SOLUTION OF A KINEMATICS PROBLEM USING A HYBRID STOCHASTIC DETERMINISTIC ALGORITHM

Abstract

The objective of this work is to present the solution of a kinematics problem through a hybrid algorithm, as well as its performance when compared to the Luus Jaakola algorithm (1973) and the Newton Interval/Generalized Bisection method. The test example, known as kin2, describes the inverse position problem applied in mechanics (Grosan and Abraham, 2008), which is represented by a system of eight nonlinear equations, resulting in ten distinct solutions. The hybrid algorithm used here (Silva, 2009) has a stochastic and deterministic nature, whose hybrid structure is composed of two methods. The first method is stochastic and is based on the Luus Jaakola algorithm (1973), and the second is deterministic in nature, based on the Hooke and Jeeves algorithm (1961). The nonlinear system originated from the kinematics problem was applied to the algorithms for a performance analysis, where the results obtained by the Hybrid Algorithm were first compared with the results of the original Luus Jaakola algorithm, and then with the results obtained by the Newton Interval/Generalized Bisection method. After the comparisons, it was verified both quantitatively and qualitatively that the Hybrid Algorithm achieved better results than the others. Finally, the efficiency of this hybrid algorithm was demonstrated in the face of the problem, in addition to justifying its applicability in this area, which can be extended to other cases as a proposal for future work.