A Game-Theoretic Predictive Control Framework with Statistical Collision Avoidance Constraints for Autonomous Vehicle Overtaking

Abstract: This work develops a control framework for the autonomous overtaking of connected and automated vehicles (CAVs) in a mixed traffic environment, where the overtaken vehicle is an unconnected but interactive human-driven vehicle. The proposed method, termed the Game-Theoretic, PRedictive Overtaking (GT-PRO) strategy, successfully decouples the longitudinal and lateral vehicle dynamics of the CAV and comprehensively coordinates these decoupled dynamics via innovative longitudinal and lateral model predictive (MPC) based controllers, respectively. To address the real-time interactive behavior of the human-driven overtaken vehicle, a dynamic Stackelberg game-based bilevel optimization is solved by the lateral controller to directly control the CAV lateral motion and predict the overtaken vehicle longitudinal responses that are subsequently shared with a stochastic MPC that governs the CAV longitudinal motion. The proposed strategy exploits a comprehensive real-world dataset, which captures human driver responses when being overtaken, to tune the game-theoretic lateral controller according to the most common human responses, and to statistically characterize human uncertainties and hence implement a collision avoidance chance constraint for the stochastic longitudinal controller. The simulation results for both polite and aggressive human response case studies of the overtaken vehicle demonstrate that the proposed GT-PRO can achieve for this range of human driver responsiveness, safer, more efficient, and more comfortable autonomous overtaking, as compared to existing autonomous overtaking approaches in the literature. Furthermore, the results suggest that the GT-PRO method is capable of real-time implementation.