Parallel index-3 formulation for real-time multibody dynamics simulations

摘要

Computational efficiency of the dynamics of large constrained multibody systems is essential in many areas of computer aided engineering and design. There are many examples of such systems in various disciplines. The involved applications include robots, vehicles, biomechanical systems and other interdisciplinary systems. Moreover, some applications like hardware-in-the-loop or human-in-the-loop devices are developed by applying real-time simulations. Parallel computing is one of the approaches to increase the computational efficiency of multibody simulations. This paper presents a new parallel formulation for real-time multibody dynamics simulations. The proposed method adopts a divide and conquer scheme. Initially, the parallel algorithm is formulated by using classical index-3 Lagrangian approach with trapezoidal rule as a numerical integrator. Subsequently, index-3 augmented Lagrangian formulations with projections are adopted to generalize the algorithm and make it more robust in case of Jacobian matrix rank deficiencies, which may occur in analysing complex systems. The performance results indiciate that real-time computations can be achieved for multibody systems with 128 DOF for three processors used, keeping the constraint errors under control.