A Dynamic Programming Algorithm for Grid-based Formation Planning of Multiple Vehicles

A common operation in multirobot systems is to generate a motion plan for multiple robots such that the robots can move in formation to achieve some desired effects. For example, in autonomous parking lots, a group of vehicles can be asked to move to another location when they block another vehicle that needs to leave the parking lot. In this paper, we present a novel grid-based planning approach for motion planning that minimizes the makespan of moving multiple vehicles from one location to another in a safe manner. Unlike most existing multirobot planning algorithms, our algorithm uses dynamic programming to compute a nearly-optimal motion plan for a large group of vehicles in polynomial time with the help of a given set of intermediate vehicle patterns. Our experimental results show that our algorithm is much faster than an exact algorithm but does not increase the minimum makespans tremendously.