Shaping Impedances to Comply With Constrained Task Dynamics

Humans are capable of managing multiple tasks simultaneously. It is widely assumed that human motor control can be emulated by impedance control. To achieve human-like behavior, however, the impedance parameters of multiple tasks may vary during task execution. We propose an algorithm that shapes task impedance as a function of the robot’s time-varying inertial properties. These properties involve virtually constrained masses and virtually constrained inertias that counteract a task in order to comply with a given constraint. In this work, we not only detect task conflicts, but also show how to handle them. Our method is able to control kinematically redundant robots. We developed a damping-design method that does not interfere with our desired Cartesian task-space behavior. The control approach was verified in experiments on a real robot. We compared our impedance shaping method with two alternative control approaches: simple impedance superposition and nullspace projection. Our method preserved the passivity while improving the Cartesian task performance of an impedance controller. The method has computational advantages, beneficial to control robots with many degrees of freedom.

[1]  Alexander Dietrich,et al.  Practical Consequences of Inertia Shaping for Interaction and Tracking in Robot Control , 2021 .

[2]  Neville Hogan,et al.  Exploiting Redundancy to Facilitate Physical Interaction , 2021, IEEE Transactions on Robotics.

[3]  N. Hogan,et al.  Energy budgets for coordinate invariant robot control in physical human–robot interaction , 2021, Int. J. Robotics Res..

[4]  Mario D. Fiore,et al.  Geometrical Interpretation and Detection of Multiple Task Conflicts using a Coordinate Invariant Index , 2020, 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[5]  Ole Madsen,et al.  An Energy-based Approach for the Integration of Collaborative Redundant Robots in Restricted Work Environments , 2020, 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[6]  Jens Kober,et al.  Learning Sequential Force Interaction Skills , 2020, Robotics.

[7]  Fanny Ficuciello,et al.  The influence of coordinates in robotic manipulability analysis , 2020 .

[8]  Sami Haddadin,et al.  Power Flow Regulation, Adaptation, and Learning for Intrinsically Robust Virtual Energy Tanks , 2020, IEEE Robotics and Automation Letters.

[9]  Uwe E. Zimmermann,et al.  Physical Human-Robot Interaction under Joint and Cartesian Constraints , 2019, 2019 19th International Conference on Advanced Robotics (ICAR).

[10]  E. Burdet,et al.  The Influence of Posture, Applied Force and Perturbation Direction on Hip Joint Viscoelasticity , 2019, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[11]  Silvio Savarese,et al.  Variable Impedance Control in End-Effector Space: An Action Space for Reinforcement Learning in Contact-Rich Tasks , 2019, 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[12]  Sami Haddadin,et al.  Valve-based Virtual Energy Tanks: A Framework to Simultaneously Passify Controls and Embed Control Objectives , 2018, 2018 Annual American Control Conference (ACC).

[13]  Dagmar Sternad,et al.  Predictability, force, and (anti)resonance in complex object control. , 2018, Journal of neurophysiology.

[14]  Richard Bearee,et al.  Task-oriented rigidity optimization for 7 DOF redundant manipulators , 2017 .

[15]  Alexander Dietrich,et al.  Passive Hierarchical Impedance Control Via Energy Tanks , 2017, IEEE Robotics and Automation Letters.

[16]  Xuwei Wu,et al.  Passivation of a Hierarchical Whole-Body Controller for Humanoid Robots , 2016 .

[17]  Hermano Igo Krebs,et al.  Summary of Human Ankle Mechanical Impedance During Walking , 2016, IEEE Journal of Translational Engineering in Health and Medicine.

[18]  Ciro Natale,et al.  Industrial implementation of a multi-task redundancy resolution at velocity level for highly redundant mobile manipulators , 2016 .

[19]  Alexander Dietrich,et al.  An overview of null space projections for redundant, torque-controlled robots , 2015, Int. J. Robotics Res..

[20]  Nikolaos G. Tsagarakis,et al.  On the role of robot configuration in Cartesian stiffness control , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[21]  Neville Hogan,et al.  A General Actuator Model Based on Nonlinear Equivalent Networks , 2014, IEEE/ASME Transactions on Mechatronics.

[22]  Tadele Shiferaw Tadele Human-friendly robotic manipulators: Safety and performance issues in controller design , 2014 .

[23]  Pierre-Brice Wieber,et al.  Hierarchical quadratic programming: Fast online humanoid-robot motion generation , 2014, Int. J. Robotics Res..

[24]  Jaeheung Park,et al.  Robot Control near Singularity and Joint Limit Using a Continuous Task Transition Algorithm , 2013 .

[25]  Etienne Burdet,et al.  Human Robotics: Neuromechanics and Motor Control , 2013 .

[26]  Carme Torras,et al.  Learning Collaborative Impedance-Based Robot Behaviors , 2013, AAAI.

[27]  Jun Nakanishi,et al.  Dynamical Movement Primitives: Learning Attractor Models for Motor Behaviors , 2013, Neural Computation.

[28]  Oussama Khatib,et al.  Prioritized multi-task motion control of redundant robots under hard joint constraints , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[29]  C. Böhmer,et al.  The Geometry of Physics: An Introduction, 3rd edn., by Theodore Frankel , 2012 .

[30]  Pierre-Brice Wieber,et al.  Kinematic Control of Redundant Manipulators: Generalizing the Task-Priority Framework to Inequality Task , 2011, IEEE Transactions on Robotics.

[31]  Stefan Schaal,et al.  Learning variable impedance control , 2011, Int. J. Robotics Res..

[32]  Darwin G. Caldwell,et al.  Learning-based control strategy for safe human-robot interaction exploiting task and robot redundancies , 2010, 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[33]  Christian Ott,et al.  Cartesian Impedance Control of Redundant and Flexible-Joint Robots , 2008, Springer Tracts in Advanced Robotics.

[34]  Bojan Nemec,et al.  Compensation of velocity and/or acceleration joint saturation applied to redundant manipulator , 2007, Robotics Auton. Syst..

[35]  Oussama Khatib,et al.  A whole-body control framework for humanoids operating in human environments , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[36]  Oussama Khatib,et al.  Synthesis of Whole-Body Behaviors through Hierarchical Control of Behavioral Primitives , 2005, Int. J. Humanoid Robotics.

[37]  Stefano Chiaverini,et al.  Interaction control of robot manipulators—six‐degrees‐of‐freedom tasks, Springer Tracts in Advanced Robotics, C. Natale, B. Siciliano, O. Khatib, F. Groen (eds), Springer: Berlin, 2003, vol. 3, 108 pp. with 36 figures, Price €42.75 ISBN: 3‐540‐00159‐X , 2005 .

[38]  P. Crago,et al.  Multijoint dynamics and postural stability of the human arm , 2004, Experimental Brain Research.

[39]  Alin Albu-Schäffer,et al.  Cartesian impedance control of redundant robots: recent results with the DLR-light-weight-arms , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[40]  Wisama Khalil,et al.  Modeling, Identification and Control of Robots , 2003 .

[41]  Rieko Osu,et al.  The central nervous system stabilizes unstable dynamics by learning optimal impedance , 2001, Nature.

[42]  N Hogan,et al.  Stability in Force-Production Tasks , 2001, Journal of motor behavior.

[43]  Paolo Rocco,et al.  Impedance control for industrial robots , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[44]  Bruno Siciliano,et al.  Six-DOF impedance control based on angle/axis representations , 1999, IEEE Trans. Robotics Autom..

[45]  Jan F. Broenink,et al.  A spatial impedance controller for robotic manipulation , 1997, IEEE Trans. Robotics Autom..

[46]  E. Bizzi,et al.  The control of stable postures in the multijoint arm , 1996, Experimental Brain Research.

[47]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[48]  N. A. Borghese,et al.  Time-varying mechanical behavior of multijointed arm in man. , 1993, Journal of neurophysiology.

[49]  Neville Hogan,et al.  Integrable Solutions of Kinematic Redundancy via Impedance Control , 1991, Int. J. Robotics Res..

[50]  Jean-Jacques E. Slotine,et al.  A general framework for managing multiple tasks in highly redundant robotic systems , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[51]  David E. Hardt,et al.  Controller Design in the Physical Domain , 1989, 1989 American Control Conference.

[52]  Neville Hogan,et al.  Controller design in the physical domain (application to robot impedance control) , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[53]  Neville Hogan,et al.  On the stability of manipulators performing contact tasks , 1988, IEEE J. Robotics Autom..

[54]  T. Yoshikawa,et al.  Task-Priority Based Redundancy Control of Robot Manipulators , 1987 .

[55]  B. Faverjon,et al.  A local based approach for path planning of manipulators with a high number of degrees of freedom , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[56]  Oussama Khatib,et al.  A unified approach for motion and force control of robot manipulators: The operational space formulation , 1987, IEEE J. Robotics Autom..

[57]  Neville Hogan,et al.  The mechanics of multi-joint posture and movement control , 1985, Biological Cybernetics.

[58]  Tsuneo Yoshikawa,et al.  Manipulability of Robotic Mechanisms , 1985 .

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

[60]  Neville Hogan,et al.  Impedance Control: An Approach to Manipulation: Part III—Applications , 1985 .

[61]  H. Asada,et al.  A Geometrical Representation of Manipulator Dynamics and Its Application to Arm Design , 1983 .

[62]  Richard P. Paul,et al.  Kinematics of Robot Wrists , 1983 .

[63]  Gianluca Garofalo,et al.  Passive Energy-based Control via Energy Tanks and Release Valve for Limit Cycle and Compliance Control , 2018, SyRoCo.

[64]  Alexander Dietrich,et al.  Passivation of Projection-Based Null Space Compliance Control Via Energy Tanks , 2016, IEEE Robotics and Automation Letters.

[65]  Diana Bohm,et al.  L2 Gain And Passivity Techniques In Nonlinear Control , 2016 .

[66]  Daniel J. Duffy,et al.  Introduction to the Boost C++ libraries : vol. II - advanced libraries , 2012 .

[67]  J. Hollerbach,et al.  Time-varying stiffness of human elbow joint during cyclic voluntary movement , 2005, Experimental Brain Research.

[68]  T. Frankel The geometry of physics : an introduction , 2004 .

[69]  Stefano Stramigioli,et al.  Modeling and IPC Control of Interactive Mechanical Systems - A Coordinate-Free Approach , 2001 .

[70]  John J. Craig,et al.  Articulated hands: Force control and kinematic issues , 1981 .

[71]  Leon O. Chua,et al.  Energy concepts in the state-space theory of nonlinear n-ports: Part I-Passivity , 1981 .

[72]  J. Willems Dissipative dynamical systems part I: General theory , 1972 .

[73]  G. Schreiber,et al.  The Fast Research Interface for the KUKA Lightweight Robot , 2022 .