Maximizing the Probability of Task Completion for Redundant Robots Experiencing Locked Joint Failures

This article considers the problem of planning a trajectory that maximizes the probability that a robot will be able to complete a set of point-to-point tasks, after experiencing locked joint failures. The proposed approach first develops a method to calculate the probability of task failure for an arbitrary trajectory based on its failure scenarios, which are efficiently computed by identifying the ranges of task point self-motion manifolds. Then, a novel trajectory planning algorithm is proposed to find the optimal trajectory with maximum probability of task completion. The planning algorithm exploits the overlap of self-motion manifold bounding boxes, as opposed to always using the shortest distance, to determine an optimal trajectory. The proposed trajectory planning algorithm is demonstrated on planar positioning 3R, spatial positioning 4R, and spatial positioning/orienting 7R redundant robots, resulting in average improvement of 17%, 22%, and 30%, respectively, compared to the best shortest distance trajectory.