Mechanically Implementable Accommodation Matrices for Passive Force Control

Robot force control implemented by means of passive mechanical devices has inherent advantages over active implementations with regard to stability, response rapidity, and physical robustness. The class of devices considered in this paper consists of a Stewart platform-type mechanism interconnected with a network of adjustable mechanical elements such as springs and dampers. The control law repertoire of such a device, imagined as a robot wrist, is given by the range of admittance matrices that it may be programmed to possess. This paper focuses on wrists incorporating damper networks for which the admittance matrices reduce to accommodation or inverse-damping matrices. We show that a hydraulic network of fully adjustable damper elements may attain any diagonally dominant accommodation matrix. We describe the technique of selecting the individual damping coefficients to design a desired matrix. We identify the set of dominant matrices as a polyhedral convex cone in the space of matrix entries, and show that each dominant matrix can be composed of a positive linear combination of a fixed set of basis matrices. The overall wrist-accommodation matrix is obtained by projecting the accommodation matrix of the damper network through the wrist kinematics. The linear combination of the dominant basis matrices projected through the wrist kinematics generates the entire space of mechanically implementable force-control laws. We quantify the versatility of mechanically implementable force-control laws by comparing this space to the space of all matrices.

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

[2]  Mark R. Cutkosky,et al.  Active Control of a Compliant Wrist in Manufacturing Tasks , 1986 .

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

[4]  Robert J. Anderson,et al.  Dynamic damping control: implementation issues and simulation results , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[5]  Neville Hogan,et al.  Stability problems in contact tasks , 1989 .

[6]  Michael A. Peshkin,et al.  Mechanical computation for passive force control , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[7]  Alain Jutard,et al.  Analysis of dynamic assembly using passive compliance , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[8]  Renjeng Su,et al.  Coupled stability characteristics of nearly passive robots , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[9]  Perry Y. Li,et al.  Passive velocity field control of mechanical manipulators , 1995, IEEE Trans. Robotics Autom..

[10]  Marcelo H. Ang,et al.  Specifying and achieving passive compliance based on manipulator structure , 1995, IEEE Trans. Robotics Autom..

[11]  Michael A. Peshkin,et al.  Synthesis and validation of nondiagonal accommodation matrices for error-corrective assembly , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[12]  Joseph Duffy,et al.  Kinestatic Control: A Novel Theory for Simultaneously Regulating Force and Displacement , 1991 .

[13]  Daniel E. Whitney,et al.  Historical Perspective and State of the Art in Robot Force Control , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

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

[15]  Michael A. Peshkin,et al.  Admittance matrix design for force-guided assembly , 1992, IEEE Trans. Robotics Autom..

[16]  Giuseppe Biorci Network and switching theory : a NATO advanced study institute , 1968 .

[17]  I. Cederbaum,et al.  A Generalization of the 'No-Amplification' Property of Resistive Networks , 1958 .

[18]  Alan S. Perelson,et al.  System Dynamics: A Unified Approach , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[19]  D. Gershon A Programmable RCC Hand , 1994 .

[20]  R. D. Hill,et al.  On the cone of positive semidefinite matrices , 1987 .

[21]  Daniel E. Whitney,et al.  Quasi-Static Assembly of Compliantly Supported Rigid Parts , 1982 .

[22]  H. Davis,et al.  Torque control of a redundantly actuated passive manipulator , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[23]  Charles A. Desoer,et al.  Basic Circuit Theory , 1969 .

[24]  J. Edward Colgate,et al.  Passive Robotics: An Exploration of Mechanical Computation , 1990, 1990 American Control Conference.

[25]  Mathukumalli Vidyasagar,et al.  Passive control of a single flexible link , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[26]  Neville Hogan,et al.  Robust control of dynamically interacting systems , 1988 .

[27]  Robert Andrew Charles The development of the passive trajectory enhancing robot , 1994 .

[28]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[29]  Josip Loncaric,et al.  Normal forms of stiffness and compliance matrices , 1987, IEEE Journal on Robotics and Automation.

[30]  Michael A. Peshkin,et al.  Programmed compliance for error corrective assembly , 1990, IEEE Trans. Robotics Autom..

[31]  J. Troccaz,et al.  An alternative to actuated robots and passive arms in medical robotics , 1993, Proceedings of the 15th Annual International Conference of the IEEE Engineering in Medicine and Biology Societ.

[32]  Wan H. Kim,et al.  Topological analysis and synthesis of communication networks , 1962 .

[33]  Shuguang Huang,et al.  A Passive Mechanism that Improves Robotic Positioning through Compliance and Constraint , 1996 .

[34]  Wyatt S. Newman,et al.  Augmented impedance control: an approach to compliant control of kinematically redundant manipulators , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[35]  Steven D. Eppinger Modeling Robot Dynamic Performance for Endpoint Force Control , 1988 .

[36]  J. Edward Colgate,et al.  Passive robots and haptic displays based on nonholonomic elements , 1996, Proceedings of IEEE International Conference on Robotics and Automation.