Decentralized optimal control for large populations of two-wheeled vehicles

In this paper, we consider decentralized optimal control for large populations of two-wheeled vehicles via mean field game theory. Specifically, the main objective is that each two-wheeled vehicle follows the average behavior (or mean field) of the whole population while achieving the overall optimal control performance without sharing their state information (position and/or velocity) with other vehicles. We first provide a general modeling framework of the two-wheeled vehicle for its position control by using balances of moments and forces that are obtained from the two electric DC motors and the vehicle chassis structure. Next, we design an optimal control for each vehicle, which is decentralized as it is a function of its own state, and the set of designed decentralized optimal controls constitutes an ϵ-Nash equilibrium. With these decentralized optimal controls, we characterize an approximated average behavior of the vehicles, and show that it is the best estimate of the actual average behavior when the population size becomes arbitrarily large. Finally, these theoretical results are validated through simulation and experiment results of large populations of two-wheeled vehicles.