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A Parallel Logarithmic Order Algorithm for General Multibody System Dynamics

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Abstract

A novel optimal order optimal resource parallel multibody algorithm with general system applicability is derived directly from the sequential recursive \(\mathcal{O}(n)\) methods and the most recent developments in recursive constraint treatments. This new Recursive Coordinate Reduction Parallelism (RCRP) is the first optimal order \({\text{(}}\mathcal{O}(\log _2 n))\) parallel direct method with a sequential implementation that is exactly the efficient \({\text{(}}\mathcal{O}{\text{(}}n)\) algorithm. Consequently, the RCRP sets new benchmarks for performance over a wide range of problem size and parallel resources. Comparisons to existing methods also demonstrate that the RCRP is presently the best general parallel method.

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References

  1. Anderson, K.S., 'An efficient modeling of constrained multibody systems for application with parallel computing', Zeitschrift für Angewandte Mathematik and Mechanik 73(6), 1993, 935–939.

    Google Scholar 

  2. Anderson, K.S., 'An order-n formulation for the motion simulation of general multi-rigid-body tree systems', Computers & Structures 46(3), 1993, 547–559.

    Google Scholar 

  3. Anderson, K.S. and Critchley, J.H., 'Improved order-n performance algorithm for the sim-ulation of constrained multi-rigid-body systems', Multibody System Dynamics 9(2), 2003, 185–212.

    Google Scholar 

  4. Anderson, K.S. and Duan, S., 'Highly parallelizable low order algorithm for the dynamics of complex multi rigid body systems', Journal of Guidance, Control and Dynamics 23(2), 2000, 355–364.

    Google Scholar 

  5. Bae, D., Kuhl, J.G. and Haug, E.J., 'A recursive formation for constrained mechanical sys-tem dynamics: Part III, Parallel processing implementation', Mechanisms, Structures, and Machines 16, 1988, 249–269.

    Google Scholar 

  6. Bae, D.S. and Haug, E.J., 'A recursive formation for constrained mechanical system dynamics: Part II, Closed loop systems', Mechanisms, Structures, and Machines 15(4), 1987, 481–506.

    Google Scholar 

  7. Bayo, E., de Jalon, J.G. and Serna, M.A., 'Modified Lagrangian formulation for the dynamic analysis of constrained mechanical systems', Computer Methods in Applied Mechanics and Engineering 71(2), 1988, 183–195.

    Google Scholar 

  8. Chung, S. and Haug, E.J., 'Hybrid variational method for multibody dynamics', International Journal for Numerical Methods in Engineering 36(1), 1993, 87–109.

    Google Scholar 

  9. Chung, S. and Haug, E.J., 'Real-time simulation of multibody dynamics on shared memory multiprocessors', Journal of Dynamic Systems, Measurement, and Control 115, 1993, 627–637.

    Google Scholar 

  10. Critchley, J.H., 'A parallel logarithmic time complexity algorithm for the simulation of general multibody system dynamics', Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, NY, 2003.

    Google Scholar 

  11. Critchley, J.H. and Anderson, K.S., 'A generalized recursive coordinate reduction method for multibody system dynamics', International Journal for Multiscale Computational Engineering 1(2&3), 2003, 181–200.

    Google Scholar 

  12. Cuadrado, J., Cardenal, J., Morer, P. and Bayo, E., 'Intelligent simulation of multibody dynam-ics: Space-state and descriptor methods in sequential and parallel computing environments', Multibody System Dynamics 4, 2000, 55–73.

    Google Scholar 

  13. Eichberger, A., Fuhrer, C. and Schwertassek, R., 'The benefits of parallel multibody simula-tion', International Journal of Numerical Methods in Engineering 37, 1994, 1557–1572.

    Google Scholar 

  14. Featherstone, R., Robot Dynamics Algorithms, Kluwer Academic Publishers, New York, 1987.

    Google Scholar 

  15. Featherstone, R., 'A divide-and-conquer articulated-body algorithm for parallel O(log n))cal-culation of rigid-body dynamics. Part 1: Basic algorithm', International Journal of Robotics Research 18(9), 1999, 867–875.

    Google Scholar 

  16. Featherstone, R., 'A divide-and-conquer articulated-body algorithm for parallel O(log n))cal-culation of rigid-body dynamics. Part 2: Trees, loops, and accuracy', International Journal of Robotics Research 18(9), 1999, 876–892.

    Google Scholar 

  17. Fijany, A. and Bejczy, A.K., 'Techniques for parallel computation of mechanical manipulator dynamics. Part II-Forward dynamics', in Advances in Robotic Systems and Control, Vol. 40, C. Leondes (ed.), Academic Press, London, 1991, 357–410.

    Google Scholar 

  18. Fijany, A. and Bejczy, A.K., 'Parallel computation of forward dynamics of manipulators', NASA Technical Brief, Report NPO-18706 12, NASA Jet Propulsion Laboratory, item #82, 1993.

  19. Fijany, A., Sharf, I. and D'Eleuterio, G.M.T., 'Parallel O(log N)algorithms for computation of manipulator forward dynamics', IEEE Transactions on Robotics and Automation 11(3), 1995, 389–400.

    Google Scholar 

  20. Fisette, P. and Peterkenne, J.M., 'Contribution to parallel and vector computation in multibody dynamics', Parallel Computing 24, 1998, 717–728.

    Google Scholar 

  21. Kane, T.R. and Levinson, D.A., Dynamics: Theory and Application, McGraw-Hill, New York, 1985.

    Google Scholar 

  22. Kasahara, H., Fujii, H. and Iwata, M., 'Parallel processing of robot motion simulation', in Proceedings IFAC 10th World Conference, 1987.

  23. Kurdila, A.J., Menon, R.G. and Sunkel, J.W., 'Nonrecursive order N formulation of multibody dynamics', Journal of Guidance, Control, and Dynamics 16(5), 1993, 838–844.

    Google Scholar 

  24. Lee, C. and Chang, P.R., 'Efficient parallel algorithms for robot forward dynamics', IEEE Transactions on Systems, Man, and Cybernetics 18(2), 1988, 238–251.

    Google Scholar 

  25. Rein, U., 'Efficient object oriented programming of multibody dynamics formalisms', in Pro-ceedings of the NATO-Advanced Study Institute on Computer Aided Analysis of Rigid and Flexible Mechanical Systems, Vol. 2. 1993, 59–69.

    Google Scholar 

  26. Roberson, R.E. and Schwertassek, R., Dynamics of Multibody Systems, Springer-Verlag, Berlin, 1988.

    Google Scholar 

  27. Stejskal, V. and Valášek, M., Kinematics and Dynamics of Machinery, Marcel Dekker, New York, 1996.

    Google Scholar 

  28. Zeid, A.A. and Overholt, J.L., 'Modeling of multibody systems connected by standard engineering joints', Mechanics of Structures and Machines 23(2), 1995, 273–307.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical, Aeronautical and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, 12180-8590, U.S.A.

    J.H. Critchley

  2. Department of Mechanical, Aeronautical and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, 12180-8590, U.S.A.

    K.S. Anderson

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  1. J.H. Critchley
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  2. K.S. Anderson
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Critchley, J., Anderson, K. A Parallel Logarithmic Order Algorithm for General Multibody System Dynamics. Multibody System Dynamics 12, 75–93 (2004). https://doi.org/10.1023/B:MUBO.0000042893.00088.c9

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  • DOI: https://doi.org/10.1023/B:MUBO.0000042893.00088.c9

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