A SIMPLE AND HIGHLY PARALLELIZABLE METHOD FOR REAL-TIME DYNAMIC SIMULATION-BASED ON VELOCITY TRANSFORMATIONS

A semi-recursive and easy-to-parallelize algorithm for real-time dynam ic simulation of open- and closed-loop multi-rigid-body systems is pre sented. The equations of motion are obtained in terms of a minimal set of relative joint coordinates using an efficient implementation of th e velocity transformation method. The open-loop velocity transformatio n matrix, which relates body translational and rotational velocities t o joint relative velocities, is computed in parallel using an extremel y simple and intuitive idea. Similarly, the open-loop projected mass m atrix is computed in parallel. Fine grain parallelization and optimum use of the cache memory are achieved by using a body-by-body procedure for the computation of vectors and matrices. Closed-loop systems are transformed into open-loop systems through the penalty formulation. Th e performance of the method is tested through an arithmetic operation count of a 45 degree of freedom open-loop model of a human body and an 18 degree of freedom closed-loop model of a heavy truck.