A class of parallel algorithms for computation of the manipulator inertia matrix

A class of parallel and parallel/pipeline algorithms for computation of the manipulator inertial matrix is presented. An algorithm based on the composite rigid-body spatial inertia method, which results in less data dependency and hence better parallelization efficiency, is used for computation of the inertia matrix. Two parallel algorithms are developed which achieve the time lower bound of O((log/sub 2/ n))+O(1) in the computation with O(n/sup 2/) processors. The architectural features required for perfect mapping of these algorithms and their communication complexity are analyzed. The performance of the algorithms when mapped on two- and one-dimensional (linear) processor arrays with nearest-neighbor connection is investigated. Mapping on the linear array results in new algorithms with a computational complexity of k/sub 1/n(log/sub 2/n)+k/sub 2/(log/sub 2/n)+k/sub 3/. A parallel/pipeline algorithm is also presented which achieves the computation time of k/sub 1/n+k/sub 2/(log/sub 2/ n)+k/sub 3/ on the linear array. An architecture-oriented approach is used in the design of the algorithms. >

[1]  Sun-Yuan Kung,et al.  On supercomputing with systolic/wavefront array processors , 1984 .

[2]  Amir Fijany,et al.  An efficient method for computation of the manipulator inertia matrix , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[3]  David E. Orin,et al.  A systolic architecture for computation of the manipulator inertia matrix , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

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

[5]  Stephen A. Cook,et al.  An overview of computational complexity , 1983, CACM.

[6]  J. Wen,et al.  New class of control laws for robotic manipulators Part 1. Non–adaptive case , 1988 .

[7]  Oussama Khatib,et al.  Dynamic control of manipulator in operational space , 1983 .

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

[9]  David E. Orin,et al.  Parallel Algorithms for Computation of the Manipulator Inertia Matrix , 1991, Int. J. Robotics Res..

[10]  Harold S. Stone,et al.  Parallel Processing with the Perfect Shuffle , 1971, IEEE Transactions on Computers.

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

[12]  Tzyh-Jong Tarn,et al.  Robust Robot Arm Control with Nonlinear Feedback , 1985 .

[13]  Tilak Agerwala,et al.  Communication Issues in the Design and Analysis of Parallel Algorithms , 1981, IEEE Transactions on Software Engineering.

[14]  John T. Wen,et al.  New class of control laws for robotic manipulators. I - Nonadaptive case. II - Adaptive case , 1988 .

[15]  H. T. Kung.  Why systolic architectures? , 1982, Computer.

[16]  Jeffrey Scott Vitter,et al.  New Classes for Parallel Complexity: A Study of Unification and Other Complete Problems for P , 1986, IEEE Transactions on Computers.

[17]  Peter M. Kogge,et al.  Parallel Solution of Recurrence Problems , 1974, IBM J. Res. Dev..

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

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

[20]  Amir Fijany,et al.  An efficient algorithm for computation of manipulator inertia matrix , 1990, J. Field Robotics.

[21]  Kai Hwang,et al.  Computer architecture and parallel processing , 1984, McGraw-Hill Series in computer organization and architecture.

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

[23]  Richard H. Lathrop,et al.  Parallelism in Manipulator Dynamics , 1985 .

[24]  Daniel Gajski,et al.  An Algorithm for Solving Linear Recurrence Systems on Parallel and Pipelined Machines , 1981, IEEE Transactions on Computers.

[25]  J. Y. S. Luh,et al.  Resolved-acceleration control of mechanical manipulators , 1980 .

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