A Simulated Annealing Approach to Coordinated Motion Planning (CG Challenge)

The third computational geometry challenge was on a coordinated motion planning problem in which a collection of square robots need to move on the integer grid, from their given starting points to their target points, and without collision between robots, or between robots and a set of input obstacles. We designed and implemented an algorithm for this problem, which consists of three parts. First, we computed a feasible solution by placing middle-points outside of the minimum bounding box of the input positions of the robots and the obstacles, and moving each robot from its starting point to its target point through a middle-point. Second, we applied a simple local search approach where we repeatedly delete and insert again a random robot through an optimal path. It improves the quality of the solution, as the robots no longer need to go through the middle-points. Finally, we used simulated annealing to further improve this feasible solution. We used two different types of moves: We either tightened the whole trajectory of a robot, or we stretched it between two points by making the robot move through a third intermediate point generated at random.