Vol. 29, No. 3, SEPTEMBER 2022 IEEE Robotics & Automation Magazine

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Displaying the world in your hands. Inventing new ways to interact. Force Dimension designs and manufactures the finest master haptic devices for leading-edge applications in research, medical, industry, and human exploration.

The ScanTrainer from Intelligent Ultrasound is an educational tool that uses real patient scans and curriculum-based teaching across obstetrics, gynecology, general medicine, and emergency medicine. The system integrated a customized delta.3 haptic device. Force Dimension Switzerland www.forcedimension.com [email protected]

Vol. 29, No. 3 SEPTEMBER 2022 ISSN 1070-9932 http://www.ieee-ras.org/publications/ram

FEATURES 10

(a)

Design, Testing, and Evolution of Mars Rover Testbeds

European Space Agency Planetary Exploration  By Martin Azkarate, Levin Gerdes, Tim Wiese, Martin Zwick, Marco Pagnamenta, Javier Hidalgo-Carrió, Pantelis Poulakis, and Carlos J. Pérez-del-Pulgar

24 Testing Gecko-Inspired Adhesives With Astrobee

Aboard the International Space Station

Readying the Technology for Space By Tony G. Chen, Abhishek Cauligi, Srinivasan A. Suresh, Marco Pavone, and Mark R. Cutkosky

34 BEAR-H

An Intelligent Bilateral Exoskeletal Assistive Robot for Smart Rehabilitation By Xiang Li, Xuan Zhang, Xiu Li, Jianjun Long, Jian’an Li, Lanshuai Xu, Gong Chen, and Jing Ye

47

(b)

Damping in Compliant Actuation

A Review By Simone Monteleone, Francesca Negrello, Manuel G. Catalano, Manolo Garabini, and Giorgio Grioli

 67 Challenges and Outlook in Robotic

Manipulation of Deformable Objects

 y Jihong Zhu, Andrea Cherubini, Claire Dune, David Navarro-Alarcon, B Farshid Alambeigi, Dmitry Berenson, Fanny Ficuciello, Kensuke Harada, Jens Kober, Xiang Li, Jia Pan, Wenzhen Yuan, and Michael Gienger

 78 FEA-Based Inverse Kinematic Control

Hyperelastic Material Characterization of Self-Healing Soft Robots By Pasquale Ferrentino, Seyedreza Kashef Tabrizian, Joost Brancart, Guy Van Assche, Bram Vanderborght, and Seppe Terryn

 89 A Review of Cable-Driven Parallel Robots ON THE COVER This issue of IEEE Robotics and Automation ­Magazine ­explores space robotics, exoskeletal robots for ­rehabilitation, soft robotics, and cable-driven robots.

Typical Configurations, Analysis Techniques, and Control Methods By Mahmoud Zarebidoki, Jaspreet Singh Dhupia, and Weiliang Xu

107 A Cable-Driven Hyperredundant Manipulator

Obstacle-Avoidance Path Planning and Tension Optimization By Dawei Xu, En Li, Rui Guo, Jiaxin Liu, and Zize Liang (Continued)

©SHUTTERSTOCK.COM/SDECORET

If you like an article, click this icon to record your opinion. This capability is available for online Web browsers and offline PDF reading on a connected device. Digital Object Identifier 10.1109/MRA.2022.3195599

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FEATURES

(Continued)

 127 Dual-Arm Control for Coordinated Fast Grabbing and Tossing of an Object

Proposing a New Approach  By Michael Bombile and Aude Billard

  139 Safety and Efficiency in Robotics

 The Control Barrier Functions Approach  By Federica Ferraguti, Chiara Talignani Landi, Andrew Singletary, Hsien-Chung Lin, Aaron Ames, Cristian Secchi, and Marcello Bonfè

A Publication of the IEEE ROBOTICS AND AUTOMATION SOCIETY Vol. 29, No. 3 September 2022 ISSN 1070-9932 http://www.ieee-ras.org/publications/ram

EDITORIAL BOARD Editor-in-Chief Yi Guo ([email protected]) Stevens Institute of Technology (USA) Editors Elena De Momi Politecnico di Milano (Italy) Jindong Tan University of Tennessee (USA) Associate Editors Ming Cao University of Groningen (The Netherlands) Feifei Chen Jiao Tong University (China) Carlos A. Cifuentes Bristol Robotics Laboratory (UK) Kingsley Fregene Lockheed Martin (USA) Antonio Frisoli Scuola Superiore Sant’Anna (Italy) Jonathan Kelly University of Toronto (Canada) Ka-Wai Kwok The University of Hong Kong (Hong Kong)

COLUMNS & DEPARTMENTS

Surya G. Nurzaman Monash University (Malaysia) Weihua Sheng Oklahoma State University (USA)

4 FROM THE EDITOR’S DESK

Yue Wang Clemson University (USA)

8 PRESIDENT’S MESSAGE

Enrica Zereik CNR-INM (Italy)



152 STANDARDS



153 WOMEN IN ENGINEERING



155 INDUSTRY ACTIVITIES



157 STUDENT’S CORNER

Houxiang Zhang Norwegian University of Science and Technology (Norway) Past Editor-in-Chief Bram Vanderborght Vrije Universiteit Brussel (Belgium) RAM Column Manager Amy Reeder (USA)

159 SOCIETY NEWS

RAM Editorial Assistant Joyce Arnold (USA)

Cover 3 CALENDAR

COLUMNS Competitions: Hyungpil Moon (Korea) Education: Andreas Müller (Austria) From the Editor’s Desk: Yi Guo (USA) Industry News: Tamas Haidegger (Hungary)

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Humanitarian Technology: Vacant Standards: Craig Schlenoff (USA) President’s Message: Frank Park (Korea) Regional Spotlight: Megan Emmons (USA) Student’s Corner: Francesco Missiroli (Germany) TC Spotlight: Yasuhisa Hirata (Japan) Women in Engineering: Karinne Ramirez Amaro (Sweden) IEEE RAS Vice-President of Publication Activities Todd Murphey (USA) RAM home page: http://www.ieee-ras.org/publications/ram IEEE Robotics and Automation Society Executive Office Peter Sobel Executive Director Amy Reeder Program Specialist [email protected] Advertising Sales Mark David Director, Business Development—Media & Advertising Tel: +1 732 465 6473 Fax: +1 732 981 1855 [email protected] IEEE Periodicals Magazines Department Kristin Falco LaFleur Senior Journals Production Manager Patrick Kempf Senior Manager Journals Production Janet Dudar Senior Art Director Gail A. Schnitzer Associate Art Director Theresa L. Smith Production Coordinator Felicia Spagnoli Advertising Production Manager Peter M. Tuohy Production Director Kevin Lisankie Editorial Services Director Dawn M. Melley Staff Director, Publishing Operations IEEE-RAS Membership and Subscription Information: +1 800 678 IEEE (4333) Fax: +1 732 463 3657 http://www.ieee.org/membership_services/ membership/societies/ras.html

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IEEE prohibits discrimination, harassment, and bullying. For more information, visit http://www.ieee.org/web/aboutus/whatis/policies/p9-26.html.

IEEE Robotics and Automation Magazine (ISSN 1070-9932) (IRAMEB) is published quarterly by the Institute of Electrical and Electronics Engineers, Inc. Headquarters: 3 Park Avenue, 17th Floor, New York, NY 10016-5997 USA, Telephone: +1 212 419 7900. Responsibility for the content rests upon the authors and not upon the IEEE, the Society or its members. IEEE Service Center (for orders, subscriptions, address changes): 445 Hoes Lane, P.O. Box 1331, Piscataway, NJ 08855 USA. Telephone: +1 732 981 0060. Individual copies: IEEE Members US$20.00 (first copy only), non-Members US$140 per copy. Subscription rates: Annual subscription rates included in IEEE Robotics and Automation Society member dues. Subscription rates available on request. Copyright and reprint permission: Abstracting is permitted with credit to the source. Libraries are permitted to

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Say Hello_to the next robotic innovator Research teams from around the globe were asked to submit their concepts on the topic of “Robotics in Healthcare” for the KUKA Innovation Award. Five teams made it to the finals and will be presenting their projects on MEDICA fair in November 2022. The award comes with a 20,000-euro prize. Meet our five finalists.

KUKA Innovation Award 2022

Team Brubotics, Vrije Universiteit Brussel and imec, Belgium “Our team developed a soft sensorized physical interface to work together with the KUKA LBR Med, enabling a rehabilitation robot with a sense of touch to capture the intention of the patient. This allows the robot to feel the patient and create a personalized and more engaging therapy.”

Team Ligō, Inventia Life Science, Australia “Ligō is reducing the lifelong impact that scarring has on burns survivors. Developed in collaboration with surgeons and 3D bioprinting experts, it treats patients in the operating theatre by 3D printing their own skin cells back into their wound to stimulate the regeneration of healthy, functional skin”.

Team ROPCA, ROPCA, Denmark “ROPCA wants to be the first in the world to offer a fully automatized ultrasound scan for Rheumatoid Arthritis. By using the LBR Med, a standard ultrasound scanner and a touchscreen display we enable the patient to scan the hands without the help of a doctor.”

Team cortEXplore, cortEXplore GmbH, Austria “Our aim is to implant micro-electrode arrays into the brain of a primate. We use our high-resolution neuronavigation system to guide the movement of a surgical robot. This allows aligning the electrodes to a planned safe insertion

www.kuka.com/InnovationAward2022

trajectory and executing a linear motion for placement at sub-millimeter and subdegree resolution.”

Team Aroki, HTIC, IIT Madras, India “Our solution aims to improve maternal and antenatal care by providing robot-assisted periodic ultrasonograms in healthcare centers. The system comprises an immersive virtual reality platform, that enhances the sonographer’s visual experience and allows them to operate the robot autonomously as well as from a remote clinical setting.”

FROM THE EDITOR’S DESK

Reconnecting the Diverse Community By Yi Guo

A

fter two years of virtual conferences, the annual flagship conference of the IEEE Robotics and Automation Society (RAS), the IEEE International Conference on Robotics and Automation (ICRA), has returned in person. When I attended ICRA in Philadelphia in May, I felt excitement in the air when people greeted each other and friends shook hands and hugged each other. It was not easy for professors, students, industry practitioners, and With more than other attendees traveling from 4,700 in-person all around the participants, nearly world to be under one roof, half of whom were while the students, this year’s COVID-19 pandemic has conference was not fully settled the largest and into its endemic stage. With youngest one ever more than 4,700 in ICRA history. in-person participants, nearly half of whom were students, this year’s conference was the largest and youngest one ever in ICRA history. Along with the exciting technical programs at ICRA, almost all RAS committees have held in-person meetings for the first time in two and a half years. After so many Zoom meetings, it felt good to network and exchange ideas freely in person with colleagues Digital Object Identifier 10.1109/MRA.2022.3188191 Date of current version: 7 September 2022

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and volunteers of the community. Our magazine, IEEE Robotics and Automation Magazine (RAM), serves as a forum, connecting the entire RAS community as well as a channel for sharing Society news and communication about activities. We made plans to enhance collaboration with RAS Technical Committees (TCs), which include publishing column articles in “TC Spotlight,” inviting TCs to propose RAM special issues (SIs), and inviting TC cochairs to join guest editor teams of SIs. We also welcome column articles from conference activities and member activities for reports on RAS-cosponsored conferences and RAS member programs and activities. At ICRA, I attended several network events, one highlight of which was the RAS Lunch with Leaders for Students. Many students at the event were first-time ICRA attendees and asked questions on career paths for robotics researchers. RAS presidents past and current, including the president-elect, were at the luncheon to talk about their first ICRA experience and offered advice to the students. This event connects the young generation and the student community with established leaders in the field. We hope that, out of the hundreds of young attendees in the room, some will rise to the top and lead the field some day in the future. With the same goal to engage the young generation and the student community, we encourage submission of RAM column articles on research life and career stories from the student and

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postdoctoral communities in our field. Interested authors may contact me or Amy Reeder, the column manager of RAM. Also, RAM has recently collaborated with IEEE Potentials, IEEE’s global magazine for students, on a theme issue on robotics and automation. Interested authors may refer to the July/ August issue of IEEE Potentials for Call for Papers [1]. Another popular social event at ICRA was the RAS Women in Engineering (WiE) Networking Event, where the RAS-WiE committee led a discussion on diversity and inclusion and initiatives to advance women in leadership. As a female robotics researcher, I have benefited from training and working with women robotics leaders. A noteworthy experience was being a member of the allfemale organizing committee of ICRA 2015 in Seattle [2]. Networking and interacting with a group of active women robotics researchers, many of whom were leaders in the field, provided an invaluable opportunity for me to broaden my vision and prepared me for leadership. I remember that Ruzena Bajcsy, Honorary General Chair of ICRA 2015, talked about her early experience as the only female robotics researcher in a meeting room in the 1990s. At this ICRA, I heard the wonderful news that Ruzena’s daughter, Klara Nahrstedt, was elected to the U.S. National Academy of Engineering this spring, which means that Ruzena and Klara became the first mother-daughter pair elected to the prestigious academy. This amazing

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news is inspiring to young women who pursue careers in the science and engineering field. As Klara stated in a fireside chat at the University of Illinois Urbana-Champaign [3], “It’s hard for female researchers for many reasons—expectations and pressures imparted on us by those around us. But to know you have a support network there to encourage you and support you, that can help a young woman develop so much confidence.” I hope that our RAS-WiE network can provide such support and encourage me nt for wome n rob ot i c s researchers to pursue a successful career in the field that is largely dominated by men. We need more exciting

news like this, so that we make real progress in fixing gender bias in science and robotics. At this ICRA, we announced the seventh RAM Best Paper award. The awarded paper “Building an Aerial– Ground Robotics System for Precision Farming: An Adaptable Solution,” by Alberto Pretto et al., was published in the September 2021 issue of RAM. We congratulate all the authors on this achievement. This September issue is a regular issue that contains 10 featured articles on space robotics, exoskeletal robots for rehabilitation, soft robotics, and cable-driven robots. I hope you enjoy reading the issue!

References [1] “Call for papers: Theme issue on robotics and automation,” IEEE Potentials, vol. 41, no. 4, pp: C2-C2, 2022. [2] L. Parker and N. M. Amato, “IEEE ICRA 2015-Celebrating the diversity of robots and roboticists [Society News],” IEEE Robot. Autom. Mag., vol. 22, no. 3, pp. 168–170, 2015, doi: 10.1109/MRA.2015.2452091. [3] A. Seidlitz, “News: Family history: Nahrstedt, Bajcsy share stage as first mother-daughter pair elected to the national academy of engineering,” Department of Computer Science, Univ. of Illinois Urbana-Champaign, Urbana, IL, USA, May 18, 2022. [Online]. Available: https://cs.illinois.edu/ news/family-history-nahrstedt-bajcsy-share -stage-as-first-mother-daughter-pair-elected-to -the-national-academy-of-engineering

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PRESIDENT’S MESSAGE

Reflections on ICRA 2022 By Frank Park

H

aving witnessed the nearly five thousand participants gathered in Philadelphia for the IEEE International Conference on Robotics and Automation (ICRA) 2022, I think it’s safe to say that in-person meetings are emphatically back. It’s true that the coronavirus continues to evolve and still stubbornly refuses to Despite some go away, and small kinks in the many travel restrictions across technology, there borders remain does appear to be in place. Still, after more than a sizable segment two years of of participants meeting remotely, the chance to for whom virtual have informal attendance is the conversations in the hallway with preferred (and, in speakers, to consome cases, the nect with both old and new only) option. friends outside meetings, and to disconnect from the distractions of daily life and rituals were, especially for me, too much to pass up. To the organizers and volunteers who organized such a tremendously successful event through the uncertainty and challenges of the pandemic, let me express my deep gratiDigital Object Identifier 10.1109/MRA.2022.3189232 Date of current version: 7 September 2022

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tude on behalf of the entire robotics community. I was struck by several trends and events at this most recent ICRA. First, the hybrid format appears here to stay for future ICRAs. Despite some small kinks in the technology, there does appear to be a sizable segment of participants for whom virtual attendance is the preferred (and, in some cases, the only) option. Second, I was particularly struck by the passion and enthusiasm of the many—including many men—who attended the RAS Women in Engineering (RAS-WiE) event. The outpouring of pent-up frustrations at the many challenges and subtle forms of discrimination that women roboticists continue to face in the workplace and at our conferences as well as at home was both a sobering revelation and a reminder of how far we as a community have to go. To the organizers of the RAS-WiE event, I wish to both thank you for your efforts and entreat you to continue to organize this event at future ICRAs. The third development that struck me was the presence of nearly 100 industry exhibitors and sponsors at ICRA 2022. It doesn’t seem that long ago when ICRAs struggled to attract half that number; the exhibitors who showed up were mostly research equipment manufacturers, lab start-ups, and publishers, with a smattering of established industrial robotics companies mixed in who often

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did not return. As noted in an article by Vice President of Industrial Activities Andrea Keay appearing in this issue of IEEE Robotics & Automation Magazine, more robotics companies have been formed in the last 10 years than in the entire history of robotics. While we are likely still far away from a “robot in every home,” the predictions of a coming wave of innovation in robotics and automation that will lead to sustainable, scalable companies, does not seem that far-fetched. To engage this new and burgeoning segment of our community, discussions are underway on the launching of a new publication designed for robotics and automation practitioners. The focus of this new publication will be on algorithms, software, designs, and systems integration as well as empirical case studies that are of nearterm benefit to practitioners. Such results are likely not ideal for our existing publications, and yet, more and more, as the robotics industry continues to expand and mature, we can expect interest in such studies to increase. I invite you to read more about the activities of our Industrial Activities Board, and to share your thoughts and feedback on how the IEEE Robotics and Automation Society can better engage with the growing segment of members from industry. 

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Design, Testing, and Evolution of Mars Rover Testbeds

European Space Agency Planetary Exploration By Martin Azkarate  , Levin Gerdes  , Tim Wiese, Martin Zwick, Marco Pagnamenta, Javier Hidalgo-Carrió  , Pantelis Poulakis, and Carlos J. Pérez-del-Pulgar 

T

his article presents the system architecture and design of two planetary rover laboratory testbeds developed at the European Space Agency (ESA). These research platforms have been developed to provide early prototypes for the validation of designs and serve the ESA’s Automation and Robotics Lab infrastructure for continuous research and testing. Both rovers have been built considering the constraints of space Digital Object Identifier 10.1109/MRA.2021.3134875 Date of current version: 14 January 2022

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systems with a sufficient level of representativeness to allow rapid prototyping. They avoid strictly space-qualified components and designs that present a major cost burden and frequently lack the flexibility or modularity that the lab environment requires for its investigations. This design approach is followed for all of the mechanical, electrical, and software aspects of the system. In this article, two ExoMars mission-representative rovers, the ExoMars Testing Rover (ExoTeR) and Martian Rover Testbed for Autonomy (MaRTA), are thoroughly described. The lessons learned and experience gained while running several research 1070-9932/22©2022IEEE

activities and test campaigns are also presented. Finally, the article aims to give an insight into how to reduce the gap between lab R&D and flight implementations by anticipating system constraints when building these platforms. This allows investigators to provide qualitative testing results that can eventually have an impact in real space missions. Current Rover Testbeds Space robotics can be considered a niche field of engineering in which the conditions given by the space environment present particular constraints to the research activities conducted in the area. Space representativeness is in a constant duel with research in terms of cost and flexibility in the processes of designing, manufacturing, and testing. This is mainly due to the technologies and development tools employed in space, which lack the mass production and community from which other engineering fields benefit. The space environment is harsh and remote and, therefore, difficult to access. Restrictions come not only from the available technology and components for space, which sometimes can be years behind their terrestrial counterparts, but even more drastically in the system mass and energy, which leads to the need for highly optimized and customized systems. One of the first questions engineers are faced with on a space mission is whether they are capable of designing a system that fulfills the mission requirements within the given mass and power budgets. Space missions are also what we call single-shot opportunities. One cannot repair during—except for certain fixes by software patches—or usually repeat a mission, which, again, puts stringent requirements on system robustness and design margins. All of these aspects eventually have a high cost impact, limiting even more space missions or activities related to space’s access to a wider community. Aware of these limitations, the Automation and Robotics Section of the ESA has embarked for years on activities for developing space robotics and, in particular, planetary rovers, in the scope of conducting R&D of key technologies for real space missions, such as ExoMars. In this article, the authors aim to demonstrate how the aforementioned constraints can be taken into account and impact the work done in the context of research as well as showcase this with specific prototyping activities. Therefore, the first goal is to describe the main challenges and design drivers in the development of laboratory planetary rover testbeds. In this context, the article highlights how MaRTA, the second-generation prototype, benefited from the experience gained and lessons learned on the design and testing of the earlier ExoTeR. Second, by providing an overview of selected test campaigns, we demonstrate how these platforms supported the actual ExoMars program rover developments. Looking at existing planetary rover testbeds, it is worth noting that NASA’s Jet Propulsion Laboratory (JPL) has led and is performing many successful planetary exploration missions with rovers. This is partially thanks to the

development of rover prototypes and testing done on Earth, typically as part of the mission programs. With the Mars Exploration Rovers (MERs) first and Curiosity later on, the same model philosophy has ensured the provision of a rover testbed throughout the different phases of the development of the mission. These were used to perform analyses of the traverse performance and predict their traversability throughout the mission by mimicking on Earth the apparent flight rover weight on Mars [1]. Among them, we could highlight the Scarecrow rover, a vehicle that shares the kinematic configuration of Curiosity and uses commercial off-the-shelf electronics, which, for years, has provided much useful data for Curiosity’s rover operations team [2]. In addition, the NASA JPL continues working on the development of new rover prototypes and platform configurations. For example, the DuAxel rover for exploration in very rough terrain, including rappelling motion, has shown promising results for potential lunar lava tube exploration missions [3]. The recently baptized Rosalind Franklin rover of the ExoMars mission is the first European rover aiming to land on Mars. Since its early conception, the ESA has been working on the development of breadboard prototypes to analyze different locomotion subsystems and their performance on a Mars-like terrain [4]. Later, in cooperation with European industrial partners, different breadboard rovers were assembled with engineering models of the electronics, software, and locomotion subsystems. National space agencies around Europe have also developed their own testbed rovers for research purposes. It is worth mentioning the Lightweight Rover Unit developed by the German Aerospace Center (DLR), an agile rover prototype used to develop several software components for autonomy [5]. The U.K. Space Agency developed the Mars Utah Rover Field Investigation, which was used to perform several field tests in collaboration with the Canadian Space Agency [6]. The French Space Agency (CNES) also developed the testbed rovers Illustrateur Autonome de Robotique mobile pour l’Exploration Spatiale (called IARES) and Autonomous Rover and Testbench for Exploration Missions (known as ARTEMIS), which were used for years for the development of the guidance, navigation, and control (GNC) software that will eventually drive Rosalind Franklin [7]. In Asia, two testbed rovers developed by JAXA are worth mentioning: Micro6 and Cuatro [8]. Both were conceived to push the technology readiness level (TRL) of failure-tolerant suspension systems and an intelligent navigation system based on novel path-planning methods. System Architecture In this section, we describe the system architecture and subsystem designs of the two ExoMars-representative laboratory rover prototypes of the ESA’s Automation and Robotics Section: ExoTeR and MaRTA, both shown in Figure 1. The ExoTeR rover concept was designed between 2008 and 2010, whereas MaRTA was developed from 2017 to 2019. While both are SEPTEMBER 2022

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conceived as scaled-down models of the ExoMars rover, ExoTeR is based on an early concept design of ExoMars, while MaRTA is more accurate in mimicking its current configuration.

Figure 1. The ExoTeR (right) and MaRTA (left) platforms side by side. The red arrow points to the parallelogram structure above the bogies on ExoTeR, which is not present in MaRTA.

ExoTeR has already been extensively used in several test campaigns, while MaRTA is still undergoing software developments and hardware integration to make it ready for testing. This section describes both systems and, in particular, highlights the differences in the design drivers and choices made based on the experience gained from testing ExoTeR. Table 1 presents a summary of all design modifications made for MaRTA that are explained throughout the section. Mechanical Design Here, we describe the mechanical design of the rover, and, in particular, we focus on three of its subsystems: the locomotion, manipulation, and mast and pan-tilt unit (PTU). It is worth noting that we do not describe other mechanical parts of the rover typically present in space systems. Our lab rovers are built to address only the pure robotic subsystems of the locomotion, manipulation, and navigation of a rover without considering other spacecraft subsystems, such as power generation and thermal control, or design aspects, for example, launch loads or radiation tolerance.

Table 1. A summary of the modifications made for MaRTA. Modification

Rationale

[M] Triple-bogie chassis design

Comply with the latest BEMA design: six-wheel steering (versus four) and no parallelogram structure

[M] Increased mass budget and payload capacity

Limitations already experienced with ExoTeR Margin for MaRTA subsystem integration

[M] Brushless motors and temperature sensors

Power–torque efficiency and better thermal behavior Temperature FDIR to avoid motor damage

[M] Modular drives design

Maintainability External routing connected to the interface plate

[M] Slimmer wheels

Mimic the effective ground pressure of the ExoMars flight system

[M] Force–torque sensors on wheels

Locomotion performance characterization and traction control implementation

[M] Arm with 6 DoF as well as longer and faster (reduced payload)

Testing experience with ExoTeR and targeting to the SFR mission scenario

[M] Stiffer and more torque-capable PTU

Limited payload and a frequent loss of calibration in ExoTeR

[M] 360° pan angle rotation of the PTU

Enable the capability to acquire full panoramic imagery

[M] Upgrade of all absolute-position sensors

Improved resolution, accuracy, and reliability of locomotion, manipulation, and PTU control

[E] Elmo Gold Twitter for motion control

Faster EtherCAT communications protocol (vs CAN) Overall product upgrade

[E] PCDE microcontroller and LCD display

Live view of the power measurement data and battery status (color LED)

[E] Emergency stop

Simply missing in ExoTeR Useful for many test procedures and operations

[E] Fiber-optic gyro sensor integration

Highly accurate measurement and tracking of the rover heading

[E] Pico-ITX OBC integration

PC104 became bulky and limiting

[E] Ethernet-based cameras

Reduced EMI with the GPS signal

[E] Mounting of MCE against walls

Improved the thermal balance inside the rover body with all avionics

[S] Current software status (both rovers)

Migrating to Ubuntu 20.04 and ROS2

BEMA: bogie electromechanical actuator; DoF: degrees of freedom; [E]: electrical; EMI: electromagnetic interference; FDIR: fault detection, isolation, and recovery; IMU: inertial measurement unit; [M]: mechanical; MCE: motion control electronics; OBC: onboard computer; PCDE: power conditioning and distribution electronics; PTU: pan-tilt unit; [S]: software; SFR: Sample Fetch Rover.

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Locomotion Subsystem The kinematic chain design on which both the ExoTeR and MaRTA rovers’ locomotions are based is known as the triple bogie. This is the actuation and passive suspension configuration chosen for the ExoMars rover’s bogie electromechanical actuator (BEMA). Its final design is actually the outcome of a series of prototyping developments that started in the early 2000s at the ESA. The triple-bogie system had interesting evolutions in design that iterated over tradeoffs among mass, complexity, and traversability performance [9]. Several of these prototypes were built and tested at the Automation and Robotics Section. The locomotion systems of ExoTeR and MaRTA were built as half-scaled versions that mimicked the ExoMars triplebogie design, each at their current times. The triple-bogie configuration basically consists of three independent bogies connected to the main body structure at the front left, front right, and rear. In contrast to the Rocker Bogie solution seen in all NASA rover missions to Mars, the triple bogie provides platform stability through its three points of attachment without the need for a differential bar across the body structure. The three attachment interfaces allow for passive rotation around the pivot assembly. Each bogie extends two horizontal levers that connect to the wheel modules. Each module consists of the following three actuators (in the order of the kinematic chain): the deployment (DEP), steering (STR), and wheel drives (DRV). In the case of ExoTeR, it did not contain steering actuators in the two middle wheels. However, ExoTeR includes a parallelogram structure at the bogies’ kinematic chain with passive linkages (see the annotation in Figure 1). This constrains the wheel motion to a straight-line translation, perpendicular to the rover chassis plane, when the bogies rotate. Despite its slightly superior tractive performances, the bogie parallelogram was eventually removed from the ExoMars design to increase the static stability limits of the rover and, at the same time, reduce even further the mass and complexity of the suspension system. On the other hand, the ExoMars mission decided to include a six-wheel steering capability with an increased angular operational range in the

Rear Bogie Assembly

latest BEMA design, which enables the full crabbing motion capability that is relevant for some approach maneuvers during scientific tasks. These two changes, together with some adaptations to the bogie lever dimensions to accommodate the wheels in the stowed position, resulted to the final ExoMars triple-bogie design [10] (see Figure 2) that MaRTA features at scale. Typically, this locomotion system is referred to as a 6 × 6 × 6 + 6 formula, as it contains a total of six wheels, out of which all are driven and steerable, and, additionally, each of them has a deployment actuator that permits the system to be stowed. This is achieved by putting the wheels upward to optimize for volume accommodation, particularly during the launch and cruise phases. Deployment actuators can be further exploited during the surface mission, permitting the implementation of a locomotion mode referred to as wheel walking. (See the “Wheel Walking: European Space Research and Technology Centre 2014 and DLR 2015” section for more details on this mode). The realization of these platform designs was accomplished by an analysis of the required forces and torques to be exerted by the rover locomotion system at any possible configuration, which leads to the selection of components for the motor drive units. In the case of ExoTeR, this resulted in dc electric Maxon brushed motors assembled with an incremental encoder at the motor back and a planetary gearbox at the output shaft. This is followed by a harmonic drive stage to further reduce the nominal speed and increase the torque capability of the system as well as, in the case of steering and deployment joints, an additional potentiometer at the output end for absolute-position sensing. Similar potentiometer sensors are installed at the three passive bogie joints attached to the base platform. ExoTeR’s platform system mass is 14 kg, with a target payload capacity of approximately 8 kg to carry other subsystems and all avionics, including the battery, actuation control electronics, and sensors. Experience with ExoTeR showed us that the payload capacity was insufficient, becoming rather limiting in cases where the manipulator was mounted. Therefore, when MaRTA was designed, a few modifications were introduced

DEP

Harness to Actuator Drive Electronics Pivot Assembly

Right Bogie Assembly

Left Bogie Assembly

STR

DRV

Figure 2. The BEMA triple-bogie kinematic chain configuration and right bogie beam with actuator locations [10].

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with respect to ExoTeR. These started with the increased base plate size, in line with the latest BEMA-scaled dimensions. Actuator components were chosen to increase the speed and torque capabilities of the locomotion system, and, therefore, enlarge the payload capacity of the platform. From the 22 kg of ExoTeR’s system mass, the total mass budget was increased to 32 kg in MaRTA. In addition, the MaRTA wheels were designed proportionally slimmer to match the current effective ground pressure of the ExoMars Rover flight system on Mars for the sake of traction performance representativeness. An eventual incident that occurred during tests with ExoTeR caused some motors to overheat and damaged its brushes and windings permanently. Because of this, a temperature sensor is also now integrated in each motor unit in MaRTA and used for thermal monitoring as well as fault detection, isolation, and recovery (FDIR) functions. In relation to the same lesson learned and in favor of maintainability, a more modular design approach was taken in MaRTA, enabling each drive module to be removed and maintained individually if needed. The externally routed motor drive harness connects directly now in MaRTA to an interface plate at the rover body. Moreover, the steering and deployment actuators are identical and interchangeable. Additionally, some components were also simply upgraded by more recent and advanced technology. The more power-efficient brushless motors were selected for MaRTA, which also improved the thermal behavior of the system; in addition, optical sensors with 12-b resolution (LIR-DA219A) were used for absolute-position sensing instead of the original wire-wound potentiometers (SP5-21A), which, in ExoTeR, showed some undesirable nonlinear behavior. Finally, each of MaRTA’s wheel modules is equipped with a force–torque sensor that provides data for future research activities, such as the performance characterization of different locomotion modes or development of traction control algorithms. Manipulator Subsystem Although the ExoMars mission does not carry a manipulator system, it was decided that developing a robotic arm

Figure 3. The ExoTeR manipulator attached to the front body wall.

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fitting the rover constraints would allow for performing relevant research in the field of robotic manipulation for future planetary exploration. This scenario has become relevant with the upcoming joint NASA–ESA Mars Sample Return campaign, where the ESA will be developing the Sample Fetch Rover (SFR). The manipulator system in Figure 3 was developed to be integrated into ExoTeR. It has five degrees of freedom (DoF), 528 mm of operational reach, and a total mass of 2.4 kg with a payload capacity of 2 kg. Its development follows the same design drivers as the locomotion system, and it has low mass and power budgets (around 10 W of nominal operation) with a high payload-to-mass ratio, which implies high reduction ratios to provide enough torque at the expense of absolute speed. The motor drive design comprises a small brushed motor; several reduction stages of planetary gear; a custom spur gear and harmonic drive with an incremental encoder at the motor end; and an absoluteposition sensor at the output shaft, i.e., a wire-wound type of potentiometer (SP5-21A). The high reduction ratio of the joints (83,200:1) and stiffness of its parts make the arm practically nonback-driveable, eliminating the need for any motor brakes to hold the position when powered off but also significantly slow (0.5°/s), following the approach of a potential space operation. In 2020, it was decided that a new robotic arm should be developed to be integrated in MaRTA, taking into consideration the lessons learned from ExoTeR’s arm. The experiments described in the “Sample Fetch Tests: ESTEC 2019” section showed us the manipulator was rather slow for R&D experimentation and testing, and its 5 DoF had impacting operational constraints. Also, ExoTeR’s arm was not designed for the SFR’s manipulation tasks, which require it to grasp sample tubes of only 100 g. The SFR scenario will be the main purpose of MaRTA’s robotic arm. The new design targets 6 DoF, allowing full unconstrained operation in 3D space, and a joint rotational speed of 8°/s. A more compact joint design is targeted with a powerful flat motor, fewer reduction stages, and no spur gear, resulting in a cylinder-shaped block design. The design foresees a total mass budget of 3 kg, with 0.9 kg of payload capacity and an operational reach of 700 mm, with the plan of accommodating a gripper end effector and leaving enough margin for sample manipulation. The power budget is also increased to approximately 20 W in nominal operation, in line with the new, more powerful motors. According to the load analysis, motor brakes will not be needed to hold the position of joints when these are powered off. A mechanical bracket interface is also designed where the arm can rest while parked in the stowed position. An upgrade in the sensors is foreseen, with absolute-position, contactless electric encoders replacing the much less reliable and less accurate potentiometer sensors. All in all, it is expected to have this robotic arm integrated in MaRTA by the end of 2021 and be of relevant use for the lab in the research activities of the autonomous fetching of sample tubes.

Mast and PTU The mast and PTU is an element present in many (if not all) planetary rover systems. The perspective view provided by sensors mounted at the top of it is not only valued by scientists but also, sometimes, necessary for accomplishing mission or engineering objectives. For the case of our lab rover prototypes, it became necessary to integrate such a system and mount camera sensors that allowed us to conduct research in the area of autonomous navigation (AutoNav). In 2014, we developed and integrated a lightweight mast and PTU system in ExoTeR. The total system mass is below 0.4 kg, while the maximum payload capacity is 0.8 kg. The two motor drive units have almost identical design for both axes, with a linear assembly of the motor, gearbox, harmonic drive, and conductive plastic potentiometer sensor (PL130). The operational range of the PTU is 300° of rotation in the pan axis and 180° in the tilt. The limited pan range favored the more simple and lightweight design of the PTU. At a later stage, this constraint would be shown to be inconvenient for certain testing scenarios. See Figure 4 for an overview of the PTU design elements. Two identical PTU sets were built and delivered that could be mounted at two different height adjustments (mast lengths), which conveniently allowed us to integrate a set into MaRTA as soon as the rover platform was delivered, thanks to both rovers having the same mechanical interface. This subsystem has enabled significant R&D activities in the areas of perception, localization, and navigation. The system is fast and easily back-drivable. Care must be taken so the tilt motor does not “fall down” when powered off, especially if more than one sensor is mounted on its top, which also offsets the center of mass of the PTU payload farther away than what it was designed for. This leads to a frequent loss of the calibration of the axis. In 2019, we decided to produce an upgraded version of this subsystem with a higher payload capacity as well Camera Bracket as a stiffer and more robust design. Apart from the more capable motor and gears assembly, we also opted to upgrade the absolute-position sensor, using an optical 12-b sensor (LIRDA219A) that provides a higher positioning accuracy than 0.1°. The new system has doubled its mass but also its payload capacity and has increased its motion range, allowing an unconstrained 360° rotation in the pan axis and 180° in the tilt. This permits pointing the cameras in any direction around the rover. Electrical Design This section describes the electrical design of the rover and focuses on the main elements of the rover avionics,

Tilt-Drive Cable

such as the motion control, power conditioning, and distribution electronics; onboard computer (OBC), and sensor suite integration. It is worth noting that we do not select spacegrade electronics or components. Our design includes neither radiation-hardened avionics nor components that are tested under the harsh space environment conditions of temperature, vacuum, and launch vibrations. We usually select commercial off-the-shelf components for embedded systems and add specific custom printed circuit board (PCB) designs for the final accommodation and integration of those. This gives us a good balance among the cost of manufacturing, design flexibility, and system engineering budgets. Further details on this process are given in the following sections. Motion Control Electronics As seen in the previous section, all of the mechanical subsystem elements can add up to more than 20 active joints among the locomotion, manipulation, and PTU commanding. It was soon understood that a centralized approach would be hardly feasible from the input–output (I/O) signaling and harness consideration points of view. Instead, a better approach is to delegate the whole joint control task to dedicated microcontrollers, i.e., servo drives, which all can then be “daisychained” to the main OBC through a single bus line. Therefore, the motion control electronics (MCE) follows a distributed (noncentralized) design approach with a network of motion control drives connected through a Fieldbus. In addition, this is in line with the design of ExoMars. In such an approach, the OBC is only in charge of defining and sending the command signals for all of the servo drives. These translate those commands into the actual power provided to each motor and control the flow of the current to achieve the commanded set point. As for the Fieldbus

Tilt Drive

Pan-Drive Cable

Pan Drive

Mast

Cable Camp

Bottom Camp

Mast Bracket

Figure 4. A schematic rendered view of the PTU design.

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protocol, several options exist, from the classic—Modbus, Profibus, or controller area network (CAN)—to the more recent ones based on real-time Ethernet. We decided to follow the choice made for ExoMars, i.e., CAN, which is a widely used protocol for motion control applications and offered us the required features in terms of the communication bit rate or number of connected nodes. Regarding the microcontroller manufacturers, several brands exist in the market. After our study, we concluded that the servo drives by Elmo Motion Control provide a compact and power-dense choice for embedded applications, both with brushed or brushless motors, with a wide range of control and feedback options that fit our design approach. For ExoTeR, we chose the Elmo Whistle SimplIQ line of drives that implement the CANopen application standard. In particular, they fulfill the DS301 communication and DS402 motor drive specifications, which are standards defined by the CAN in automation organization. Each Elmo Whistle, similar to a matchbox in size, can control a motor with a bus voltage range of 12–60 V and a maximum current of 1–20 A. Motor feedback control can be achieved via incremental or absolute encoders, Hall effect sensors, resolvers, or potentiometers with specific feedback ports or generic I/O digital and analog inputs. All of these features allow us to control the full range of active joints present in our platforms. In ExoTeR, a total of 23 drives had to be mounted: 16 for locomotion, two for the PTU, and five for the arm. A custom PCB was designed and manufactured that could hold up to four Elmo Whistles. Several samples of this PCB were printed to integrate the avionics for locomotion and PTU control. Additionally, a dedicated PCB for the manipulator with a capacity to host five Whistles was manufactured. The split of the MCE in PCBs and modules aimed at modularity (such as being able to connect/disconnect the arm) and maintainability

(the capability to swap out MCE cards easily in the case of failures). The resulting accommodation of the avionics architecture, including the MCE, is shown in Figure 5. The experience with ExoTeR showed that certain control tasks could reach the CAN bus maximum bit rate of 1 Mb/s and required a higher bandwidth to perform. The need for faster control of the rover platform joints pushed our next design to move to another communication standard. Therefore, for MaRTA, we decided to upgrade the motor drives and opted for the Elmo Gold Twitter. This choice meant an even smaller footprint; more efficient and power-dense drives; reduced electromagnetic interference (EMI); and a faster communication protocol based on Ethernet for Control Automation Technology (EtherCAT), with a maximum bit rate of 100 Mb/s. In addition, the force–torque sensors installed in each of the wheel modules of MaRTA provide an interface to EtherCAT as well and can, therefore, be connected to the main OBC through the same EtherCAT bus. The Elmo Gold Twitter also implements CANopen over the EtherCAT application standard and provides the same flexibility of I/O and feedback control options as the Whistles in ExoTeR. All of these synergies were positively considered for MaRTA’s system integration.

Power Conditioning and Distribution Electronics As the name suggests, the power conditioning and distribution electronics (PCDE) distribute the power coming from a source, and this needs to be conditioned before reaching the different avionics components. The design of this subsystem starts with a system power budget analysis that allows us to dimension the system and identify the different levels of voltage and current needed. This also permits us to first size the power source, i.e., the battery capacity and discharge parameters, and, finally, select a proper battery that will allow for sufficient time of continuous operation. Battery For ExoTeR, this resulted in a battery with an energy capacity of 8.5 Ah at 28.8 V and capable of providing up to 245 W. For synergetic purposes, the same battery was kept for MaRTA’s PCDE design at the cost of a shorter operational autonomy, this being reduced from approximately 3 h in ExoTeR to about 2h in MaRTA. The PCDE can also run the system from a Locomotion MCE standard laboratory power supply. The selection of the input source—battery Pan and Tilt MCE or external supply—is done through a Manipulator MCE diode placed in series with each PC104 OBC source, which also allows batteries to PCDE be hot-swapped. The PCDE then converts and regulates the input power into the different voltage lines needed by the system avionics, typically rangFigure 5. ExoTeR’s avionics integrated in the rover body chassis. PCDE: power conditioning and distribution electronics. ing from among 24, 12, 5 and 3.3  V. 16

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We selected TRACO Power dc–dc converters for the different stages because they are efficient and reliable components that provide galvanic insulation between the primary and secondary lines. The current deliverable by each dc–dc converter is sized according to the power budget, and the output is further protected with fuses. In the case of ExoTeR, the PCDE is a rather simple design with little intelligence onboard and limited to the functions just described. In MaRTA, we decided to add a microcontroller within the PCDE board to control certain additional functionalities and provide more useful data. The battery status is displayed on an LCD screen at the back of the rover. Similarly, the consumption of several power lines is monitored, including the total power currently running the rover. The current measurements of the PCDE can be helpful to find potential issues and degradation in the electronics. A colored LED alerts the operator when the battery is low and needs to be replaced. An emergency stop function is also implemented within the PCDE that can accept emergency signals coming from three sources: a physical push button at the deck of the rover, similar remote emergency switch that communicates with the rover PCDE through a radio link, or specific telecommand message sent from the rover OBC to the PCDE. Regardless of the source, an incoming emergency signal effects cutting the power to all motors in the platform and stopping any active motion, yet the rest of the avionics and logic power to the MCE are maintained to allow for potential recovery actions and proceed with any test execution. OBC and Sensor Integration Here, we address the topic of integrating the elements that are most relevant to our actual robotics field. These are the OBC and sensors used by the rover that are the source of the data needed for implementing many important functionalities. Looking at the proprioceptive type of sensors, relevant examples would be accelerometers, gyroscopes, or full threeaxis inertial measurement units (IMUs). Also worth mentioning within this group are the motor encoders and other sensors that belong to the control of the mobility system, which were properly addressed in the “Mechanical Design” section. A sensor present in all of our lab rover prototypes is the Sensonor STIM-300 IMU, a small-footprint sensor with three-axis gyros and accelerometers that uses microelectromechanical system (MEMS) technology to provide 3D orientation data. Other sensors we have opted to mount on MaRTA are the Level Developments SOLAR dual-axis inclinometer or the KVH DSP1760 Fiber Optic Gyroscope, which, together, can provide full rover attitude estimation by tracking the gravity vector and rover azimuth, respectively. As for the exteroceptive sensors, the most widely used ones would be cameras, and, within this type, certainly, the optical sensor cameras [red, green, blue (RGB) or monochrome] are the most relevant due to their low cost, miniature size, ease of integration, and heritage as well as in terms of the algorithms available for image data processing.

Similarly, stereo camera rigs are commonly used to provide depth information. Depth data are essential for any navigation application since it forms the basis for two key functionalities, localization and mapping. The relevance of stereo cameras is highlighted in space robotics applications, given the existence of space-grade sensors of this kind. This is why both ExoTeR and MaRTA are equipped with several stereo cameras (the FLIR Bumblebee BB2 and XB3), typically one dedicated to localization mounted at the rover body rim pointing downward and close to the ground, and another one for mapping and navigation mounted on top of a mast with pan-tilt pointing capability from a higher-perspective viewpoint. Other exteroceptive sensors, such as depth cameras (RGB-Depth cameras), time-of-flight cameras, and laser sensors or lidars, have been used in our lab for some dedicated tests; however, we do try to limit their use in our applications and research activities due to the lack of existing space-qualified sensors of this type. While we try to be representative in the types of sensors we use, it is important to note that we do not use space-grade or qualified components in this regard, which would make our research unaffordable. Similarly, when it comes to choosing the OBC, we opt for embedded computers used in a wide range of robotics applications. Trying to be representative of a space-grade processing module would require working with an expensive and considerably complex LEON4 architecture, with the accompanying limitations on software developments and prototyping activities. The first computer in ExoTeR was selected from the PC104 form factor due to its flexibility and modularity as well as the ability to customize the computer stack and interface ports by selecting and adding specific layers, such as FireWire, CAN bus, or Wi-Fi modules. However, the stack soon became quite bulky, and the availability of processors was limited to slightly old and low-power units. Therefore, at the point of selecting the OBC for MaRTA, we decided to unify and upgrade the OBCs in both rovers with embedded systems from the Pico-ITX form factor. At the moment, both rovers have almost identical OBCs, which is obviously a convenience, carrying relatively new and powerful Intel processors within a 64-b x86 system architecture. Communications between processing modules in space is typically done through point-to-point SpaceWire interface links, and wireless communications use ultrahigh frequency antennas and implement protocols for satellite communications. In our case, these are replaced by Ethernet and Wi-Fi standard communications for convenience of use in a lab environment. Human–Machine Interface, Thermal, and EMI Considerations The electrical design of the rover is completed taking into consideration other aspects at the system level. One of them is related to grounding and harness routing to minimize the EMI as much as possible. We followed well-known recommended practices for limiting the EMI and protecting SEPTEMBER 2022

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data-sensitive lines. Additionally, many lessons learned were taken out of the experience gained from ExoTeR, which, during tests, suffered drops in the communication link or sudden blackouts of detected global navigation satellite systems (GNSS) satellites. We discovered that FireWire cables tend to badly interfere with the GNSS signal, so, in MaRTA, we opted to use Ethernet cameras (Gigabit Ethernet), instead of inheriting the FLIR Bumblebee stereo cameras mounted on ExoTeR. We also took the aforementioned EMI suppression design practices thoroughly into account when designing the PCDE of MaRTA and integrating the rest of the avionics components; e.g., the rover chassis was used as a common ground plane. Another important aspect is the operational thermal limits of the devices, in particular, the high temperatures reached by the power-dense MCE. In MaRTA, MCEs are mounted against the front and rear metallic walls of the rover (the side and top walls are removable covers), essentially turning them to heat-sink radiators. Additionally, both ExoTeR and MaRTA feature small fans that provide cooling by flowing external cold air to the warm components inside and extracting warm air toward the outside. A final consideration is given to the human–machine interface and the accessibility and maintainability of components. For example, providing external access to internal ports, such as Ethernet, USB or graphics, or easing the access to the other avionics ports and cables to debug or replace efficiently, especially for time-constrained operational conditions. Similarly, enclosures are optimized for easy removal to access internal components and later readjustment without the need for any tools. Software Design The already-mentioned balance toward space representativeness in our system architecture is similarly applied to the software design. ExoTeR and MaRTA are lab rover prototypes allowing for the quick iteration and demonstration of technologies, where space qualification cannot and does not have to be achieved. Consequently, the focus of our software developments is on the algorithms and not so much on the optimization and qualification aspects of the software engineering that would be needed to run in space hardware. While we keep ourselves aware of the computational complexity of the developed algorithms, we do not invest in system integration optimizations. Further details on this are given in the following sections, where the selection of the running operating system (OS) and the use of well-known robotic frameworks are discussed. These considerations support a modular approach to the developments conducted by our research lab, which includes many short-stay members. Finally, we elaborate on some activities that the ESA has conducted to reduce the gap between lab developments and flight software implementations. In this section, we do not make references to modifications or design changes introduced for MaRTA, and the details provided apply to both rovers equally. This is because 18

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software developments and changes along the years are applied to and integrated in both rovers. OS For years now, the OS in use in all of our lab rover platforms is Ubuntu, which is free and open source. This popular Linux distribution based on Debian is continuously improved and maintained by the open source community, offering a biyearly long-term support (LTS) release, with standard support guaranteed for at least five years. The main reason for this selection is the stability of the system and vast adoption of this Linux distribution around the world. Similarly, many of the developments done in research labs and institutes in the world are carried out on Ubuntu, and software libraries are often released for Ubuntu systems. This is also the case for the robotics frameworks that we discuss in the “Use of Robotics Frameworks” section. The main drawback with Ubuntu is the lack of real-time application support since its standard kernel is based on a best-effort approach. Whereas a real-time method could potentially improve the rover control based on kinematic and dynamic computations, the generally slow dynamics of our system make this feature less noticeable in reality, and, therefore, we usually do not impose hard real-time requirements on our lab rover developments. Eventually, pre-emption and scheduling capabilities can be added to the system using the PREEMPT_RT kernel patch or Xenomai, a real-time development framework cooperating with the Linux kernel that has been continuously supported on Ubuntu LTS releases. An alternative and space-representative option would be Real-Time Executive for Multiprocessor Systems, a realtime OS used in most ESA missions today [11]. However, this would hinder many developments of our fast-paced research activities by introducing issues with system configurations and hidden dependencies. Additionally, it would prevent us from using any of the general-purpose open source robotics frameworks available to the community, which play an integral part in all of our applications’ software development approaches. Use of Robotics Frameworks Robotics frameworks have grown increasingly popular in the last two decades, with the ROS becoming the default framework in almost every robotics lab. There are a handful of robotics frameworks available, most of them providing useful tools for data visualization, logging, and debugging along with a plethora of implemented software packages that range from low-level drivers to full robot navigation solutions. However, the most important aspect that these frameworks brought is the change in the paradigm with respect to developing applications. As it is explained hereafter, they made applications inherently highly modular. Originally, these frameworks were developed for providing a communication middleware between independent components. The middleware is a common language, with standard defined interfaces, that any component can use to

talk to another component. A component defines the interfaces to communicate and receive data and fulfills the specific task or function for which it is meant. A developer can focus on a library to implement a particular function and easily embed this within the framework’s component to transmit or receive data. The modularity of this development approach is inherently implied, allowing the ease of replacement or switching between components with the same interface and providing a standardized component configuration. Additionally, the deployment of a modular system can be such that a crashed component does not bring down the entire system, and FDIR can be more efficient. When our time to make a decision on which framework to use arrived (in the early 2010s), the shortlisted finalists were ROS, Robot Construction Kit (RoCK), and Generator of Modules. Eventually, the RoCK framework developed by German Research Center for Artificial Intelligence (DFKI) ranked at the top due to its more formal and structured approach in software engineering. Based on the ORoCoS Real-Time Toolkit, RoCK includes real-time logging capabilities, modular deployment and component introspection, and a state machine implemented at the component level that allows for the control of its lifecycle. Despite the larger ROS community, having a direct line of contact with the RoCK developers at the DFKI turned out to be a significant advantage. While we have also used ROS for some particular developments and testing, the core software stack of our lab rovers has grown and developed in the RoCK framework. However, during recent years, the RoCK framework community and development activity have been significantly reduced, with limited updates and overall releases. On the other side, ROS published the second generation of its framework, integrating many of the formal approaches and software engineering aspects that RoCK included. Eventually, in the last year, we have started migrating some components to ROS2 and are currently considering a full migration to the second generation of this popular framework.

Human Interfaces

Without detailing the entirety of our software architecture stack, Figure 6 shows a setup of some components that has been of interest for some project support activities and test campaigns that are detailed later in the “Test Campaigns” section. This configuration was used for the assessment of operational aspects, mainly utilizing, switching between, and potentially blending various operation modes. From left to right, the figure visualizes the remote interfaces for human interaction down to the drivers to access the different hardware elements. 3D Robot Operations Control System (3DROCS) represents the rover monitoring and control station (MCS), which is the base development from which the flight MCS for the ExoMars mission has been derived [12]. The telemetry/telecommand component running onboard the rover takes care of implementing the communication protocol with 3DROCS by translating and passing the telecommands further down to the lower-level components and gathering all relevant data from different sources to generate the telemetry packets. The operators can also use a joystick to control the rover, and an arbiter makes sure that mutually exclusive access by either of the components is guaranteed to avoid conflicts. The rover can be controlled by direct body-level motion commands or using higher-level navigation functions following waypoints. The perception chain models the environment and increases the awareness of the rover surroundings, both onboard and at the remote station by forwarding the generated maps. The localization estimate is computed by the odometry component, which fuses the data from different sensors. Further details about the implementation and theoretical principles behind several of the components shown in Figure 6 can be found in the references given throughout the “Test Campaigns” section. Bridging the Gap to Space As already stated in this section’s introduction, we do not seek space qualification, nor is our objective to produce or develop

HW Access Motion

PTU Control

Joystick

Command Arbiter

Locomotion Switcher

TM/TC

Locomotion Control

Wheel Walking

Waypoint Navigation 3DROCS

Platform Driver

IMU

Odometry Mapping DEM Generation

Camera

Trigger*

Figure 6. A simplified overview of ExoTeR’s principal TM/TC components. TC: telecommands; TM: telemetry; DEM: digital elevation map.

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flight software. The OS and robotics framework on our lab rovers facilitate fast developments and functional algorithmic demonstrations, and this creates a gap for a potential path to flight. That is where the reliability, availability, maintainability, and safety (RAMS) requirements applied to the software development and testing become relevant. The ESA has developments where the RAMS requirements for software development are taken into consideration at their foundations. The most relevant reference in this regard is the TASTE framework (https://taste.tools/). In constant development for more than a decade, TASTE is a development environment composed of a set of tools where software components can be developed and automatically deployed in specific target platforms, which include spacegrade boards and OSs. It provides a graphical and textual development environment for the definition and implementation of functions and interfaces and an automated process for the generation of glue code to run them on the selected target system. It also facilitates the validation and verification of software by analytical and statistical tools. The development of TASTE started with the aim to build functional blocks for satellite missions. However, the approach to robotics and, particularly, for the planetary exploration missions is quite different from that of their orbital counterparts, and TASTE lacked the tools to address this at its origins. In 2016, an ESA activity named Space Automation and Robotics General Controller (SARGON) took the first steps to extend the capabilities of TASTE to build robotics applications. ExoTeR was used as the target platform to deploy the application built for the final demonstration of SARGON. These efforts were continued within the European Space Robotics Control and OS (ESROCOS) (https://www .h2020-esrocos.eu/), an activity that is part of the European Commission’s Horizon 2020 program. Since the completion of ESROCOS, several activities of the Space Robotics Cluster of Horizon 2020 have used TASTE as their development and deployment framework for planetary robotics applications with field test demonstrations [13]. These activities are bridging the existing gap between laboratory developments and flight software. TASTE can deploy components on machines running Ubuntu and use bridge tools to communicate with ROS and RoCK applications. Eventually, it could fully replace these frameworks for our lab developments and reduce the gap to space. Test Campaigns In this section, we provide a brief description of the main test campaigns performed with ExoTeR that have driven our lab research activities for the last five years. These are chronologically introduced, and references to previous publications are provided for further details. While MaRTA is now at a ready state for testing activities, there have not yet been any relevant test campaigns that we considered reporting. The intent of describing these campaigns is to demonstrate how the results from testing these subscale 20

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designs can eventually influence a real mission rover development and serve ESA mission teams to be better informed of the challenges and technologies needed for different mission case scenarios. Wheel Walking: European Space Research and Technology Centre 2014 and DLR 2015 Wheel walking refers to a rover locomotion mode that synchronizes the motion of the wheel-driving motor with another motor that is connected through a lever, or leg, that can be used to swing the wheel back and forth, following a pattern that increases traction on soft soils. In the case of ExoMars, this second motor is referred to as the deployment motor since it is used to stow and deploy the wheels for an efficient accommodation during the spacecraft cruise phase. The triple-bogie locomotion system has a total of six deployment motors, one for each wheel (see the “Mechanical Design” section). Motivated by the difficulties that MER rovers had traversing the Martian surface, even getting stuck in loose soil several times, and inspired by the peristaltic motion demonstrated on Lavochkin’s planetary rover prototypes [14], a project was started to implement and evaluate the wheel walking locomotion pattern on ExoTeR. The expected outcome was an improved tractive performance in challenging conditions, such as sandy terrains or high slopes, where the nominal roving motion was subject to high slip ratios. The improved locomotion capabilities were validated in a comprehensive set of tests, showing the reduced slip ratios of wheel walking compared to the standard mode. A first test campaign was conducted in European Space Research and Technology Centre (ESTEC) at the end of 2014, and the encouraging results motivated a second test campaign at the DLR’s Robotics and Mechatronics Center facilities in Munich in early 2015 (see Figure 7), making use of the significantly larger testbed and different soil types available there, allowing us to validate our results in a wider set of test conditions. Further details on this can be found in [15]. These campaigns were instrumental to demonstrate the need of this capability for the ExoMars mission and motivated further research [16] that eventually led to wheel walking being implemented as a locomotion mode on ExoMars. Remote Rover Operations: CNES 2015 and 2016 The objective of the remote rover operation campaigns was to assess the readiness level and adequacy of the procedures and decision-making processes established for the future ExoMars Rover Operations Control Center (ROCC). Two campaigns in consecutive years took the ExoTeR rover to CNES facilities in Toulouse. In parallel, a rover operations center was temporarily arranged at ESTEC, emulating the conditions of the ROCC. In 2015, the campaign focused on the egress phase of the mission. The objective was to validate whether the telemetry data coming from the rover together with the

tools available at the control center were sufficient to evaluate the potential hazards and decide on the egress direction in full situational awareness to minimize the risk of failure. Our team in the Site d’Essai pour les Rovers Mobiles (SEROM) field in Toulouse (see Figure 8) orchestrated up to five egress scenarios, adding several hazards and hidden traps for the operations team in ESTEC. The campaign was a success, demonstrating that the operations team was capable of identifying any potential risk and verifying the procedural telecommands and telemetry checks to guarantee the safe egress of the rover. In 2016, the focus was set on demonstrating postegress operations, with the commissioning activities involving the rover and lander platform and a subsequent traverse toward the first scientific target and experiment cycle. However, the campaign started with another rehearsal of the egress operation, which was considered adequate due to the confidence gained in the previous campaign. While the egress itself was successful, it did condition the rest of the operations considerably by setting the rover in a challenging terrain trafficability situation for the upcoming activities, and it eventually failed to accomplish them. Despite the unaccomplished objectives on the latter, both campaigns provided many important lessons for the ExoMars mission rover operations team and served to validate numerous rover and control center functionalities. More details on these campaigns can be found in [17]. GNC Algorithm Development: ESTEC 2017 Previous campaigns identified the need to include additional navigation functionalities onboard the rover systems. This would allow the performance of more complex operations, including longer traverses. First, a trajectory control algorithm was designed and implemented in ExoTeR. Instead of following the classic control theory approach with a proportional-integral-derivative-type control, our controller uses geometrical relations, making it much more intuitive to the operator and easy to tune. Thus, the controller parameters are defined using rover dimensions and the mechanical constraints of the locomotion system. Moreover, the provided path as the input comprises any finite number of waypoints without a fixed distance between them. The controller takes care of smoothly transitioning between waypoints and finding the directional vector toward which to steer the rover at any point in time. The algorithm was experimentally validated at the Planetary Robotics Lab in ESTEC in 2017. Filip and Azkarate [18] provide more details on the algorithm implementation and testing results. In parallel, a path-planning algorithm was developed that could dynamically replan the path of the rover along the traverse when needed. The planner uses a novel technique based on the fast-marching method to significantly reduce the computational time while maintaining the features of other grid-based planners, such as the optimality and smoothness (no angle restrictions) of the generated paths. The planner was extended with the capability to also

plan global paths at the beginning of a traverse. These two capabilities were finally combined, making the planner able to reason in a multilayer approach, with lower-resolution grids in the global frame and higher-resolution ones in the local frame and both outputs connected as a single planned path. The algorithm was experimentally validated at the Planetary Robotics Lab (PRL) in summer 2017 (see ­Figure  9), making use of the aforementioned trajectory control algorithm to follow the planned paths.

Figure 7. ExoTeR at the DLR performing a wheel walking test.

Figure 8. ExoTeR ready for remote operations tests at SEROM (CNES).

Figure 9. ExoTeR during the algorithm validation tests at the PRL.

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Finally, the experiments were taken outdoors for a longer traverse in a planetary analog terrain located in the vicinity of ESTEC. These experiments demonstrated the functionality and robustness of both algorithms in a Mars representative scenario completing a trajectory of approximately 100 m. More details about the algorithm implementation and testing results can be found in [19]. ExoMars ROCC: Aerospace Logistics Technology Engineering Company 2018 and 2019 Following the validation of the algorithms described in the “GNC Algorithm Development: ESTEC 2017” section, the rover was ready to execute more complex navigation tasks. These included the nominal traverse mode of ExoMars at the time, used for following a path provided from the ground control station. In 2018, ExoMars was getting ready for its launch, foreseen for summer 2020, yet the ground test model (GTM) rover to be delivered to the ExoMars ROCC at the Aerospace Logistics Technology Engineering Company SpA. (ALTEC) in Turin was not yet fully assembled due to ongoing subsystem qualification activities. Given the previous experience with ExoTeR in the Remote Rover Operations campaigns and more complex capabilities integrated into the system, it was decided to temporarily use it at the ROCC instead of the GTM so that the infrastructure facilities and tools could be tested and prepared. The rover commanding interface was enhanced and adapted to work with the 3DROCS software tool, i.e., the rover control,

Figure 10. ExoTeR at the ROCC inauguration event on 30 May 2019.

Figure 11. The ExoTeR performing a sample fetching test at the PRL.

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operations planning, and monitoring station used in ExoMars. It also implemented the same telecommands protocol specified for the commanding of Rosalind Franklin. The first campaign of ExoTeR in ALTEC was performed during summer 2018 and served to validate the tools, interfaces, and operational procedures, including the training of the staff operators in ALTEC. ExoTeR returned to ESTEC when the ExoMars mission finally confirmed the inclusion of the AutoNav functionality onboard the rover. Therefore, it was decided to integrate this functionality on ExoTeR as well. Thanks to the support of our colleagues at CNES, who provided us with their AutoNav implementation for ExoMars, we were able to quickly integrate and demonstrate the capability. In early 2019, ExoTeR was sent again to ALTEC, and several tests were executed, making use of the newly added AutoNav functionality. This campaign culminated with the ExoMars ROCC inauguration event shown in Figure 10. Sample Fetch Tests: ESTEC 2019 With the imminently foreseen launch of ExoMars, our lab started to put the focus on the next ESA rover mission to Mars, the SFR. As already mentioned in the “Mechanical Design” section, a robotic arm was developed that can be integrated at the front panel of ExoTeR’s chassis. This enabled the possibility of working on this highly relevant phase of the SFR mission, i.e., the sample fetching part. Coupled with the path-planning algorithm development work described in the “GNC Algorithm Development: ESTEC 2017” section, the planner was further extended to not only plan the motion of the rover platform toward the sample location but also include the trajectory planning of the robotic arm. The same fast-marching method was used to find the optimal arm trajectory and synchronize it with the rover platform motion while avoiding any collision of the arm with the rover or environment. In the first experimental campaign [20], the actual grasping of the samples was not performed due to the missing gripper development (see Figure 11). However, at the moment, the lab is working toward integrating such a mechanism together with the perception means to detect the sample and precisely estimate its full pose, to perform a complete demonstration of the sample fetching scenario. Conclusion Two lab rover testbeds, ExoTeR and MaRTA, built as scaleddown prototypes of the ExoMars rover design, have been introduced. Their robotic subsystems have been thoroughly described with a focus on the mechanical, electrical, and software design aspects. Several lessons learned from and the design changes between the rovers were also discussed. These platforms have been of great use to provide project support to ExoMars and other R&D activities of the Automation and Robotics Section of the ESA to increase the TRL of different robotics building blocks.

The test campaigns described demonstrate how the ExoMars mission has used the ExoTeR platform on numerous occasions to get qualitative results in a short time. These served as derisking actions to flexibly identify potential solutions outside of the tight project schedule and contractual constraints. As the ExoMars mission is approaching its launch date, these platforms will provide support to the following SFR mission, with specific campaigns in the field of autonomous sample fetching. In parallel, they will continue to contribute to the conception, demonstration, and maturation of identified key technologies of future robotics missions. Acknowledgment The authors would like to thank the members of the Automation and Robotics Section—who, for years, have contributed to the design and work of these rover platforms—for their guidance and comments on the elaboration of this article, namely, Michel Van Winnendael, Gianfranco Visentin, and Luc Joudrier. References [1] M. Heverly et al., “Traverse performance characterization for the mars science laboratory rover,” J. Field Robot., vol. 30, no. 6, pp. 835–846, 2013, doi: 10.1002/rob.21481. [2] E. Graser, S. McGill, A. Rankin, and A. Bielawiec, “Rimmed wheel performance on the Mars Science Laboratory Scarecrow rover,” in Proc. IEEE Aerospace Conf., 2020, pp. 1–12, doi: 10.1109/AERO47225.2020.9172666. [3] I. A. Nesnas et al., “Axel and DuAxel rovers for the sustainable exploration of extreme terrains,” J. Field Robot., vol. 29, no. 4, pp. 663– 685, 2012, doi: 10.1002/rob.21407. [4] M. Apfelbeck et al., “ExoMars phase B2 breadboard locomotion sub-system test campaign,” in Proc. Adv. Space Technol. Robot. Automat. (ASTRA), 2011. [5] M. J. Schuster et al., “Towards autonomous planetary exploration,” J. Intell. Robot. Syst., vol. 93, nos. 3–4, pp. 461–494, 2019, doi: 10.1007/ s10846-017-0680-9. [6] M. Balme et al., “The 2016 U.K. Space Agency Mars Utah Rover Field Investigation (MURFI),” Planetary Space Sci., vol. 165, pp. 31–56, Jan. 2019, doi: 10.1016/j.pss.2018.12.003. [7] A. Torres et al., “Robotic planetary exploration: Autonomous navigation in cluttered unknown environments,” in Proc. 42nd Int. Conf. Environ. Syst., 2012, p. 3619, doi: 10.2514/6.2012-3619. [8] T. Kubota, “An overview of JAXA space robotics activities,” in Proc. 13th Int. Symp. Artif. Intell., Robot. Automat. Space (i-SAIRAS), 2016. [9] N. Patel, R. Slade, and J. Clemmet, “The ExoMars rover locomotion subsystem,” J. Terramech., vol. 47, no. 4, pp. 227–242, 2010, doi: 10.1016/j. jterra.2010.02.004. [10] P. Poulakis, “Overview and development status of the ExoMars rover mobility subsystem,” in Proc. 13th Symp. Adv. Space Technol. Robot. Automat. (ASTRA), 2015. [11] F. Nicodemos, O. Saotome, and G. Lima, “RTEMS core analysis for space applications,” in Proc. III Brazilian Symp. Comput. Syst. Eng., 2013, pp. 125–130. [12] F. Martinez Fadrique, R. Sánchez-Beato Fernández, M. Barrera, P. Franceschetti, and L. Joudrier, “ExoMars 2020: Rover Operations Con-

trol System design as part of the Rover Operations Control Center (ROCC),” in Proc. SpaceOps Conf., 2018, doi: 10.2514/6.2018-2405. [13] J. Ocon, “Using the ERGO framework for space robotics in a planetary and an orbital scenario,” in Proc. 14th Int. Symp. Artif. Intell., Robot. Automat. Space (i-SAIRAS), 2018. [14] P. Ehrenfreund, C. Krafft, H. Kochan, and V. Pirronello, Laboratory Astrophysics and Space Research, vol. 80. Springer Science & Business Media, 1998. [15] M. Azkarate et al., “First experimental investigations on Wheel Walk ing for improving triple-bogie rover locomotion performances,” in Proc. 13th Symp. Adv. Space Technol. Robot. Automat. (ASTRA), 2015. [16] T. Wiese, “3D kinematic modeling and evaluation of rough-terrain locomotion modes for an ExoMars-like mobility subsystem,” M.Sc thesis, Technische Universität München, Munich, Germany, 2017. [17] M. Azkarate et al., “Remote rover operations: Testing the ExoMars egress case,” in Proc. 13th Int. Symp. Artif. Intell., Robot. Automat. Space (i-SAIRAS), 2016. [18] J. Filip and M. Azkarate, “Trajectory control for autonomous planetary rovers,” in Proc. 14th Symp. Adv. Space Technol. Robot. Automat. (ASTRA), Jun. 2017. [19] C. J. Pérez-del Pulgar, J. Sánchez, A. Sánchez, M. Azkarate, and G. Visentin, “Path planning for reconfigurable rovers in planetary exploration,” in Proc. IEEE Int. Conf. Adv. Intell. Mechatron. (AIM), 2017, pp. 1453–1458, doi: 10.1109/AIM.2017.8014223. [20] J. R. Sánchez-Ibáñez, G. J. Paz-Delgado, P. Romeo-Manrique, C. J. Pérez-del Pulgar, and M. Azkarate, “Coupled path and motion planning for a rover-manipulator system,” in Proc. 15th Symp. Adv. Space Technol. Robot. Automat. (ASTRA), May 2019.

Martin Azkarate, University of Malaga, 29016, Spain, and HE Space for the European Space Agency, Noordwijk, 2200 AG, The Netherlands. Email: [email protected]. Levin Gerdes, University of Malaga, Malaga, 29016, Spain, and HE Space for the European Space Agency, Noordwijk, 2200 AG, The Netherlands. Email: [email protected]. Tim Wiese, HE Space for the European Space Agency, Noordwijk, 2200 AG, The Netherlands. Email: [email protected]. Martin Zwick, European Space Agency, Noordwijk, 2200 AG, The Netherlands. Email: [email protected]. Marco Pagnamenta, Anybotics, Zurich, 8050, Switzerland. Email: [email protected]. Javier Hidalgo-Carrió, University of Zurich, Zurich, 8050, Switzerland. Email: [email protected]. Pantelis Poulakis, European Space Agency, Noordwijk, 2200 AG, The Netherlands. Email: [email protected]. Carlos J. Pérez-del-Pulgar, University of Malaga, Malaga, 29016, Spain. Email: [email protected].  SEPTEMBER 2022

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Testing Gecko-Inspired Adhesives With Astrobee Aboard the International Space Station Readying the Technology for Space By Tony G. Chen* , Abhishek Cauligi* , Srinivasan A. Suresh , Marco Pavone , and Mark R. Cutkosky *Tony G. Chen and Abhishek Cauligi contributed equally to this work. Digital Object Identifier 10.1109/MRA.2022.3175597 Date of current version: 27 May 2022

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G

ecko-inspired adhesives can allow freeflying space robots to grasp and manip­ ulate large items or anchor themselves on smooth surfaces. In this article, we report on the first tests conducted using geckoinspired adhesives on a gripper attached to an Astrobee free-flying robot operating inside the International Space Station (ISS). We present results from on-ground testing as well as two on-orbit sessions conducted during early 2021. Recorded data demonstrated that an adhesive gripper for Astrobee could provide 3.15 N of force for manual perching. The adhesives functioned as anticipated, despite a

1070-9932/22©2022IEEE

lengthy storage period. The results also highlighted some considerations for future adhesive gripping in space with free-flying robots. We discuss these topics along with system design considerations for successful implementation aboard the ISS, raising the readiness of this technology for a spacegrade environment. Overview Gecko-inspired adhesives are a promising technology to enable free-flying space robots to grasp and manipulate large items or anchor themselves on smooth surfaces. They can function in vacuum, withstand extreme temperatures and radiation [1], [2], and allow robots to apply gentle forces to objects in orbit without having to enclose features as with a conventional gripper. Hence, they work on flat and gently curved surfaces that would otherwise be difficult to grapple. With these properties, they have been proposed as a solution for grasping and retrieving space debris. Grasping experiments have been conducted with simulated satellites floating on gas bearings in the Jet Propulsion Laboratory’s Robodome and aboard the NASA zerogravity parabolic flight airplane [3]. Additional terrestrial grasping experiments have been conducted in partnership with the Japan Aerospace Exploration Agency [4]. In this article, we report on the first tests conducted using gecko-inspired adhesives on a gripper attached to an Astrobee free flyer operating inside the ISS. The tests were conducted in March 2021, using grippers launched in July 2019, and kept in storage on the ISS. We first provide a brief background on gecko-inspired adhesives and their applicability toward tasks carried out by assistive free-flying robots [or assistive free flyers (AFFs)]. We present the gripper design and requirements for gripping flat and gently curved surfaces with the Astrobee free flyer. We then present the results of tests conducted on ground and on orbit. The tests revealed that the adhesives functioned as anticipated, despite a lengthy storage period, but they also highlighted some considerations for future adhesive gripping in space. To provide a drop-in replacement for the existing gripper, we designed an active system that uses a sensor to trigger a motor that loads the adhesives. It is important to load the adhesives only when all of the adhesive pads have established coplanar contact with a surface. However, in comparison to robot arms on a fixed base or even quadrotors on Earth, the ability of free flyers in microgravity to make final adjustments to velocity and orientation is quite limited. This limitation motivates our recommendation in the section “Conclusions and Future Work” that future adhesive grippers use passive suspensions and passively triggered grippers to align to a surface and load the adhesives for a firm grip. Contributions The contributions of this article are as follows: 1) The primary contribution of this article is to present a system that meets the requirements of being launched into orbit and integrated with the Astrobee free flyer.

2) We additionally report on tests conducted aboard the ISS both manually by astronauts and with Astrobee. In this respect, the work advances the technology readiness level (TRL) of gecko-inspired adhesives for deployment in space from TRL-3 (experiments from ground-based benchmarks) to TRL-5 (testing in a relevant environment). 3) As a result of the tests and the system development and integration challenges addressed, we present recommendations for future use of gecko-inspired adhesives on freeflying robots in microgravity. Background The grippers and experiments reported here take advantage of two technologies: gecko-inspired adhesives and free-flying robots for use in space. We briefly review them here with references to publications providing further details. Gecko-Inspired Adhesives Geckos are remarkable for their ability to run on vertical and even overhanging surfaces. To accomplish this feat, they use a hierarchy of features on the surfaces of their toes that terminate in tiny spatular tips less than 1 µm across. The dry adhesive features conform intimately to smooth and rough surfaces and achieve adhesion using primarily van der Waals forces. An important characteristic of gecko adhesion is that it is directional and, therefore, controllable. The gecko sticks only when its adhesive features are parallel to the gripped surface and from the gecko’s palm out toward the tips of its toes (i.e., in the direction a gecko would load them when climbing up a wall). Relaxing the tangential load eliminates the adhesion and allows a gecko to lift its feet with low effort [5]. The same principle underlies directional synthetic geckoinspired adhesives, albeit with less sophisticated terminal features. Figure 1 shows side views of the microwedge adhesives made of silicone rubber. These adhesives were used in prior work to explore space-related applications, for example, using planar robots floating on gas bearings [3], [6].

60 µm 90 µm

Load

Contact Area (a)

(b)

Figure 1. (a) Gecko toe and microscopic view of angled setal stalks with spatular tips ( 75%, the second order of Ogden for m > 58% and the Yeoh model for m > 89%. Consequently, these last three constitutive models are not stable for large strains and cannot be considered as an adequate hyperelastic models for the use of the self-healing material in large strain applications. Focusing on soft robotics, therefore, the neo-Hookean and the firstorder Ogden law were selected as possible candidates for modeling the material behavior. Table 2 shows the norm of residuals and the RMSE of the fitted neo-Hookean and first order of the Ogden constitutive law. The neo-Hookean model shows slightly lower values for both the norm of residuals and RMSE. This means that the fitting for this constitutive law is slightly more accurate in comparison to the fit of the first-order Ogden law. In addition, in Figure 3(c), it is visible that although very similar, the absolute value of the residuals of the neo-Hookean model is for each strain slightly lower than the Ogden law. As such, it can be concluded that the neo-Hookean model provides the best approximation of the hyperelastic behavior of the DBPM-F5000-r0.5 material. The resulting fitting parameter are presented in the last column of Table 2.

(a)

Stress (MPa)

0.3 0.25 0.2 0.15 0.1

Ref Healed

0.05 0 0

20

40

60 80 Strain (%)

100

120

140

Figure 4. Stress-strain tensile tests until fracture of an undamaged reference sample (red) and five samples that healed after being cut completely in half using a healing procedure at 80 °C for 40 min (blue).

Table 3. Recovery of the mechanical properties after healing. Mech Prop

Symbol Unit Undamaged Healed RMSE

Young’s Modulus

E

MPa 0.68

0.7

0.01

First Material Constant

C10

Mpa 0.109

0.107

0.03

Mpa 1.150

1.153

0.02

Compressibility D1 factor Fracture stress vmax

kPa

316

304

4

Fracture strain emax

%

128

117

2

Healing efficiency

%

/

96.3

1.4

h v max h e max

%

/

91.3

1.8

hE

%

/

103.4

0.8

(b)

Figure 5. (a) The linear pressure controller system is composed of a syringe driven by a stepper motor and an digital pressure sensor. (b) 30 × 50 × 50 cm with the Pneunet actuator and RGBD camera.

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Characterization of the Healing Performance In the case of self-healing elastomers, the fitting of the neo-Hookean model on pristine and healed samples allows to validate the healing ability of the DPBMFT5000-r0.5 material, measured using uniaxial tensile testing of a Focusing on soft robotics, series of six samples (Figure 4). One pristine therefore, the neo-Hookean sample was fractured in a tensile test with a and the first-order Ogden strain ramp om 1%s −1 to derive the fracture law were selected as properties, the fracture stress ^v maxh and the possible candidates for fracture strain ^m maxh . The other five samples modeling the material were cut completely in half, reconnected, and behavior. subsequently healed at 80 °C for 40 min (Figure 4). Next, these samples were subjected to a tensile test upon fracture with the same strain ramp. When comparing the hyperelastic stress-strain relation, it can be seen that the mechanical properties of the healed samples are recovered for strains up to 100%. Traditionally, the healing efficiency can be defined based on the recovery of the fracture stress or the fracture strain (h v max = v max, healed /v max, ref , h emax = e max, healed /e max, ref ). In Table 3, the averages of the mechanical properties derived in the tensile test until fracture are presented as well as the RMSE of the mean value on the results. For these healing tests, high healing efficiencies of 91% ^h e maxh and 96% ^h v maxh were achieved, respectively based on the strain and the stress. The healed samples did not break at the location of the healed cut, which further illustrates excellent healing performance. In addition, the Young’s modulus is

used to evaluate the healing, as illustrated in Table 3. It is derived by a linear regression in the 0–5% strain interval and recovered with 103%. However, E, σmax, and emax provide information on the recovery of the mechanical behavior at very low stains (0–5%), and very high strains (110–130%). By fitting the neo-Hookean model on both pristine and healed samples, the recovery of the mechanical behavior can be evaluated across the entire strain window (0–130%), by checking the recovery of the material parameters. Table 3 illustrates the material parameters C10 and D1 for both pristine and healed samples. It can be concluded that these parameters only differ slightly after healing, showing excellent recovery of the hyperelastic behavior after healing. FEA Simulation in SOFA In this work, SOFA [13], [20] is selected as the FEA simulator. The design presented in Figure 2(b) is imported in SOFA and meshed with about 64,000 tetrahedrons, while the DPBM-FT5000-r0.5 material is modeled with the neo-Hookean parameters C10 and D1, obtained in the “Results of the Fitting” section. The density of the material is t = 1.02 g cm 3 . The ODE solver used is a Euler implicit solver, and the convergence solver is a sparse LDL solver. Characterization Setup for the Actuator The final aim is to build an inverse kinematic controller with the FEA simulation working in the control scheme. Therefore, the simulation result has to be validated experimentally, to ensure that it is accurate enough to be used in an inverse kinematic controller. To do so, a dedicated test bench that permits to control the inner pressure and characterize the actuator using motion tracking is built (Figure 5). Figure 5(a) shows the linear pressure controller system. The outlet of the 60 mL syringe is connected to the actuator and a digital pressure sensor by a tee male connector. The plunger of the syringe is attached to the nut by a 3D-printed interface, making it possible to linearly move by rotating the leadscrew,

x θ

y (a)

(b)

(c)

Figure 6. (a) An image of the actuator at 0.76 bar with nine blue markers. The figure also illustrates how the bending angle H is geometrically calculated as the angle between the origin and the tip. (b) SOFA simulation with the selected nodes (green) in the meshed simulated actuator that coincide with the centroids of the nine blue markers on the actuator prototype. (c) A segmented image, with in white, the highlighted position of the marker on a black background. The clustering is visible too, with the centroids of the markers in red.

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which is coupled to a stepper motor. Furthermore, the validation setup is composed of a 30 × 50 × 50 cm plexiglass box in which a RGBD camera is installed [Figure 5(b)]. The camera tracks the position of the centroids of nine blue markers on the actuator during bending [Figure 6(a)]. In the FEA, nine corresponding nodes are selected and their position is tracked during the simulation shown in Figure 6(b) (green dots). The FEA model, with integrated neo-Hookean model, is validated by comparing the position of the markers on the actuator with the selected nodes in the FEA simulation. To estimate the position of the markers, the camera is first calibrated with Zhang calibration method [21], after which the images of the camera are streamed through a robotic operating system and elaborated through a segmentation algorithm that highlights the blue

markers in white, on a black background as shown in Figure 6(c). Finally, the frames of the segmented images are sent to a clustering algorithm, that recognizes the number of markers on the pneumatic actuator and calculates the centroid position through the camera calibration. Validation of the FEA Simulation The experiments are made for two different orientations of the bending actuator in comparison to the gravitational field (g); an upward bending with the gravity force that act against the motion [Figure 7(c)] and a downwards bending with the gravity force assisting it [Figure 7(d)]. Both orientations are tested for three different pressures; 0.3 bar, 0.5 bar and 0.76 bar.

Camera Rest Position Camera at 0.3 Bar FEA at 0.3 Bar Camera at 0.5 Bar FEA at 0.5 Bar Camera at 0.76 Bar FEA at 0.76 Bar

FEA at 0.3 Bar Camera at 0.3 Bar FEA at 0.5 Bar Camera at 0.5 Bar FEA at 0.76 Bar Camera at 0.76 Bar

Upwards Bending Configurations

–40 –60 –80

y Position (mm)

100

80

Bending Angle (°)

–20

0

20 40 60 80 x Position (mm) (a)

60 40 20 0 0

100

Downward Bending Configurations

60 40 20 0

0.6

0.8

1

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(f)

Figure 7. (a)-(b) The bending of the actuator at 0.3 bar, 0.5 bar and 0.76 bar in two different configuration in comparison to the gravitational field; upwards and downwards bending. The dashed lines are the nodes selected in the SOFA simulation, while the x-symbols are the centroids of the marker detected by the camera. (c)-(d) Camera images of the bending configurations. (e)-(f) The bending angle versus the normalized time for the three pressure inputs.

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When comparing the SOFA simulation (dashed lines) with the experimental tracking of the markers (crosses), it can be seen that the FEA model simulates well the bending characteristic for both configurations [Figure 7(a) and (b)]. The RMSE, calculated between the marker’s centroids positions detected by camera and the simulation positions (Table 4), is below 1 mm for each pressure and configuration. This accuracy is sufficiently high such that this simulation can be used in the control scheme of a soft gripper. Furthermore, it can be seen that the simulation can take into account the direction of the gravitational field, which is important in soft gripper applications, in which the gripper rotates in the 3D space. Furthermore, Figure 7(e) and (f) show the bending angle for the three pressure inputs as function of the normalized time, to demonstrate that the FEA simulation matches the reality for a bending action involving bending under an increasing pressure up to 0.3, 0.5 and 0.76 bar. The dashed lines are the data from the camera and the continuous lines are retrieved from SOFA simulations. Inverse Controller Based on the validated FEA model, the inverse kinematic controller can be designed (Figure 8). An inverse controller of the bending angle is developed, defined as the angle between a vertical line through the base of the actuator and a segment through the base of the actuator and the tip [Figure 6(a)]. As seen in Figure 8, starting from a desired bending angle (Θd), the controller will minimize the error between the desired value and the measured one (Θm). This error is multiplied by a gain matrix K, that provides the input for the SOFA scene, implemented using two important plugins: the Model Order Reduction plugin

Table 4. The RMSE between the marker’s centroids position and FEA simulation positions for each pressure level and for the two bending directions. Bending Direction

Unit

0.3 bar

0.5 bar 0.76 bar

RMSE for upward bending

mm

0.94

0.83

0.81

RMSE for downward bending

mm

0.98

0.86

0.83

θd

+ – θm

e

P

K

Actuation Setup + Camera

Figure 8. The inverse control scheme.

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[22] and the SoftRobots.Inverse plugin [13]. The first conserves the DoF of the scene object but decreases drastically the number of tetrahedrons in the mesh (from 64,000 to 12), accelerating the scene performance in terms of frame per second. The SoftRobots.Inverse plugin [13] allows to resolve the inverse problem, calculating the pressure P needed to reach the desired angle based on the FEA simulation. This pressure is sent to the actuation system that tracks and estimate the actual angle with a camera, which works as feedback in the control scheme. The designed controller has a maximum speed of 20 Hz. Figure 9(a)–(d) show the results of the experiments of the bending angle’s inverse controller. The pressure value retrieved from the inverse problem solver in SOFA, for this experiment, is about 0.5 bar. In particular to demonstrate the self-healing ability of the Diels-Alder polymer that is used in this article, the finger will undergo two damage/healing cycles. In each case, the actuator was damaged severely as seen in Figure 9(e)–(f). However, these large damages can be healed by heating the actuator for 40 min to 90 °C. After healing, identical to the “Validation of the FEA Simulation” section, the experiments are repeated in the two different configurations with respect the gravitational field. Figure 9(a) and (c) shown the trends of bending angle Θ as a function of time, for both configurations, while Figure 9(b) and (d) illustrates the relative estimated error between the desired bending angle and the bending angle measured by the camera feedback. From the plots, it is clear that for the undamaged actuator (in blue) and the healed actuator, both for first (in magenta) and second damage/healing cycle (in black), the measured bending angle converge to the desired bending angle, confirming that after healing the actuator properties are recovered. Conclusions and Future Work In this article, a methodology is presented to develop an inverse kinematic controller for soft pneumatic robots based on an experimental characterization of the hyperelastic materials from which the system is constructed. It is illustrated that via uniaxial tension and compression test, hyperelastic constitutive models can be fitted on the experimental data, which can be used in a FEA model of the actuator. This methodology was tested for a self-healing Pneunet actuator developed out of a Diels-Alder polymer. Although in total five hyperelastic models, including Mooney-Rivlin, neo-Hookean, Yeoh, and Ogden first- and second-order laws, were fitted on the stress-strain data of the Diels-Alder material, the neo-Hookean proved to form the best fit for the entire strain window of 0–130%, in which these selfhealing materials can be used. To further validate the neo-Hookean model, the material constants were used in a FEA simulation in SOFA, an open source software, to simulate the bending behavior of Pneunet actuator. In addition, a prototype was made via compression moulding of the Diels-Alder material and its

Inverse Control for Bending Angle

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Inverse Control for Bending Angle

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30 20 10 0

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–10 0

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First Damage

Second Damage

(e)

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Figure 9. The results of the actuator reaching a desired bending angle using the inverse kinematic controller. The experiments were performed for both the (a), (b) upwards and (c), (d) downwards configuration, on the pristine (undamaged) actuator and on the actuator that underwent two damage/healing cycles. (e), (f) The first and second damage.

motion during actuation was tracked on a characterization setup with a pressure controller and motion tracking camera. The FEA simulation, and the embedded neoHookean model, were validated by comparing the simulation and the experimental characterization. For different pressures and different configurations in comparison to the gravitational field, RMSEs of less than 1 mm were detected between tracked markers on the actuator prototype and corresponding selected nodes in the FEA simulations. This illustrates that only with a limited material characterization, actuator models can be developed with an accuracy that is sufficient for a wide variety of soft robotic applications. This validated FEA model, was used in a feedback inverse control scheme. In particular, SOFA simulation

resolves the inverse problem, and it is tested in bending angle, for an actuator that undergoes to two damage/healing cycles. The results are promising and show that the selfhealing material doesn’t lose mechanical properties and performance. In future works, this approach will be extended for multimaterial applications. Furthermore, the controller can evolve toward a dynamic controller in the future, as in the material model can be extended including viscoelastic properties. In this way the actuator can be tested in dynamic conditions, for example with sinusoidal or more complex controller inputs. Acknowledgment This research is funded by the EU FET Project SHERO (828818). Seyedreza Kashef Tabrizian is funded by the EU SEPTEMBER 2022

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Marie Curie ITN project SMART (860108). The FWO (Fonds Wetenschappelijk Onderzoek) funded the work through personal grants of Terryn (1100416N). A special thanks goes to SOFA consortium, in particular to its coordinator, Hugo Talbot for the license releasing of the private plugin, SoftRobots.Inverse. References [1] T. G. Thuruthel, Y. Ansari, E. Falotico, and C. Laschi, “Control strategies for soft robotic manipulators: A survey,” Soft Robot., vol. 5, no. 2, pp. 149–163, 2018, doi: 10.1089/soro.2017.0007. [2] S. Terryn, J. Brancart, D. Lefeber, G. Van Assche, and B. Vanderborght, “Self-healing soft pneumatic robots,” Sci. Robot., vol. 2, no. 9, 2017, doi: 10.1126/scirobotics.aan4268. [3] C. Duriez, J. Allard, F. Faure, P. Bensoussan, H. Delingette, and S. Cotin, “Ep4a: Software and computer based simulator research: Development and outlook sofa—An open source framework for medical simulation,” Simul. Healthcare, vol. 2, no. 4, pp. 284–285, 2007, doi: 10.1097/ SIH.0b013e31815f61bc. [4] L. Marechal, P. Balland, L. Lindenroth, F. Petrou, C. Kontovounisios, and F. Bello, “Toward a common framework and database of materials for soft robotics,” Soft Robot., vol. 8, no. 3, pp. 284–297, 2021, doi: 10.1089/ soro.2019.0115. [5] S. Terryn et al., “A review on self-healing polymers for soft robotics,” Materials Today, vol. 47, 2021, doi: 10.1016/j.mattod.2021.01.009. [6] M. W. Hannan and I. D. Walker, “Kinematics and the implementation of an elephant’s trunk manipulator and other continuum style robots,” J. Robot Syst., vol. 20, no. 2, pp. 45–63, 2003, doi: 10.1002/ rob.10070. [7] B. A. Jones and I. D. Walker, “Kinematics for multisection continuum robots,” IEEE Trans. Robot., vol. 22, no. 1, pp. 43–55, 2006, doi: 10.1109/TRO.2005.861458. [8] C. Della Santina, A. Bicchi, and D. Rus, “On an improved state parametrization for soft robots with piecewise constant curvature and its use in model based control,” IEEE Robot. Autom. Lett., vol. 5, no. 2, pp. 1001–1008, 2020, doi: 10.1109/LRA.2020.2967269. [9] I. A. Gravagne, C. D. Rahn, and I. D. Walker, “Large def lection dynamics and control for planar continuum robots,” IEEE/ASME Trans. Mechatron., vol. 8, no. 2, pp. 299–307, 2003, doi: 10.1109/ TMECH.2003.812829. [10] D. Trivedi, A. Lotfi, and C. D. Rahn, “Geometrically exact models for soft robotic manipulators,” IEEE Trans. Robot., vol. 24, no. 4, pp. 773–780, 2008, doi: 10.1109/TRO.2008.924923. [11] S. Grazioso, G. D. Gironimo, and B. Siciliano, “A geometrically exact model for soft continuum robots: The finite element deformation space formulation,” Soft Robot., vol. 6, no. 6, pp. 790–811, 2019, doi: 10.1089/soro.2018.0047. [12] F. Faure et al., “Sofa: A multi-model framework for interactive physical simulation,” in Soft Tissue Biomechanical Modeling for Computer Assisted Surgery. Berlin: Springer-Verlag, 2012, pp. 283–321. [13] C. Duriez et al., “Framework for online simulation of soft robots with optimization-based inverse model,” in Proc. IEEE Int. Conf. Simulation, Modeling, and Programming for Auto. Robots (SIMPAR), 2016, pp. 111–118, doi: 10.1109/SIMPAR.2016.7862384.

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[14] A. Rodríguez, E. Coevoet, and C. Duriez, “Real-time simulation of hydraulic components for interactive control of soft robots,” in Proc. IEEE Int. Conf. Robot. Autom. (ICRA), 2017, pp. 4953–4958, doi: 10.1109/ ICRA.2017.7989575. [15] S. Terryn, J. Brancart, E. Roels, G. Van Assche, and B. Vanderborght, “Room temperature self-healing in soft pneumatic robotics: Autonomous self-healing in a Diels–Alder polymer network,” IEEE Robot. Autom. Mag., vol. 27, no. 4, pp. 44–55, 2020, doi: 10.1109/ MRA.2020.3024275. [16] E. Roels et al., “Processing of self-healing polymers for soft robotics,” Adv. Materials, 2021. [Online]. Available: https://onlinelibrary. wiley.com/doi/abs/10.1002/adma.202104798, doi: 10.1002/adma. 202104798. [17] L.-R. Wang and Z.-H. Lu, “Modeling method of constitutive law of rubber hyperelasticity based on finite element simulations,” Rubber Chemistry Technol., vol. 76, no. 1, pp. 271–285, 2003, doi: 10.5254/ 1.3547739. [18] A. Goriely, S. Budday, and E. Kuhl, “Neuromechanics: From neurons to brain,” Adv. Appl. Mech., vol. 48, pp. 79–139, 2015. [19] K. Romanov, “The drucker stability of a material,” J. Appl. Mathematics Mech., vol. 65, no. 1, pp. 155–162, 2001, doi: 10.1016/S0021-8928(01) 00017-X. [20] J. Allard et al., “Sofa—An open source framework for medical simulation,” vol. 125, pp. 13–18, 2007. [21] Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 22, no. 11, pp. 1330–1334, 2000, doi: 10.1109/34.888718. [22] O. Goury and C. Duriez, “Fast, generic, and reliable control and simulation of soft robots using model order reduction,” IEEE Trans. Robot., vol. 34, no. 6, pp. 1565–1576, 2018, doi: 10.1109/TRO.2018.2861900.

Pasquale Ferrentino, Brubotics, Vrije Universiteit Brussel, and Imec, Elsene, 1050, Belgium. Email: pasquale.ferrentino@ vub.be. Seyedreza Kashef Tabrizian, Brubotics, Vrije Universiteit Brussel, and Imec, Elsene, 1050, Belgium. Email: seyedreza. [email protected]. Joost Brancart, Physical Chemistry and Polymer Science, Vrije Universiteit Brussel, Elsene, 1050, Belgium. Email: [email protected]. Guy Van Assche, Physical Chemistry and Polymer Science, Vrije Universiteit Brussel, Elsene, 1050, Belgium. Email: guy.van [email protected]. Bram Vanderborght, Brubotics, Vrije Universiteit Brussel, and Imec, Elsene, 1050, Belgium. Email: bram.vanderborght@ vub.be. Seppe Terryn, Brubotics and Physical Chemistry and Polymer Science, Vrije Universiteit Brussel, and Imec, Elsene, 1050, Belgium. Email: [email protected]. 

©SHUTTERSTOCK.COM/OCIACIA

A Review of Cable-Driven Parallel Robots Typical Configurations, Analysis Techniques, and Control Methods

By Mahmoud Zarebidoki

, Jaspreet Singh Dhupia , and Weiliang Xu

C

able-driven parallel robots (CDPRs) have applications in large workspaces and at high operating speeds, which necessitates considering the mass and elasticity of cables for accurate analyses of kinematics, dynamics, workspace, trajectory planning, and control. In this article, first, the typical CDPR configurations along with their application areas are summarized. Then, various approaches, such as optimizing cable and motor configurations or integrating additional elements to the structure of CDPRs that can be used for workspace geometry optimization, are discussed. Afterward, different models for the cables with mass and Digital Object Identifier 10.1109/MRA.2021.3138387 Date of current version: 29 March 2022

1070-9932/22©2022IEEE

elasticity, such as Irvine’s sagging or spring dampers studied in the literature for integrating into the kinematics and dynamics equations, are reported. Later, along with reviewing different approaches for trajectory planning of planar and spatial CDPRs, advances in configuration optimization for collisionfree trajectory planning are addressed. Finally, kinematic and dynamic control algorithms to handle the effect of mass and elasticity of the cables and robust and adaptive control algorithms to tackle structured and unstructured uncertainties, such as in the mass and moment of the moving platform (MP) and external disturbances, are reported. Background Flexible cables are used instead of rigid links in CDPRs for connecting the base platform (BP) to the MP. In these robots, SEPTEMBER 2022

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cables are wound or unwound using electrical motors, winches, and pulleys to move the MP. CDPRs have several advantages over conventional link-based robots because of their ability to generate higher velocities and accelerations because of a lower inertia, large workspace, and a high load capacity [1], [2]. The initial ideas on cable-controlled robotic systems originate from a master thesis [3] in 1984. SkyCam [4] and RoboCrane [5] are considered the first applied robots of this kind, developed in the 1980s to carry a recording camera and to perform a pick-and-place task, respectively. In the 1990s, the first research about the problem of tension distribution of cables was studied in [6], where adding additional cables for constraining the MP was proven. The first classification of CDPRs based on the number of cables and degrees of freedom (DoF) was introduced in [7]. By the turn of the century, along with a broadened research about CDPRs in academics, their practicality in the industry in applications to different tasks, such as pick and place, rehabilitation, and 3D printing, was proven.

b2

Actuators

b3

b1 Hefty Cable

Massless Cables MP

Fhefty

Effect of Hefty Cables on Force Direction Fmassless

(a) Elastic Cables

(b) BP

BP Optimum Design

Redundant Sample

MP

MP (c)

Figure 1. (a) Hefty cables with mass and their effect on the kinematics and dynamics. (b) Effect of elasticity of cables in CDPRs. (c) Minimum-time trajectory optimization by changing the cable configuration, adapted from [50].

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Different characteristics of cables, such as material, density, and elasticity, can influence the static and dynamic behavior of a CDPR [2]. Among these characteristics, the effect of the mass and elasticity of cables on CDPR performance is often studied in the literature for accurate robot analysis. The mass of a cable can be ignored if its tension is considerably greater than its weight [8]. However, a large cable mass is required in applications with a large workspace, which cannot be ignored in the kinematics and dynamics formulation [9]–[20]. For example, a Five-hundred-meter Aperture Spherical radio Telescope (FAST) was designed in China; it is the largest single-dish radio telescope in the world. The feed cabin of this mechanism is supported and driven by cables within a reflector with a curvature of radius 300 m [21]. Other examples of large-workspace CDPRs are MARIONET-CRANE [22] and COGIRO [11], which were developed for handling and assembling heavy parts within the workspace dimensions of 15 m × 15 m × 15 m and 15 m × 11 m × 6 m, respectively. These applications need a large workspace, so the modeling of cables with mass [Figure 1(a)] should be integrated into the kinematics and dynamics equations. The elasticity of a cable can strongly affect the performance and efficiency of a CDPR, especially for applications with a higher speed [18], [23], [25]–[29]. In 1995, it was shown experimentally that CDPRs can generate accelerations of more than 400 m/s2 [2]. Later, a highspeed spatial CDPR was introduced in [1] capable of accelerating up to 43 g and a maximum speed of 13 m/s. In such applications, it is necessary to consider the elasticity of cables and its effect on resulting displacements and vibration during the formulation of the kinematics and dynamics of the system [Figure 1(b)]. Therefore, the cable models used in the literature consider 1) cables with no mass and no elasticity; 2) elastic cables with no mass; 3) cables with mass and no elasticity, assuming them to have a straight line or hefty contours; or 4) cables with both mass and elasticity. Incorporating a lightweight structure and its modularity makes CDPRs more reconfigurable and scalable than traditional rigid robots. Various cable and motor configurations are studied in the literature to describe frameworks for optimal trajectory planning [30]–[33] and optimal workspace generation [30], [34]–[46]. Moreover, the cables can wrap around obstacles [33] or collide with each other in a cluttered environment. Therefore, [30] and [34] have considered changing the configuration by changing the connection point to the BP or MP [Figure 1(c)] to avoid collisions in the approaching phases. Compared to previous literature reviews [47], [48] on cable-driven robots, this article covers research that considers the mass and elasticity of cables for subsequent analysis and configuration optimization of CDPRs in more detail. Common CDPR Design Configurations and Applications CDPRs can be categorized into different types based on their configuration, the number of cables, and the DoF. A

CDPR with M cables and N DoF is an incompletely restrained positionPlanar Translational Planar Translational and Rotational ing mechanism (IRPM), if M # N. For such a configuration, the robot cannot resist arbitrary applied wrenches. However, considering (a) (b) (c) (d) gravity or other applied forces, one or Spatial Translational Spatial Translational and Rotational more poses of an IRPM may exist where the robot is in stable or unstable equilibrium. If M = N + 1, the robot can be a completely restrained positioning mechanism (CRPM) in certain poses. In this case, possible tension distributions form a 1D subspace in the M-dimensional space of (e) (f) (g) (h) cable forces, making it comparably simple to solve. If M 2 N + 1, the robot is a redundantly restrained Figure 2. Different types of CDPRs: (a) 2–2 planar IRPM, (b) 3–2 planar CRPM, (c) 3–3 planar IRPM, (d) 4–3 planar CRPM, (e) 3–3 spatial IRPM, (f) 4–3 spatial CRPM, (g) 6–6 positioning mechanism (RRPM). In spatial IRPM, and (h) 8–6 spatial RRPM [57]. this case, based on the robot configuration, there might be infinitely many solutions for the tension distribution in the cables; there- Kinematics and Dynamics fore, two significant problems should be solved. The first is In this section, research on the kinematics and dynamics of to find out if there is at least one solution for tension distri- CDPRs considering and not considering the mass and elasbution; the second, if there are many solutions, is how to ticity of the cables are reviewed. Compared to serial robots, find continuous smooth ones along a trajectory [2], [51]. Different configurations of CDPRs consisting of IRPMs, CRPMs, and RRPMs can operate in a suspended configuraTable 1. Typical applications with corresponding tion where the robot relies on gravity to be balanced. In this CDPR configurations. case, suspended CRPMs and RRPMs will have the maxiApplication Type References mum of N cables under tension [52]. This issue makes notable differences in a CDPR’s analysis as all slack cables should Pick and place Planar CRPM [140] be ignored. Spatial IRPM [5], [34], [64], [65], [68], Different typical configurations of CDPRs are illustrated in [118], [135] Figure 2, and typical applications corresponding to different Simulator Spatial CRPM [26], [27], [103] configurations of CDPRs are presented in Table 1. The followRadio telescope Spatial IRPM [21], [88], [137] ing sections discuss different research aspects of IRPMs, CRPMs, and RRPMs involving kinematics, dynamics, workRehabilitation Planar CRPM [94], [109], [110], [124], [144]–[152] space, trajectory planning, and control. In addition to the basic architecture of CDPRs, other conSpatial IRPM [109], [125], [153]–[155] figurations were also proposed in the literature by replacing 3D printing Spatial IRPM [156], [157] some of the cables with other elements, such as rigid links, Spatial CRPM [158]–[161] revolute joints, springs, and extension limbs. In [53] and [54], Camera carrier, Planar CRPM [162], [163] a telescopic spine and an extensible limb provide appropriate Inspection, and pressure to the MP to maintain all of the cables in tension. Spatial IRPM [4], [98], [104], [108], so on [164], [165] The force and torque capacity of the MP can be modified by applying the required ballast force. On the other hand, the Painting and Planar IRPM [78], [92], [93], [166], [167] robot’s reachable workspace decreases as these elements’ so on Spatial RRPM [168] length and swing angle are limited. In [55], a cable-driven Logistics Spatial RRPM [143], [169], [170] mechanism with Cartesian motion was introduced. The robot consists of a rigid-link Cartesian mechanism that is Maritime Spatial IRPM [172], [173] driven with a cable loop with stationary actuators. Springs Aerial Spatial IRPM [174]–[177] have also been integrated into the structure of CDPRs for Spatial RRPM [178] constraining the robot without adding extra cables and actuaJoystick Spatial IRPM [24], [171], [179] tors [56] or for optimizing and enhancing the required workspace [44], [45]. SEPTEMBER 2022

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the forward kinematics (FK) for parallel robots is more complex to solve. It is even more difficult in the case of CDPRs because of the unilateral nature of cables, which requires them to always be in tension. Inverse kinematics (IK) is easier than the FK to solve for parallel robots and CDPRs with ideal cables with no mass and elasticity. Furthermore, the hefty shape of the cables makes A positive effect of the the IK problem quite complex. In this case, five-bar mechanism on both the position parameters and cable tensions decreasing the drive are unknowns, and some of the equations are not torques and increasing algebraic. Therefore, approaches that are effithe load-carrying cient with ideal cables cannot be used for IK capacity of the robot analysis. By assuming a hefty elastic model for the was demonstrated. cables, solving the IK problem becomes even more complex as the cable configuration considers both hefty shape and elongation of the tensioning cables [58]. The details about elastic and hefty cable models and their effect on the kinematics and dynamics are explained in the sections “Cables with Mass,” “Research Works Considering Elastic Cables,” and “Research Works Considering Cables With Both Mass and Elasticity.” Research Works Assuming Massless Inelastic Cables The Newton–Euler method was widely used for deriving the dynamics equations of both planar and spatial CDPRs [5], [26], [59], [60]. In this approach, the position vector of each cable and applied forces and wrenches on the MP were calculated for deriving the dynamics equations. In [61], a new Jacobian matrix was constructed with a chosen set of variables arising from dynamics analysis using the Lagrangian method. The dynamics equation presented in [59] has six variables corresponding to the position and orientation coordinates for the six DoF of the MP. However, the new Jacobian matrix employed Cartesian coordinates of the vertices of the MP consisting of nine variables, which reduces the computation time for workspace definition. In [62], the FK was studied using the multilayer perception type neural network approach, which is faster than numerical approaches. A backpropagation procedure was utilized for training the network. In [63], an approach for finding the lowest stable equilibrium pose of suspended CDPRs with an arbitrary number of cables was studied. In this approach, the potential energy of MP is minimized using the branch-andbound algorithm. The kinematics of the collaborative transport of cablesuspended payloads by four mobile cranes was examined in [64]. The estimation of kinematic errors caused by 92

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machining, assembly, and operation was studied to improve the exact positioning of the MP. Moreover, in [65], an IK analysis of three quadrotors carrying a payload was presented. The IK problem has infinitely many solutions for this configuration. However, when the tensions of the cables are also specified, the IK problem is shown to have a finite number of solutions. Different approaches are used in the literature to account for the effect of the winding mechanism for improving the dynamic performance of the CDPRs [66]. In [67], reflective pulleys were integrated into the MP to improve the kinematics and dynamics of the robot. These reflective pulleys must have the same radius as the ones at the BP to compensate for their impacts. However, according to [2], pulleys have a significant effect only on the kinematics of small CDPRs and can otherwise be neglected. In [68], a five-bar mechanism was used to move the MP of a spatial IRPM. A positive effect of the five-bar mechanism on decreasing the drive torques and increasing the load-carrying capacity of the robot was demonstrated. In [28] and [66], the dynamics of pulleys and winches were considered for deriving kinematics and dynamics equations of a spatial and a planar robot using geometrical approaches. Cables With Mass Two approaches have been proposed in the literature for analyzing the kinematics and dynamics of CDPRs, considering the mass of cables. The first approach assumes cables as straight elements, and the second one accounts for their hefty or catenary shape. In terms of the first approach, in [14], the cables were assumed as straight lines with varying mass and velocity. Dynamics equations of a 4–3 planar IRPM were derived using the Lagrangian method. In [15], the virtual work and Newton–Euler methods were used to analyze the dynamics of the MPs and cables of the FAST, respectively. In [13], cables were modeled as cylinder elements. The motion analysis of a 7–6 CRPM was studied using the “bushing” joint of ADAMS software. The second approach was applied in [19], where the cable configuration (Figure 3) is represented with a hyperbolic function,

y ^ x h = k cosh ` x + c 1 j + c 2, (1) k

where k = H/q, q is the distributed mass of the cable, H is the horizontal tension force, and c 1 and c 2 are two constants that can be evaluated from the boundary conditions. Dynamic equations were derived for a hefty configuration of the cables considering aerodynamic forces acting on the robot by discretizing the cable into a series of N elastic segments joined at nodes [9]. The lumped-mass method was used to develop partial differential equations, which were solved using the adaptive Runge–Kutta algorithm. In [10], besides considering the mass of cables, the dynamics of pulleys were integrated for kinetostatic

analysis. In [16], (1) was simplified for statics analysis, where a linear relationship was derived between the forces in the cables and the externally applied wrench to the robot’s MP. Finally, in [69], an interval-analysis-based algorithm was used to solve the direct geometric–static problem of spatial IRPMs. The algorithm finds all possible equilibrium poses of an MP considering slack in the cables along with its mass.

Research Works Considering Cables With Both Mass and Elasticity The Irvine sagging-cable model [25], [74] is mostly used for deriving kinematic and dynamic equations considering both the mass and elasticity of cables. In this formulation, the ordinary differential equations for the coordinates of point A, which is the cable’s connection point to the MP (Figure 3), are defined as

Research Works Considering Elastic Cables Transversal vibrations of cables can be neglected relative to axial vibrations. In [29], the axial and transversal vibration of a 7–6 CDPR was studied. It was shown that the transversal vibration contributes only 1.4% of the total vibration amplitude. The nonlinear stiffness characteristic of a cable that was used for a CDPR is shown in Figure 4(a). Cables are mostly modeled as axial springs [Figure 4(b)] for CDPRs with elastic cables. In this case, the elongation TL of a cable is calculated as TL = K c Tc, where K c and Tc are the stiffness and the tension applied to a cable, respectively. The cable’s stiffness can have linear or nonlinear behavior. However, most of the literature considers a linear stiffness, K c = EA/L, where E is Young’s modulus of the cable material, A is the cable cross-sectional area, and L is the cable length at rest. In [70], the IK and FK of a 7–6 IRPM with elastic cables were presented under the assumption that the tensions must be lower than a fixed threshold to avoid breaking the cables. In [29], a vibration analysis of general 6-DoF CDPRs was presented. The natural frequencies of the multibody system were analyzed to demonstrate that a cable manipulator can be designed to be stiff enough for special applications. In [71], the Euler–Lagrange formulation was used to derive the dynamic equations by first calculating the kinetic and potential energy of the MP and elastic cables. In [72] and [73], the cables were considered straight elements with elasticity and a damping coefficient having an inverse relation with the cable length. The Euler–Lagrange formulation was used to derive the dynamics equation.

m sinh -1 V - sinh -1 c V f H p L xA = H + , (2) EA tg

tgL

2 H 2 + V 2 - H 2 + ^V - tgLh2 tgL + VL , (3) tg EA 2EA

yA =

where V is the horizontal tension force, and E, A, L, H, and t were described earlier in the sections “Cables with Mass” and “Research Works Considering Elastic Cables.” This model was used for setting up the cable configuration in [17] and [19], where the dynamics and kinematics modeling of the FAST was derived. The kinematic and force singularities were analyzed to improve the real‐time controllability of the system. In [24], the static displacement of cables was computed and used for IK analysis and stiffness of general

Cable Force

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Elongation ∆l (a) ∆l1

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Figure 3. The catenary shape of cables considering the mass of the cables. (Source: [19]; used with permission.)

Figure 4. (a) The nonlinear behavior of a cable used for a CDPR and (b) elastic cables considered as linear springs for kinematics and dynamics analyses.

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CDPRs. In [25], the FK of spatial IRPMs was solved using a numerical continuation scheme. The FK was solved for nondeformable cables and then extended to find the solution for deformable cables. In [11], Irvine’s sagging-cable model was linearized and used for a stability and stiffness analysis. The cable tensions were computed and used to solve an IK problem of spatial CDPRs. Other approaches are also employed for kinematics and dynamics analyses, accounting for both the mass and elasticity of the cables. In [27], the port-Hamiltonian method was used to derive dynamic equations by calculating the MP’s and cables’ total kinetic and potential energies. In [12], a linear spring model with mass was used for the cables. Ordinary differential equations were derived using the lumped-mass method. The finite-difference method was used for the discretization of the equations. In [28], the same spring model was used for the cables. The Newton–Euler method was used to derive the dynamics equations considering the dynamics of actuators and pulleys. Hefty elastic cable models are also used for stiffness analysis. In [75], the static stiffness was evaluated using the MP pose-error variation by considering a hefty elastic cable model for the cables. The dynamic stiffness was analyzed by identifying the robot’s natural frequencies. In [49] and [76], the stiffness matrix of spatial CDPRs was calculated numerically. A homogenization of this stiffness matrix was introduced in [49] and can be used for design purposes. Workspace The CDPR workspace studies presented in the literature divide the overall workspace into three zones. A controllable or wrench-closure workspace (WCW) is related to every position of the MP in the configuration space, where the tensions in cables are greater than zero [77]. A wrench-feasible workspace (WFW) refers to the positions of the MP where a positive lower and upper bound are considered for the

tension in cables, while the CDPR can resist any external wrenches in each set. Workspace of Planar CDPRs A 2–2 repetitive workspace IRPM with serial link support was presented in [78]. The robot was used for painting, and the repetitive workspace means that the BP can be shifted several times during the painting process. The effect of geometrical parameters, such as the anchor point’s location for the serial manipulator on the workspace configuration, was analyzed. For planar CRPMs, the WCW of a 4–3 CRPM with different MP angles was determined in [77], composed of conic sections. In [79], a variant of Bland’s pivot rule was used to determine the WCW of planar and spatial CRPMs. A system of inequalities arising from static equilibrium was converted into a system of equations, which results in a more efficient workspace calculation compared to that obtained by numerical methods. In [80], the effect of prestressed cables on the WCW was reported. The prestress stable WCW was defined as a subset of the WCW, where an increase in the prestress level leads to an increase in the overall stiffness of the mechanism. In [35], a collision-free workspace of reconfigurable constrained robots in cluttered spaces was studied. The critical support lines of obstacles [Figure 5(a)], the topological constraints, and the convex hull-mapping method were used to define the collision-free workspace [Figure 5(b)]. Here, the critical support lines are determined by connecting the farthest points of two consecutive obstacles.

Angle

Workspace of Spatial CDPRs Regarding the workspace of spatial IRPMs, the effects of different parameters, such as the size of the MP and BP and the MP rotation angle on the workspace geometry, were investigated in [81] and [82]. The results show that, when the degree of orientation of the MP is zero, the largest workspace is obtained. In [83], the boundaries of the WCW for spatial CDPRs with more than six cables were defined. For such robots, the WCW consists of cubic surfaces, like the WCW of the Gough– Stewart robot. In [84], a feasible dynamic workspace was determined 30 analytically considering a prescribed MP set of accelerations for the MP. In [85], 15 the improved workspace of a 4–6 0 IRPM was presented considering the Cables inertia of MPs, external wrenches, and –15 centrifugal and Coriolis matrices. However, it was shown that the –30 Critical improved workspace was around 32% 1,000 1,000 Support Lines smaller than the general workspace. 0 0 of Obstacles Y (mm) –1,000 –1,000 The workspace of a CDPR is always X (mm) determined and characterized by the (a) (b) tension status of its driving cables. Therefore, the relative tension distribuFigure 5. (a) Critical support lines of obstacles were used for defining the collision-free tion among the cables is an appropriate workspace, adapted from [35]. (b) The collision-free workspace of a three-cable CDPR with different orientations in a three-obstacle area [35]. measure to evaluate the quality of the 94

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Tension (N)

workspace. In [86], the determination × 105 of an optimal tension factor value for 2.2 Curve Shape of Tensions and Singularities generating an optimized workspace H1 2 was studied. The tension factor was H2 determined as the minimum tension H3 1.8 over the maximum tension of the cables. When this factor approaches 1.6 zero, the MP is located near the work1.4 space boundary. By a similar analogy, if the factor approaches one, the MP is 1.2 0 50 100 150 200 250 300 350 400 positioned far from the workspace Time (s) boundary. In [38], a translational contour crafting RRPM with 12 cables was Figure 6. The curve shapes of tensions and resulting singularities of a CDPR with cables presented. The cable tensions were with mass. (Source: [88]; used with permission.) used to approximate the maximum structure size built using this manipulator, considering vari- software was used to improve the rotational workspace of an ous loading conditions. In [87], the worst possible exerted 8–6 RRPM. Different cable configurations were tested to wrench on the MP was considered the key wrench to define demonstrate that the cable configuration can increase the the controllable workspace of spatial CRPMs. rotational workspace efficiently. For CDPRs with a large workspace, such as the FAST, the The second approach was used in [46], where an articmass of cables was used for workspace analysis and studying ulated gripper was integrated into the MP of a conthe force singularities [88]. The plot of tension versus time strained robot. The gripper augments the boundaries of (Figure 6) has six singular sections, where the cable tensions the workspace by grabbing an external structure, which are uncertain. These six sections divide the shell workspace allows the MP to reach outside its standard configuration evenly into six segments. To tackle this problem, adding a tie- space. In [45], springs were integrated into the structure down cable for handling force singularities and improving the of planar and spatial CRPMs (Figure 7). Their effect on workspace was recommended. the MP wrench was investigated by varying their number In [89], an analytical solution method solved the static or quasi-static problem of the FAST. The calculation time of this method is lower than iterative methods, which makes it useful Springs for real-time control. In [90], the kinetostatic solution of RRPMs for three different selection criteria consisting of 1) minimizing the tension in the cables, 2) maximizing the tension in the cables, and 3) minimizing the deviation between the cable tension and the mean tension is presented. Each criterion can be used for different applications with different requirements. Cables (a) 3

3

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z (m)

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Workspace Optimization by Optimizing the Configuration Two approaches are used in the literature for optimizing the workspace of CDPRs. The first approach analyzes the effect of different cable and motor configurations. The second approach considers integrating different elements, such as springs, into their structure. The first approach was used to evaluate the WCW of two configurations of a 7–6 CRPM, “WIRO-6.1” and “WIRO4.3,” and a 9–6 RRPM, “WIRO-6.3,” using numerical approaches [40]–[42]. The results showed that WIRO-6.3 has the largest workspace. The same approach was used in [39], and three different cable configurations of 7–6 CRPMs were compared. In [37], the maximum acceptable distance between the geometric center and the mass center of the MP was used as the performance index. The placement of motors and winches was optimized to have a more load-carrying capability with a larger workspace. In [36], Wire Center

–1

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–2

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–3

–4 –4

–1

0 x (m)

1

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–4 –4

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Figure 7. Integrating springs to CDPRs for having the desired workspace, b) workspace of the CDPR by adding springs, c) workspace without adding the springs. (Source: [45]; used with permission.)

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and location. To maximize the WFW, the desirable spring parameters were calculated using a quadratic programming-based optimization scheme with lower and upper bounds on the cable tensions. In [44], a differential mechanism [Figure 8(a)] was used for pulling two cables using just one For this robot, rotating actuator. The workspace of a CRPM with and arms were used at the top without this mechanism was analyzed using concorners of the signpost for vex theory and linear algebra. In [43], a cableoptimal force generation loop structure [Figure  8(b)] was integrated over the entire plane of into a planar CDPR to provide an unlimited and the signpost. singularity-free orientation workspace. However, the cable loop also results in occasional rotational motions of the MP, so-called parasitic inclinations, which were modeled and assessed in this work. Bar linkages and springs were used for the static balancing of a planar CDPR in [91]. This mechanism decreases the forces that must be applied to the MP across the workspace. It also helped to have a minimum desirable tension in the cables to conserve the workspace geometry.

out-of-plane motion in [92]. A numerical method was used to compute the minimum-time trajectory satisfying the velocity and acceleration constraints for a given path. Another 2–2 IRPM was introduced in [93] for removing graffiti from highway signs. For this robot, rotating arms were used at the top corners of the signpost for optimal force generation over the entire plane of the signpost. The workspace was divided into 20 sections wide by 20 sections high, and image processing was applied to isolate graffiti from nongraffiti in these sections. Then, the robot path was generated by connecting the coordinates of each section. Regarding CRPMs and RRPMs, in [94], a reconfigurable 4–3 CRPM was designed for lower limb rehabilitation. The cable attachment points on the BP can move to balance the external wrenches during the limb motion. The area of the wrench-closure zone was increased for this mechanism using different actuation configurations. Different methods are used for the minimum-time trajectory planning of CRPMs and RRPMs. In [50], the effects of the configuration of cables, the corresponding switching points, and the number of cables were optimized for the minimum-time trajectory planning of a 4–3 CRPM. In [59], a minimum-time trajectory-planning approach of redundant and nonredundant cable robots was presented. This approach reduced the differential equations of the robot dynamics to a system of second-order differential equations in terms of path parameters using the specified desired path.

Trajectory Planning of Spatial CDPRs Most of the literature about the trajectory planning of spatial CDPRs is related to IRPMs. Point-to-point trajectory planning is one of the most frequent methods for spatial CDPRs, where different approaches are employed to ensure acceleration continuity and zero velocity at target points. In [95], a hypocycloid curve [Figure 9(a)] was used to connect the consecutive target points with zero instantaneous velocity to obtain the desired trajectory. Target points can be outside the static workspace of the mechanism, which guarantees a wider zone of achievable workspace. In [96], generic trajectory Trajectory Planning of Planar CDPRs expressions of a 3–3 CDPR were derived using trigonometric In terms of trajectory planning of IRPMs, a two-link serial functions. The feasible target points were defined, and viable robot was attached to the MP of a 2–2 IRPM to limit its areas between two consecutive points were selected for indirect trajectories. In [97], an S - Sp plane was used to devise dynamically Spring feasible point-to-point trajectories and Differential Mechanism periodic trajectories. In this approach, Pulley the unilateral cable tension constraints Cable were explicitly converted to geometrical constraints in the S - Sp plane. The other approaches for the trajecMotors tory planning for CDPRs include an End Effector (Unlimited Rotation) IRPM carrying a camera presented in Actuated With One Motor [98]. This approach used the feedback (a) (b) of the current positions and velocities Figure 8. (a) A differential mechanism used for a CDPR instead of adding motors. of the camera and the object to calcu(b) Increasing the rotational capability of CDPRs by cable loop. (Source: [43]; used with permission.) late the goal position and velocity of Trajectory Planning Trajectory planning of CDPRs is more challenging than for traditional parallel robots as the lengths and tensions of cables must remain within acceptable bounds to avoid cable sagging during operation [47], [48]. For CRPMs and RRPMs, all of the DoFs of the MP can be controlled, which makes the trajectory planning problem easier. For IRPMs, the WCW does not exist, which makes the trajectory planning complicated.

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1.5 Cable 3

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0 X

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(a)

(b)

Figure 9. (a) Hypocycloid curves were used for trajectory planning with zero velocity at the target points [95]. (b) A 6–3 spatial RRPM equivalent to a 3–3 purely translational IRPM using a parallelogram. (Source: [99]; used with permission.)

the camera. In [99] and [100], a parallelogram configuration minimum energy consumption when the robot is maneuverof cables was used to change the feasible dynamic motions ing periodic trajectories was determined. This was achieved of a 6–6 IRPM [Figure 9(b)]. Each parallelogram consists of by minimizing the second norm of the cable tension vector. two parallel cables sharing the same length. The robot can A rapid calibration method was developed to reduce the demove like a 3–3 purely translational CDPR, while the MP ori- ployment time using a laser rangefinder and plumb lines susentation remains approximately the same. pended from each cable origin. In this case, the horizontal Since fewer cables are used in IRPMs than CRPM or distance between the plumb lines can be measured quickly RRPM, the payload can have additional DoF and exhibit and precisely. swaying motions or oscillations. A trajectory planner was In a cluttered environment, the cables can wrap around implemented for a 4-6 IRPM to eliminate unwanted oscilla- obstacles or tangle with each other [33]. Therefore, optimized tions using a zero-vibration input-shaping scheme [101]. collision-free path planning is studied in the literature to tackle Motion in 3D space was mirrored to two vertical planes per- this problem. In [33], a homotropy-signature augmented graph pendicular to each other, and afterward, the natural frequency [Figure 10(a)] was used for path planning of an IRPM in an area was calculated for planar IRPMs with two cables. with polygonal obstacles. Two different trajectories connecting In terms of considering the mass and elasticity of the the same start and end points are homotopic if one can continucables, a trajectory-planning approach was presented in [102] ously deform into the other without intersecting any obstacle. for a 6-6 IRPM considering a virtual equivalent spring model for the cables. The trajectory-planning technique Xg permitted the MP to move beyond its τ1 static workspace in a controlled, preO1 Reconfigurable MP dictable manner. –τ2 Regarding the trajectory planning of CRPMs and RRPMs, a robot was O2 designed in [103] for simulating underwater forces, such as the buoyancy τ2 for a walking humanoid robot. The τ3 Xs simulator robot followed the desired O3 trajectories, ensuring a smooth path while avoiding any perturbation in the (a) (b) cables. In [104], the trajectory planning of a 4–3 CRPM for sensing and Figure 10. (a) x 1 and x 2 are homotopic, but x 3 is not homotopic to x 1 and x 2 [33]. mapping of an aquatic environment (b) A CDPR with a reconfigurable MP for collision-free path planning. (Source: [34]; used was presented. Trajectory planning for with permission.) SEPTEMBER 2022

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This approach helps to find the shortest path between the start and end points. In [31], a piecewise linear interpolation method was introduced. In this approach, any target points above cable exit points can be connected in sequence via some intermediate points in the static workspace. Accordingly, the intermediate points can be accurately selected to avoid collisions between cables and obstacles. In [32], the path planning of a 6–6 IRPM was studied using the higher-dimensional continuation method of Henderson [105]. The approach provides a systematic way of transitioning through two configurations while ensuring cable tensions are inside their allowable bounds. The method is flexible enough to accommodate the collision constraints of the robot. Changing the cable configuration at the MP or BP level is another approach to tackle cable and obstacle collisions. In [34], a reconfigurable MP [Figure 10(b)] was designed for pick and place in cluttered areas. The configuration of the MP can be changed to avoid collisions with obstacles while reducing the duration of motion. In [30], the cable connection points on the BP can be positioned at a large but discrete set of possible locations ensuring minimal cable collisions. A feasibility map was generated to determine the minimum sets of configurations for following a prescribed path. Control Using cables makes the control of CDPRs more challenging than that for traditional rigid-link parallel robots. In this case, control laws should be designed to keep all tensions positive while attaining the desired control performance [106]. In addition, it is difficult to control the position and orientation of the MP precisely because of the low stiffness of such mechanisms. Therefore, some widely used control methods must be modified to meet the special properties of cables [48]. Both kinematic and dynamic controllers are implemented on CDPRs. Kinematic control techniques are based on an IK transformation [107], which feeds the reference values to the cables corresponding to the assigned MP trajectory. Dynamic controllers consider the nonlinear dynamics of the robot. Control of CDPRs Assuming Massless Inelastic Cables In terms of kinematic controllers, in [108], a proportionalderivative (PD) controller was used for a spatial object-tracking IRPM. The feedback from the gyro sensor, inertial measurement unit (IMU), and encoders were used for calculating position errors. In [109], a proportional-integral-derivative (PID) force servo system improved the loading accuracy and speed of a reconfigurable CDPR used for limb rehabilitation. The employed force servo system had a good tracking ability in the standard rehabilitation frequency band, meeting the requirements for rehabilitation. In [110], a two-part controller was designed for a 3–2 planar CRPM used for arm rehabilitation. The low-level controller was used for tension distribution through three cables, and the high-level controller was used for calculating assistive forces. The assistive force 98

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generated a virtual guidance field around a nominal path using impedance control to improve the movement accuracy and execution time. In terms of dynamic controllers, feedback linearization (FL) control was used in [106] and [111] for CRPMs, ensuring positive tension in cables using linear and quadratic programming. The control input was chosen as DV + G, where V = ep - K P e - K D eo, e is the error in position, and D and G are inertia and gravity matrices, respectively. In [112], FL control was augmented by adding a reference governor. This reference governor operates under the receding horizon strategy by generating admissible reference signals. This approach offered an efficient way to predict the system’s future states using the error dynamics. In [113], the controller shortened the phase trajectory to dampen the oscillation of the nonlinear system. An oscillation number was defined as an index to evaluate the oscillatory nature of the nonlinear system, and the FL was used to minimize it. Mechanical systems may interact with a disturbed environment [114]. Besides, there would be uncertainties in different mechanical parameters of the CDPRs, such as the mass and moment of inertia of the MP and the diameter of cable pulleys. Therefore, using adaptive and robust controllers can help achieve more accurate trajectory tracking. A robust PID controller was presented in [115] for a spatial CRPM to handle structured and unstructured uncertainties in the robot parameters, such as the mass and inertia of the MP. The vector of internal tension, which was obtained based on the null space of the robot’s transposed Jacobian matrix, was used to ensure positive tension in the cables. To derive the control action xr, the pseudoinverse of the inaccurate Jacobian matrix Jt was used:

xr =

Jt (Jt T Jt) - 1 c K P e + K D eo + K I 8e ^ s h ds m, (4) t

0

where e is the error in the position of the MP, and K P, K D, and K I are positive definite diagonal gain matrices. In [116], three control algorithms—pole placement, sliding mode, and adaptive sliding mode—were implemented on a planar CRPM using feedback from a vision-based system. The adaptive sliding-mode controller had the best efficiency to handle uncertainties tackling the chattering phenomena. Sk = K – K reference was used as the sliding surfaces, where the elements in K and K reference corresponded to the x, y, and i DoF of the MP. Zarebidoki et al. [117] implemented an adaptive control algorithm and FL control on a 6–6 IRPM. The results were compared to demonstrate the efficiency of the adaptive controller to compensate for the uncertainties in the mass and moment of inertia of the MP and sinusoidal disturbances. In [118], a robust sliding-mode controller was implemented to a spatial IRPM carried by a helicopter. The helicopter produced gross motion, while the robot performed both translational and rotational movements. This method properly estimates the bound of the helicopter’s motion, allowing the cable robot to be stabilized even when the helicopter’s motion is

unknown. In [119], an adaptive controller was implemented to eliminate cable interference in a spatial CRPM during translational motion. Repulsive forces were generated when cables were near to collision. The minimum distance between the two cables was calculated using the Karush–Kuhn–Tucker conditions method. In [120], 2½D visual servo control was implemented on an 8–6 suspended RRPM. The vision algorithm provided feedback for the trajectory tracker to increase the robustness of the system. In [121], a nonlinear continuous-time generalized predictive control was used for a 4–2 RRPM. The controller design was based on the finite-horizon continuous-time minimization of a quadratic cost function. The cost function was chosen as the error between the desired trajectory and the predicted positions considering constraints on cable tensions. In [122], robust control of an 8–6 suspended RRPM balancing between PD and sliding-mode controllers was presented. The controller provides good accuracy and repeatability considering uncertainties in the MP’s mass. Neural network controllers, like one using an adaptive multilayer neural network, were presented in [123] for a planar IRPM to compensate for the perturbed conditions. A term was added to the central controller considering the dynamics of actuators and gearboxes to provide a priori bounded tension command for the cables. In [124], a neural network controller with an adjustable tracking error was used for a 4–3 planar rehabilitation robot. The controller aims to follow the desired trajectory by allowing an adjustable tracking error, enabling the human subject to freely move the limb inside this error area with an adjustable assistance level. The algorithm helps obtain a better rehabilitation efficiency using a compensating dynamic model implemented through an adaptive neural network. In terms of fuzzy controllers, an adaptive control law was presented in [125] for a 3–6 upper limb rehabilitation IRPM. A fuzzy tuner was employed to adjust control parameters based on position errors in the presence of external uncertainties in the environment and time-varying dynamic properties of the human arm for the robot-aided rehabilitation. In terms of RRPMs, along with an appropriate control scheme, a real-time embeddable algorithm for cable tension distribution is required. Therefore, different redundancy resolution approaches are used that also assist in ensuring positive tension in the cables. In [126], a noniterative real-time-compatible tension distribution algorithm within a dual-space feedforward scheme was implemented on an 8–6 suspended RRPM. In [127], an analytic–iterative scheme was used for redundancy resolution of a 4–2 RRPM. This scheme utilizes a convex optimization problem with inequality constraints of the manipulator structure and cable dynamics. The Karush– Kuhn–Tucker theorem is used to analyze the optimization problem, and a tractable and iterative search algorithm is proposed to implement the redundancy resolution. In [28], [128], and [129], the tension distributions of an 8-6 RRPM were studied by converting the problem into an optimization problem using p-norms of the cable tension as a cost function. In

this approach, the tension distributions are continuous along trajectories and differentiable at most of the points. In [130], a new flexible cost function with the ability of intuitive tuning was used for the optimal tension distribution of different configurations of CDPRs. The cost function is chosen as a combination of fixed logarithmic barrier and p-norm functions. This method avoids undesired discontinuous accelerations of actuators and guarantees continuous differentiability of In terms of RRPMs, along the actuator forces. In [131], a passive plant was with an appropriate established by considering cable pretension, which control scheme, a real-time results in a strictly positive controller for planar embeddable algorithm for RRPMs. The controller uses actuator saturation cable tension distribution prevention techniques and the solution to a linear is required. programming problem to ensure strictly positive tension in the cables. In [132], a model predictivecontrol strategy was used for RRPMs, explicitly addressing the cable tension limits. It means that the cable tension distribution can be performed as an integral part of the main model-based control architecture. In [133], a new methodology for positive tension distribution in CDPRs without having any redundancy resolution approach is presented. The controller incorporates a positive saturation-type function to map the control effort into a positive range. In this case, a nonlinear disturbance observer compensates for the saturation effects. The stability of the proposed control scheme is verified through Lyapunov’s second method. Controllers Considering the Mass of Cables The controllers reviewed in this section consider the mass and sagging of cables during the robot dynamics and aim to compensate for their effect for achieving exact positioning. A hybrid position/force PID controller was presented in [134] to tackle the pseudodrag problem of flexible cables in the FAST. The controller receives feedback from both the cable force error and position error. The tracking error achieved using this controller is about 2 mm, which assures the accuracy requirement for the FAST. In [135], a mobile wheeled CDPR was introduced, where the Gibbs–Appell method was used to derive the dynamics equation considering the mass of cables. This equation was used in the feedback law for FL to eliminate nonlinearities. The fuzzy method has also been used to control CDPRs with hefty cables and tune the controller gains. A fuzzy model reference learning controller was presented in [136] for a largeworkspace robot, consisting of a direct fuzzy controller, a reference fuzzy inverse model, and a fuzzy learning part. The direct fuzzy controller was adjusted so that the SEPTEMBER 2022

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closed-loop system acted like a prespecified reference model using the fuzzy learning mechanism. In [137], an inverse dynamics analysis of the FAST was derived using the Lagrangian method. Random wind forces acting on the cabin (MP) were simulated, and a PD fuzzy controller was implemented to handle the vibrations induced by the wind. In [138], passivity-based control of a planar 2-1 CRPM using a modified input torque and output tip rate for establishing a passive input–output mapping was presented. A lumped-mass method was used to model the dynamics considering the changing stiffness and mass of the cable wrapped around a winch. Controllers Considering the Elasticity of Cables Different approaches are employed to control the effect of elasticity and vibration of CDPRs. One approach is to separate the fast and slow motion of the system. In [71], dynamic equations of a spatial IRPM were rewritten to the standard form of the singular perturbation approach. A corrective term was added to the rigid part of the controller to guarantee the asymptotic stability of the fast dynamics. The Tikhonov theorem was used to separate slow and fast variables for stability analysis. In [139], a composite robust adaptive method was presented for a 4–3 planar CRPM. A fast control term, K v (Lo 1 - Lo 2), was added to compensate for the longitudinal vibrations, where L 1 and L 2 are the vectors of the tensioned and free cable lengths, respectively, and K v is a diagonal matrix. In [140], the MP’s undesired vibration was separated from its desired equation of motion by neglecting the second- and higher-order terms of the motion errors to form a linear parametric variable dynamic system. A robust vibration compensator was designed using the H 3 method to control the system. In [23] and [141], PD, PID, and fuzzy PID controllers were used for a 7–6 spatial CRPM and a 4–3 planar CRPM. The fuzzy method was used to tune the gains of the PID controller, and an online dynamic minimum torque estimation was used to ensure positive tensions in the cables. System responses showed that the fuzzy PID controller is more robust than the PID controller when encountering disturbances from the elastic cables. IMUs and encoders were used to detect the fast and slow dynamic movements of the MP in [73]. Their feedback was used in the FL controller to estimate the precise position and orientation of the MP, and a Kalman filter was used to smooth the noises in the process. In [72], the MP vibration was considered as a process noise. To achieve a tradeoff between the control input and the tracking error, the FL gains were obtained using the linear quadratic Gaussian method. A Lyapunov analysis demonstrated that a system with damping less than a specified minimum value could be stable with this approach. In [142], a mechanical reaction-based stabilizer was used for nonmodelbased vibration control of CDPRs. The stabilizer was composed of three actuators attached to a pendulum in a perpendicular arrangement mounted on the MP. The stabilizer needed only the actuators’ directly measurable position and 100

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velocity to form its closed-loop control feedback signals. In [143], a linear decoupled model of an 8–6 suspended RRPM with elastic cables was derived using modal analysis. The model is projected in the modal space yielding six decoupled second-order transfer functions for six DoFs of the robot, which can be easily controlled with standard single-input, single-output techniques. Conclusion and Outlook In this review, different design configurations and applications of planar and spatial CDPRs have been presented. Along with reviewing new and emerging research aspects of CDPRs with massless inelastic cables, the effects of considering the mass and elasticity of cables on the kinematics, dynamics, and control were emphasized. Achieving configuration optimization by changing motor and cable placements or adding additional elements for having a larger workspace and collision-free trajectory planning were addressed. Moreover, robust and adaptive controllers for compensating uncertainties in the robot’s parameters and disturbances were reported. This review reveals some outstanding research aspects concerning the CDPRs, listed as follows. 1) In terms of considering the mass and elasticity of the cables, most of the literature considers linear behavior for the cables. The kinematics and dynamics considering the nonlinear elastic behavior of the thin cables still require investigation. Moreover, a framework for carrying out the comprehensive formulation for the kinematics and dynamics considering mass, nonlinear elasticity, and environmental effects, such as temperature and wind, still needs to be developed. Furthermore, only a few research works [69], [88], [102] have reported the effect of mass and elasticity of the cables on the workspace and trajectory planning. 2) While several investigations of CDPRs have been reported, the combination of traditional serial and parallel robots with CDPRs for constructing hybrid manipulators is still in its infancy. CDPRs can be integrated into traditional manipulators to cover some DoF of the system. However, kinematics, dynamics, workspace, trajectory planning, and control will require further investigation in such configurations. 3) The application of CDPRs for underwater applications or fluid environments has been little studied in the literature. However, a large workspace and lightweight structure can enable a CDPR to be suitable for such applications. This type of implementation requires considering the effect of fluid forces such as buoyancy and drag force on the MP and cables during dynamics analysis and control implementation. Efficient control algorithms need to be developed for such CDPR applications to handle the nonlinear dynamics arising from fluid forces. 4) CDPRs have several advantages over other robotic solutions in terms of easier modularity, scalability, and reconfigurability, which can be further enhanced by

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Mahmoud Zarebidoki, University of Auckland, Auckland, 1010, New Zealand. Email: [email protected]. Jaspreet Singh Dhupia, University of Auckland, Auckland, 1010, New Zealand. Email: [email protected]. Weiliang Xu, University of Auckland, Auckland, 1010, New Zealand. Email: p.xu@auckland. ac.nz. 

A Cable-Driven Hyperredundant Manipulator

Obstacle-Avoidance Path Planning and Tension Optimization By Dawei Xu, En Li

M

, Rui Guo

anipulators with a hyperredundant and large aspect ratio are becoming more commonly used to detect complex and narrow spaces. The hyperredundant feature confers advantages for such manipulator types in comparison to traditional manipulators. However, they also introduce path-planning challenges. Due to the characteristics of hyperredundancy, there are countless inverse kinematics solutions, and the path-planning method that is used for traditional manipulators cannot be directly applied to these Digital Object Identifier 10.1109/MRA.2021.3111832 Date of current version: 6 October 2021

1070-9932/22©2022IEEE

, Jiaxin Liu, and Zize Liang

hyperredundancy manipulators in terms of the number of calculations or adaptability of the algorithm. Based on the typical working methods for these devices, this article proposes a phased path-planning method to simplify the problem. In the first stage, an improved artificial potential field method, which generates repulsion passively to avoid problems such as path oscillation, is proposed to obtain a guiding trajectory for the end of the manipulator. In the second stage, a joint-following algorithm is proposed to obtain all of the joint postures when the end of the manipulator moves along the guide trajectory. The joint-following algorithm converts the path planning into an optimal search and then sequentially determines the position of SEPTEMBER 2022

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each link to obtain the manipulator pose. Such a conversion also allows the algorithm to reduce the tension while avoiding obstacles. The simulations and experiments demonstrate that the proposed path-planning method can effectively complete the obstacle-avoidance path planning for a hyperredundant manipulator. It also has the ability to optimize the cable tension while avoiding obstacles, which is important for the efficiency, stability, and safety of the cabledriven mechanism. Previous Research Owing to the development of modern manufacturing, the industrial environment and large-scale equipment are becoming more complex. This results in the creation of dimly lit, narrow spaces, such as pipelines, aluminum electrolytic cell cathodes, and aircraft wing box structures. In such spaces, there are complex obstacles, making it challenging for people or equipment to enter and causing difficulties for assessment and maintenance. The existing equipment for the assessment of such spaces, such as industrial endoscopes, can only perform simple operations manually in a small area and cannot handle difficult tasks in more complex and extensive environments. In this context, a type of manipulator with hyperredundancy and a large aspect ratio has gained significant attention [1]. It has gradually demonstrated its advantages in complex and narrow spaces, which include aircraft assembly, pipeline maintenance [2], and medical surgery applications [3], and it is receiving attention [4]. In our previous work, we designed a cable-driven, snakelike manipulator with joints that have two degrees of freedom (DoF). Based on its kinematics model and the rigid body torque balance, a tension model was established to describe the relationship between the posture of the manipulator and the cable tension [5]. By exploiting its hyperredundant DoF, this type of manipulator can achieve obstacle-avoidance movement in complex and narrow spaces, and it also has the potential to achieve other goals, such as posture optimization. The obstacle-avoidance function needs to be realized through path planning, which will determine the posture of each joint. Therefore, posture optimization can also be realized. For manipulators, the purpose of path planning is to find a path from the start to the stop point. The number of possible paths is often greater than one. The start and stop points are usually given by the end position of the manipulator in the Cartesian space. The manipulator realizes the end movement by controlling the rotation of each joint, but, for a hyperredundant manipulator, the mapping from the end positions to the joint angles involves more than one set. This makes path planning particularly complicated, especially when there are obstacles in the environment. To find answers to these problems, especially that of the end position to the joint angles, early research focused on the inverse solution through numerical methods. Nakamura and 108

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Hanafusa [6] used the inverse solution algorithm based on the damped least-squares method to solve the inverse kinematics. In addition, Omisore et al. [7] used a deep neural network to predict the appropriate damping coefficient based on the location and distance information of the target point. Yang et al. [8] used an improved weighted minimum norm method. Kelemen et al. [9] used the Jacobian matrix with weights to solve joint space paths satisfying the avoidance constraints of the joint limit, kinematic singularities, and obstacles. Wang et al. [10] used an improved artificial potential field method to determine the joint velocity by the obstacles and then used the Jacobian matrix to perform a closed-loop iteration to make the end position converge to the target value. Such approaches require a way of introducing the obstacleavoidance goal into the pseudo-inverse calculation formula, which is sometimes difficult, and the methods are not universal. Therefore, some techniques that combine pseudo-inverse methods and heuristic algorithms have been proposed that use heuristic approaches to simplify the calculation of the pseudo-inverses or achieve obstacle avoidance. For example, Marcos et al. [11] used genetic algorithms and closed-loop pseudo-inverse methods for path planning and obstacle avoidance. Zhang and Wang [12] used the length of the vertical vector from the obstacle to the link and the range of the obstacle to determine whether there was a collision. Then, the inverse solution is converted into an optimization problem with inequality constraints, which can be solved with a dual neural network. Although these methods show some adaptability and scalability, they need to be combined with pseudo-inverse methods, and they rely on the decoupling characteristics of the specific mechanical structure. This makes it difficult to directly apply them to redundant manipulators, especially considering that the computational complexity increases sharply with an increase in the redundancy. Therefore, for the redundant manipulators, especially hyperredundant manipulators, some methods that are based on heuristic algorithms that do not require a pseudoinverse have been proposed. Chen et al. [13] proposed an algorithm that uses intermediate points that can avoid obstacles. The idea of the algorithm is to find an intermediate point between the starting and target points in the joint space that can avoid obstacles. The position of the intermediate point is searched by a genetic algorithm that is based on collision detection, the amount of joint motion, and the end path length. Ram et al. [14] proposed an inverse solution with obstacle avoidance based on a two-way particle swarm optimization (PSO) algorithm. The idea of this method is to fix the first and end joints of the manipulator and decouple it into two shorter manipulators at a certain joint. Afterward, the two-way PSO is used to search for the solution in the joint space. In addition, a type of “follow-the-leader” planning method for snake robots [15] can also be applied to snake-like manipulators. Conkur [16] proposed an end-following

method that uses plane analytical geometry to match the redundant manipulator and path curve. Palmer et al. [17] used the quadratic planning algorithm to match the key points of the manipulator with the discrete space curve to apply the algorithm to spatial path planning. Xiong et al. [18] used the geometric constraints between the links to solve the joint position that makes the joint motion as small as possible to obtain an inverse solution of the manipulator under a certain end position. This study proposes a cable-driven, snake-like manipulator with hyperredundant DoF to perform surveillance and detection in a complex and narrow space. It requires avoiding obstacles and the use of redundant DoF to optimize the posture to meet the other requirements, such as reducing the cable tension. Therefore, we tend to adopt a planning method based on a heuristic algorithm to improve the adaptability and scalability. To reduce the complexity, we first searched for a suitable end-guide trajectory in the workspace, and then, along this trajectory, we used a heuristic algorithm to calculate the posture of the manipulator that can avoid the obstacles. Numerous methods in the field of mobile robots can be applied when searching for the end-guide trajectory. The common method is to rasterize the environment space and use a suitable search algorithm to find a feasible path. Hart et al. [19] and Yao et al. [20] searched for the paths based on the A-star algorithm and its improved algorithm. Meanwhile, Tuncer and Yildirim [21] used genetic algorithms to search for feasible paths with the shortest path as the goal and they set the fitness function to a negative value when the path encountered obstacles. In addition, LaValle [22] proposed a rapidly exploring random tree (RRT) method that is based on random sampling. This was achieved by using tree nodes to describe the path and growing the tree with a sampling method. Furthermore, Wang et al. [23] weighted the vector pointing to the target and random direction as the growth direction, and they adjusted the weights according to the obstacles to obtain a better solution and avoidance ability. In addition, Khatib et al. [24] proposed a method based on an artificial potential field. By calculating the virtual force, the robot moves from a high potential position to a low position to complete the path search and obstacle avoidance. In general, although the described methods may achieve an obstacle-avoidance path search, the grid method is complicated in terms of calculating the large-scale 3D space, and neither the grid nor RRT method can guarantee the straightness and smoothness of the path [25]. The relatively less straight and less smooth path has no effect on the mobile robot. However, it may cause a jump in the joint space trajectory and affect the obstacle avoidance of the other joints for a hyperredundant manipulator moving along the trajectory. We adopted a trajectory search method based on an artificial potential field. For this type of method, it is often necessary to choose a reasonable attractive or repulsive coefficient [26] or function [27] to avoid problems, such as

falling into a local extreme, oscillating near obstacles, or having excessive obstacle avoidance. In this study, we provide an overview of the artificial potential field method and propose an attraction-offset method to improve the performance of the artificial potential field method. In summary, based on the established kineWe tend to adopt a matics and cable tension model, this article proplanning method based poses a path-planning method with obstacle on a heuristic algorithm to avoidance. The path of the manipulator in a improve the adaptability narrow space with obstacles is planned using and scalability. an improved artificial potential field method and the joint-following algorithm. Furthermore, cable tension optimization can be realized to reduce the maximum cable tension during the movement of the manipulator by using its redundant DoF. System Components Overview As shown in Figure 1, the robot system consists of a snakelike manipulator, cable-driven mechanism, and propulsion platform. The root of the manipulator is connected to a cabledriven mechanism, and they are placed on the propulsion platform together, where they cooperate to make the manipulator meander forward or backward like a snake to enter the depths of the narrow space. Manipulator The manipulator is composed of links and 2-DoF joints in series. It has a total of 20 DoF. The structures of the joints and links are illustrated in Figure 2. The joint adopts a design similar to that of Hooke’s hinge to achieve 2 DoF. The diameter of the joint is 60 mm, and both ends were connected to a link. Three cables were fixed on each joint to fully control its 2 DoF. The cables of all of the joints pass through the presequence joints in turn, and they finally reach the cable-driven mechanism at the root of the manipulator. Cable-Driven Mechanism Manipulator

Propulsion Platform Figure 1. The composition of the robot system.

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Yoke

Cam Bearing

Cable Hole

Connect Flange

Diamond Ring (a)

(b)

Figure 2. The structure of a single (a) joint and (b) link.

Screw Nut

Cable Seat

Trapezoidal Screw Motor

Tension Sensor Sliding Rail Figure 3. The structure of the cable driver.

Front Disk Rear Disk

Figure 4. The cable-driven mechanism.

Servo Motor

Gear Rack

Load Platform

Figure 5. The linear sliding table.

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Slideway

Cable-Driven Mechanism Each cable was independently driven by a cable driver, as shown in Figure 3. When the motor drives the lead screw to rotate, the cable seat slides back and forth to drive the cable that is fixed on it. Thirty cable drivers were divided into two circles inside and outside to form a barrel, and they constitute the entire cable-driven mechanism together with the front and rear disks, as shown in Figure 4. This layout is based on two considerations: 1) make the drive mechanism more compact and easier to install on the various pushing platforms and 2) align the cable drivers and cable holes of the joints to make the cable path more straight in the circumferential direction. Propulsion Platform To simplify the kinematics model and facilitate the production, we used a linear sliding table as the pushing platform. A linear sliding table is presented in Figure 5. Its motor can drive the sliding platform on the guide rail to move the robot back and forth. Its effective stroke is 2,000 mm so that the manipulator can be fully extended or retracted.

Path-Planning Framework The task of the manipulator is to carry an end effector (such as a camera) into a narrow space and bypass obstacles to reach the working point. The moving path from the initial to working positions cannot be obtained simply by end curve fitting or joint space planning because of the narrow space and obstacles. A path-planning algorithm with an obstacle-avoidance function is required in this case. For the hyperredundant manipulator with 20 DoF in this study, the computational complexity of the inverse solution method increases rapidly. In addition, it is difficult to find a suitable way, such as those in [9] and [10] to map the obstacle-avoidance requirement to the matrix parameters. The global search method has a large calculation amount, and the obtained postures cannot guarantee smoothness. Therefore, according to the working characteristics of the manipulator, we can decompose the path planning into stages. The typical workflow of a snake-like manipulator is to select an entry point according to the distribution of the obstacles and position of the operating point. The propulsion platform is then used to send the manipulator to the operating space. At the same time, with the redundant DoF, the

manipulator can bypass obstacles and make the end reach the working point. According to these characteristics, the manipulator needs to continuously change its posture with the cooperation of the propulsion platform to avoid obstacles. Therefore, we divided its path planning into two stages: ●●  A collision-free curve from the entry to work points was generated by a trajectory search method that was used as the guide trajectory for the end of the manipulator. ●●  The end of the manipulator moves along the aforementioned curve with a small step size, and, while forwarding, a joint-following algorithm is utilized to adjust and optimize the posture of each joint according to the obstacles and other information. Because all of the joint postures of each step in the second stage are known, the joint angles of each step can be calculated and then combined into a sequence to obtain the joint path of the entire motion. End-Guide Trajectory Search The purpose of the end trajectory search is to find a collisionfree path from the entry to working points in the workspace. This trajectory guides the actual movement of the manipulator. Therefore, two conditions should be considered: 1) the curve should stay away from the obstacles, and 2) it should be as straight as possible and smooth. Basic Idea The end-guide trajectory is a spatial curve in the workspace (Cartesian space); it should avoid all of the obstacles. To address such challenges, numerous methods can be used as references in the path-planning search of mobile robots. Among them, the artificial potential field method with direct modeling and simple calculations has attracted our attention. The artificial potential field method generally establishes an attractive potential field at the target point, and it establishes a repulsive potential field around the obstacles. As a result, each position in the entire search space has a certain potential energy. The closer it is to the target point, the lower the potential energy, and the target point is the place with the smallest potential energy, such as a basin. Around the obstacles are places with greater potential energy, such as mountain peaks. The mobile robot (moving point) begins from the starting position, and it slides down in the direction of decreasing potential energy, which is generally in the negative direction of the potential energy gradient, until it reaches the target point. In the specific implementation, it needs to configure two functions, which are usually called the attraction and repulsion functions. Their results are often interpreted as the speed to determine the direction and distance of the next move. Therefore, the configuration of these two functions has a significant influence on the search. In some cases, such as if inappropriate coefficients are used or mismatches occur between the gravitational and repulsive functions, there can be problems: the moving

point can fall into a local extreme value, oscillate near the edge of an obstacle, or show excessive obstacle avoidance. To avoid these issues, we reconsidered the basic idea of the artificial potential field method and proposed an improved method. First, according to the basic idea of the method, the target point is trying to pull the moving point, and the obstacles are trying to push it away. The combined results of these two trends The task of the manipulator can determine the next position of the moving is to carry an end effector point. The pulling of the target point is expected (such as a camera) into a to be global, whereas the pushing of obstacles is narrow space and bypass often limited to its surroundings [28]. The obstacles to reach the purpose of pulling is to move the moving point working point. toward the target point at any position, and it finally reaches the target point. Meanwhile, the purpose of pushing is to keep the moving point away from an obstacle when it is close to one. Based on these two points, we can consider that the repulsive speed can be passively generated based on the pulling speed. That is, the repulsive speed is calculated according to the pulling speed and position of the obstacle in the current local area. Therefore, the repulsive speed is only used to offset the original tendency of the moving point to move toward the obstacle. The remaining moving trends in the other directions are still generated by the pulling speed. This ensures the global requirement of advancing the moving point toward the target. Because the repulsive speed is not calculated independently, the problem of mismatching between the attraction and repulsion functions can be avoided. In addition, to allow the moving point to escape after falling into a local area, we designed a mechanism that is described as follows. When the final calculated moving speed is too small, and the current position is far from the target point, it is deemed to have fallen into a local extreme value. Then, we can increase the original pulling speed by a certain multiple until the final calculated speed reaches the requirement of escape. Improved Artificial Potential Field Method The main process of the improved artificial potential field method is illustrated in Figure 6. The initial pulling speed Vpull is calculated as follows:

d target ) Vpull_max d target # R target R = Vpull * target , (1) Vpull_max d target 2 R target

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is the speed deceleration radius of the target. The area beyond this range is considered far away from the target, so the initial pulling speed remains at its maximum. Then, according to the number of obstacles in the current area, the repulsive speed calculation is divided into two types: single and multiple obstacles. It should be noted that all of the obstacles in this study were spherical. For obstacles that consist of various shapes in practice, multiple balls were used. For a single obstacle, the repulsive speed calculation is shown in Figure 7(a). First, we can calculate the speed offset coefficient h offset as follows:

Start Calculate Initial Pull Speed Calculate Passive Repulse Speed

Calculate Final Speed

Speed Is Too Slow

Yes



Increase Weight of Pull Speed

h offset =

f c R obs - d obs m, (2) R obs - robs

where robs is the radius of the obstacle, R obs is the action range of the obstacle, d obs is the distance between the current moving point and obstacle, and the function f is a monotonically increasing function whose domain and value range are both [0,1]. Then, by decomposing the pulling speed in the direction of the repulsion, Vpull - a and Vpull - b can be obtained. l - a can be calculated According to the offset coefficient, Vpull as follows:

No Move

Reach Target Yes Stop

Figure 6. A flow chart of the improved potential field method.



l - a = ^1 - h offseth ) Vpull - a .(3) Vpull

Vpull-b

(1) Vrep-b

′ Vpull

(2)

Pobs Vpull ′ Vpull-a

(1) Vrep-a

(2) Vrep-a

Vpull-a

θ (2)

(1)

Pobs

robs (a)

(b)

Figure 7. A schematic of the passive repulsion for (a) a single obstacle and (b) multiple obstacles.

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Vpull

(2) Vrep-b

Robs

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l - a and Vpull - b yields the final pullFinally, combining Vpull l V . ing speed pull

l - a + h pull ) Vpull - b, (4) Vpulll = Vpull

where h pull is the pulling coefficient, and the initial value is one. When the final speed is too small, it gradually increases until it meets the requirements. For multiple obstacles, there are various repulsive directions, and they are often not orthogonal. If the pulling speed is still decomposed in the way described, there will be a variety of decomposition results. Therefore, we decomposed each repulsive direction according to the direction of the pulling velocity, as shown in Figure 7(b). The components Vrep - a in the direction of the pulling speed and Vrep - b, which is perpendicular to the direction of the pulling speed, are calculated by h offset ) cos (i)|V pull | h offset 1 1



|Vrep - a | = )



|Vrep - b | = h offset ) sin (i) |Vpull |, (6)

|Vpull |

h offset = 1

(5)

where i is the angle between the direction of the repulsive speed and opposite direction of the pulling speed. When considering Vrep - a for all of the obstacles, they are merged as follows:

sum) (1) (2) (n) |V (rep - a | = max (|V rep - a |, |V rep - a |, f, |V rep - a |), (7)

With regard to Vrep - b for all of the obstacles, they are merged according to the normal vector summation method:

(sum)

(1)

(2)

(n)

V rep - b = V rep - b + V rep - b + g + V rep - b .(8) The final pulling speed Vpulll can be determined as follows:



(sum)

(sum) Vpulll = Vpull + V rep - a + h pull ) V rep - b (9)

In summary, starting from the initial point, the moving point moves toward the target point step by step under the combined action of the passive repulsive and pull speeds, and it finally reaches the target point. By fitting all of the waypoints as a curve, the final guide trajectory can be obtained. Joint-Following Algorithm Basic Idea The second stage of path planning uses the end-guide trajectory and joint-following method to obtain the obstacleavoidance path. Joint following means that, when the end of the manipulator moves along the guiding trajectory, the

other joints follow in turn and avoid the obstacles. Because the manipulator can bend only at the joint, if the other joints repeat the trajectory of the end joint in the joint space, the manipulator posture in the actual workspace will have unexpected situations, such as colliding with the obstacles. At the same time, in this case, the potential flexibility of the proximal joint will be lost. Therefore, it is necessary to specially design the joint-following algorithm Xiong et al. [18] proposed an improved algorithm that moves each joint in turn according to the geometric constraints of the joints to make the movement more reasonable and flexible. This study learns from its idea and proposes the following method with the obstacle-avoidance ability, and it cooperates with the end-guide trajectory search algorithm from the previous section to complete obstacle-avoidance path planning for the hyperredundant manipulator. In addition, due to the adoption of the optimization search algorithm to move the joints, cable tension optimization can also be easily introduced as a secondary goal of path planning. By using the hyperredundancy of the manipulator, obstacle avoidance and tension optimization can be realized at the same time. Algorithm Flow The obstacle-avoidance algorithm uses the current posture of the manipulator as the initial condition and plans the new positions of each link one by one to obtain a new posture that can allow the end of the manipulator to reach the target position. When planning each link position, the following points should be considered: 1) obstacles must be avoided, 2) the amount of movement should be as small as possible, and 3) the root joint needs to meet the requirements of the propulsion platform (such as moving along a straight line). The expected position of the end of the manipulator at the beginning of the algorithm was derived from the trajectory that was searched for in the previous section. This trajectory guides the manipulator forward. Therefore, when planning, the end of the manipulator does not need to fall on this trajectory, but it allows a deviation. The joint-following algorithm is divided into the forward and reverse planning parts, as shown in Figure 8. In forward planning, the position of each link is planned from joint n to joint 1. While planning joint 1 and joint 2, whether the constraint of the sliding table can be satisfied must be considered, and, if it cannot be satisfied, reverse planning is required. The reverse planning design makes full use of the existing plan results when the position of the root joint does not meet the requirements. It adjusts the position of the root joint individually according to the current planned pose, then it reversely plans from the root to the end, and finally it checks the position of the end joint. The main process in forward planning is Jn–J3 and J2J1 planning. For Jn–J3 planning, as shown in Figure 8(b), general link or root planning must be performed according to SEPTEMBER 2022

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whether the currently planned link is within the reachable area of joint 2. The purpose of the branch judgment is to finish complete planning ahead of schedule when the currently planned joint can reach the sliding table so as to improve efficiency. For J2J1 planning, as shown in Figure 8(c), root

planning is directly carried out to try to place the end joint on the slider segment. If it fails, root-free planning is performed to execute reverse planning. As mentioned earlier, reverse planning involves planning from joint 1 to joint n. Therefore, for J1–Jn planning, as

Start

Current is Joint 2 No

Yes

J1~Jn Planning

J2J1 Planning

Jn~J3 Planning

No

Reach slider table?

Reach slider table?

End is near target?

No

Yes

No

Yes

Yes

Stop

Forward Planning

Reverse Planning

(a) Start

Joint is Within the Reach Area of J2 No

Yes

Start

Start Root Planning

Fail

General Link Planning

Root Planning

Success

Fail

Root-Free Planning

General Link Planning

Success

Stop (Reach Slider Segment)

Stop (Next Link) (b)

Stop (Reach Slider Segment)

Stop (Need Reverse Planning) (c)

Stop (Reach Slider Segment) (d)

Figure 8. Flowcharts of the joint-following algorithm: the (a) overall process and (b) Jn–J3, (c) J2J1, and (d) J1–Jn planning processes.

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shown in Figure 8(d), only general link planning is required. The core modules of the algorithm are general link, root, and root-free planning, which are explained separately in the following sections. General Link Planning Symbol Convention As shown in Figure 9, from the root to the end of the manipulator are the first joint, second joint, and up to the 11th joint. The 11th joint is at the end of the manipulator without a rotation mechanism. Their positions are represented by J(1), J(2),  …, J(11). The link between the first and second joints is the first link, and so on in a similar fashion. The position of a link is represented by the joint positions at both of its ends. The joint after link k is J (k), and the previous joint is J (k - 1) . Planning Method Consider the kth link as an example to illustrate the linkplanning method. The purpose of link planning is to deterk) k + 1) mine the new position of link k ( J (new , J (new ). As shown in Figure 10, suppose that the new position of link k + 1 has been determined in the previous planning step; its new posik + 1) (k + 2) tion is ( J (new , J new ). According to the mechanical structure, the end of link k coincides with the root of link k + 1; therefore, the new end position of link k has been determined. It only needs to find the new position of its root; that is, only k) needs to be ascertained. J (new According to the design of the joint mechanism, the angle formed by links k and k + 1 must be within the maximum k) bending angle i max of joint k + 1. Therefore, J (new can be (k + 1) located only on spherical crown M, which takes J new as the center and the extension line of link k + 1 as the axis; the cone apex angle is 2i max . From this, the work of planning the new link position is kh refined to find a suitable point on crown M as J^new . This point requires the link to meet two points: 1) avoid obstacles and 2) reduce the amount of movement as much as possible. For this problem, in terms of finding a suitable location in a certain space, an optimization search algorithm, such as the PSO or firefly algorithm, can be used. These often use a fitness function to measure how “appropriate” a location is and, then, a search strategy to find the most suitable location in the given undetermined parameter space. Therefore, for link planning in this study, the search space and fitness function must be determined Undetermined Parameters and Search Space The search target is the coordinates (X, Y, Z) of joint k in the workplace, which is generally expressed by the axis rotation angle z and bending angle i:

X = L ) sin (i) ) sin (z) * Y = L ) sin (i) ) cos (z), (10) Z = L ) cos (i)

where L is the length of the link. Considering the variables z and i, it is noted that z has a period of 2r; that is, ^i, zh and (i, z + 2r) are the same position. Therefore, if z and i are the undetermined parameters to build the search space, there may be extreme values on both sides of the space, which is not conducive to searching. Therefore, for convenience, we projected spherical crown  M onto the bottom surface of its spherical cap to obtain a projection circle, as shown in Figure 11. Any point on the projection circle corresponds to a point on spherical crown M, one by one. If x and y are points in the projection plane, then X=x

*Y = y



2

2

Z= L -x -y

Link(2)

Link(1) J (1)

, (11)

Link(3) J (3)

J (2)

2

Link(10)

J (4)

J (11)

J (10)

Figure 9. The symbols for the joints and links.

J (k+2) (k+2)

J (k+1)

J (k)

J new (k+1)

J new

Spherical Crown M

(k)

J new Figure 10. The single-link planning.

z

Spherical Crown M

θ φ

(X, Y, Z ) y

x

Projection Circle y (x, y) x Figure 11. A projection of the spherical crown.

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where (x, y) is in the following space:



{x, y | x 2 + y 2 = L2 cos 2 ^i maxh}. (12)



In this space, the extreme value of the fitness function is consistent with spherical crown M. Finally, the undetermined parameters are (x, y), and the search space is " x, y | x 2 + y 2 = L2 cos 2 (i max) , . Fitness Function The fitness function must weigh the obstacle avoidance and joint movement. For the obstacle avoidance, it can directly set the fitness to infinity when a collision is detected. However, to measure the amount of joint movement, there are different methods. For the limited root joint, we expect that, by being closer to the root joint, there will be a smaller change in the joint position during forward planning. According to [18], these requirements can be met when the joint is as close as possible to the extension line of the last position of the link. Therefore, in forward planning, fitness is defined as the angle a between ( k) k) . In the case of reverse planthe vectors J (k) J (k +1) and J J (new ning, the end joint is not as limited as the root joint, but it is still expected to be as close as possible to the last position. ( k) ( k) . Therefore, the fitness is defined as d = J J new Finally, the fitness function is a forward Q f it = * d reverse .(13) 3 collision



Collison Detection Considering that each point needs to be judged when searching for the optimal position, this study uses the following methods to simplify the calculation of the collision detection. For example, when planning the position of the kth link, obstacles that are located outside the sphere that crown M is on will definitely not collide with the kth link and can be eliminated in advance. They satisfy the following formula:

αobs βobs

γ > βobs

γ < βobs Pobs (k+1) Jnew

(k+1) Jnew

(k+2) Jnew

(k+2) Jnew

(a)

(b)

Figure 12. The collision detection for (a) angle b obs and (b) two cases of angle c.

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k +1) J (new - Pobs 2 L + robs , (14)

where Pobs is the center position of the obstacle, robs is the radius of the obstacle, and L is the length of the kth link. Then, some obstacles that are inside the sphere but still outside the cone will not collide with the kth link, and they can also be eliminated. They satisfy the following formula:

a obs - b obs

$ i max, (15)

k +1) Pobs and where a obs is the angle between the vectors J (new (k + 2) (k +1) . J new J new b obs is the angle between the kth link and the obstacle when the edge of the link is assumed to be tangential to the obstacle, as shown in Figure 12. It can be calculated as follows:



b obs = arcsin c

R link + robs , m (16) k +1) J (new Pobs

where R link is the radius of the kth link. Next, for the remaining obstacles, it is necessary to evaluk) ate whether it collides with the kth link according to J (new when searching for the optimal position. Specifically, when the following formula is satisfied, a collision occurs:

c 1 b obs (17)

k +1) (k) J new and vecwhere c is the angle between the link axis J (new (k + 1) J P . tor new obs With this technique, before the search starts, some obstacles can be eliminated, and b obs for each obstacle can be obtained. Then, b obs for the discriminant can be used to quickly detect collisions during the search. In summary, by analyzing the constraints of the mechanical structure, we converted the link planning into an optimization search and determined the suitable undetermined parameters and search space. Then, the angle or distance was used to quantify the amount of link movement while planning in different directions, and the obstacleavoidance function was realized by the collisiondetection and fitness functions.

Root Planning and Root-Free Planning The manipulator that is described in this study often needs to be used with a propulsion platform. Here, we used a linear sliding table. Because the cable-driven mechanism is fixed on the sliding table, the root of link 1, that is, joint 1, is always located on a line segment determined by the sliding table, which is called the slider segment. Its length is the effective stroke of the sliding table, and its direction is parallel to the direction of movement of the sliding table. Then, according to the constraints of the joint mechanism, it is easy to see that joint 2 should be located in a bulletshaped area with the slider segment as the axis, as shown in Figure 13. When deciding the position of link 2, the optimal position on spherical crown M should meet the following three

conditions simultaneously: 1) the link should be away from the obstacles, 2) it should be within the bullet area of J2, and 3) it should be as close as possible to the slider segment. Therefore, the fitness function is updated as ∞ collision Q fit = * ∞ not in the bullet area , (18) d slider other situation



where d slider is the distance from the position on crown M to the slider segment. Once the location of J2 is determined, it is easy to directly calculate the location of J1 through the geometric constraints. If root planning is carried out during the Jn–J3 planning, the obtained positions of J2 and J1 are actually the positions of J(m) and J (m - 1), where m $ 3. Because J (m - 1) is already on the slider segment, the positions of the remaining joints can be directly calculated along the line of the slider segment. If the point that meets these three conditions does not exist, this means that, based on the current new positions of the other links and obstacles that have been obtained, joint 1 cannot fall on the slider segment. At that time, root-free planning is required to obtain the J1 position as close as possible to the slider segment, and then reverse planning should be performed. The method of root-free planning is basically the same as that of root planning, except that the constraint that J2

must be in the bullet-shaped area is abandoned, and, after obtaining J2, it continues to search for the location of J1. In summary, for each phase of the joint-following algorithm, the fitness function is shown in Table 1, where a is the k) , d slider is the distance angle between J (k) J (k + 1) and J (k) J (new (k) from J new to the slider segment, and d is the distance from k) J (k) to J (new . Cable Tension Optimization Due to the large aspect ratio, necessity of rigidity during work, and lack of support points, the cable needs to provide a large tension. A larger tension will not only affect the control, but it will also cause a larger cable deformation and increase the end-position error. In severe cases, it may even cause accidents. Therefore, it is necessary to optimize the cable tension. According to the tension model of the manipulator, the cable tension varies with the posture [5]. The path planning of this study involves the planning of the joint posture, that is, planning the link position. Therefore, the optimization of the cable tension can be added to path planning. In path planning, the part that involves the joint posture is link planning, which is carried out step by step. In each step, the posture was determined by an optimization search. Therefore, the idea of tension optimization is to find the cable with the maximum tension of each joint according to the current posture while planning the link position. Then, we can take the goal of reducing the tension of these cables as the second goal of the optimization search.

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Table 1. The definition of Qfit in different phases. Phase Forward

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Next, we need to answer three questions: how to 1) determine which cable has a higher tension, 2) adjust the posture to reduce the tension of the specified cable, and 3) map the target of the posture adjustment into the optimization search. Each link and the two half joints that are connected to its two ends can be regarded as a rigid body. Then, the manipulator can be regarded as 10 rigid bodies that are connected in series through a diamond shaft. In our previous study, we established a cable tension model for a rigid body. As shown in Figure 14, for each rigid body, the two axes of the

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body, and T is the torque that is generated by the corresponding force. By starting from the rigid body at the end of the manipulator, solving the equation in turn, and putting the result into F1 + F2 + F3 + FS1 + FS2 = - ^FG + FP1 + FP2 + FC1 + FC2h ) , T1 + T2 + T3 + TS1 + TS2 = - ^TG + TP1 + TP2 + TC1 + FC2h the rigid body’s balance equation, this technique can solve  (19) the tension for all of the cables. Therefore, for question 1, during each step of path planning, by using the current pose where F1, F2, and F3 are the cable tensions, FG is the gravi- and (19), the relative magnitude of the current cable tension ty of the rigid body, FC1 and FC2 represent the lateral pres- can be obtained, and the largest one can be determined. sure that is generated by a cable that passes through the For question 2, in the previous work, we discovered and rigid body, FP1 and FP2 are the pressures from the dia- verified a characteristic of the cable tension according to the mond shaft of the postsequence rigid body to support it, tension model. If a rigid body rotates slightly while the size FS1 and FS2 are the support from the presequence rigid and direction of the load are almost unchanged, the change in diamond shaft can be used as the rotation axis to establish the moment balance equation:

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Figure 17. A comparison of the moving process. In each part of the figure, the postures of the dashed manipulator are obtained by normal planning, while the solid are obtained by tension-optimization planning. Posture at (a) the beginning of the path, (b) one-third of the path, (c) two-thirds of the path, and (d) the end of the path.

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Figure 19. The (a) snake-like manipulator and (b) obstacle environment.

the cable tension is positively correlated with the change in its length: when the cable becomes longer, the tension becomes larger; when the cable becomes shorter, the tension decreases. Therefore, when planning the link position, the adjustment of the posture in the direction of reducing the length of the selected cable can be used to reduce the cable tension. 120

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∞ Q fit = * ∞

For question 3, in the optimization search, the result mainly depends on the fitness function. Therefore, the goal of reducing the cable length can be achieved by constructing a new fitness function. First, under the assumption that there are no other restrictions, such as obstacles, we can calculate the root position of the link that makes the selected cable have the shortest length, defined as J t . Subsequently, in the optimization search, for the position of J new, making it closer to J t shortens the corresponding cable length. Therefore, in the fitness function, a variable that measures the distance between J new and J t can be used to represent the degree of the cable length reduction, that is, the degree of the cable tension reduction. For the fitness function of general link planning, an angle is used to represent the amount of linkage movement. To ensure the comparability of these two variables, the angle X k + 1) (k) J new and between vectors J (new (k + 1) (k) J new J t is used to represent the distance between J new and J t . Finally, the new fitness function in general link planning is as follows: forward reverse . collision (20) For root planning, because the root joint can move along the slider segment, its possible location J t is not fixed. The original fitness function uses the distance of some position to the slider segment. Thus, the distance from this position to a line is also used here to represent its proximity to J t . This line passes through J t, and it is parallel to the slider segment. Finally, during root planning, the fitness function is updated: h1 ) a + h2 ) X

Q fit = * d  ∞



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collision not in the bullet area . (21) other situation

Because any secondary goals will consume the redundancy, and the joints in the different positions have different

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(b) Figure 20. The moving process of the manipulator: the (a) normal and (b) tension-optimization paths.

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The manipulator was placed along the y-axis, and its end was placed at the origin point. The manipulator has 10 joints, and each link is 140 mm in length and 60 mm in diameter. It should be noted that the line in Figure 15 is the central axis of the links, and the diameter of the link is not shown; this is the same for subsequent figures as well. The obstacle is a cylinder that is represented by spheres; its center coordinate is (120, 430, –120), length is 60 mm, and radius is 140 mm. First, we simulated normal planning without tension optimization. The moving process of the manipulator is shown in Figure 16. The joints near the end successfully avoided the obstaSimulation and Experiment cles. The following process for the other joints was also In this section, we establish simulations and actual experi- smooth and continuous, and the path of the manipulator mental environments for obstacle-avoidance path planning. met expectations. Next, we simulated another path-planning method by Simulation using tension optimization. According to the optimization This simulation mainly verifies the functional effectiveness of method, we assume that the load of the joint does not the algorithm and effect of the tension optimization. We change significantly every time the manipulator moves. designed a real environment based on this and configured the Therefore, we enable tension optimization only of the last three joints to observe its effect. A comparison of the movobstacles as shown in Figure 15. ing process between normal planning and tension-optimization planning is shown in Figure 17. After the enabled tension optimi33 38.5 zation, the manipulator can still avoid obstacles. At the same time, the pos38 32.5 tures of the last three joints are differ0 50 100 0 50 100 ent from normal planning. The (a) (b) postures of the other joints also 20 change relative to their situations in 20 10 normal planning, which becomes more obvious after the end joint 10 0 0 50 100 0 50 100 enters the inside of the cylinder obsta(c) (d) cle. These changes show that the X in 15 20 the fitness function plays its role of 15 adjusting the postures of the joints 10 10 under the premise of satisfying obsta5 0 50 100 0 50 100 cle avoidance. In addition, it can be (e) (f) seen that tension optimization has a 10 10 negative effect on the smoothness of 5 5 the overall path. This indicates that any task that relies on posture adjust0 0 ment will “consume” the redundant 0 50 100 0 50 100 DoF of the manipulator, causing it to (g) (h) lose a certain degree of flexibility. 6 4 The tension model was also used to 4 2 estimate the maximum cable tension of 2 each joint according to the posture of 0 50 100 0 50 100 the manipulator at each step. A com(i) (j) Normalized Time parison of the path and tension-optimization paths is shown in Figure 18. Figure 21. A comparison of the actual maximum cable tension for joints (a) 1, (b) 2, When tension optimization was (c) 3, (d) 4, (e) 5, (f) 6, (g) 7, (h) 8, (i) 9, and (j) 10. The dashed line represents normal enabled, the maximum cable tensions planning, the solid line signifies the tension-optimization planning, and the horizontal line is the respective mean. of the last three joints were reduced to Tension (kgf)

requirements for the tension optimization, a different h 1 and h 2 to each joint could be presented to achieve a better balance for the flexibility and tension optimization. The tension optimization is not added to reverse planning because the highest-priority goal at that time is to make the root joint meet the constraints of the propulsion platform. In summary, when tension optimization is enabled, the fitness function in each phase of the joint-following algorithm is shown in Table 2. In addition to the parameters in Table 1, in k + 1) (k) k + 1) (k) J new and J (new Table 2, X is the angle between J (new J t , and ^kh d line is the distance from J new to the line that passes through J t and parallel to the slider segment.

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through the cylinder smoothly, and they avoided the obstacles well. The actual path of the manipulator matched the plan. Due to the tension optimization, the postures of the end joints were adjusted in comparison to those in the normal path, which, in turn, leads to the posture adjustment of their presequence The tension optimization joints. Therefore, we can see that the posture of the does not simply reduce manipulator is different for the two moving prothe tension, but, within cesses. In addition, due to the limitation of the a certain range, it makes motor speed, this also causes the tension-optithe tension distribution mization path to take a longer execution time. between the cables more Figure 21 shows the maximum tension of balanced and reasonable. each joint that is detected by the tension sensor during the two processes. Because of the difference in their execution times, to compare their tension, we normalized their times. In contrast to the simulation, the actual tension curve is significantly more complicated due to the influence of

varying degrees. This proves the effectiveness of the tensionoptimization method, and it shows that a joint following the algorithm has the ability to achieve the second goal in addition to the obstacle-avoidance goal. We also noticed that tensions increased in the middle joints. We believe that this is because, in essence, the tension that is provided by the cables must be sufficient to support the manipulator itself, and the relationship between the tension must comply with the physical balance principle. Therefore, the tension optimization does not simply reduce the tension, but, within a certain range, it makes the tension distribution between the cables more balanced and reasonable. This is conducive to improving the performance of the motor control and reducing the motor deceleration ratio to improve the efficiency. Experiment We built a snake-like manipulator with 10 joints and 20 DoF. Its arm length is 1.4 m, and an obstacle environment that is similar to the simulation was also built, as shown in Figure 19. We executed the two paths that were obtained from the previous simulation, and the moving processes of the normal and tension-optimization paths are shown in Figure 20. In both processes, the end of the manipulator moved along the expected path, and the other joints also followed it well. Similar to the simulation, the joints near the end passed

(a) Figure 22. The moving process of the manipulator without obstacles: the (a) normal and (b) tension-optimization paths. (Continued)

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friction, deformation, acceleration, and deceleration. However, it can still be observed that the tension of the three joints at the end is reduced after the optimization is enabled, which is more obvious on average. In the described experiment, both obstacle avoidance and tension optimization have impacts on the postures of the joints, and the priority of obstacle avoidance is higher; thus, to better observe the tension optimization, we conducted an experiment without obstacles. In this investigation, the normal and tensionoptimized paths were executed, and the movement trajectory of the end of the manipulator under the two paths was the same. Figure 22 shows the processes of these two paths. Although the moving target of the end of the manipulator is the same, when tension optimization is enabled, the

postures of the joints are changed as the manipulator advances. Figure 23 shows the maximum tension of each joint during the two processes. From this, we can see that the tension of the last three joints is still decreasing after tension optimization is enabled. This, once again, proves the key idea of this study: tension optimization can be performed in path planning. However, we also noticed that, after optimization is enabled, the tension of the end three joints is not always smaller, and the tension of the other joints has increased. We believe that there are several reasons for this. First, tension optimization is performed in the search for the new position of each joint; these searches are carried out in sequence, and the influence between joints is not considered during each search.

(b) Figure 22. (Continued) The moving process of the manipulator without obstacles: the (a) normal and (b) tension-optimization paths. 124

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However, for the manipulator, the force between the joints varies with the posture of each joint and tension of each cable. Second, in the implementation method of tension optimization, the specific method of adjusting the joint posture to reduce the tension has certain limitations. The positive correlation between the cable length and tension is not established at all times. In addition, the cable tension is not only related to the load and posture of the manipulator but also to its dynamic process. The tension optimization based on path planning cannot change factors other than the posture. Therefore, for cable-driven manipulators, careful consideration is required with regard to what kind of tension or tension distribution we expect to design a more comprehensive optimization method. In summary, from these simulations and experiments, the improved artificial potential field method and obstacle-avoidance-following method all reach the desired requirements and demonstrate their design features, such as better trajectory smoothness and adaptability as well as the ability to achieve the second goal while avoiding obstacles. Therefore, we believe that the obstacle-avoidance path-search algorithm in this study achieves the design goal, and it is effective for a hyperredundant, snake-like manipulator.

Acknowledgment This work was supported by the National Key Research and Development Program of China under grant 2018YFB1307400, the National Natural Science Foundation of China under grant 61873267. The authors appreciate the comments and valuable suggestions of reviewers and editors to improve the quality of the article.

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Conclusions This study proposes an obstacleavoidance path-planning method for cable-driven, hyperredundant manipulators. This method is based on the improved artificial potential field method to find the trajectory to guide the end of the manipulator. The joint-following algorithm is used to plan the path of each joint and avoid obstacles. In addition, the pathplanning method can also achieve cable tension optimization while avoiding obstacles. We carried out simulations of the path-planning method and built a 10-joint cable-driven, hyperredundant, snake-like manipulator system and performed obstacle-avoidance path-planning experiments. In the simulation and experiment, the effectiveness of the path-planning method was verified, and the effect of tension optimization was shown as well. We also noticed that path planning is broken down into the planning of each link position, which leads to a lack of global ability to perceive and adjust the manipulator’s posture. This makes it difficult for the tension-optimization algorithm to consider multiple joints at the same time and also

sometimes require multiple forward and reverse planning processes to obtain a suitable new manipulator posture. In addition, the method used to implement the tension optimization is based on the assumption that the cable length and tension are positively correlated, which limits the adaptability of the optimization method when the manipulator moves quickly and substantially. In future research, a superior method of transmitting the end joint changes to the root joints will be developed. In addition, path planning will also be performed in a global way to plan the positions of all of the joints at the same time to fully utilize the flexibility of the hyperredundant manipulator and provide a basis for better tension optimization, which determines the direction for reducing cable tension more directly.

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Dawei Xu, Department of Automation, North China Electric Power University, Baoding, 071003, China and the State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China. Email: [email protected]. En Li, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China. His current research interests include advanced robotics, sensor networks, and optical measurements. Email: [email protected]. Rui Guo, Electric Power Research Institute, State Grid Shandong Electric Power Company, Jinan, 250000, China. Email: [email protected]. Jiaxin Liu, State Grid Liaoning Electric Power Company Limited, Shenyang, 110000, China. Email: [email protected]. Zize Liang, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China. Email: [email protected].

Dual-Arm Control for Coordinated Fast Grabbing and Tossing of an Object Proposing a New Approach

By Michael Bombile

P

icking up objects and tossing them on a conveyor belt are activities generated on a daily basis in industry. These tasks are still done largely by humans. This article proposes a unified motion generator for a bimanual robotic system that enables two seven-degree-of-freedom robotic arms to grab and toss an object in one swipe. Unlike classical approaches

Digital Object Identifier 10.1109/MRA.2022.3177355 Date of current version: 3 June 2022

1070-9932/22©2022IEEE

and Aude Billard

that grab the object with quasi-zero contact velocity, the proposed approach is able to grasp the object while in motion. We control the contact forces prior to and following impact so as to stabilize the robots’ grip on the object. We show that such swift grasping speeds up the pick-and-place process and reduces energy expenditure for tossing. Continuous control of the reach, grab, and toss motion is achieved by combining a sequence of timeinvariant dynamical systems (DSs) in a single control framework. We introduce a state-dependent modulation SEPTEMBER 2022

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function to control the generated velocity in different directions. The framework is validated in simulation and on a real dual-arm system. We show that we can precisely toss objects within a workspace of 0.2 # 0.4 m 2 . Moreover, we show that the algorithm can adapt on-the-fly to changes in object location. Background on Bimanual Robot Systems Swift robot manipulation of objects in an unstructured and dynamic environment is crucial for industry. In logistics, for instance, the booming of e-commerce and its related challenges have increased the need to speed up the pace of pickand-place operations. In current applications, robots usually pick up and release the products with almost zero contact velocity. One solution to speed up the process is to move from this quasi-static approach toward a dynamic one Unlike classical approaches where robots are allowed to grab and release prodthat grab the object with ucts with nonzero contact velocities. This can quasi-zero contact velocity, be achieved by designing robot controllers that the proposed approach is are aware of induced im­­ pacts. Planning impact is able to grasp the object challenging due to noise in perception and conwhile in motion. trol. In that regards, one important aspect is to generate motion robust to imprecision as to when and how much impact is incurred. Moreover, the motion should be robust throughout the task from grabbing with impact to release, be it by placing, handing over, or tossing of the object.

(a)

(b)

Figure 1. Illustrations of a dual-arm manual and robotic pick-andplace operations. (a) A human dual-arm grabbing and placing objects in a palletizing task within a Vanderlande facility. (Source: Photo courtesy of Vanderlande.) (b) A pair of two real and simulated real KUKA LBR IIWA robots grabbing an open box (top) and an object containing a small moving object inside (bottom).

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In this article, we consider the problem of grabbing and releasing an object in one swipe with a dual-arm robotic system. The desired manipulation task is motivated by the need to perform fast pick-and-place or pick-and-toss operation in a depalletizing context (see Figure 1). Such repetitive and physically demanding work is usually performed by humans for the lack of similarly fast, precise, and robust bimanual robot systems. The bimanual tasks envisioned here extend the complexity of the control problem as it requires, in addition to controlling for impact, enforcing the coordination of the two arms. A poorly coordinated system, where one arm reaches the object before the other, would lead to uncontrolled impact. Bimanual pick-and-toss requires precise coordination before and after contact with the object. Coordination at contact ensures that the object is not set off balance at pickup. Once contact is established, the resulting interaction forces need to be controlled to ensure a stable grasp and to induce the desired velocity on the object for proper tossing. Controlling robustly coordinated motions of multiarm systems opens the door to a larger variety of tasks. Besides depalletizing, this could include manipulations that are too complex or heavy for a single robot and require two or more robotic arms. Some applications could be the fast picking up of open trays or cases, fast picking up of luggage from an airport’s conveyor belt, and so forth. Dual-arm control has been extensively studied; see, for instance, [1] for a review. Several methods have been proposed to coordinate multiple robots’ motion [2]–[4], to control simultaneously robots’ motion and forces [5]–[8], and to optimize contact forces at run time, using two robot manipulators [9], or a humanoid robot in [10], using quadratic programming (QP). All previous cited works assume that the object is already grasped by the robot and focus on the postcontact manipulation phase. The free motion phase and its transition toward the contact phase and after the contact phase for placing and tossing were not considered. A first approach to smoothly coordinate two robotic arms in freespace motion and when making simultaneous contact based on DS was proposed in our group [11]. This approach uses a virtual object to constrain and coordinate the motion of the robots. However, it did not control for force at contact. Our group extended this further in [12] to propose a DS that could generate both motion and forces for the dual-arm system. Yet these two approaches still assumed quasi-static grab with end-effector velocities vanishing as they approach the grasping points on the object. Moreover, they ignored the problem of tossing or placing the object once in hand. Recently, an impact-aware controller formulated within a QP framework was presented in [13] and was applied to dualarm grabbing of a box with a contact velocity of 0.15 m/s. This work offers a powerful approach to control impact with nonzero contact velocities. The QP scheme, however, relies on a planning of the grasping motion, making it less robust to imprecise perception or dynamic changes of the object’s pose. In our work, instead, we use as motion generators autonomous DSs for their fast and time-independent replanning

abilities and their robustness to perturbations. The bimanual coordination problem is formulated using the Extended Cooperative Task Space representation [14]. We subsequently combine this flexible planning trajectory with a QP to handle the balancing of force constraints. Assuming prior but approximate knowledge of the object’s mass and the friction coefficient, the QP generates online interaction wrenches that achieve stable grasp subject to contacts’ constraints. The scope of this article being motion generation, we leave aside the impact dynamics and assume that the associated states’ jumps remain within the robots’ limits. The interested reader is referred to [15] for the control of impact with states jump mitigation and to [13] or [16] for explicit enforcement of hardware limits during impact generation. The Proposed Approach In the considered dual-arm task, the robotic system is required to reach and swiftly grasp an object and then either toss it, by releasing it at a desired position and with a specific velocity, or place it at a desired location. A schematic illustrating the considered task is given in Figure 2, where the tasks phases are depicted. To induce the desired motion on the object when fast picking and when tossing requires that the two robots’ arms adopt the required velocity just prior to impact (for fast picking) and prior to release (when tossing). To obtain this behavior, the robot arms must transit, at contact and release time, through desired states expressed in both position and velocity simultaneously. Unlike attractors, these transitory states are not equilibrium points, and therefore, the robotic system can only transit through such states. Thus, to realize the desired task in a robust way, we proposed an approach based on modulated DSs (MDSs), where state-dependent functions shape locally the generated motion of the robot—prior to contact or

release of the object—such that the motion aligns first with the desired velocity while moving toward the desired contact or release position. Therefore, for a dual-arm system that requires coordination, to realize fast grabbing and afterward a tossing task, we formulate at the position level (the control of orientation is described in “Orientation Control”) the following MDS. xo = M (x) fn (x) + f g (x), (1)



where x = 8xxRB ! R 6 is the state vector of the DS with x L and x R representing respectively the position of the left and right robot of the dual-arm system. fn (x) ! R 6 is the nominal DS that generates the coordinated motion toward transitory attractors located in the vicinity of the desired positions. L

Orientation Control To control the orientation task, which consists of driving the current orientation of the hth end effector represented by the rotation matrix R ch ! R 3#3 toward its desired value R dh ! R 3#3, we define a state vector pih ! R 3 using the axis/angle representation of the relative orientation, d R ch _ (R dh)< R ch . Hence, p ih _ in (d R ch), where n ! R 3 and i ! R represent respectively the axis and the angle associated with the rotation matrix d R ch . With pih defined as mentioned previously, its desired h value is located at the origin, that is p i d = 0. Thus, similarly to the position task, if we assume a linear or LPV DS for the orientation, we can write po ih = A i (pih - pi d ) = A i pih, h

where A i ! R 3 # 3 is the dynamic matrix chosen to be negative definite ( A i 1 0) to ensure asymptotic converges of pih toward its attractor 0 (lim t " 3 pih = 0) . Such convergence indicates the matching R ch with R dh . The angular velocity associated with the orientation DS is obtained as follows ~ h = L p h po ih = L p h A i pih, -1

Σl

Σ ol Σ vl

where L ph _ L hin (R hc )< with L hin ! R 3 # 3 a matrix mapping the angular velocity to the time derivative of orientation state vector p h and given by [20]

Σr

Σabs Σo

Z

Σ or

Σ vr

-1

ΣW

Y

X

Figure 2. A schematics illustration of the considered dual-arm task, which can be seen as succession of two main phases: a free motion phase when reaching (red dashed line) and a constrained motion phase when in contact and executing the placing or tossing motion (blue and green dashed lines). R w and R o are the world and the object frame. R l and R r denote respectively the end-effector frames of the left and right robot, while R o l and R o r denote respectively their desired grasping configuration on the object side. R i and R o i are respectively the ith end effector’s and object’s grasp configuration frames, while R v i denotes the ith frame of a virtual or auxiliary attractor that shapes the trajectory for impact, with index (i / left, right).

L hin = I 3 # 3 - i [ n h ]# + 1- sin c i [ n h]#2 , 2 f sin c 2 i p 2 where i sin ci = sin i and [ n h ]# ! R 3 # 3 denotes a skewsymmetric matrix associated with n h . To coordinate the position and the orientation task, the latter was coupled to the position task using a statedepend coefficient h (x) function of the error on the absolute position: h (x) = 1- exp (-(v/< x abs - x abs d < + f)), where v 2 0 is a scalar that tunes how fast h (x) varies within [0, 1] . The orientation state vector [0, 1] is now computed as pih _ i n ( ) R ch ), with ) R ch _ (R )h (h))< R ch . Here R )h(h) denotes the rotation matrix computed from the spherical interpolation between a resting orientation R hr and the desired orientation R dh as function of h (x). When h (x) " 0, R )h(h) " R hr . and when h (x) " 1, R )h(h) " R dh .

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f g (x) represents the equivalent grasping force in the motion space, whereas M (x) ! R 6 # 6 is the state-dependent modulation matrix that shapes locally the motion generated by fn (x). It is defined as M (x) = E (x) K (x) E < (x) ! R 6 # 6, (2)



where E (x) ! R 6 # 6 and K (x) ! R 6 # 6 are block-diagonal matrices, respectively, of state-dependent orthonormal basis and gains for the left and right robotic arm. They are respectively defined as E (x) = diag {E L (x), E R (x)} and K (x) = diag {K L (x), K R (x)}. In E (x), each basis E h (x) = [e h1 e h2 e h3]



. xdo

eL2

xdL

→L n

eL1 eL3

! R 3 # 3 with h = {L, R} is designed such that its first vector e h1 is aligned with the intended impact direction at contact. (The direction of impact is not limited to be normal to the contact surface but can also have other orientations.) That .h .h .h is e h1 = x d / x d = x dh - x ht / x hd - x ht , where [x hd x d] denotes the desired impact or tossing state of the hth robot, and x ht is the transitory attractor defined at a distance t of x hd, such that x ht = x hd + E h (x) [- t 0 0] < . Thus, as illustrated in Figure 3 for the case of grabbing with impact, each robot is driven first toward a transitory attractor x ht before being moved with the appropriate orientation along e h1 toward x hd, the real attractor. In K (x), each robot’s gain matrix K h (x) ! R 3 # 3 has entries mr hij (x) defined as

xdR

→ nR

xo xtL

xRt eR 1

eR3 eR2

Figure 3. A geometric representation of orthonormal basis E L (x), E R (x) and an illustration of modulation region (green ellipsoid) within which the dark-red cylindrical region represents the activation of the normal distance to the vector x dh - x th .

h

mr ij (x)

=)

h

a (x) m ij (x) + (1 - a (x))

if i = j , (3) if i ! j

h

a (x) m ij (x)

where m hij (x) ! R 1 represent the state-dependent scalar terms defined in the “Stability and Convergence to Attractors” section, and a (x) ! [0, 1] activates the modulation when the robots are in the vicinity of their desired attractors. The modulation is active in a region defined by an ellipsoid along the vector x hd - x ht , as illustrated in Figure 3. To characterize the modulation, we define three activation parameters namely: d radial, d normal, and d tangent, which represent distances

0.4 α (x) = 1 xrelease xtransist xinitial x xretract

Z (m)

0.2

0

–0.2

–0.4 –0.4

–0.2 0 X (m)

0.2

0.2

0.2

0.2

0

Z (m)

Z (m)

Z (m)

0.8 0

–0.2

–0.2 –0.2

0

0.2

X (m)

0.6

0

0.4 0.2

–0.2 –0.2

0 X (m)

0.2

–0.2

0

0.2

0

X (m)

Figure 4. An example of the flow of generated motion outside and within the modulated region (thick dotted blue line), where the motion is shaped to pass through the desired release position (red dot). The activation of the modulation terms z radial (x), z normal (x), and z tangent (x) are shown respectively on the three bottom panels.

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with their origin at x ht in the basis E h (x). These distances are measured respectively in 3D, in 2D normal to e h1, and in 1D along e h1 . Accordingly, we define associated activation functions z i (x h) ! [0, 1] with i = {radial, normal, h tangent} as z i (x h) = 1/1 + e -a i (d i - Ci (x )), where C hi (x h) represents state-dependent distances of the robot given by C hi (x h) = [(x h - x ht ) < E h (x h) R i (E h (x h)) < (x h - x ht )] 1/2 . R i ! R 3 # 3 are diagonal matrices that select the considered directions of E h (x). The elements of R i are mainly zero but are one at index(es) of the desired direction(s). Hence, a (x) in (3), is designed such that a (x) = 1/2 R 2h = 1 z radial (x h). The behavior of the DS as it generates the desired motion is show in Figure 4 along with the activation of the modulation functions z i (x). Modulation-Based Coordinated Control The motion coordination of the dual-arm system, in this work, exploits the cooperative task space representation [14], which relates the states of each robot to the cooperative coordinates formed by the absolute and relative states of the dualarm system. The coordination is achieved by controlling the two robots’ cooperative coordinates and mapping the resulting motion to each robot. Thus, assuming that the nominal DS fn (x) is linear, the coordinated motion that it generates can be written as:

fn (x) = xo = T -b 1 ATb (x - x )), (4) > l A

where Tb = 6-(1I/32) I 3 I(13 /2) I 3@ ! R 6 # 6 is a matrix that maps the two robot positions (x L and x R) to the absolute position x abs ! R 3 and relative position x rel ! R 3 of the dual-arm system, such that abs L 8xxrel B = Tb 8xxRB and where I 3 is a 3 × 3 unit matrix. In (4), 6#6 A!R denotes the dynamics or gain matrix, which is negative definite (A 1 0) to ensure stability and convergence to a given attractor x ) . The coordination is thus achieved by controlling the dynamics of x abs and x rel, which amounts to controlling respectively the two robots’ joint motion and their relative displacement and thereby their synchronization. The resulting motion of x abs and x rel is then mapped through T -b 1 to each robot’s motion. The modulation shapes the behavior of the nominal DS in the region where it is active. This shaping must preserve the DS stability and convergence properties of the nominal DS fn (x) toward its equilibrium points x ) . Stability and Convergence to Attractors Based on the previous work [17] on single robot, we can state the following proposition for dual-arm system. Proposition 1 For any given state {x ! R 3 ; a (x) = 1, f nh (x) ! 0} , setting the state-dependent coefficients of the modulation matrix K h (x) as

h

m ij (x)



= (e hi ) < f mh i (x)

f nh (x) < e hj , (5) f (x) < f nh (x) h n

the motion generated by (1) will be governed by the DS f mh i (x). Moreover, if f mh i (x) is a stable linear or linear parameter-varying (LPV) DS, for instance, of the form of (4), the state x will asymptotically reach its attractor x ) while maintaining the coordination between the robots of the dual-arm system. That is, lim t " 3 x - x ) = 0. Proof: See “Proof of Proposition 1.” Generation of Impact Velocity To generate the desired grabbing impact velocities with the dual-arm system, we introduce the following proposition. Proof of Proposition 1 Substituting (5) in (2) and then in (1) and multiplying by diag " (e Li )