On the discretized dubins traveling salesman problem

This paper deals with minimizing the visitation cost of a kinematic constrained vehicle through a set of targets. We are motivated by real-world scenarios that include motion planning for manned and unmanned marine and aerial vehicles and motion planning for robots, just to name some possible application outlets. We discretize the original continuous problem and explicitly formulate it as an integer optimization problem. Then we analyze its performance and develop an upper bound as a function of the discretization level and the number of targets. The suggested linkage between discretization level, number of targets and performance provides an opportunity to guide discretization level choices for the solution of motion planning scenarios.