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Parallel conjugate gradient algorithms for manipulator dynamic simulationParallel conjugate gradient algorithms for the computation of multibody dynamics are developed for the specialized case of a robot manipulator. For an n-dimensional positive-definite linear system, the Classical Conjugate Gradient (CCG) algorithms are guaranteed to converge in n iterations, each with a computation cost of O(n); this leads to a total computational cost of O(n sq) on a serial processor. A conjugate gradient algorithms is presented that provide greater efficiency using a preconditioner, which reduces the number of iterations required, and by exploiting parallelism, which reduces the cost of each iteration. Two Preconditioned Conjugate Gradient (PCG) algorithms are proposed which respectively use a diagonal and a tridiagonal matrix, composed of the diagonal and tridiagonal elements of the mass matrix, as preconditioners. Parallel algorithms are developed to compute the preconditioners and their inversions in O(log sub 2 n) steps using n processors. A parallel algorithm is also presented which, on the same architecture, achieves the computational time of O(log sub 2 n) for each iteration. Simulation results for a seven degree-of-freedom manipulator are presented. Variants of the proposed algorithms are also developed which can be efficiently implemented on the Robot Mathematics Processor (RMP).
Document ID
Document Type
Conference Paper
Fijany, Amir
(Jet Propulsion Lab., California Inst. of Tech. Pasadena, CA, United States)
Scheld, Robert E.
(Jet Propulsion Lab., California Inst. of Tech. Pasadena, CA, United States)
Date Acquired
September 6, 2013
Publication Date
December 15, 1989
Publication Information
Publication: Proceedings of the 3rd Annual Conference on Aerospace Computational Control, Volume 2
Subject Category
Computer Systems
Accession Number
Distribution Limits
Work of the US Gov. Public Use Permitted.

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