Abstract
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.
Highlights
In current research and industrial applications, there is a need for fast multibody (MBS) dynamics simulations
The results were competitively set against analogous divide-and-conquer algorithm (DCA) algorithm [17] that solves forward dynamics problem by using acceleration based Newton–Euler’s equations, and the closed-loops were enforced by the application of pseudo-inverses
A novel Hamiltonian based divide-andconquer algorithm (HDCA) algorithm is presented for the simulation of constrained multirigid body system dynamics possessing closed-loop topologies
Summary
In current research and industrial applications, there is a need for fast multibody (MBS) dynamics simulations. Due to the advances in the robotics field, there has been a growing attention to the development of efficient, low order algorithms for the simulation of open-loop and closed-loop kinematic chain system dynamics [5,6,7]. As Hamilton’s canonical equations are expressed in terms of velocities and momenta of the system and the possible constraints are usually imposed at the velocity level, many sources indicate profitable characteristics of the Hamiltonian approach from the numerical point of view Various authors exploited this approach for real-time simulations of vehicles [29], in the analyses of MBS subjected to intermittent motion [30], and in the development of penalty methods for constrained mechanical system dynamics [31]. 2 introduces basic concepts and definitions exploited in the paper and demonstrates novel Hamiltonian based parallel formulation for multi-rigid-body system dynamics possessing closed-loop chains. Original contributions of the paper are summarized in the last section
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