A parallel Hamiltonian formulation for forward dynamics of closed-loop multibody systems

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• 作者：K. Chadaj ; P. Malczyk ; J. Frączek
• 关键词：Forward dynamics ; Closed ; loop systems ; Hamilton’s canonical equations ; Parallel algorithm ; Divide and conquer ; Joint coordinates
• 刊名：Multibody System Dynamics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：39
• 期：1-2
• 页码：51-77
• 全文大小：2422KB
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Optimization; Electrical Engineering; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-272X
• 卷排序：39

文摘

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.