Geometry‐based efficient rata coordination for manipulators with kinematic redundancy

Abstract

AbstractThe redundancy resolution problem for kinematically redundant serial chain manipulators is addressed. In this article we present a generalization of the geometry‐based rate allocation algorithm, developed initially for only a minimum norm solution, to obtain the optimal joint rate solution for any specified objective function, with or without weightage. This generalization is made possible through a physial interpretation of the common pseudoinverse‐based gradient solution scheme, and by developing a modified formulation for the objective function as a minimum criterion not with respect to the origin of the joint rate space, but with respect to another point in the joint rate space represented by the gradient of the specified objective. Application examples of the algorithm including procedures of solution are demonstrated using 7R manipulators with two generic types of geometry. Moreover, a closed form optimal solution for the class of 7R anthropomorphic arms is also given. © 1995 John Wiley & Sons, Inc.