Optimal Solution of the Generalized Dubins Interval Problem

Abstract

The problem addressed in this paper is motivated by surveillance mission planning with curvature-constrained trajectories for Dubins vehicles that can be formulated as the Dubins Traveling Salesman Problem with Neighborhoods (DTSPN). We aim to provide a tight lower bound of the DTSPN, especially for the cases where the sequence of visits to the given regions is available. A problem to find the shortest Dubins path connecting two regions with prescribed intervals for possible departure and arrival heading angles of the vehicle is introduced. This new problem is called the Generalized Dubins Interval Problem (GDIP) and its optimal solution is addressed. Based on the solution of the GDIP, a tight lower bound of the above mentioned DTSPN is provided which is used to steer sampling-based algorithm to determine a feasible solution that is close to the optimum.