Editorial: Soft Robotic Modeling and Control: Bringing Together Articulated Soft Robots and Soft-Bodied Robots

Successful soft robot modeling approaches appearing in the recent literature have been based on a variety of distinct theories, including traditional robotic theory, continuum mechanics, and machine learning. Though specific modeling techniques have been developed for and validated against already realized systems, their strengths and weaknesses have not been explicitly compared against each other. In this article, we show how three distinct model structures, a lumpedparameter model, a continuum mechanical model, and a neural network, compare in capturing the gross trends and specific features of the force generation of soft robotic actuators. In particular, we study models for fiber-reinforced elastomeric enclosures (FREEs), which are a popular choice of soft actuator and that are used in several soft articulated systems, including soft manipulators, exoskeletons, grippers, and locomoting soft robots. We generated benchmark data by testing eight FREE samples that spanned broad design and kinematic spaces and compared the models on their ability to predict the loading–deformation relationships of these samples. This comparison shows the predictive capabilities of each model on individual actuators and each model’s generalizability across the design space. While the neural net achieved the highest peak performance, the first principles-based models generalized best across all actuator design parameters tested. The results highlight the essential roles of mathematical structure and experimental parameter determination in building high-performing, generalizable soft actuator models with varying effort invested in system identification.

[1]  Manfred Morari,et al.  Efficient interior point methods for multistage problems arising in receding horizon control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[2]  Jamie Paik,et al.  Modeling, Design, and Development of Soft Pneumatic Actuators with Finite Element Method   , 2016 .

[3]  J. Morimoto,et al.  Design of physical user–robot interactions for model identification of soft actuators on exoskeleton robots , 2019, Int. J. Robotics Res..

[4]  Dmitry Berenson,et al.  Improving Soft Pneumatic Actuator fingers through integration of soft sensors, position and force control, and rigid fingernails , 2016, 2016 IEEE International Conference on Robotics and Automation (ICRA).

[5]  Antonio Bicchi,et al.  Compliant design for intrinsic safety: general issues and preliminary design , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[6]  N. N. Ansari,et al.  The interrater and intrarater reliability of the Modified Ashworth Scale in the assessment of muscle spasticity: limb and muscle group effect. , 2008, NeuroRehabilitation.

[7]  Agamemnon Krasoulis,et al.  Model-based control of individual finger movements for prosthetic hand function , 2019, bioRxiv.

[8]  Daniela Rus,et al.  Dynamics and trajectory optimization for a soft spatial fluidic elastomer manipulator , 2016, Int. J. Robotics Res..

[9]  Christopher D. Rahn,et al.  Design of an artificial muscle continuum robot , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[10]  Christopher G. Atkeson,et al.  Physical human interaction for an inflatable manipulator , 2011, 2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[11]  Cecilia Laschi,et al.  Neural Network and Jacobian Method for Solving the Inverse Statics of a Cable-Driven Soft Arm With Nonconstant Curvature , 2015, IEEE Transactions on Robotics.

[12]  Antonio Bicchi,et al.  Optimality principles in variable stiffness control: The VSA hammer , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[13]  Jonathan Rossiter,et al.  Bodily Aware Soft Robots: Integration of Proprioceptive and Exteroceptive Sensors , 2017, ICRA.

[14]  Stephen P. Boyd,et al.  CVXGEN: a code generator for embedded convex optimization , 2011, Optimization and Engineering.

[15]  W. H. Bowers,et al.  Anatomy of the proximal interphalangeal joint. , 1994, Hand clinics.

[16]  Paolo Dario,et al.  Soft Robot Arm Inspired by the Octopus , 2012, Adv. Robotics.

[17]  Kamran Mohseni,et al.  Controlling the deformation space of soft membranes using fiber reinforcement , 2020, Int. J. Robotics Res..

[18]  Shinji Doki,et al.  Sensorless control of permanent-magnet synchronous motors using online parameter identification based on system identification theory , 2006, IEEE Transactions on Industrial Electronics.

[19]  Arnau Garriga-Casanovas,et al.  Energy-shaping control of soft continuum manipulators with in-plane disturbances , 2020, Int. J. Robotics Res..

[20]  M. Chen,et al.  An intention driven hand functions task training robotic system , 2010, 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology.

[21]  Filip Ilievski,et al.  Soft robotics for chemists. , 2011, Angewandte Chemie.

[22]  Hao-Chi Chang,et al.  Sliding mode control on electro-mechanical systems , 1999 .

[23]  Useok Jeong,et al.  Reliability analysis of a tendon-driven actuation for soft robots , 2020, Int. J. Robotics Res..

[24]  Manuel G. Catalano,et al.  On the motion/stiffness decoupling property of articulated soft robots with application to model-free torque iterative learning control , 2020, Int. J. Robotics Res..

[25]  Charles C. Kemp,et al.  Model predictive control for fast reaching in clutter , 2016, Auton. Robots.

[26]  Jing Wang,et al.  Hand Rehabilitation Robotics on Poststroke Motor Recovery , 2017, Behavioural neurology.

[27]  Marc D. Killpack,et al.  Configuration Estimation for Accurate Position Control of Large-Scale Soft Robots , 2019, IEEE/ASME Transactions on Mechatronics.

[28]  Robert J. Wood,et al.  Modeling of Soft Fiber-Reinforced Bending Actuators , 2015, IEEE Transactions on Robotics.

[29]  Girish Krishnan,et al.  Designing systems of fiber reinforced pneumatic actuators using a pseudo-rigid body model , 2017, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[30]  William Harwin,et al.  Error correction movement for machine assisted stroke rehabilitation , 2001 .

[31]  Samia Nefti-Meziani,et al.  Novel Design of a Soft Lightweight Pneumatic Continuum Robot Arm with Decoupled Variable Stiffness and Positioning , 2017, Soft robotics.

[32]  Rashid K. Abu Al-Rub,et al.  Design and prototyping soft–rigid tendon-driven modular grippers using interpenetrating phase composites materials , 2020, Int. J. Robotics Res..

[33]  Adriano Fagiolini,et al.  Decoupled nonlinear adaptive control of position and stiffness for pneumatic soft robots , 2020, Int. J. Robotics Res..

[34]  M Giorelli,et al.  Hybrid parameter identification of a multi-modal underwater soft robot , 2017, Bioinspiration & biomimetics.

[35]  David Wingate,et al.  Learning nonlinear dynamic models of soft robots for model predictive control with neural networks , 2018, 2018 IEEE International Conference on Soft Robotics (RoboSoft).

[36]  Jérémie Dequidt,et al.  Kinematic modeling and observer based control of soft robot using real-time Finite Element Method , 2016, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[37]  Neville Hogan,et al.  Impedance Control: An Approach to Manipulation: Part II—Implementation , 1985 .

[38]  W. Harwin,et al.  Using haptics technology to deliver motivational therapies in stroke patients: concepts and initial pilot studies , 2001 .

[39]  Barbara Mazzolai,et al.  The softness distribution index: towards the creation of guidelines for the modeling of soft-bodied robots , 2019, Int. J. Robotics Res..

[40]  Xiangrong Shen,et al.  Simultaneous Force and Stiffness Control of a Pneumatic Actuator , 2007 .

[41]  H. Taghirad,et al.  Nonlinear Control , 2021, Control Theory for Physicists.

[42]  Jennifer K. W. Chesnutt,et al.  Artery Buckling: New Phenotypes, Models, and Applications , 2012, Annals of Biomedical Engineering.

[43]  Mats Jackson,et al.  Bending angle prediction and control of soft pneumatic actuators with embedded flex sensors: a data-driven approach , 2017 .

[44]  C. Walsh,et al.  A soft robotic exosuit improves walking in patients after stroke , 2017, Science Translational Medicine.

[45]  Javad Taghia,et al.  Position Control of Soft-Robots with Rotary-Type Pneumatic Actuators , 2012, ROBOTIK.

[46]  E. G. Cruz,et al.  Weakness is the primary contributor to finger impairment in chronic stroke. , 2006, Archives of physical medicine and rehabilitation.

[47]  William Harwin,et al.  A novel method for computing natural path for robot assisted movements in synthetic worlds , 2001 .

[48]  Pierre Lopez,et al.  Modeling and control of McKibben artificial muscle robot actuators , 2000 .

[49]  Christopher G. Atkeson,et al.  Robots with inflatable links , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[50]  Iqbal Husain,et al.  Online Parameter Estimation and Adaptive Control of Permanent-Magnet Synchronous Machines , 2010, IEEE Transactions on Industrial Electronics.

[51]  Cecilia Laschi,et al.  Soft robot perception using embedded soft sensors and recurrent neural networks , 2019, Science Robotics.

[52]  Alin Albu-Schäffer,et al.  The DLR lightweight robot: design and control concepts for robots in human environments , 2007, Ind. Robot.

[53]  Hao Jiang,et al.  Model-free control for soft manipulators based on reinforcement learning , 2017, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[54]  Tianmiao Wang,et al.  A soft manipulator for efficient delicate grasping in shallow water: Modeling, control, and real-world experiments , 2020, Int. J. Robotics Res..

[55]  Daniela Rus,et al.  Whole arm planning for a soft and highly compliant 2D robotic manipulator , 2014, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[56]  Sungho Jo,et al.  Deep Full-Body Motion Network for a Soft Wearable Motion Sensing Suit , 2019, IEEE/ASME Transactions on Mechatronics.

[57]  Erwin-Christian Lovasz,et al.  New Advances in Mechanisms, Transmissions and Applications , 2014 .

[58]  Kostas E. Bekris,et al.  Adaptive tensegrity locomotion: Controlling a compliant icosahedron with symmetry-reduced reinforcement learning , 2019, Int. J. Robotics Res..

[59]  Marc D. Killpack,et al.  Comparing model-based control methods for simultaneous stiffness and position control of inflatable soft robots , 2020, Int. J. Robotics Res..

[60]  Alin Albu-Schäffer,et al.  The KUKA-DLR Lightweight Robot arm - a new reference platform for robotics research and manufacturing , 2010, ISR/ROBOTIK.

[61]  Zheng Li,et al.  Robotic Glove with Soft-Elastic Composite Actuators for Assisting Activities of Daily Living. , 2019, Soft robotics.

[62]  Ian D. Walker,et al.  Field trials and testing of the OctArm continuum manipulator , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[63]  Fionnuala Connolly,et al.  Automatic design of fiber-reinforced soft actuators for trajectory matching , 2016, Proceedings of the National Academy of Sciences.

[64]  Juš Kocijan,et al.  Modelling and Control of Dynamic Systems Using Gaussian Process Models , 2015 .

[65]  L. Cooper,et al.  When Networks Disagree: Ensemble Methods for Hybrid Neural Networks , 1992 .

[66]  Arianna Menciassi,et al.  Feedback Control of Soft Robot Actuators via Commercial Flex Bend Sensors , 2017, IEEE/ASME Transactions on Mechatronics.

[67]  Yuval Tassa,et al.  Infinite-Horizon Model Predictive Control for Periodic Tasks with Contacts , 2011, Robotics: Science and Systems.

[68]  Wolfram Burgard,et al.  The limits and potentials of deep learning for robotics , 2018, Int. J. Robotics Res..

[69]  TrimmerBarry Soft Robot Control Systems: A New Grand Challenge? , 2014 .

[70]  C. David Remy,et al.  Nonlinear System Identification of Soft Robot Dynamics Using Koopman Operator Theory , 2018, 2019 International Conference on Robotics and Automation (ICRA).

[71]  E. A. Susanto,et al.  The effects of post-stroke upper-limb training with an electromyography (EMG)-driven hand robot. , 2013, Journal of electromyography and kinesiology : official journal of the International Society of Electrophysiological Kinesiology.

[72]  W. Rymer,et al.  Extrinsic flexor muscles generate concurrent flexion of all three finger joints. , 2002, Journal of biomechanics.

[73]  Edward C. Smith,et al.  Fluidic Composite Tunable Vibration Isolators , 2010 .

[74]  Kody M. Powell,et al.  Nonlinear modeling, estimation and predictive control in APMonitor , 2014, Comput. Chem. Eng..

[75]  Brian Byunghyun Kang,et al.  Exo-Glove: A Wearable Robot for the Hand with a Soft Tendon Routing System , 2015, IEEE Robotics & Automation Magazine.

[76]  Jiping He,et al.  RUPERT: An exoskeleton robot for assisting rehabilitation of arm functions , 2008, 2008 Virtual Rehabilitation.

[77]  Evren Samur,et al.  Quasi-static modeling of a novel growing soft-continuum robot , 2019, Int. J. Robotics Res..

[78]  S. Shankar Sastry,et al.  Decentralized nonlinear model predictive control of multiple flying robots , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[79]  Marc D. Killpack,et al.  Simultaneous position and stiffness control for an inflatable soft robot , 2016, 2016 IEEE International Conference on Robotics and Automation (ICRA).

[80]  Xiaoping Chen,et al.  Hierarchical control of soft manipulators towards unstructured interactions , 2021, Int. J. Robotics Res..

[81]  Jay H. Lee,et al.  Model predictive control technique combined with iterative learning for batch processes , 1999 .

[82]  Marc D. Killpack,et al.  Control of a pneumatically actuated, fully inflatable, fabric-based, humanoid robot , 2015, 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids).

[83]  Ruxu Du,et al.  Design and Analysis of a Bio-Inspired Wire-Driven Multi-Section Flexible Robot , 2013 .

[84]  Kaspar Althoefer,et al.  TMTDyn: A Matlab package for modeling and control of hybrid rigid–continuum robots based on discretized lumped systems and reduced-order models , 2020, Int. J. Robotics Res..

[85]  R. Ogden,et al.  A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models , 2000 .

[86]  Robert J. Wood,et al.  Soft Robotic Grippers for Biological Sampling on Deep Reefs , 2016, Soft robotics.

[87]  Girish Chowdhary,et al.  Open Loop Position Control of Soft Continuum Arm Using Deep Reinforcement Learning , 2018, 2019 International Conference on Robotics and Automation (ICRA).

[88]  Antonio Bicchi,et al.  Adaptive simultaneous position and stiffness control for a soft robot arm , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[89]  S. M. Hadi Sadati,et al.  Mechanics of Continuum Manipulators, a Comparative Study of Five Methods with Experiments , 2017, TAROS.

[90]  Robert J. Wood,et al.  Soft robotic glove for combined assistance and at-home rehabilitation , 2015, Robotics Auton. Syst..

[91]  L. Der-Yeghiaian,et al.  Robot-based hand motor therapy after stroke. , 2007, Brain : a journal of neurology.

[92]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[93]  R. Brent Gillespie,et al.  Comparison and experimental validation of predictive models for soft, fiber-reinforced actuators , 2019, Int. J. Robotics Res..

[94]  Gamini Dissanayake,et al.  Planning under uncertainty using model predictive control for information gathering , 2006, Robotics Auton. Syst..

[95]  Kevin C. Galloway,et al.  Interaction Forces of Soft Fiber Reinforced Bending Actuators , 2017, IEEE/ASME Transactions on Mechatronics.

[96]  Xiangjie Liu,et al.  Feedback-Assisted Iterative Learning Model Predictive Control with Nonlinear Fuzzy Model , 2014 .

[97]  Jamie Paik,et al.  Soft pneumatic actuator-driven origami-inspired modular robotic “pneumagami” , 2020, Int. J. Robotics Res..

[98]  Yi Sun,et al.  A Fully Fabric-Based Bidirectional Soft Robotic Glove for Assistance and Rehabilitation of Hand Impaired Patients , 2017, IEEE Robotics and Automation Letters.

[99]  Marc D. Killpack,et al.  Real-time evolutionary model predictive control using a graphics processing unit , 2017, 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids).

[100]  William C. Messner,et al.  The design and development of Branch Bot: a branch-crawling, caterpillar-inspired, soft robot , 2019, Int. J. Robotics Res..

[101]  Lakmal Seneviratne,et al.  A unified multi-soft-body dynamic model for underwater soft robots , 2018, Int. J. Robotics Res..

[102]  Robert J. Webster,et al.  Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review , 2010, Int. J. Robotics Res..

[103]  Luis Moreno,et al.  Hand Exo-Muscular System for Assisting Astronauts During Extravehicular Activities. , 2019, Soft robotics.

[104]  A. Timmermans,et al.  Technology-assisted training of arm-hand skills in stroke: concepts on reacquisition of motor control and therapist guidelines for rehabilitation technology design , 2009, Journal of NeuroEngineering and Rehabilitation.

[105]  Kevin J. MacKenzie,et al.  Finger length and distal finger extent patterns in humans. , 2002, American journal of physical anthropology.

[106]  Oliver Brock,et al.  A novel type of compliant and underactuated robotic hand for dexterous grasping , 2016, Int. J. Robotics Res..

[107]  Edward M Chapman,et al.  Modeling and analysis of hydraulic piston actuation of McKibben fluidic artificial muscles for hand rehabilitation , 2019, Int. J. Robotics Res..

[108]  Charles Mansel Best,et al.  Position and Stiffness Control of Inflatable Robotic Links Using Rotary Pneumatic Actuation , 2016 .

[109]  Maarten Steinbuch,et al.  Learning-based identification and iterative learning control of direct-drive robots , 2005, IEEE Transactions on Control Systems Technology.

[110]  Vadim I. Utkin,et al.  A control engineer's guide to sliding mode control , 1999, IEEE Trans. Control. Syst. Technol..

[111]  W. T. Dempster,et al.  SPACE REQUIREMENTS OF THE SEATED OPERATOR, GEOMETRICAL, KINEMATIC, AND MECHANICAL ASPECTS OF THE BODY WITH SPECIAL REFERENCE TO THE LIMBS , 1955 .

[112]  Zheng Li,et al.  Model-based online learning and adaptive control for a “human-wearable soft robot” integrated system , 2019, Int. J. Robotics Res..

[113]  E. A. Susanto,et al.  Efficacy of robot-assisted fingers training in chronic stroke survivors: a pilot randomized-controlled trial , 2015, Journal of NeuroEngineering and Rehabilitation.

[114]  Kohei Nakajima,et al.  Algebraic approach towards the exploitation of “softness”: the input–output equation for morphological computation , 2020, Int. J. Robotics Res..

[115]  Callie Branyan,et al.  Soft Snake Robots: Investigating the Effects of Gait Parameters on Locomotion in Complex Terrains , 2018, 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[116]  Alin Albu-Schäffer,et al.  Robots Driven by Compliant Actuators: Optimal Control Under Actuation Constraints , 2013, IEEE Transactions on Robotics.

[117]  Manuel G. Catalano,et al.  Variable impedance actuators: A review , 2013, Robotics Auton. Syst..

[118]  Sami Haddadin,et al.  Antagonistic Impedance Control for Pneumatically Actuated Robot Joints , 2016, IEEE Robotics and Automation Letters.

[119]  Lawrence F. Shampine,et al.  The MATLAB ODE Suite , 1997, SIAM J. Sci. Comput..

[120]  C. David Remy,et al.  Force Generation by Parallel Combinations of Fiber-Reinforced Fluid-Driven Actuators , 2018, IEEE Robotics and Automation Letters.

[121]  F Gomes de Almeida,et al.  Reduced-Order Thermodynamic Models for Servo-Pneumatic Actuator Chambers , 2006 .

[122]  Cecilia Laschi,et al.  Model-Based Reinforcement Learning for Closed-Loop Dynamic Control of Soft Robotic Manipulators , 2019, IEEE Transactions on Robotics.

[123]  A. Banerjee,et al.  Large deflection of cantilever beams with geometric non-linearity: Analytical and numerical approaches , 2008 .

[124]  Jérémie Dequidt,et al.  Software toolkit for modeling, simulation, and control of soft robots , 2017, Adv. Robotics.

[125]  Christian Duriez,et al.  Fast, Generic, and Reliable Control and Simulation of Soft Robots Using Model Order Reduction , 2018, IEEE Transactions on Robotics.

[126]  Hong Ren Wu,et al.  A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators , 1994, IEEE Trans. Autom. Control..

[127]  Behzad Taheri,et al.  Force and Stiffness Backstepping-Sliding Mode Controller for Pneumatic Cylinders , 2014, IEEE/ASME Transactions on Mechatronics.

[128]  Sridhar Kota,et al.  A Continuum Model for Fiber-Reinforced Soft Robot Actuators , 2018 .

[129]  Ian D. Walker,et al.  A Neural Network Controller for Continuum Robots , 2007, IEEE Transactions on Robotics.

[130]  Cecilia Laschi,et al.  Control Strategies for Soft Robotic Manipulators: A Survey. , 2018, Soft robotics.

[131]  Hui Yang,et al.  A soft manipulator for efficient delicate grasping in shallow water: Modeling, control, and real-world experiments: , 2020 .

[132]  Wesley Roozing,et al.  An efficient leg with series–parallel and biarticular compliant actuation: design optimization, modeling, and control of the eLeg , 2019, Int. J. Robotics Res..

[133]  Silvia Appendino,et al.  Human Finger Kinematics and Dynamics , 2014 .

[134]  Alin Albu-Schäffer,et al.  A Unified Passivity-based Control Framework for Position, Torque and Impedance Control of Flexible Joint Robots , 2007, Int. J. Robotics Res..

[135]  F. G. Martins Tuning PID Controllers using the ITAE Criterion * , 2022 .

[136]  Christian Duriez,et al.  Control Design for Soft Robots Based on Reduced-Order Model , 2019, IEEE Robotics and Automation Letters.

[137]  William S. Harwin,et al.  Minimum Jerk Trajectory Control for Rehabilitation and Haptic Applications , 2002, ICRA.

[138]  Stefan Schulz,et al.  Compliant Robotics and Automation with Flexible Fluidic Actuators and Inflatable Structures , 2012 .

[139]  Daniel P. Ferris,et al.  'Body-in-the-Loop' Optimization of Assistive Robotic Devices: A Validation Study , 2016, Robotics: Science and Systems.

[140]  Jessica Burgner-Kahrs,et al.  Tendon-driven continuum robots with extensible sections—A model-based evaluation of path-following motions , 2019, Int. J. Robotics Res..

[141]  Sridhar Kota,et al.  Design and Modeling of Generalized Fiber-Reinforced Pneumatic Soft Actuators , 2015, IEEE Transactions on Robotics.

[142]  Jack A. Jones,et al.  Inflatable robotics for planetary applications , 2001 .

[143]  Simona Celi,et al.  Modeling biomechanical interaction between soft tissue and soft robotic instruments: importance of constitutive anisotropic hyperelastic formulations , 2020, Int. J. Robotics Res..

[144]  Geoffrey A. Hollinger,et al.  A generalizable equilibrium model for bending soft arms with longitudinal actuators , 2019, Int. J. Robotics Res..

[145]  Stephen P. Boyd,et al.  OSQP: an operator splitting solver for quadratic programs , 2017, 2018 UKACC 12th International Conference on Control (CONTROL).

[146]  E. Burdet,et al.  Robot-assisted rehabilitation of hand function. , 2010, Current opinion in neurology.

[147]  F. Miyazaki,et al.  Bettering operation of dynamic systems by learning: A new control theory for servomechanism or mechatronics systems , 1984, The 23rd IEEE Conference on Decision and Control.

[148]  R. Ham,et al.  Compliant actuator designs , 2009, IEEE Robotics & Automation Magazine.

[149]  Cagdas D. Onal,et al.  Design and control of a soft and continuously deformable 2D robotic manipulation system , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[150]  Sridhar Kota,et al.  Model based control of fiber reinforced elastofluidic enclosures , 2017, 2017 IEEE International Conference on Robotics and Automation (ICRA).

[151]  J. Edward Colgate,et al.  Design of components for programmable passive impedance , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[152]  Kyungwoo Lee Large deflections of cantilever beams of non-linear elastic material under a combined loading , 2002 .

[153]  Manuel G. Catalano,et al.  Adaptive synergies for the design and control of the Pisa/IIT SoftHand , 2014, Int. J. Robotics Res..

[154]  Daniela Rus,et al.  Design, kinematics, and control of a soft spatial fluidic elastomer manipulator , 2016, Int. J. Robotics Res..

[155]  Mariangela Manti,et al.  Multiobjective Optimization for Stiffness and Position Control in a Soft Robot Arm Module , 2018, IEEE Robotics and Automation Letters.

[156]  Phil F. Culverhouse,et al.  Robust Adaptive Control of an Uninhabited Surface Vehicle , 2015, J. Intell. Robotic Syst..

[157]  Filip Ilievski,et al.  Multigait soft robot , 2011, Proceedings of the National Academy of Sciences.

[158]  R. Ogden Non-Linear Elastic Deformations , 1984 .

[159]  Oleg Ivlev Soft fluidic actuators of rotary type for safe physical human-machine interaction , 2009, 2009 IEEE International Conference on Rehabilitation Robotics.

[160]  Hai-Chao Han,et al.  Artery buckling analysis using a four-fiber wall model. , 2014, Journal of biomechanics.

[161]  Steven Laureys,et al.  Spasticity after stroke: Physiology, assessment and treatment , 2013, Brain injury.

[162]  Sheng Quan Xie,et al.  Accurate multivariable arbitrary piecewise model regression of McKibben and Peano muscle static and damping force behavior , 2018, Smart Materials and Structures.

[163]  Cosimo Della Santina,et al.  Using Nonlinear Normal Modes for Execution of Efficient Cyclic Motions in Soft Robots , 2018, ArXiv.

[164]  Walter F. Mascarenhas,et al.  The divergence of the BFGS and Gauss Newton methods , 2013, Math. Program..

[165]  Stephen P. Boyd,et al.  Fast Model Predictive Control Using Online Optimization , 2010, IEEE Transactions on Control Systems Technology.

[166]  J. R. Cueli,et al.  Iterative nonlinear model predictive control. Stability, robustness and applications , 2008 .

[167]  Radhika Nagpal,et al.  Design and control of a bio-inspired soft wearable robotic device for ankle–foot rehabilitation , 2014, Bioinspiration & biomimetics.

[168]  Elizabeth T Hsiao-Wecksler,et al.  Design and analysis of coiled fiber reinforced soft pneumatic actuator , 2018, Bioinspiration & biomimetics.

[169]  Helmut Hauser,et al.  Morphologically induced stability on an underwater legged robot with a deformable body , 2019 .

[170]  D. Rus,et al.  Design, fabrication and control of soft robots , 2015, Nature.

[171]  Chi Wang,et al.  Engineering with rubber - how to design rubber components - 2nd edition , 1992 .

[172]  Zhi Qiang Tang,et al.  A Novel Iterative Learning Model Predictive Control Method for Soft Bending Actuators , 2019, 2019 International Conference on Robotics and Automation (ICRA).

[173]  K. Tong,et al.  Sensorimotor Control of Tracking Movements at Various Speeds for Stroke Patients as Well as Age-Matched and Young Healthy Subjects , 2015, PloS one.

[174]  Jamie Paik,et al.  Soft Pneumatic Actuator Fascicles for High Force and Reliability , 2017, Soft robotics.

[175]  Marc D. Killpack,et al.  Comparison of linearized dynamic robot manipulator models for model predictive control , 2017, 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids).

[176]  Matthew M. Williamson,et al.  Series elastic actuators , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[177]  Cosimo Della Santina,et al.  Dynamic control of soft robots interacting with the environment , 2018, 2018 IEEE International Conference on Soft Robotics (RoboSoft).

[178]  S. Kirker,et al.  A new electromechanical trainer for sensorimotor rehabilitation of paralysed fingers: A case series in chronic and acute stroke patients , 2008, Journal of NeuroEngineering and Rehabilitation.

[179]  Claire J. Tomlin,et al.  Learning-based model predictive control on a quadrotor: Onboard implementation and experimental results , 2012, 2012 IEEE International Conference on Robotics and Automation.

[180]  Gaurav Singh,et al.  Parameter estimation and modeling of a pneumatic continuum manipulator with asymmetric building blocks , 2018, 2018 IEEE International Conference on Soft Robotics (RoboSoft).

[181]  Edward M Chapman,et al.  Modeling and analysis of hydraulic piston actuation of McKibben fluidic artificial muscles for hand rehabilitation , 2019 .

[182]  Siddharth Sanan,et al.  Pneumatic Torsional Actuators for Inflatable Robots , 2014 .

[183]  Mariangela Manti,et al.  Stiffening in Soft Robotics: A Review of the State of the Art , 2016, IEEE Robotics & Automation Magazine.

[184]  Marc D. Killpack,et al.  A New Soft Robot Control Method: Using Model Predictive Control for a Pneumatically Actuated Humanoid , 2016, IEEE Robotics & Automation Magazine.

[185]  Antonio Bicchi,et al.  Fast and "soft-arm" tactics [robot arm design] , 2004, IEEE Robotics & Automation Magazine.

[186]  Marc D. Killpack,et al.  Comparing Model Predictive Control and input shaping for improved response of low-impedance robots , 2015, 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids).

[187]  Axel Graser,et al.  Modeling and Control of Fluidic Robotic Joints with natural compliance , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[188]  Mark W. Tibbitt,et al.  Matryoshka-Inspired Micro-Origami Capsules to Enhance Loading, Encapsulation, and Transport of Drugs. , 2019, Soft robotics.

[189]  P. Parks,et al.  Liapunov redesign of model reference adaptive control systems , 1966 .

[190]  Marc D. Killpack,et al.  Model Predictive Control for Pneumatically Actuated Soft Robots , 2016 .

[191]  N. Hogan An organizing principle for a class of voluntary movements , 1984, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[192]  Jochen J. Steil,et al.  Hybrid Analytical and Data-Driven Modeling for Feed-Forward Robot Control † , 2017, Sensors.

[193]  Hong Kai Yap,et al.  Design of a Soft Robotic Glove for Hand Rehabilitation of Stroke Patients with Clenched Fist Deformity using Inflatable Plastic Actuators , 2016 .