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This paper proposes an efficient computational framework for longitudinalvelocity control of a large number of autonomous vehicles (AVs) and develops atraffic flow theory for AVs. Instead of hypothesizing explicitly how AVs drive,our goal is to design future AVs as rational, utility-optimizing agents thatcontinuously select optimal velocity over a period of planning horizon. With alarge number of interacting AVs, this design problem can become computationallyintractable. This paper aims to tackle such a challenge by employing mean fieldapproximation and deriving a mean field game (MFG) as the limiting differentialgame with an infinite number of agents. The proposed micro-macro model allowsone to define individuals on a microscopic level as utility-optimizing agentswhile translating rich microscopic behaviors to macroscopic models. Differentfrom existing studies on the application of MFG to traffic flow models, thepresent study offers a systematic framework to apply MFG to autonomous vehiclevelocity control. The MFG-based AV controller is shown to mitigate traffic jamfaster than the LWR-based controller. MFG also embodies classical traffic flowmodels with behavioral interpretation, thereby providing a new traffic flowtheory for AVs.

A Game-Theoretic Framework for Autonomous Vehicles Velocity Control: Bridging Microscopic Differential Games and Macroscopic Mean Field Games