Repeatable Redundant Manipulator Control Using Nullspace Quasivelocities

This paper presents a repeatable control scheme for redundant manipulators. It is developed in terms of physically meaningful variables, a concept closely related to integrability and homogeneity. This approach sheds a different light on some well-known phenomena related to redundant manipulator control. The control is developed by determining enough physically meaningful variables to describe the manipulator's motions in the task and nullspaces, in a manner that allows them to be controlled independently. These variables are then used to develop physically meaningful controller error signals. As a consequence, all configurations in the workspace are repeatable, except for those at, or very close, to a kinematic singularity. The approach is illustrated on a 6DOF planar manipulator.

[1]  A. A. Maciejewski,et al.  Obstacle Avoidance , 2005 .

[2]  Christine Chevallereau,et al.  Efficient method for the calculation of the pseudo inverse kinematic problem , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[3]  Yong-San Yoon,et al.  Trajectory planning of redundant robots by maximizing the moving acceleration radius , 1992, Robotica.

[4]  J. Hollerbach,et al.  Programming and control of kinematically redundant manipulators , 1984, The 23rd IEEE Conference on Decision and Control.

[5]  A. Liegeois,et al.  Automatic supervisory control of the configuration and behavior of multi-body mechanisms , 1977 .

[6]  François G. Pin,et al.  Resolving kinematic redundancy with constraints using the FSP (full space parameterization) approach , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[7]  Giuseppe Oriolo,et al.  Nonholonomic behavior in redundant robots under kinematic control , 1997, IEEE Trans. Robotics Autom..

[8]  Olav Egeland,et al.  Task-space tracking with redundant manipulators , 1987, IEEE Journal on Robotics and Automation.

[9]  T. Shamir,et al.  Repeatability of redundant manipulators: mathematical solution of the problem , 1988 .

[10]  D. D. Carlson,et al.  A new solution method for the inverse kinematic joint velocity calculations of redundant manipulators , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[11]  John M. Hollerbach,et al.  Redundancy resolution of manipulators through torque optimization , 1987, IEEE J. Robotics Autom..

[12]  Bruno Siciliano,et al.  Kinematic control of redundant robot manipulators: A tutorial , 1990, J. Intell. Robotic Syst..

[13]  A. A. Maciejewski,et al.  Repeatable generalized inverse control strategies for kinematically redundant manipulators , 1993, IEEE Trans. Autom. Control..

[14]  Shaheen Ahmad,et al.  Predicting the drift motion for kinematically redundant robots , 1992, IEEE Trans. Syst. Man Cybern..

[15]  Oussama Khatib,et al.  Inertial Properties in Robotic Manipulation: An Object-Level Framework , 1995, Int. J. Robotics Res..

[16]  John J. Craig,et al.  Introduction to Robotics Mechanics and Control , 1986 .

[17]  T. Shamir.  Remarks on some dynamical problems of controlling redundant manipulators , 1990 .

[18]  Charles A. Klein,et al.  The nature of drift in pseudoinverse control of kinematically redundant manipulators , 1989, IEEE Trans. Robotics Autom..

[19]  D. Dawson,et al.  Robust control of robots by the computed torque law , 1991 .

[20]  Sukhan Lee,et al.  An extension to operational space for kinematically redundant manipulators: kinematics and dynamics , 2000, IEEE Trans. Robotics Autom..

[21]  Li Li,et al.  Controlling chaotic robots with kinematical redundancy. , 2006, Chaos.

[22]  Christian H. Fedrowitz,et al.  A simplified criterion for repeatability and its application in constraint path planning problems , 2000, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113).

[23]  Charles A. Klein,et al.  Repeatable pseudoinverse control for planar kinematically redundant manipulators , 1995, IEEE Transactions on Systems, Man, and Cybernetics.

[24]  Oussama Khatib,et al.  Dynamic Performance and Modular Design of Redundant Macro-/Minimanipulators , 2008 .

[25]  Yunong Zhang,et al.  Minimum-Energy Redundancy Resolution of Robot Manipulators Unified by Quadratic Programming and its Online Solution , 2007, 2007 International Conference on Mechatronics and Automation.

[26]  Anthony A. Maciejewski,et al.  Singularities, Stable Surfaces, and the Repeatable Behavior of Kinematically Redundant Manipulators , 1994, Int. J. Robotics Res..

[27]  Charles A. Klein,et al.  Review of pseudoinverse control for use with kinematically redundant manipulators , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[28]  Omar Bouattane,et al.  θ(1) time quadtree algorithm and its application for image geometric properties on a mesh connected computer (MCC) , 1995, IEEE Transactions on Systems, Man, and Cybernetics.

[29]  Jonghoon Park,et al.  Characterization of instability of dynamic control for kinematically redundant manipulators , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[30]  Ranjan Mukherjee,et al.  Design of holonomic loops for repeatability in redundant manipulators , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[31]  Giuseppe Oriolo,et al.  Control of redundant robots on cyclic trajectories , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[32]  Dragomir N. Nenchev,et al.  Redundancy resolution through local optimization: A review , 1989, J. Field Robotics.

[33]  Homayoun Seraji.  Task options for redundancy resolution using configuration control , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[34]  Denis Gillet,et al.  On Achieving Periodic Joint-Motion for Redundant Robots , 2008 .

[35]  T. Fukuda,et al.  Decentralized control of redundant manipulators: a control scheme that generates a cyclic solution to the inverse problem , 1999, 1999 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (Cat. No.99TH8399).

[36]  Yu-Che Chen,et al.  On the existence and characteristics of solution paths at algorithmic singularities [kinematically redundant arms] , 1998, IEEE Trans. Robotics Autom..

[37]  J. T. Wang.  Redundancy Resolution of Robotic Manipulators Using Normalized Generalized Inverses , 1995 .

[38]  Andrew A. Goldenberg,et al.  A Solution to the Inverse Kinematics of Redundant Manipulators , 1985, 1985 American Control Conference.

[39]  Shugen Ma,et al.  Local torque minimization for redundant manipulators: a correct formulation , 1996, Robotica.

[40]  John Baillieul,et al.  Kinematic programming alternatives for redundant manipulators , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[41]  Shuzhi Sam Ge,et al.  A unified quadratic-programming-based dynamical system approach to joint torque optimization of physically constrained redundant manipulators , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[42]  Vijay Kumar,et al.  On singular behaviors of impedance-based repeatable control for redundant robots , 2001, J. Field Robotics.

[43]  Kevin A. O'Neil,et al.  Divergence of linear acceleration-based redundancy resolution schemes , 2002, IEEE Trans. Robotics Autom..

[44]  Zsolt Kemény,et al.  Redundancy resolution in robots using parameterization through space , 2003, IEEE Trans. Ind. Electron..

[45]  Adi Ben-Israel,et al.  Generalized inverses: theory and applications , 1974 .

[46]  J. Bay.  Geometry and Prediction of Drift-Free Trajectories for Redundant Machines Under Pseudoinverse Control , 1992 .