Parallel Algorithms for Computation of the Manipulator Inertia Matrix

This article presents the development of an O(log 2 N) parallel algorithm for the manipulator inertia matrix. It is based on an efficient serial algorithm that uses the composite rigid- body method. Recursive doubling is used to reformulate the linear recurrence equations that are required to compute the diagonal elements of the matrix. It results in O(log 2 N) levels of computation. Computation of the off-diagonal ele ments involves N linear recurrences of varying size, and a new method, which avoids redundant computation of position and orientation transforms for the manipulator, is developed. The O(log 2 N) algorithm is presented in both equation and graphic forms that clearly show the parallelism inherent in the algorithm. The relationship between the number of pro cessors required and the order of the computation is also given for several versions of parallel algorithms for the inertia matrix.

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

[2]  Richard H. Lathrop,et al.  Parallelism in Manipulator Dynamics , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

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

[4]  David E. Orin,et al.  Systolic architectures for the manipulator inertia matrix , 1988, IEEE Trans. Syst. Man Cybern..

[5]  David E. Orin,et al.  Alternate Formulations for the Manipulator Inertia Matrix , 1991, Int. J. Robotics Res..

[6]  John S. Bay.  Constrained motion of a 3-D manipulator over unknown constraints : the robotic groping problem / , 1988 .

[7]  Daniel Gajski,et al.  Essential Issues in Multiprocessor Systems , 1985, Computer.

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

[9]  C. S. George Lee,et al.  Efficient parallel algorithm for robot inverse dynamics computation , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[10]  Harold S. Stone,et al.  A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations , 1973, IEEE Transactions on Computers.

[11]  Amir Fijany,et al.  A class of parallel algorithms for computation of the manipulator inertia matrix , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

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

[13]  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.

[14]  Yuan F. Zheng,et al.  Mathematical modeling of a robot collision with its environment , 1985, J. Field Robotics.

[15]  K. W. Olson,et al.  Systolic architecture for computation of the Jacobian for robot manipulators , 1987 .

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