An example of computing the failure-tolerant workspace area for a planar kinematically redundant robot

Robots are frequently employed in structured environments for automating repetitive tasks. To extend their application to remote or hazardous environments, one must guarantee some measure of failure tolerance. One way to do this is to use kinematically redundant robots that have additional degrees of freedom. They are inherently robust to locked joint failures but the size of the reachable workspace after a failure depends on the design (and control) of the robot. The existence of such a workspace can be guaranteed by imposing a suitable set of artificial joint limits prior to a failure, however, this also limits the reachable pre-failure workspace. This work demonstrates how one can calculate an optimal tradeoff between pre-failure and post-failure workspace by determining the appropriate artificial joint limits. This is illustrated on a three degree-of-freedom planar robot generated from a PA-10 robot.