  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.
