Explicit solutions for optimal Maneuver-based motion planning

In this paper, we examine the problem of optimal motion planning for a continuous dynamical system whose dynamics are described using a formal language, defined by a finite-state machine called a Maneuver Automaton. Any string in the language describes a feasible motion for the dynamical system. It is shown that, under appropriate technical conditions, the set of "sensible" strings in the language, that is, the set of words which describe optimal motions for some choice of initial and final configurations, is finite. This leads to a finite partition of the configuration space, into a number of critical regions associated to each sensible string. Hence, an explicit, exact and finite representation of optimal motion plans, and the corresponding costs, can be computed. The theory and the explicit optimal control solution are demonstrated on an sailboat steering example.