Motion Planning and Goal Assignment for Robot Fleets Using Trajectory Optimization

This paper is concerned with automating fleets of autonomous robots. This involves solving a multitude of problems, including goal assignment, motion planning, and coordination, while maximizing some performance criterion. While methods for solving these sub-problems have been studied, they address only a facet of the overall problem, and make strong assumptions on the use-case, on the environment, or on the robots in the fleet. In this paper, we formulate the overall fleet management problem in terms of Optimal Control. We describe a scheme for solving this problem in the particular case of fleets of non-holonomic robots navigating in an environment with obstacles. The method is based on a two-phase approach, whereby the first phase solves for fleet-wide boolean decision variables via Mixed Integer Quadratic Programming, and the second phase solves for real-valued variables to obtain an optimized set of trajectories for the fleet. Examples showcasing the features of the method are illustrated, and the method is validated experimentally.