Parallel Algorithms for Computation of the Manipulator Inertia Matrix

This paper presents the development of an O(log 2 N) parallel algorithm for the manipulator inertia matrix. It is based on the most efficient serial algorithm which uses the composite rigid body method. Recursive doubling is used to reformulate the linear recurrence equations which 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 elements 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 which clearly show the parallelism inherent in the algorithm.