Redundancy resolution through local optimization: A review

Kinematically redundant manipulator arms and other robotic mechanisms provide a means for solving sophisticated motion tasks but require complex research on both mechanical and control problems. So far, many works have been published on kinematic redundancy, however, a systemization is missing. In this article an attempt for such a systemization is presented. It has been limited to methods for redundancy resolution through local optimization. Until now, these methods are most widely used, and it is expected also that they will prevail in the near future. A classification is suggested and the performance capabilities of the methods are discussed and compared. Two reference tables are provided; One of them lists references for different problems on kinematic redundancy as: mechanical design, dexterity measures, multicriteria optimization, global optimization, control design and computational considerations. The other table displays existing publications classified according to the application area of redundant robotic-mechanisms.

[1]  Kenneth J. Waldron,et al.  A study of a kinematically redundant manipulator structure , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[2]  Mathukumalli Vidyasagar,et al.  Optimal trajectory planning for planar n-link revolute manipulators in the presence of obstacles , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[3]  Tsuneo Yoshikawa,et al.  Analysis and Control of Articulated Robot Arms with Redundancy , 1981 .

[4]  Pradeep K. Khosla,et al.  Automatic generation of kinematics for a reconfigurable modular manipulator system , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[5]  Ian D. Walker,et al.  Subtask performance by redundancy resolution for redundant robot manipulators , 1988, IEEE J. Robotics Autom..

[6]  Christine Chevallereau,et al.  A new method for the solution of the inverse kinematics of redundant robots , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[7]  M. Christodoulou,et al.  Kinematic control and obstacle avoidance for redundant manipulators , 1986, 1986 25th IEEE Conference on Decision and Control.

[8]  Alain Fournier,et al.  Cooperation of two manipulators in assembly tasks , 1984 .

[9]  John M. Hollerbach,et al.  OPTIMUM KINEMATIC DESIGN FOR A SEVEN DEGREE OF FREEDOM MANIPULATOR. , 1985 .

[10]  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.

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

[12]  Olav Egeland,et al.  Cartesian Control of a Class of Redundant Manipulators , 1986 .

[13]  Yoshihiko Nakamura,et al.  Optimal Redundancy Control of Robot Manipulators , 1987 .

[14]  Tsuneo Yoshikawa,et al.  Analysis and Control of Robot Manipulators with Redundancy , 1983 .

[15]  S. R. Searle.  Generalized Inverse Matrices , 1971 .

[16]  Rajiv V. Dubey,et al.  Redundant robot control for higher flexibility , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[17]  L. Sciavicco,et al.  A dynamic solution to the inverse kinematic problem for redundant manipulators , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[18]  Kazem Kazerounian,et al.  An alternative method for minimization of the driving forces in redundant manipulators , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[19]  Oussama Khatib,et al.  Object manipulation in a multi-effector robot system , 1988 .

[20]  Charles A. Klein,et al.  Dynamic simulation of a kinematically redundant manipulator system , 1987, J. Field Robotics.

[21]  Pyung Chang,et al.  A closed-form solution for the control of manipulators with kinematic redundancy , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

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

[23]  Andrew K. C. Wong,et al.  A singularities avoidance approach for the optimal local path generation of redundant manipulators , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[24]  J. Y. S. Luh,et al.  Industrial robots with seven joints , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[25]  Rajiv V. Dubey,et al.  An efficient gradient projection optimization scheme for a seven-degree-of-freedom redundant robot with spherical wrist , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[26]  오세영.  An Inverse Kinematic Solution for Kinematically Redundant Robot Manipulators , 1984 .

[27]  J. Y. S. Luh,et al.  Resolved-acceleration control of mechanical manipulators , 1980 .

[28]  Yoshihiko Nakamura,et al.  Control of Articulated Robots with Redundancy , 1986 .

[29]  Daniel C. H. Yang,et al.  Feasibility evaluation of dynamically linearized kinematically redundant planar manipulators , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

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

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

[32]  Shugen Ma,et al.  Redundancy Decomposition Control for Multi-Joint Manipulators , 1988 .

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

[34]  S. Chiu,et al.  Control of redundant manipulators for task compatibility , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

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

[36]  Bruno Siciliano,et al.  A solution algorithm to the inverse kinematic problem for redundant manipulators , 1988, IEEE J. Robotics Autom..

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

[38]  Bernard Roth,et al.  Special grasping configurations with dexterous hands , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[39]  Charles W. Wampler,et al.  Some facts concerning the inverse kinematics of redundant manipulators , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[40]  S. Shankar Sastry,et al.  Dynamic control of redundant manipulators , 1989, J. Field Robotics.

[41]  John Baillieul,et al.  Avoiding obstacles and resolving kinematic redundancy , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

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

[43]  Charles W. Wampler,et al.  Manipulator Inverse Kinematic Solutions Based on Vector Formulations and Damped Least-Squares Methods , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[44]  C. S. George Lee,et al.  Residue arithmetic VLSI array architecture for manipulator pseudo-inverse Jacobian computation , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

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

[46]  Charles W. Wampler,et al.  Inverse kinematic functions for redundant manipulators , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[47]  John M. Hollerbach,et al.  Redundancy resolution of manipulators through torque optimization , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[48]  Yoshihiko Nakamura,et al.  Inverse kinematic solutions with singularity robustness for robot manipulator control , 1986 .

[49]  K. S. Banerjee.  Generalized Inverse of Matrices and Its Applications , 1973 .

[50]  D. E. Whitney,et al.  The mathematics of coordinated control of prosthetic arms and manipulators. , 1972 .

[51]  K.G. Shin,et al.  Coordination of dual robot arms using kinematic redundancy , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[52]  John M. Hollerbach,et al.  Local versus global torque optimization of redundant manipulators , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[53]  Miomir Vukobratović,et al.  Contribution to Control of Redundant Robotic Manipulators in an Environment with Obstacles , 1986 .

[54]  Daniel E. Whitney,et al.  Resolved Motion Rate Control of Manipulators and Human Prostheses , 1969 .

[55]  Pyung Hun Chang,et al.  A closed-form solution for inverse kinematics of robot manipulators with redundancy , 1987, IEEE J. Robotics Autom..

[56]  H. Das,et al.  Inverse kinematic algorithms for redundant systems , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[57]  Daniel Henry Gottlieb.  Robots and topology , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[58]  Tsuneo Yoshikawa,et al.  Manipulability and redundancy control of robotic mechanisms , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

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

[60]  Rajiv V. Dubey,et al.  Redundant robot control using task based performance measures , 1988, J. Field Robotics.

[61]  John Baillieul,et al.  A constraint oriented approach to inverse problems for kinematically redundant manipulators , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[62]  Mei-Hua Liu,et al.  Multivariable self-tuning control of redundant manipulators , 1988, IEEE J. Robotics Autom..

[63]  Peter D. Lawrence,et al.  General inverse kinematics with the error damped pseudoinverse , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[64]  Yoshihiko Nakamura,et al.  Redundancy of space manipulator on free-flying vehicle and its nonholonomic path planning , 1989 .

[65]  Pyung Chang.  A closed-form solution for inverse kinematics of robot manipulators with redundancy , 1987, IEEE Journal on Robotics and Automation.

[66]  John M. Hollerbach.  EVALUATION OF REDUNDANT MANIPULATORS DERIVED FROM THE PUMA GEOMETRY. , 1985 .

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

[68]  Andrew K. C. Wong,et al.  A singularities avoidance method for the trajectory planning of redundant and nonredundant robot manipulators , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[69]  Robert Judd,et al.  A performance measure for computing the reverse kinematic solution for robots with redundant degrees of freedom , 1985, 1985 24th IEEE Conference on Decision and Control.

[70]  Miomir Vukobratovic,et al.  A dynamic approach to nominal trajectory synthesis for redundant manipulators , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[71]  J. Kenneth Salisbury,et al.  Articulated Hands , 1982 .

[72]  Pietro Morasso,et al.  The Inverse Kinematic Problem for Anthropomorphic Manipulator Arms , 1982 .

[73]  Tsuneo Yoshikawa,et al.  Dynamic manipulability of robot manipulators , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[74]  中村 仁彦,et al.  Kinematical studies on the trajectory control of robot manipulators , 1985 .

[75]  Ashitava Ghosal,et al.  A New Approach for Kinematic Resolution of Redundancy , 1988, Int. J. Robotics Res..

[76]  Charles A. Klein,et al.  Dexterity Measures for the Design and Control of Kinematically Redundant Manipulators , 1987 .

[77]  Shugen Ma,et al.  Redundancy decomposition control for multi-joint manipulator , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[78]  J. Salisbury,et al.  Design and control of a redundant mechanism for small motion , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.