车道保持模型预测控制中车辆模型简化推导及仿真分析

Simplified Derivation of Vehicle Models for Lane-Keeping Model Predictive Control and Simulation Analysis

为提高车道保持控制中算法的计算效率,构建了模型预测控制(MPC)算法,基于刚体动力学推导出单轨车辆模型,并考虑横、纵向轮胎作用力特性作为标准车辆模型,在此基础上,忽略偏滑角和轮胎滑移率,推导出了简化车辆模型,该模型用线性方程表达车辆航向角变化率,省去轮胎模型,从而降低了MPC约束方程的复杂度。综合考虑跟踪误差、控制量及其变化率的代价项作为目标函数,对标准车辆模型和简化车辆模型的控制效果进行了仿真对比分析,结果表明,简化车辆模型在车道保持模型预测控制中取得了与标准车辆模型相近的控制效果,同时避免了车速接近0时无法求解轮胎模型的问题,且显著缩短了MPC优化求解耗时。

To improve calculation efficiency of lane-keep control algorithm,a Model Predictive Control(MPC)algorithm for lane-keeping was constructed.A single-rail vehicle model was derived based on rigid body dynamics.The standard vehicle model was based on rigid body dynamics and considered lateral and longitudinal tire force characteristic.Based on that,a simplified vehicle model was derived by assuming zero slip angle and slip ratio.The simplified model formulated yaw rate using linear equations and eliminated the tire model,thereby reducing the complexity of the constraint equations in the MPC.Considering the tracking error,control input,and the cost item of its change rate as the objective function,the control effect of standard vehicle model and simplified vehicle model were compared and analyzed.The results show that the simplified vehicle model achieves similar control performances to the standard model in lane-keeping MPC and avoids the problem of being unable to solve the tire model when the vehicle speed is close to zero.Additionally,the simplified model significantly reduces the computational time required for MPC optimization.