Abstract: A non-cooperative model predictive control strategy is proposed to address the problem of co-piloting control between drivers and automation systems. First, a two-degree-of-freedom vehicle model is used to model the lateral control of the vehicle, then a human-automation co-piloting control model is established based on the trajectory tracking and steering input, and the cost functions of the driver and automation system are proposed. Then, the driver and automation system are described as a non-cooperative game using game theory principles, and the Nash equilibrium solution of the human-automation steering input is obtained. Finally, the influence of different weight matrices in the cost function on the human-automation control is verified through a Simulink/CarSim joint simulation experiment. The research results show that the weight matrix that mainly affects the vehicle trajectory is the lateral deviation weight matrix and the steering input weight matrix, while the steering input increment weight matrix affects the convergence speed of the steering input.Therefore, in the human-automation co-piloting strategy, the vehicle can be driven stably, safely, and efficiently by rationally allocating the size of the weight matrix.

Key words: human-automation co-driving; game theory; model predictive control; Nash equilibrium

摘要： 针对驾驶人和自动化系统共驾控制的问题，文章提出了一种非合作模型预测控制策略。 首先基于二自由度汽车模型对车辆横向控制进行建模；其次建立了人机共驾控制模型，依据 轨迹跟踪和转向输入提出了驾驶人和自动化系统的代价函数；再次利用博弈论的原理将驾驶 人和自动化系统描述为一种非合作博弈状况，求解了人机转向输入的纳什均衡解；最后通过 Simiulink/CarSim 联合仿真实验验证了代价函数中不同权重矩阵对人机控制的影响。研究表 明，主要影响车辆轨迹的权重矩阵为横向偏差权重矩阵和转向输入权重矩阵，而转向输入增 量权重矩阵影响的是转向输入的收敛速度，因此，在人机共驾策略中可以通过合理分配权重 矩阵的大小使车辆在行驶中的稳定安全且高效。

关键词: 人机共驾；博弈论；模型预测控制；纳什均衡