The +1 Method: Model-Free Adaptive Repositioning Policies for Robotic Multi-Agent Systems

Abstract

Robotic multi-agent systems can efficiently handle spatially distributed tasks in dynamic environments. Problem instances of particular interest, and generality are the dynamic traveling repairman problem, and the dynamic vehicle routing problem. Operational policies for robotic fleets solving these two problems take decisions in an online setting with continuously arriving demands to optimize service level, and efficiency, and can be classified along several lines. First, some require a model of the demand, e.g., based on historical information, while others work model-free. Second, they are designed for different operating conditions from light to heavy system load. Third, they work in a time-invariant or time-varying setting. We present a novel class of model-free operational policies for time-varying demands, which have performance independent of the load factor, a combination of properties not achieved by other operational policies in the literature. The underlying principle of the introduced policies is to send available robots to recent service request locations. In simple terms, they rely on sending more than one robot for every service request arriving to the system. This leads to an advantage in scenarios where demand is non-uniformly distributed, and correlated in space, and time. We provide performance guarantees for both the time-invariant, and the time-varying cases as well as for correlated demand. We verify our theoretical results numerically. Finally, we apply our operational policy to the problem of mobility-on-demand fleet operation, and demonstrate that it outperforms model-based, and complex algorithms across all load ranges, despite its simplicity.