Highly Parallelizable Low-Order Dynamics Simulation Algorithm for Multi-Rigid-Body Systems

A new efficient procedure is presented for the determination of the dynamic equations of motion for complex multibody systems and their subsequent temporal integration using parallel computing. The method is applicable to general systems of rigid bodies, which may contain arbitrary joint types, multiple branches, and/or closed loops. The method is based on the explicit determination of constraint forces at key joint locations and the subsequent highly efficient determination of system state time derivatives. The algorithm uses a novel hybrid direct and iterative solution scheme that allows a substantially higher degree of parallelization than is generally obtainable using the more conventional recursive O(N) procedures. It is shown that at the coarsest level the parallelization obtainable easily exceeds that indicated by the topology of the system. The procedure can produce a theoretical time optimal O(log2N) performance for chain systems on computational throughput with O(N) processors. Numerical results indicate that this procedure performs particularly well relative to other parallel multibody formulations in situations where the number of degrees of freedom are large and the number of bodies that make up the system is greater than the number of computing processors available, the multibody systems involve branches, or the applied forces within the system are rapidly changing or are discontinuous. An estimate for the parallel efficiency of the algorithm is obtained by combining a theoretical bound for parallel complexity with an approximated overhead cost for parallel implementation. (Author)