri et al. 2017), we compared the torque tracking performance of two subsequent generations of actuators used on our back-support device. Figure 5 illus-

Fig. 5 Torque tracking performance of two generations of actuators (non-elastic and PEA) under the same controller. Top: torque-acceleration relationship shows reduction in perceived inertia. Bottom: corresponding increase in torque bandwidth

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trates two manifestations of closed-loop torque tracking, and represents in red a non-elastic traditional actuator and in blue the PEA. Given the same closed-loop torque controller, the output inertia (left plot) is represented as the relation between residual interaction torque and the angular acceleration of a joint controlled with zero-torque reference. The slope for the PEA is considerably lower than for the nonelastic actuator, indicating that the perceived inertia is reduced substantially by the parallel spring. The right plot illustrates the improvement in torque bandwidth as estimated from following a torque chirp.

3.3 Electrical Energy Consumption Electrical energy consumption is another aspect of interest for actuators on wearable robots. Recent work on the Robo-Mate active back-support has estimated the effect of the parallel elasticity in the energy consumption via simulation (Toxiri et al. 2019a). In line with the results presented above, this comparison is between a non-elastic actuator (red line in Fig. 6) and a PEA (blue line in Fig. 6). The two actuators are selected for comparable torque capacity during the task of interest. Figure 6 shows substantially lower electrical power consumption associated with the use of parallel elasticity. A more detailed analysis of the different losses is presented in (Toxiri et al. 2019a). Fed with data from three subjects, the simulation predicted a reduction of electrical energy consumption well over 50%.

Fig. 6 Simulated electrical energy consumption of two different actuators during the activity illustrated in Fig. 2. PEA, represented by the solid blue line, is a parallel-elastic actuator. Represented by the solid red line is a non-elastic actuator selected for comparable torque capacity. This figure shows data from one of the subjects considered, while the average predicted reduction across all subjects is well over 50% (Toxiri et al. 2019a)

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4 Conclusion/Considerations With reference to the back-support exoskeleton described above and its target task of lifting, our results associate the use of parallel elasticity with several advantages. The requirement for mechanical power output from the geared motor is relaxed, which in principle enables more convenient design choices, e.g., impacting cost and weight. The different actuator design also improves torque tracking performance, which positively impacts the biomechanical effectiveness of the exoskeleton as well as the user comfort. Finally, a preliminary analysis additionally points at a clear reduction in electrical energy consumption, which would impact the tradeoff between battery weight and duration.

References Coenen, P., Kingma, I., Boot, C. R. L., Bongers, P., & Van Dieën, J. (2014). Cumulative mechanical low-back load at work is a determinant of low-back pain. Occupational and Environmental Medicine, 71(5), 332–337. De Looze, M. P., Kingma, I., Thunnissen, W., Van Wijk, M. J., & Toussaint, H. M. (1994). The evaluation of a practical biomechanical model estimating lumbar moments in occupational activities. Ergonomics, 37(9), 1495–1502. Koopman, A. S., Toxiri, S., Power, V., Kingma, I., van Dieën, J. H., Ortiz, J., & de Looze, M. P. (2019). The effect of control strategies for an active back-support exoskeleton on spine loading and kinematics during lifting. Journal of Biomechanics, 91, 14–22. Masood, J., Ortiz, J., Fernández, J., Mateos, L. A., & Caldwell, D. G. (2016). Mechanical design and analysis of light weight hip joint parallel elastic actuator for industrial exoskeleton. In: 2016 6th IEEE International Conference on Biomedical Robotics and Biomechatronics (BioRob) (pp. 631–636). IEEE. Toxiri, S., Calanca, A., Ortiz, J., Fiorini, P., & Caldwell, D. G. (2017). A parallel-elastic actuator for a torque-controlled back-support exoskeleton. IEEE Robotics and Automation Letters, 3(1), 492–499. Toxiri, S., Koopman, A. S., Lazzaroni, M., Ortiz, J., Power, V., de Looze, M. P., et al. (2018a). Rationale, implementation and evaluation of assistive strategies for an active back-support exoskeleton. Frontiers in Robotics and A, I, 5. Toxiri, S., Calanca, A., Poliero, T., Caldwell, D. G., & Ortiz, J. (2018b). Actuation requirements for assistive exoskeletons: Exploiting knowledge of task dynamics. In: International Symposium on Wearable Robotics (pp. 381–385). Springer, Cham. Toxiri, S., Verstraten, T., Calanca, A., Caldwell, D. G., & Ortiz, J. (2019a). Using parallel elasticity in back-support exoskeletons: a study on energy consumption during industrial lifting tasks. In: 2019 Wearable Robotics Association Conference (WearRAcon) (pp. 1–6). IEEE. Toxiri, S., Näf, M. B., Lazzaroni, M., Fernández, J., Sposito, M., Poliero, T., et al. (2019). Backsupport exoskeletons for occupational use: An overview of technological advances and trends. IISE Transactions on Occupational Ergonomics and Human Factors. https://doi.org/10.1080/247 25838.2019.1626303.

Considerations and conclusions

Considerations Philipp Beckerle, Maziar Ahmad Sharbafi, Peter P. Pott, André Seyfarth, and Tom Verstraten

Summarizing and discussing the contents of the previous chapters, we provide biological, engineering, bioinspiration, and application considerations of bioinspired actuators for robotics.

1 Biological Considerations Biomechanics and motor control are mirroring systems which may solve the task at a similar level of complexity but with quite different means. Biomechanical template models have been developed over the last two decades for different movement types and subfunctions. It still remains as an open task to systematically translate these insights on organization of the motor system on the mechanical level into the corresponding control programs on the neural level. The novel concept of the sensor-motor map may help to identify the matching neural structures to achieve a desired motor task with corresponding motor subfunctions as described for legged locomotion.

2 Engineering Considerations From an engineering perspective, elastic actuators are a promising concept to approach the biomechanical role model. Despite technical constraints, the multitude of implementations provides various advantages, e.g., safe human-machine P. Beckerle (B) · M. A. Sharbafi · P. P. Pott · A. Seyfarth · T. Verstraten Elastic Lightweight Robotics Group, Technische Universität Dortmund, Robotics Research Institute, Otto-Hahn-Straße 8, 44227 Dortmund, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2021 P. Beckerle et al. (eds.), Novel Bioinspired Actuator Designs for Robotics, Studies in Computational Intelligence 888, https://doi.org/10.1007/978-3-030-40886-2_13

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interaction and improved energy efficiency. To further advance functional capabilities and size/weight, system integration and combinations of multiple actuators appear to be promising routes to follow. However, consistent and hybrid actuator combinations pose new control challenges to be tackled, which is also connect to the mechanical configuration of actuator(s) and springs. Hence, a broad mechatronic view is required to define and approach technical specifications considering transducers, gearing, and springs as well as sensors and control. Elastic actuation is not a purely mechanical problem and systems have to be addressed in the static and dynamic behavior as well as time and frequency domain. Resonance and anti-resonance play an important role when it comes to energy efficient operation in close human machine interaction such as prosthetics and orthotics. Energy efficiency is not only a green goal but defines battery size and weight given a desired operational time. Lastly, the chosen control strategy plays an important role for the systems’ performance and allows a wide range of behavior.

3 Bioinspiration Considerations Engineers have attempted to develop bioinspired actuators for locomotion, but efforts have failed to approach biological actuators’ characteristics. The bioinspired features are at the control architecture or the mechanical design level, such as embedding (adjustable) compliance. Different approaches of variable impedance actuators design address some aspects of biological actuation. Recent studies revealed other novel key features of biological muscles that are uninvestigated in robotics and locomotion. We highlighted an extensive capability in studying muscle properties such as redundancy, motor unit recruitment, and compliant functionality, with a view toward design and control of actuators in robots. For example, using multiple small actuators with adjustable impedance, which can be discretely recruited, is a novel method that is now accessible with new actuation technologies. Kinematically redundant actuators such as the DMA, and pneumatic artificial muscles (PAM) are two instances of engineered actuators benefiting from this potential. The PAMs are already used in different robots as the energy injection source, but, in the electric-pneumatic actuators (EPA), they also function as the adjustable compliance to increase efficiency and robustness of the motion. Since providing the exact features of biological muscle with state-of-the-art actuators is still not feasible with today’s technology, researchers recently started to use the animal muscles and even growing living cells to actuate robots. Different aspects presented here are entirely new and have primarily been introduced in the last couple of years. This growing interest in designing bioinspired actuators shows tremendous potential for future research not only in robotics but also in related research fields such as gait assistance and rehabilitation.

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4 Application Considerations We have discussed how actuators with elastic elements can lead to considerable improvements in terms of energy efficiency, peak power reduction, bandwidth and weight reduction. Practical implementations in the CYBERLEGS prosthesis and in the assistive back-support exoskeleton built at IIT confirm these findings. However, one must bear in mind that compliant actuators link kinematics to dynamics. When these differ from the expected patterns, the springs may lose effectiveness, and more complex mechanisms such as the energy transfer mechanism in the CYBERLEGS prosthesis may cease to work as expected. In other words, a good understanding of the actuators, the task at hand and the interaction between the user and the device are crucial elements for designers of compliant actuators.

Conclusions Philipp Beckerle, Maziar Ahmad Sharbafi, Peter P. Pott, André Seyfarth, and Tom Verstraten

Abstract This book outlines technical concepts to approach muscle-like actuation. We conclude on the immense potential of developing such devices for robotic applications.

While research still seems to be far away from creating real muscle-like actuators, this book outlines promising actuation approaches as well as the immense potential of developing such devices for diverse robotic applications. To this end, the analysis and understanding of biological muscles is a key step to provide engineering implications for actuator design. For instance, the muscle fiber acts like a linear spring with adjustable rest length in case of isometric contractions followed by stretch. While this feature of biological muscles is already applied in robotic actuators through the integration of compliant elements, further analysis is required to understand more sophisticated biomechanical and neuromechanical principles and to consider them in actutator design. Depending on the complexity of the task to be solved, actuation design can rely on simplistic 1-D models of muscle fibers or whole muscles as well as sophisticated 3-D descriptions. Going beyond the mechanical part of the muscle, the coordination of the neuromuscular and the musculoskeletal systems should be considered in actuator design and control. Therefore, neuromechanical modeling is proposed as a means to understand neural recruitment and force transfer and to mimic it through signal processing and control. In combination with biomechanical template models, this might lead to sensor-motor maps, which could reveal the organization of the human motor system on the mechanical land the neural level. In analyzing the general technical specifications of elastic actuators, we advocate a system wide perspective going beyond the actual electromechanical transducer, mechanical elements, as well as compliances and considering also sensors, P. Beckerle (B) · M. A. Sharbafi · P. P. Pott · A. Seyfarth · T. Verstraten Elastic Lightweight Robotics Group, Technische Universität Dortmund, Robotics Research Institute, Otto-Hahn-Straße 8, 44227 Dortmund, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2021 P. Beckerle et al. (eds.), Novel Bioinspired Actuator Designs for Robotics, Studies in Computational Intelligence 888, https://doi.org/10.1007/978-3-030-40886-2_14

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processing, and control. Issues of how to design the static and dynamic behavior of technical actuators might be answered through bioinspiration from the human muscle as mentioned above. Moreover, actuator topologies, multi-actuator systems, and system dynamic characteristics such as resonance and antiresonance are important design options. The latter, especially, influence energy efficiency and, thereby, influence battery size and weight, which outlines the importance of system integration. Going beyond classic elastic actuation concepts, key features of the biological muscles could be implemented in robotic applications. This concerns redundancy and motor unit recruitment, which relies on combining multiple actuators in an overall actuation system and can increase its reliability, versatility, and performance. Possible solutions range from combining two actuators to cellular arrangements of various small actuators and might include different actuation principles, e.g., electromechanical and pneumatic. Clearly biomimetic examples are kinematically redundant actuators, which implement the functions of human muscle sarcomeres, and pneumatic artificial muscles that resemble human muscle force generation by contraction. Furthermore, clutch mechanisms might extend the stiffness variation functionality of muscle-inspired actuators. Using (synthetically-grown) biological muscles themselves as actuators in robotics might be a future technical solution, but could also enforce our efforts in understanding muscle function. As a prime application example of bioinspired actuators, wearable robots are entering commercial market and might lead humanity into an era of robot-assisted living. The potential of wearable robots is strongly depending on actuator technologies, which are subject to challenging requirements regarding safety, reliability and durability, size and weight, and energy efficiency as well as user experience. Compliant actuators are especially promising for assistive applications such as exoskeletons or prosthetics: human joints exhibit a linear component in the torqueangle relationship during many tasks, e.g., walking and lifting loads, which makes them suitable for elastic elements. The presented case studies imply how bioinspired actuation, kinematics, and controls can improve assistive device performance and efficiency, but also that user experience influences which technical solutions are suitable. Comparing the biomechanical and neuromechanical insights (see Part II) to recent actuator implementations (Part III) and cutting edge approaches to increased bioinspiration (Part IV) outlines: 1. 2.

a gap between what is understood about biological human actuators and what is implemented in their technical counterparts. even the understanding of the biological foundations is limited.

Accordingly, future research should follow two paths, namely getting a deeper understanding of the function of the biological role model as well as following the route of implementing what is already understood. Moreover, technical implementations of biological concepts in robotics have proven to be very strong tools to improve the understanding of the underlying biomechanical and neuromechanical principles.

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Hence, an iterative approach towards developing both research directions appears to be the right way to promote the field of bioinspired actuators as a whole. Through following this line, the authors of this book believe that not only humanlike performance, but also versatility, efficiency, and perturbation-rejection characteristics could be achieved and implemented in assistive robotics to, finally, serve future demands of humanity.