A Mean Field Game Approach to Swarming Robots Control

Abstract

Controlling the collective behavior through individuals of swarming robots to accomplish the tasks which are beyond the capability of an individual robot is an important yet challenging problem for both research and industry communities, since the relationship between individual behavior and collective behavior for swarming robots still remain unclear. To bridge this gap, mean field game is applied using two coupled PDEs where the backward equation is used to understand the behavior of individual robots while the forward equation governs the evolution of the robots' distribution. The proposed approach aims to provide an optimal control strategy for each individual such that the desired swarm distribution generated by random forest regression can be tracked. The discrete mean field game is solved numerically to find the optimal control where the running cost is learned instead of directly given. Our proposed approach is illustrated by an example with the data from NYC taxi trips.