Minimum-Time Escape from a Circular Region for a Dubins Car

We investigate the problem of finding paths that enable a robot modeled as a Dubins car (i.e., a constant-speed finite-turn-rate unicycle) to escape from a circular region of space in minimum time. This minimum-time escape problem arises in marine, aerial, and ground robotics in situations where a safety region has been violated and must be exited before a potential negative consequence occurs (e.g., a collision). Using the tools of nonlinear optimal control theory, we show that a surprisingly simple closed-form feedback control law solves this minimum-time escape problem, and that the minimum-time paths have an elegant geometric interpretation.