A Learning-Based Method for Computing Self-Motion Manifolds of Redundant Robots for Real-Time Fault-Tolerant Motion Planning

Abstract

The focus of this research is to develop a learning-based method that computes self-motion manifolds (SMMs) efficiently and accurately to enable real-time global fault-tolerant motion planning. The proposed method first develops a learnable, closed-form representation of SMMs based on Fourier series. A cellular automaton is then applied to cluster workspace locations having the same number of SMMs and group SMMs with similar shape by homotopy classes, such that the SMMs of each homotopy class can be accurately learned by a neural network. To approximate the SMMs of an arbitrary workspace location, a neural network is first trained to predict the set of homotopy classes belonging to this workspace location. For each set of homotopy classes, another neural network is trained to approximate the Fourier series coefficients of the SMMs, and the joint configurations along the SMMs can be retrieved using the inverse Fourier transform. The proposed method is validated on planar 3R positioning, spatial 4R positioning, and spatial 7R positioning and orienting robots, using 10 000 randomly sampled workspace locations each. The results show that the proposed method can approximate SMMs with high accuracy and is much faster than the traditionally used nullspace projection method, a sampling-based method, and a grid-based method. The performance of the proposed method in real-time fault-tolerant motion planning applications is also demonstrated using the simulation of the spatial 7R robot and physical experiments on a planar 3R robot. Due to the computational efficiency of the proposed method, both robots are able to quickly plan trajectories which maximize the likelihood of task completion after the failure of one arbitrary joint.