Parallel O(log N) algorithms for computation of manipulator forward dynamics

In this paper, two parallel O(log N) algorithms for the computation of manipulator forward dynamics are presented. They are based on a new O(N) algorithm for the problem which is developed from a new factorization of mass matrix M. Specifically, a factorization of the inverse M/sup -1/ in the form of a Schur complement is derived. The new O(N) algorithm is then developed as a recursive implementation of this factorization. It is shown that the resulting algorithm is strictly parallel, that is, it is less efficient than other algorithms for serial computation of the problem. However, to our knowledge, it is the only algorithm that can be parallelized to derive both a time-optimal O(logN) - and processor-optimal - O(N) - parallel algorithm for the problem. A more efficient parallel O(logN) algorithm based on a multilevel exploitation of parallelism is also briefly described. In addition to their theoretical significance, these parallel algorithms allow a practical implementation due to their simple architectural requirements. >

[1]  J. Baumgarte.  Stabilization of constraints and integrals of motion in dynamical systems , 1972 .

[2]  R. Cottle.  Manifestations of the Schur complement , 1974 .

[3]  D. Heller.  Some Aspects of the Cyclic Reduction Algorithm for Block Tridiagonal Linear Systems , 1976 .

[4]  D. Heller.  Direct and iterative methods for block tridiagonal linear systems. , 1977 .

[5]  The Complexity of Parallel Evaluation of Linear Recurrences , 1977, JACM.

[6]  R. Roberson.  Constraint Stabilization for Rigid Bodies: an Extension of Baumgarte’s Method , 1978 .

[7]  J. Y. S. Luh,et al.  On-Line Computational Scheme for Mechanical Manipulators , 1980 .

[8]  David E. Orin,et al.  Efficient Dynamic Computer Simulation of Robotic Mechanisms , 1982 .

[9]  Gene H. Golub,et al.  Matrix computations , 1983 .

[10]  R. Featherstone.  The Calculation of Robot Dynamics Using Articulated-Body Inertias , 1983 .

[11]  C. S. George Lee,et al.  Efficient Parallel Algorithm for Robot Inverse Dynamics Computation , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  Giuseppe Rodriguez,et al.  Kalman filtering, smoothing, and recursive robot arm forward and inverse dynamics , 1987, IEEE Journal on Robotics and Automation.

[13]  Oussama Khatib,et al.  A unified approach for motion and force control of robot manipulators: The operational space formulation , 1987, IEEE J. Robotics Autom..

[14]  C. S. George Lee,et al.  Efficient parallel algorithms for robot forward dynamics computation , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[15]  Hironori Kasahara,et al.  Parallel Processing of Robot Motion Simulation , 1987 .

[16]  D. E. Rosenthal.  Triangularization of equations of motion for robotic systems , 1987 .

[17]  C. S. George Lee,et al.  Efficient parallel algorithms for robot forward dynamics computation , 1988, IEEE Trans. Syst. Man Cybern..

[18]  G. B. Sincarsin,et al.  Dynamics of an elastic multibody chain: part a—body motion equations , 1989 .

[19]  P. C. Hughes,et al.  EFFICIENT ALGORITHMS FOR THE DYNAMICAL SIMULATION OF STRUCTURALLY FLEXIBLE MANIPULATORS , 1989 .

[20]  R. Scheid,et al.  Efficient conjugate gradient algorithms for computation of the manipulator forward dynamics , 1989 .

[21]  G. B. Sincarsin,et al.  Dynamics of an elastic multibody chain: Part B—Global dynamics , 1989 .

[22]  Abhinandan Jain.  Unified formulation of dynamics for serial rigid multibody systems , 1991 .

[23]  Amir Fijany,et al.  Parallel algorithms and architecture for computation of manipulator forward dynamics , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[24]  Amir Fijany,et al.  Techniques for Parallel Computation of Mechanical Manipulator Dynamics. Part II: Forward Dynamics , 1991 .

[25]  Antal K. Bejczy,et al.  Techniques for Parallel Computation of Mechanical Manipulator Dynamics. Part II: Forward Dynamics , 1991 .

[26]  Antal K. Bejczy,et al.  Parallel Computation Systems for Robotics: Algorithms and Architectures , 1992, Parallel Computation Systems for Robotics.

[27]  Amir Fijany,et al.  Asparc: an Algorithmically Specialized Parallel Architecture for Robotics Computations , 1992, Parallel Computation Systems for Robotics.

[28]  Scott McMillan,et al.  Toward super-real-time simulation of robotic mechanisms using a parallel integration method , 1992, IEEE Trans. Syst. Man Cybern..

[29]  G. D'Eleuterio,et al.  Dynamics of an elastic multibody chain: Part C - Recursive dynamics , 1992 .

[30]  Guillermo Rodríguez-Ortiz,et al.  Spatial operator factorization and inversion of the manipulator mass matrix , 1992, IEEE Trans. Robotics Autom..

[31]  Inna Sharf,et al.  An Iterative Approach to Multibody Simulation Dynamics Suitable for Parallel Implementation , 1993 .

[32]  G. B. Sincarsin,et al.  Dynamics of an elastic multibody chain: Part D—Modelling of joints , 1993 .

[33]  Amir Fijany,et al.  A fast algorithm for parallel computation of multibody dynamics on MIMD parallel architectures , 1993 .

[34]  Amir Fijany,et al.  Fast parallel Preconditioned Conjugate Gradient algorithms for robot manipulator dynamics simulation , 1994, J. Intell. Robotic Syst..

[35]  Amir Fijany,et al.  Schur complement factorizations and parallel O(log N) algorithms for computation of operational space mass matrix and its inverse , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.