Journal Article

Adaptive control of kinematically redundant robots

SHENGWU LUO, SHAHEEN AHMED and MOHAMED ZRIBI

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 14, issue 3, pages 225-253
Published in print September 1997 | ISSN: 0265-0754
Published online September 1997 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/14.3.225
Adaptive control of kinematically redundant robots

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A redundant robot has more degrees of freedom than those needed to position the Robert end-effector uniquely. In a usual robotic task, only end-effector position trajectory is specified. The joint position trajectory is unknown, and it must be selected from a self-motion manifold for a specified end-effector. In many situations, the robot dynamic parameters such as the link mass, inertia, and joint viscous friction are unknown. The lack of knowledge of the joint trajectory and the dynamic parameters make it difficult to control redundant robots.

In this paper we show, through careful formulation of the problem, that the adaptative control of redundant robots can be addressed as a reference-velocity traking problem in the joint space. A control law ensures bounded estimation of the unknown dynamic parameters of the robot, and the convergence to zero of the velocity traking error is derived. To ensure the joint motion on the self-motion manifold remains bounded, a homeomorphic transformation is found. This transformation decomposes the dynamics of the velocity tracking error into a cascade system consisting of the dynamics in the end-effector error coordinates and the dynamics on the self-motion manifold. The dynamics on the self-motion manifold is shown to be related to the concept of zero dynamics. In the shown that, if the reference joint trajectory is selected to optimize a certain type of objective function, then stable dynamics on the self-motion manifold result. This ensures the overall stability of the adaptive system. Detailed simulations are given to test the theoretical developments. The proposed adaptive scheme does not require measurements of the joint acceleration or the inversion of the inertia matrix of the robot.

Journal Article.  0 words. 

Subjects: Mathematics

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