A Hybrid Approach for Estimating the Failure-Tolerant Workspace Size of Kinematically Redundant Robots

Previous work has shown that it is possible to guarantee a reachable workspace for a kinematically redundant robot after an arbitrary locked-joint failure if one artificially restricts the range of its joints prior to the failure. Identifying the optimal articial joint limits has been the subject of previous work to maximize this so-called “failure-tolerant workspace.” Unfortunately, these techniques are not feasible for a highly redundant robot operating in a spatial workspace. This work presents a novel hybrid technique for estimating the failure-tolerant workspace size for robots of arbitrary kinematic structure and any number of degrees of freedom performing tasks in a 6D workspace. The method presented combines an algorithm for computing self-motion manifold ranges to estimate workspace envelopes and Monte-Carlo integration to estimate orientation volumes to create a computationally efficient algorithm. This algorithm is then combined with the coordinate ascent optimization technique to determine optimal artificial joint limits that maximize the size of the failure-tolerant workspace of a given robot. This approach is illustrated on multiple examples of robots that perform tasks in 3D planar and 6D spatial workspaces.