Optimal torque and stiffness control in compliantly actuated robots

Anthropomorphic robots that aim to approach human performance agility and efficiency are typically highly redundant not only in their kinematics but also in actuation. Variable-impedance actuators, used to drive many of these devices, are capable of modulating torque and passive impedance (stiffness and/or damping) simultaneously and independently. Here, we propose a framework for simultaneous optimisation of torque and impedance (stiffness) profiles in order to optimise task performance, tuned to the complex hardware and incorporating real-world constraints. Simulation and hardware experiments validate the viability of this approach to complex, state dependent constraints and demonstrate task performance benefits of optimal temporal impedance modulation.

[1]  Antonio Bicchi,et al.  Design and Control of a Variable Stiffness Actuator for Safe and Fast Physical Human/Robot Interaction , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[2]  Emanuel Todorov,et al.  Iterative linearization methods for approximately optimal control and estimation of non-linear stochastic system , 2007, Int. J. Control.

[3]  G. Hirzinger,et al.  A new variable stiffness design: Matching requirements of the next robot generation , 2008, 2008 IEEE International Conference on Robotics and Automation.

[4]  Alan F. Blackwell,et al.  Programming , 1973, CSC '73.

[5]  Alin Albu-Schaffer,et al.  Optimal Control for Maximizing Link Velocity of Robotic Variable Stiffness Joints , 2011 .

[6]  David Q. Mayne,et al.  Differential dynamic programming , 1972, The Mathematical Gazette.

[7]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[8]  L. Bittner L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishechenko, The Mathematical Theory of Optimal Processes. VIII + 360 S. New York/London 1962. John Wiley & Sons. Preis 90/– , 1963 .

[9]  Neville Hogan,et al.  Impedance Control: An Approach to Manipulation: Part I—Theory , 1985 .

[10]  Jack M. Winters,et al.  Analysis of Fundamental Human Movement Patterns Through the Use of In-Depth Antagonistic Muscle Models , 1985, IEEE Transactions on Biomedical Engineering.

[11]  Alin Albu-Schäffer,et al.  The DLR hand arm system , 2011, 2011 IEEE International Conference on Robotics and Automation.

[12]  Marc Toussaint,et al.  An Approximate Inference Approach to Temporal Optimization in Optimal Control , 2010, NIPS.

[13]  Yoshinori Watanabe,et al.  Antagonistic muscle-like actuator and its application to multi-d.o.f. forearm prosthesis , 1997, Adv. Robotics.

[14]  J. W. Humberston Classical mechanics , 1980, Nature.

[15]  Alin Albu-Schäffer,et al.  Optimal control for exploiting the natural dynamics of Variable Stiffness robots , 2012, 2012 IEEE International Conference on Robotics and Automation.

[16]  Neville Hogan,et al.  Impedance Control: An Approach to Manipulation , 1984, 1984 American Control Conference.

[17]  Stephen P. DeWeerth,et al.  Novel Nonlinear Elastic Actuators for Passively Controlling Robotic Joint Compliance , 2007 .

[18]  E. Bizzi,et al.  Neural, mechanical, and geometric factors subserving arm posture in humans , 1985, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[19]  M. Spong Modeling and Control of Elastic Joint Robots , 1987 .

[20]  M. L. Chambers The Mathematical Theory of Optimal Processes , 1965 .

[21]  Sethu Vijayakumar,et al.  Exploiting Variable Stiffness in Explosive Movement Tasks , 2011, Robotics: Science and Systems.

[22]  Jun Nakanishi,et al.  Exploiting Passive Dynamics with Variable Stiffness Actuation in Robot Brachiation , 2012, Robotics: Science and Systems.

[23]  Sethu Vijayakumar,et al.  Optimal variable stiffness control: formulation and application to explosive movement tasks , 2012, Auton. Robots.

[24]  W. L. Nelson Physical principles for economies of skilled movements , 1983, Biological Cybernetics.

[25]  J. Betts Survey of Numerical Methods for Trajectory Optimization , 1998 .

[26]  Joel E. Chestnutt,et al.  The Actuator With Mechanically Adjustable Series Compliance , 2010, IEEE Transactions on Robotics.

[27]  Sean R Eddy,et al.  What is dynamic programming? , 2004, Nature Biotechnology.

[28]  J. Salisbury,et al.  Active stiffness control of a manipulator in cartesian coordinates , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[29]  Bram Vanderborght,et al.  MACCEPA, the mechanically adjustable compliance and controllable equilibrium position actuator: Design and implementation in a biped robot , 2007, Robotics Auton. Syst..