Locking underactuated robots by shrinking their manifolds of free-swinging motion

When a robot suffers a Free Swing Joint Failure, it becomes underactuated since some of its actuated joints become passive. If the joints that remain actuated are locked, the robot can perform uncontrollable free-swinging motions that are dangerous due to the risk of collision. This is typically corrected by using brakes or redundant actuators, which are costly solutions. In this paper, we propose an alternative method to secure underactuated robots after Free Swing Joint Failure without brakes or redundant actuators, by taking the healthy actuated joints to what we call "locking configurations". At these configurations, the manifolds along which the underactuated robot performs free-swinging motions degenerate into points, suppressing such uncontrollable motions. We present a discretization and clustering method to find locking configurations by detecting the degeneracy of free-swinging manifolds into points, introducing two criteria to confirm if these configurations are stable, by checking if passive joint velocities are forbidden or if any external wrench can be balanced by the healthy actuators. Several examples illustrate the method, including serial and parallel underactuated robots with varying numbers of failed actuators.