Approximate optimum paths of robot manipulators under realistic physical constraints

A method is developed for planning the point-to-point path that the manipulator may adopt to minimize a specified performance index, under the realistic physical constraints on Joint torques, accelerations, velocities and position limits. The purpose of such path planning is either to provide the best input for the manipulator controller or to evaluate the arm performance for various designs. Because there is no analytic function available for describing the optimum path, cubic spline functions are proposed for an approximation. For a selected number of polynomial segments, the flexible polyhedron search is used to search for the optimum path arrangement. During the search period, it is often necessary to convert an infeasible arrangement into a feasible one. Methods for these required conversions have been studied. The number of concatenated polynomials is increased until there is no significant improvement on the approximation. Computer programs have been written to implement the algorithm.