Mathematics

We consider two problems in planning and controlling a class of vehicles along planar routes. The vehicle is supposed to move forward only with a given velocity profile, and to have bounds on its turning radius. This model, sometimes referred to as the "Dubins's vehicle", is relevant to the kinematics of road vehicles as well as aircraft cruising at constant altitude, or sea vessels. We consider first the optimal control problem consisting in minimizing the length travelled by the vehicle starting from a generic configuration to connect to the specified route. A feedback law is proposed, such that straight routes can be approached optimally, while system is asymptotically stabilized. A generalization to curved paths is also described. In the second part, we will consider the problem of optimal coordinated conflict management scheme for a simplified model of traffic, where several Dubins' vehicles share their operational space with possibly conflicting requirements on minimization of path length. A technique to minimize total fuel consumption while guaranteeing safety against collisions is described, in the hypothesis of full cooperation among agents. A decentralized implementation of such a scheme is then introduced, and its features as a hybrid control scheme are described. Finally, we discuss the tradeoff between performance and fault tolerance that goes with decentralization, and assess it by extensive simulation trials. Links with work at U.C. Berkeley on optimization under a non--cooperative assumption will be considered.