Unified GPU-Parallelizable Robot Forward Dynamics Computation Using Band Sparsity

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.

I. Introduction

In robot simulation, the acceleration of the robot system must be computed for any applied force (forward dynamics, or FD) [1]. Albeit being a thoroughly explored subject, fast FD computation remains a relevant issue in emerging subfields of robotics. For example, while hyper-redundant robots for dexterous manipulation provide opportunities for working in complex environment  [2], their large degree of freedoms (DOF) poses new challenges to fast simulation. In addition, given a kinematic reference trajectory of a robot, we can generate dynamically feasible trajectories using the concept of dynamics filter proposed in [3], by largely evaluating dynamics with sampled states around the reference and different control inputs. An optimal trajectory can then be selected  [4]. Such applications involving a vast number of FD calculations also require high computational efficiency and motivate our current research on accelerating FD computation using CPU-GPU platform.