T-4-1-2 Comparative Study of Two Methods Using Relative Coordinates for Constrained Rigid Body System

Abstract

In this study, we compared the efficiencies of two famous methods which use relative coordinates for forward dynamics : the original fully recursive algorithm and modified recursive algorithm. The fully recursive algorithm is modified a little bit for improvement by using the same form of velocity transformation as the modified recursive algorithm. To compare the efficiencies, we expressed the number of multiplications and divisions as a function of system parameters. By varying the parameters, we check the effect of parameters on the efficiencies and it turned out that the fully recursive algorithm is more efficient for the system with long chains, while the modified recursive algorithm is more efficient for the parallel system with many constraints. In the results, two algorithms showed equal efficiency for the number of bodies in chain, n=9∿13 with variation by the number of constraints and parallelism.