A Parallel Recursive Hamiltonian Algorithm for Forward Dynamics of Serial Kinematic Chains

Chadaj, Krzysztof; Malczyk, Paweł; Frączek, Janusz

doi:10.1109/tro.2017.2654507

Cited by 21 publications

(22 citation statements)

References 43 publications

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“…This, unfortunately, leads to a situation where the term T δ | |t f doesn't vanish when explicit dependency of h on reaction forces appears. We can, however, overcome this problem by adding variation of Equation (2) to the cost functional (26) and an auxiliary adjoint variable evaluated at time t = t f . Equation (2) can be rewritten as:…”

Section: The Adjoint Methodsmentioning

confidence: 99%

“…Multiple representations of equations of motion may be employed to model a MBS. Recent works of the authors [25][26][27] have demonstrated that by using a constrained Hamilton's canonical equations, in which Lagrange multipliers enforce constraint equations at the velocity level, one can obtain more stable solutions for DAEs as compared to acceleration-based counterparts. 28,29 This phenomenon is partially connected with differential index reduction of the resultant Hamilton's equations.…”

Section: Introductionmentioning

confidence: 99%

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Hamiltonian direct differentiation and adjoint approaches for multibody system sensitivity analysis

Maciąg

Malczyk

Frączek

2020

Numerical Meth Engineering

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The design of multibody systems involves high fidelity and reliable techniques and formulations that should help the analyst to make reasonable decisions. Given that constrained equations of motion for the simplest of multibody systems are highly nonlinear, determining the sensitivity terms is a computationally intensive and complex process that requires the application of special procedures. In this article, two novel Hamiltonian-based approaches are presented for efficient sensitivity analysis of general multibody systems. The developed direct differentiation and the adjoint methods are based on constrained Hamilton's canonical equations of motion. This formulation provides solutions, which are more stable as compared to the results of direct integration of equations of motion expressed in terms of accelerations due to a reduced differential index of the underlying system of differential-algebraic equations and explicit constraint imposition at the velocity level.The proposed Hamiltonian based methods are both capable of calculating the sensitivity derivatives and keeping the growth of constraint violation errors at a reasonable rate. The Hamiltonian-based procedures derived herein appear to be good alternatives to existing methods for sensitivity analysis of general multibody systems.

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Section: The Adjoint Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hamiltonian direct differentiation and adjoint approaches for multibody system sensitivity analysis

Maciąg

Malczyk

Frączek

2020

Numerical Meth Engineering

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“…The Articulated Body Algorithm (ABA) [15] was combined with the DCA in [6] to deliver significant speedups in computation times. Hamilton's canonical equations were used in [7,8] and showed good properties regarding the satisfaction of kinematic constraints. Augmented Lagrangian methods with configurationand velocity-level mass-orthogonal projections have also been employed [28]; the resulting algorithm has been proven to behave robustly during the simulation of mechanical systems with redundant constraints and singular configurations.…”

Section: Related Workmentioning

confidence: 99%

“…Moreover, the height of an upper part of such tree should be minimized and the lower part of the tree should be designed in a way to distribute the computational load as evenly as possible over the available processing units. Therefore, the real problem is to design a good assembly-disassembly tree for a given mechanism so that the tree could be efficiently mapped onto the architecture of a given parallel resource, either it is a shared memory computer (as in this paper) or it is a graphics processor unit (as analyzed in [8]). The specifics of the binary tree creation for various multibody system topologies can found in other references [6,16,28,33].…”

Section: Parallel Implementationmentioning

confidence: 99%

Index-3 divide-and-conquer algorithm for efficient multibody system dynamics simulations: theory and parallel implementation

et al. 2018

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There has been a growing attention to efficient simulations of multibody systems, which is apparently seen in many areas of computer-aided engineering and design both in academia and in industry. The need for efficient or real-time simulations requires highfidelity techniques and formulations that should significantly minimize computational time. Parallel computing is one of the approaches to achieve this objective. This paper presents a novel index-3 divide-andconquer algorithm for efficient multibody dynamics simulations that elegantly handles multibody systems in generalized topologies through the application of the augmented Lagrangian method. The proposed algorithm exploits a redundant set of absolute coordinates. The trapezoidal integration rule is embedded into the formulation and a set of nonlinear equations need to be solved every time instant. Consequently, the Newton-Raphson iterative scheme is applied to find the system

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“…In previous papers [33,34], the authors proposed a Hamiltonian based divide-andconquer algorithm (HDCA) for open-loop multi-rigid body dynamics. In this paper, the HDCA algorithm is significantly extended and generalized to deal with systems possessing closed-loop and coupled-loops topologies.…”

Section: Introductionmentioning

confidence: 99%

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

2016

Self Cite

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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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A Parallel Recursive Hamiltonian Algorithm for Forward Dynamics of Serial Kinematic Chains

Cited by 21 publications

References 43 publications

Hamiltonian direct differentiation and adjoint approaches for multibody system sensitivity analysis

Hamiltonian direct differentiation and adjoint approaches for multibody system sensitivity analysis

Index-3 divide-and-conquer algorithm for efficient multibody system dynamics simulations: theory and parallel implementation

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

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