Two approaches to singularity-consistent motion of nonredundant robotic mechanisms

In this paper we discuss the relation between the two approaches to velocity command generation for nonredundant robotic mechanisms, which the two groups of the authors proposed recently and independently of each other. It will be shown analytically that the singularity-consistent null space based approach, and the split Jacobian approach, are equivalent. Analysis of the behavior at a singularity will be presented from the viewpoint of both approaches. An analytical example will be used to demonstrate the theoretical results.

[1]  Masaru Uchiyama,et al.  Singularity-consistent path tracking: a null space based approach , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

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

[3]  Masaru Uchiyama,et al.  Experimental teleoperation of a nonredundant slave arm at and around singularities , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[4]  T. Shamir,et al.  The Singularities of Redundant Robot Arms , 1990, Int. J. Robotics Res..

[5]  Masaru Uchiyama,et al.  Teleoperation based on the adjoint Jacobian approach , 1997 .

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

[7]  Masaru Uchiyama.  Study of the Computer Control of the Motion of a Mechanical Arm : 3rd Report, Dynamic Vision and Visual Feedback , 1979 .

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

[9]  Bruno Siciliano,et al.  Review of the damped least-squares inverse kinematics with experiments on an industrial robot manipulator , 1994, IEEE Trans. Control. Syst. Technol..

[10]  Nazareth Bedrossian,et al.  Characterizing spatial redundant manipulator singularities , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[11]  Dragomir N. Nenchev,et al.  Tracking Manipulator Trajectories With Ordinary Singularities: A Null Space-Based Approach , 1995, Int. J. Robotics Res..

[12]  Joel W. Burdick,et al.  A classification of 3R regional manipulator singularities and geometries , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[13]  Kosei Kitagaki,et al.  Robot Control System ARS/A for Research , 1990, J. Robotics Mechatronics.

[14]  Jon C. Kieffer,et al.  Differential analysis of bifurcations and isolated singularities for robots and mechanisms , 1994, IEEE Trans. Robotics Autom..

[15]  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.

[16]  Beno Benhabib,et al.  Singularity analysis of mechanisms and robots via a velocity-equation model of the instantaneous kinematics , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[17]  David R. Smith,et al.  Higher order singularities of regional manipulators , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

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

[19]  Harvey Lipkin,et al.  A new method of robotic rate control near singularities , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[20]  J. Kieffer.  Manipulator Inverse Kinematics for Untimed End-Effector Trajectories With Ordinary Singularities , 1992 .

[21]  Gerd Hirzinger,et al.  Redundant motions of non-redundant robots a new approach to singularity treatment , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[22]  M. Uchiyama.  A Study of Computer Control of Motion of a Mechanical Arm : 1st Report, Calculation of Coordinative Motion Considering Singuler Points , 1979 .

[23]  Kosei Kitagaki,et al.  A Robot Control System for Research: ARS/A , 1989 .