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Parallel algorithm for constrained multibody system dynamics with many degrees of freedom

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Języki publikacji
EN
Abstrakty
EN
This paper presents a parallel formulation for efficient multibody dynamics simulations with many degrees of freedom. The proposed method adopts a divide and conquer scheme and is formulated by using augmented Lagrangian formulation. The algorithm can accommodate situations, in which the Jacobian matrix is rank deficient, which may occur in analysing complex systems with redundant constraints and in singular positions. In addition, the constraint violation errors are kept under control of the user at position, velocity and acceleration levels. The method treats open and closed loop multibody systems in the same manner. Numerical experiments confirmed good performance of the formulation in the case of modest parallel computing resources available, especially for multibody systems with many degrees of freedom. Due to these characteristics the algorithm can be regarded as a tool for efficient dynamics simulations for general multibody systems.
Rocznik
Strony
779--791
Opis fizyczny
Bibliogr. 32 poz., rys., wykr.
Twórcy
autor
autor
  • Institute of Aeronautics and Applied Mechanics Faculty of Power and Aeronautical Engineering Warsaw University of Technology Nowowiejska 24, 00-665 Warsaw, POLAND, pmalczyk@meil.pw.edu.pl
Bibliografia
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  • Anderson K.S. and Duan S. (2000): Highly parallelizable low-order dynamics simulation algorithm for multi-rigid-body systems. – Journal of Guidance, Control and Dynamics, vol.23, pp.355-364.
  • Bae D.S. and Haug E.J. (1987): A recursive formulation for constrained mechanical system dynamics: Part I: Open loop systems. – Mechanics of Structures and Machines, vol.15, pp.359-382.
  • Bae D.S. and Haug E.J. (1988a): A recursive formulation for constrained mechanical system dynamics: Part II: Closed loop systems. – Mechanics of Structures and Machines, vol.15, pp.481-506.
  • Bae D.S., Kuhl J.G. and Haug E.J. (1988b): A recursive formulation for constrained mechanical system dynamics: Part III. Parallel processor implementation. – Mechanics of Structures and Machines, vol.16, pp.249-269.
  • Bayo E. and Ledesma R. (1996): Augmented Lagrangian and mass-orthogonal projection methods for constrained multibody dynamics. – Nonlinear Dynamics, vol.9, pp.113-130.
  • Blajer W. (2002): Augmented Lagrangian formulation: geometrical interpretation and application to systems with singularities and redundancy. – Multibody System Dynamics, vol.8, pp.141-159.
  • Chung S. and Haug E.J. (1993): Real-time simulation of multibody dynamics on shared memory multiprocessors. – Journal of Dynamic Systems, Measurement, and Control, vol.115, pp.627-637.
  • Critchley J. and Anderson K.S. (2004): A parallel logarithmic order algorithm for general multibody system dynamics. –Multibody System Dynamics, vol.12, pp.75-93.
  • Cuadrado J., Cardenal J. and Bayo E. (1997): Modeling and solution methods for efficient realtime simulation of multibody dynamics. – Multibody System Dynamics, vol.1, pp.259-280.
  • Cuadrado J., Cardenal J., Morer P. and Bayo E. (2000): Intelligent simulation of multibody dynamics: Space-state and descriptor methods in sequential and parallel computing environments. – Multibody System Dynamics, vol.4, pp.55-73.
  • Cuadrado J., Dopico D., Naya M. and Gonzalez M. (2004): Penalty, semi-recursive and hybrid methods for MBS real time dynamics in the context of structural integrators. – Multibody System Dynamics, vol.12, pp.117-132.
  • De Jalon G. and Bayo E. (1994): Kinematic and Dynamic Simulation of Multibody Systems. The Real- Time Challange. – Berlin: Springer Verlag.
  • Featherstone R. (1983): The calculation of robot dynamics using articulated-body inertias. – International Journal of Robotics Research, vol.2, pp.13-30.
  • Featherstone R. (1999a): A divide-and-conquer articulated body algorithm for parallel calculation of rigid body dynamics. part 1: Basic algorithm. – International Journal of Robotics Research, vol.18, pp.867-875.
  • Featherstone R. (1999b): A divide-and-conquer articulated body algorithm for parallel calculation of rigid body dynamics. part 2: Trees, loops, and accuracy. – International Journal of Robotics Research, vol.18, pp.876-892.
  • Featherstone R. (2008): Rigid Body Dynamics Algorithms. – Springer.
  • Fijany A. and Bejczy A.K. (1991): Techniques for parallel computation of mechanical manipulator dynamics. part II: Forward dynamics. – Control and Dynamics Systems, vol.40, pp.357-410.
  • Fijany A., Sharf I. and D’Eleuterio G. (1995): Parallel algorithms for computation of manipulator forward dynamics. – IEEE Transactions on Robotics and Automation, vol.11, pp.389-400.
  • Fisette, P. and Peterkenne J.M. (1998): Contribution to parallel and vector computation in multibody dynamics. – Parallel Computing, vol.24, pp.717-728.
  • Jain A. (1991): Unified formulation of dynamics for serial rigid multibody systems. – Journal of Guidance, Control, and Dynamics, vol.14, pp.531-542.
  • Kasahara H., Fujii H. and Iwata M. (1987): Parallel processing of robot motion simulation. – In Proceedings IFAC World Congress, Munich.
  • Malczyk P. and Frączek J. (2009a): Lagrange multipliers based divide and conquer algorithm for dynamics of general multibody systems. – In Proceeding of the ECCOMAS Multibody Dynamics 2009 Thematic Conference, (CD-ROM) (Warsaw, Poland, 29th June - 2nd July 2009), K. Arczewski, J. Frączek and M. Wojtyra, Eds.
  • Malczyk P. and Frączek J. (2009b): Evaluation of parallel efficiency in modeling of mechanisms using commercial multibody solvers, – The Archive of Mechanical Engineering, vol.LVI, No.3, pp.237-249.
  • Malczyk P., Frączek J. and Cuadrado J. (2010): Parallel index-3 formulation for real-time multibody dynamics simulations. – To appear in Proceedings of the 1st Joint International Conference on Multibody System Dynamics, May 25-27, 2010, Lappeenranta, Finland.
  • Mattson T.G., Sanders B.A. and Massingill B.L. (2005): Patterns for Parallel Programming. – Addison-Wesley, Boston.
  • Mukherjee R. and Anderson K. (2007): Orthogonal complement based divide-and-conquer algorithm for constrained multibody systems. – Nonlinear Dynamics, vol.48, pp.199-215.
  • OpenMP. Application program interface (2008): Specification for parallel programming, version 3.0. – Available online at http://www.openmp.org.
  • Rodriguez G. (1987): Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics. – IEEE Journal of Robotics and Automation, vol.6, pp.624-639.
  • Saha S.K. and Schiehlen W.O. (2001): Recursive kinematics and dynamics for parallel structured closed-loop multibody systems. – Mechanical Structures and Machines, vol.29, No.2, pp.143-175.
  • Walker M.W. and Orin D.E. (1982): Efficient dynamic computer simulation of robotic mechanisms. – ASME Journal of Dynamic Systems, Measurements, and Control, vol.104, pp.205-211.
  • Yamane K. and Nakamura Y. (2009): Comparative study on serial and parallel forward dynamics algorithms for kinematic chains. – International Journal of Robotics Research, vol.28, No.5, pp.622-629.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ5-0004-0055
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