Inverse Kinematic Solutions With Singularity Robustness for Robot Manipulator Control

[+] Author and Article Information
Yoshihiko Nakamura

Automation Research Laboratory, Kyoto University, Uji, Kyoto 611, Japan

Hideo Hanafusa

Department of Mechanical Engineering, Ritsumeikan University, Kiktaku, Kyoto 603, Japan

J. Dyn. Sys., Meas., Control 108(3), 163-171 (Sep 01, 1986) (9 pages) doi:10.1115/1.3143764 History: Received April 06, 1986; Online July 21, 2009


The singularity problem is an inherent problem in controlling robot manipulators with articulated configuration. In this paper, we propose to determine the joint motion for the requested motion of the endeffector by evaluating the feasibility of the joint motion. The determined joint motion is called an inverse kinematic solution with singularity robustness, because it denotes feasible solution even at or in the neighborhood of singular points. The singularity robust inverse (SR-inverse) is introduced as an alternative to the pseudoinverse of the Jacobian matrix. The SR-inverse of the Jacobian matrix provides us with an approximating motion close to the desired Cartesian trajectory of the endeffector, even when the inverse kinematic solution by the inverse or the pseudoinverse of the Jacobian matrix is not feasible at or in the neighborhood of singular points. The properties of the SR-inverse are clarified by comparing it with the inverse and the pseudoinverse. The computational complexity of the SR-inverse is considered to discuss its implementability. Several simulation results are also shown to illustrate the singularity problem and the effectiveness of the inverse kinematic solution with singularity robustness.

Copyright © 1986 by ASME
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