Parallel Algorithms for Computation of the Manipulator Inertia Matrix

Abstract

This article presents the development of an O( log2 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( log2 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( log2 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.