An Illustration of Numerical Algebraic Methods for Workspace Estimation of Cooperating Robots after Joint Failure

We consider the estimation of the post-failure workspace of two two-link serial robots where the free-swinging failure of one robot’s last joint is handled by having the functional robot grasp the final link of the broken robot. We present an algorithm for finding the optimal placement of such synergistic robot arms and the optimal grasp point on the final link of the broken robot. To determine whether a point in the pre-failure workspace of the broken robot remains in the post-failure workspace, we solve an inverse kinematics problem in the form of a polynomial system. Homotopy continuation provides an efficient means for solving such polynomial systems, so we use the software package Bertini. Finally, Monte-Carlo methods are used to estimate the post-failure workspace.