Invariant Configuration-Space Bubbles for Revolute Serial-Chain Robots

This paper adapts the invariant-set motion planner (ISMP) for robot motion planning. We derive control invariant subsets of configuration-space bubbles lifted into the state-space. The resulting sets guarantee collision avoidance since they are both constraint admissible and control invariant. We present a command governor that enforces the positive invariance of the constraints in closed-loop. This governor can be used to transform any nominal tracking controller into a constraint enforcing controller. We use these control invariant sets to quantify a relationship between velocity and control authority that enables collision avoidance. We demonstrate our invariant-sets through an illustrative numerical example.