Game Theoretic Modelling of a Human Driver’s Steering Interaction with Vehicle Active Steering Collision Avoidance System

Development of vehicle active steering collision avoidance systems calls for mathematical models capable of predicting a human driver’s response so as to reduce the cost involved in field tests whilst accelerate product development. This article provides a discussion on the paradigms that may be used for modelling a driver’s steering interaction with vehicle collision avoidance control in path-following scenarios. Four paradigms, namely decentralized, noncooperative Nash, noncooperative Stackelberg and cooperative Pareto are established. The decentralized paradigm, developed based on optimal control theory, represents a driver’s interaction with the collision avoidance controllers that disregard driver steering control. The noncooperative Nash and Stackelberg paradigms are used for predicting a driver’s steering behaviour in response to the collision avoidance control that actively compensates for driver steering action. These two are devised based on the principles of equilibria in noncooperative game theory. The cooperative Pareto paradigm is derived from cooperative game theory to model a driver’s interaction with the collision avoidance systems that take into account the driver’s target path. The driver and the collision avoidance controllers’ optimization problems and their resulting steering strategies arise in each paradigm are delineated. Two mathematical approaches applicable to these optimization problems, namely the distributed Model Predictive Control and the Linear Quadratic dynamic optimization approaches are described in some detail. A case study illustrating a conflict in steering control between driver and vehicle collision avoidance system is performed via simulation. It was found that variation of driver path-error cost function weights results in a variety of steering behaviours which are distinct between paradigms.