Efficient parallel formulation for dynamics simulation of large articulated robotic systems

This paper presents a recursive and parallel formulation for the dynamics simulation of large articulated robotic systems based on the Hamilton's canonical equations. Although Hamilton's canonical equations exhibit many advantageous features compared to their acceleration based counterparts, it appears that there is a lack of dedicated parallel algorithms for multi-rigid body dynamics simulation based on such formulation. In this paper we consider open-loop kinematic chains that are connected by kinematic joints. Initially, the standard set of Hamilton's canonical equations are joined together with the constraint equations at the velocity level. The formulation allows to determine the system's joint velocities and impulsive constraint forces in a divide and conquer framework. This operation results in logarithmic numerical cost in parallel implementation. Subsequently, the time derivatives of the total joint momenta are evaluated at the constant expense. In case of sequential implementation, the entire algorithm exhibits linear computational cost. The proposed method is exact, non-iterative and does not require the direct calculation of the system's Hamiltonian nor its partial derivatives. Numerical test cases reveal negligible energy drift without the use of any additional constraint stabilization techniques. The results are compared against more standard acceleration based formulation and the preliminary outcome from real-life physical experiment.