Unified GPU-Parallelizable Robot Forward Dynamics Computation Using Band Sparsity

Abstract

This letter proposes a unified GPU-parallelizable approach for robot forward dynamics (FD) computation based on the key fact that parallelism of prevailing FD algorithms benefits from the essential band sparsity of the joint space inertia (JSI) matrix or its inverse. The existing FD algorithms are categorized into three classes: direct JSI algorithms, propagation algorithms, and constraint force algorithms. Their associated systems of linear equations are transformed into a set of block bidiagonal (the first and second classes) and tridiagonal (the third class) linear systems, which can be conveniently and efficiently parallelized over the existing CPU-GPU programming platforms using various state-of-the-art parallel algorithms, such as parallel all-prefix sum (scan) and odd-even elimination. This high-level perspective allows unified and efficient implementation of all three classes of algorithms and also other potentially efficient algorithms, with the bonus that different algorithms can be swiftly compared to recommend problem-specific solutions.