Multiple solution algorithm with applications to robot kinematics

Abstract

In this work, we present a new framework devoted to the numerical solution of nonlinear algebraic systems. The algorithm is composed by a symbiotic organisms search and a repulsion technique. The systematic repetition of a metaheuristic algorithm in order to find the full set of solutions tends to fail since, at times, the same solution is found over and over again. The methodology proposed here, incorporating a repulsion technique, changes the behavior of the symbiotic organisms search, allowing for a better probability of finding a high number of solutions. We tested the methodology in two examples, one of which is the inverse kinematics problem for PUMA robot. We present a detailed study of the effect that some control parameters have, showing how to increase the probability of identifying more solutions. Overall, the results validate the enhancement attained by the methodology in finding the full set of solutions of the problem.