Immersion and invariance control for an antagonistic joint with nonlinear mechanical stiffness

Tendon controlled robots with nonlinear mechanical tendon stiffness are becoming more and more popular. With the appropriate actuation, the joint position and the stiffness between motor and link side can be prescribed at the same time. In this paper, the modeling of tendon-driven elastic systems with nonlinear couplings is recapitulated. Based on the Immersion and Invariance (I&I) framework a control law is developed that takes trajectories of the desired joint position and the pretension as input. The contribution of this paper are the application of the I&I framework to tendon-controlled systems with variable stiffness which requires to consider the internal degrees of freedom to realize the pretension, respectively the mechanical joint stiffness. But also, and even more importantly, the handling of nonlinear transmission elements between the motor and the joint link is included. The performance and sensitivity is analyzed by simulating an antagonistically driven robot joint.

[1]  Gianluca Palli.  Model and control of tendon actuated robots , 2007 .

[2]  Donald Russell,et al.  Implementation of variable joint stiffness through antagonistic actuation using rolamite springs , 1999 .

[3]  Alessandro Astolfi,et al.  Nonlinear and adaptive control with applications , 2008 .

[4]  John Kenneth Salisbury,et al.  Mechanical bandwidth as a guideline to high-performance manipulator design , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[5]  Alin Albu-Schäffer,et al.  On the Passivity-Based Impedance Control of Flexible Joint Robots , 2008, IEEE Transactions on Robotics.

[6]  Hiroaki Kobayashi,et al.  On Tendon-Driven Robotic Mechanisms with Redundant Tendons , 1998, Int. J. Robotics Res..

[7]  S. Gruber,et al.  Robot hands and the mechanics of manipulation , 1987, Proceedings of the IEEE.

[8]  Stephen P. DeWeerth,et al.  Biologically Inspired Joint Stiffness Control , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[9]  William Towsend,et al.  The Effect of Transmission Design on Force-Controlled Manipulator Performance. , 1988 .

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

[11]  Hiroaki Kobayashi,et al.  Adaptive neural network control of tendon-driven mechanisms with elastic tendons , 2003, Autom..

[12]  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.

[13]  Bram Vanderborght,et al.  Exploiting Natural Dynamics to Reduce Energy Consumption by Controlling the Compliance of Soft Actuators , 2006, Int. J. Robotics Res..

[14]  Antonio Frisoli,et al.  A Method for Modeling and Control Complex Tendon Transmissions in Haptic Interfaces , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[15]  J. Slotine,et al.  On the Adaptive Control of Robot Manipulators , 1987 .

[16]  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.

[17]  Gerd Hirzinger,et al.  Feedback linearization and simultaneous stiffness-position control of robots with antagonistic actuated joints , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[18]  Matthew T. Mason,et al.  Robot Hands and the Mechanics of Manipulation , 1985 .

[19]  Stephen C. Jacobsen,et al.  Antagonistic control of a tendon driven manipulator , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[20]  Patrick van der Smagt,et al.  Antagonism for a Highly Anthropomorphic Hand–Arm System , 2008, Adv. Robotics.

[21]  Yoshihiko Nakamura,et al.  Skill of compliance with controlled charging/discharging of kinetic energy , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

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

[23]  Stephen C. Jacobsen,et al.  The UTAH/M.I.T. Dextrous Hand: Work in Progress , 1984 .

[24]  Alin Albu-Schäffer,et al.  Impedance control for variable stiffness mechanisms with nonlinear joint coupling , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.