This paper presents a novel recursive divide-and-conquer formulation for the simulation of complex constrained multibody system dynamics based on Hamilton's canonical equations (HDCA). The systems under consideration are subjected to holonomic, independent constraints and may include serial chains, tree chains, or closed-loop topologies. 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 system dynamics based on the Hamiltonian formulation. The developed HDCA formulation leads to a two-stage procedure. In the first phase, the approach utilizes the divide and conquer scheme, i.e., a hierarchic assembly-disassembly process to traverse the multibody system topology in a binary tree manner. The purpose of this step is to evaluate the joint velocities and constraint force impulses. The process exhibits linear O(n) (n -number of bodies) and logarithmic O(log 2 n) numerical cost, in serial and parallel implementations, respectively. The time derivatives of the total momenta are directly evaluated in the second parallelizable step of the algorithm. Sample closed-loop test cases indicate very small constraint violation errors at the position and velocity level as well as marginal energy drift without any additional form of constraint stabilization techniques involved in the solution process. The results are comparatively set against more standard acceleration based Featherstone's DCA approach to indicate the performance of the HDCA algorithm.

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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.

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