A mixed integer programming model for timed deliveries in multirobot systems

We present a solution that enables robots to operate in long-duration missions with minimal interruption for recharging or refreshing other resources. Consider a set of deployed “task robots” that request resources (e.g. batteries) from a distribution center, which can deploy “delivery robots” to fulfill those requests. We address the scheduling problem with multiple incoming time-bound requests from the task robots. Our proposed framework incorporates priorities on working robots that can be adjusted by a human operator during scheduling, since mission priorities can change over time. The framework allows a relaxed delivery schedule when available resources are scant and permits dynamic re-routing of delivery robots. The problem is posed as a variant of the Vehicle Routing Problem with Time Windows, and solved as a Mixed Integer Quadratic Program using a branch and bound based solver. We present the specific case of a battery distribution system and validate the results in simulation.