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Analysis and Experimentation of Transpose Jacobian-based Cartesian Regulators

Published online by Cambridge University Press:  01 May 1999

Rafael Kelly
Affiliation:
División de Física Aplicada, CICESE, Apdo. Postal 2615, Adm. 1, Carretera Tijuana–Ensenada Km. 107, Ensenada, B. C., 22800 (Mexico ). E-mail: rkelly@cicese.mx
Angel Coello
Affiliation:
División de Física Aplicada, CICESE, Apdo. Postal 2615, Adm. 1, Carretera Tijuana–Ensenada Km. 107, Ensenada, B. C., 22800 (Mexico ). E-mail: rkelly@cicese.mx

Abstract

Transpose Jacobian-based controllers represent an attractive approach to robot control in Cartesian space. These controllers attempt to drive the robot end-effector posture to a specified desired position and orientation without solving either the inverse kinematics nor computing the robot inverse Jacobian. A wide class of transpose Jacobian-based regulators obtained from the energy shaping plus damping injection technique is analyzed in this paper. Our main theoretical contribution is the introduction of a novel analysis which does not invoke any assumption on Jacobian singularities to ensure local asymptotic stability for a family of nonredundant robots. The performance of four transpose Jacobian-based regulators is illustrated via experimental tests conducted on a direct-drive vertical arm.

Type
Research Article
Copyright
© 1999 Cambridge University Press

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