Application of Open-Loop Stackelberg Equilibrium to Modeling a Driver's Interaction with Vehicle Active Steering Control in Obstacle Avoidance

The increasing use of active front steering (AFS) technology for obstacle avoidance raises the question of drivers' interaction with vehicle automation. Mathematical models capable of representing such interaction are in demand for driver behavior study. This paper presents the application of open-loop Stackelberg equilibrium to modeling a driver's interaction with vehicle AFS control in an obstacle avoidance scenario, where both the driver and the AFS controller are exerting steering control to the vehicle. In this paper, such driver-AFS interactive steering control is modeled as a leader-follower game. Mathematical expressions of the driver's and the AFS controller's steering control strategies are derived using the linear quadratic dynamic optimization approach and the distributed model predictive control (DMPC) approach. These two approaches are found to give identical control gains, which suggest their equivalence in representing driver-AFS interaction. The DMPC approach is found to consume far less computation time due to its numerical nature. Mathematical modifications to the steering control strategies are then introduced to allow practical implementation for a future experimental study. Simulation results including time histories of steering angles and vehicle responses are illustrated and discussed.