On the Discretized Dubins Traveling Salesman Problem

This research deals with a variation of the traveling salesman problem in which the cost of a tour, during which a kinematically constrained vehicle visits a set of targets, has to be minimized. We are motivated by scenarios that include motion planning for unmanned aerial, marine, and ground vehicles, just to name a few possible application outlets. We discretize the original continuous problem and explicitly formulate it as an integer optimization problem. Then we develop performance bounds as a function of the discretization level and the number of targets. The inclusion of a discretization level provides an opportunity to achieve tighter bounds, compared to what has been reported in the literature. The suggested linkage between discretization level, number of targets, and performance may guide discretization level choices for the solution of motion planning scenarios. We perform a numerical study that quantifies the performance of the suggested approach.