Parallelism in Manipulator Dynamics

Lathrop, Richard H.

doi:10.1177/027836498500400207

Cited by 122 publications

(19 citation statements)

References 19 publications

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“…This trend can be observed in early works in this field, e.g., [14][15][16]. In 1999, Featherstone [17] developed truly optimal-time, logarithmic order divide-and-conquer algorithm (DCA) for the dynamics of tree-like topologies as well as closed-loop multibody systems.…”

Section: Introductionmentioning

confidence: 90%

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

2016

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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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Section: Introductionmentioning

confidence: 90%

“…The shift matrix S CO is defined analogously to (14). Let us note that the spatial momentum vectors transform in the same way as spatial force vectors.…”

Section: Derivatives Of Canonical Momentamentioning

confidence: 99%

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

2016

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“…The R(n), p,,, RiP'(n), PFT(n), and PCT(n) associated with each stage of insertion are listed in Table 2. The PFT and PCT of this mapping are found to be PFT = ( 13,15,7 ) and PCT = ( 6, 7, 7 ); the cost of this mapping is 22 units, and the Gantt chart of this suboptimal mapping is shown in Fig. 4.…”

Section: End Wbmmentioning

confidence: 99%

“…It is unlikely that further substantial improvements in computational efficiency can be achieved. Nevertheless, some improvements could be achieved by taking advantage of particular computation structures [4], customized algorithms/architectures for specific manipulators [5,6], parallel computations [3,7], and scheduling algorithms for muitiprocessor systems [8][9][10][11]. This paper presents two efficient mapping algorithms for scheduling the robot inverse dynamics computation of an n-jointed manipulator to be executed on a multiprocessor system with processor finishing time and interprocessor communication time considered in the system.…”

Section: Introductionmentioning

confidence: 99%

Efficient mapping algorithms for scheduling robot inverse dynamics computation on a multiprocessor system

Lee

Chen

1990

IEEE Trans. Syst., Man, Cybern.

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This paper presents two efficient mapping algorithms for scheduling the robot inverse dynamics computation consisting of m computational modules with precedence relationship to be executed on a multiprocessor system consisting ofp identical homogeneous processors with processor and communication costs to achieve minimum computation time. An objective function is defined in terms of the sum of the processor finishing time and the interprocessor communication time. The minimax optimization is performed on the objective function to obtain the best mapping. This mapping problem can be formulated as a combination of the graph partitioning and the scheduling problems, both have been known to be NP-complete. Thus, to speed up the searching for a solution, two heuristic algorithms were proposed to obtain fast but suboptimal mapping solutions. The first algorithm utilizes the level and the communication intensity of the task modules to construct an ordered priority list of ready modules and the module assignment is performed by a weighted bipartite matching algorithm. For a near-optimal mapping solution, the problem can be solved by the heuristic algorithm with simulated annealing. These proposed optimization algorithms can solve various large-scale problems within a reasonable time. Computer simulations were performed to evaluate and verify the performance and the validity of the proposed mapping algorithms. Finally, experiments for computing the inverse dynamics of a six-jointed PUMA-like manipulator based on the Newton-Euler dynamic equations were implemented on an NCUBE/ten hypercube computer to verify the proposed mapping algorithms. Computer simulation and experimental results are compared and discussed.

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“…In other words, the computational cost of the n recurrences in Eqs. (17), (23), (24), (28), and (29) is determined by that of the largest ones, i.e., for i = I, which are of size n. Furthermore, the computational cost of all the O(n 2) terms in Eqs. (16), (19)- (22), (25)- (27), and (30) is determined by the cost of one term since for each column n terms are computed in parallel and the computation for n columns, as will be discussed later, is overlapped.…”

Section: )mentioning

confidence: 99%

Parallel algorithms and architecture for computation of manipulator forward dynamics

Fijany

Bejczy

Proceedings. 1991 IEEE International Conference on Robotics and Automation

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Parallelism in Manipulator Dynamics

Cited by 122 publications

References 19 publications

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

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

Efficient mapping algorithms for scheduling robot inverse dynamics computation on a multiprocessor system

Parallel algorithms and architecture for computation of manipulator forward dynamics

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