Motion-Planning for Unicycles using the Invariant-Set Motion-Planner

This paper adapts the invariant-set motion-planner to systems with unicycle-like dynamics. The invariant-set motion-planner is a motion-planning algorithm that uses the positive-invariant sets of the closed-loop dynamics to find a collision-free path to a desired target through an obstacle filled environment. The main challenge in applying the invariant-set motion-planner to unicycles is that the positive invariant sets of the unicycle under discontinuous feedback control have complex geometry. Thus, we develop numerically efficient mathematical tools for detecting collisions. We demonstrate the invariant-set motion-planner for unicycles in an automated perpendicular parking case study.