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 redand 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.

There are currently two existing methods to compute the fault-tolerant workspace of a redundant robot arm for a given set of artificial joint limits. However, both of these methods are very computationally expensive. This article proposes using a mixture density network to learn the probability that a rotation angle belongs to the fault-tolerant rotation ranges. A difference filter is used to remove outlying rotation angles predicted by the network, and the remaining rotation angles are grouped together to generate the fault-tolerant workspace. Because this method is highly computationally efficient, it can be used alongside a genetic algorithm to compute the optimal artificial joint limits to maximize the area of the fault-tolerant workspace for a given robot arm. The predicted fault-tolerant workspace is compared to the actual fault-tolerant workspace, which proves the effectiveness of this algorithm. The computational speed of this proposed algorithm is roughly 390 times faster than the traditional method. Finally, a trajectory is placed within the fault-tolerant workspace predicted by the proposed method, and the experimental results show that this trajectory is tolerant to arbitrary joint failures.