On a Traveling Salesman Problem with Dynamic Obstacles and Integrated Motion Planning

This paper presents a variant of the Traveling Salesman Problem (TSP) with nonholonomic constraints and dynamic obstacles, with optimal control applications in the mining industry. The problem is discretized and an approach for solving the discretized problem to optimality is proposed. The proposed approach solves the three subproblems (waypoint ordering, heading at each waypoint and motion planning between waypoints) simultaneously using two nested graph-search planners. The higher-level planner solves the waypoint ordering and heading subproblems while making calls to the lower-level planner that solves the motion planning subproblem using a lattice-based motion planner. For the higher-level motion planner A* search is used and two different heuristics, a minimal spanning tree heuristic and a nearest insertion heuristic, are proposed and optimality bounds are proven. The proposed planner is evaluated on numerical examples and compared to Dijkstras algorithm. Furthermore, the performance and observed suboptimality are investigated when the minimal spanning tree heuristic cost is inflated.