Analysis and Control of Robot Manipulators with Kinematic Redundancy

Abstract

A c1osed-form solution formula for the kinematic control of manipulators with
\nredundancy is derived, using the Lagrangian multiplier method. Differential
\nrelationship equivalent to the Resolved Motion Method has been also derived.
\nThe proposed method is proved to provide with the exact equilibrium state for
\nthe Resolved Motion Method. This exactness in the proposed method fixes the
\nrepeatability problem in the Resolved Motion Method, and establishes a fixed
\ntransformation from workspace to the joint space. Also the method, owing to the
\nexactness, is demonstrated to give more accurate trajectories than the Resolved
\nMotion Method.
\nIn addition, a new performance measure for redundancy control has been developed.
\nThis measure, if used with kinematic control methods, helps achieve
\ndexterous movements including singularity avoidance. Compared to other measures
\nsuch as the manipulability measure and the condition number, this measure
\ntends to give superior performances in terms of preserving the repeatability property
\nand providing with smoot.her joint velocity trajectories.
\nUsing the fixed transformation property, Taylor's Bounded Deviation Paths
\nAlgorithm has been extended to the redundant manipulators.