Time optimal control for collision avoidance recovery of two unicycles.

摘要

This thesis addresses the problem of steering two identical Dubins unicycles back to desired constant headings in minimum time after a collision avoidance event. A canonical terminal condition for a collision avoidance controller is that the unicycles are a minimum distance from each other and with equal heading. For this terminal condition, we derive, based on the Pontryagin maximum principle, a time optimal "recovery controller" that returns the unicycles to their desired headings without incurring further collision avoidance events and while maintaining a minimum safe separation. As an intermediate step of the problem, we obtain a Dubins-like theorem on the feasible time optimal paths for a two unicycle system when one unicycle steers straight while the other's goal is to reach a desired heading. This result provides the first Dubins-like theorem available for the case of a unicycle navigating in the presence of a time-varying state constraint.