Analytic minimum-norm solution for rate coordination in redundant manipulators

Abstract

In this article, we present a novel method that results in efficient minimum norm solution for the rate coordination problem in redundant manipulators. The theory is developed based upon a geometric interpretation that, for minimum norm criterion, vectors orthogonal to constraint space should pass through the origin of the solution space. It is shown that, for any spatial manipulator with 1, 2, or 3 degrees of redundancy, the minimum norm rate solution can be derived in analytic closed form. An example of the analytic formulation is given for a 3R planar case, substantiated with simulation results. The behavior of this algorithm in nonredundant and near singular situations is also discussed. The method offers an equivalent but much more efficient alternative to using the pseudoinverse in redundancy resolution and, in fact, is applicable to any underdetermined linear system. An alternative formulation of pseudoinverse arrived at in the course of the development is also presented. © 1992 John Wiley & Sons, Inc.