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We propose a torque overlay-based robust steering wheel angle control method of electrical power steering (EPS) for a lane-keeping system of automated vehicles. The proposed method consists of an augmented observer and a nonlinear damping controller to guarantee the semi-global uniform ultimate boundedness of the steering wheel angle tracking error using only steering wheel angle feedback. The key idea of the proposed method is that the system functions with unknown parameters and external disturbance, along with their derivatives, are combined into an augmented state variable for designing the nonlinear observer in the absence of Lipschitz conditions. The augmented observer is designed in order to estimate the full state and disturbance. The nonlinear damping controller is developed via backstepping to suppress the angle tracking error using the input-to-state stability property when the estimation error becomes large. Since the proposed method is designed based on torque overlay, a torque integration using basic functions of the EPS for the steering wheel angle control is available for driver convenience. Furthermore, no modification of the EPS is required. The performance of the proposed method was validated through experimentation with a test vehicle. Index Terms-Lateralcontrol, Backstepping control, Automated vehicle control, Electric power steering, Stability NOMENCLATURE • θ h : Steering wheel angular position [deg] • θ h d : Desired steering wheel angular position [deg] • ω h : Steering wheel angular velocity [deg/s] • θ m : Motor angular position [deg] • ω m : Motor angular velocity [deg/s] • i: Current input of the motor [A] • T : Input torque of EPS system (T = K t i) [N·m] • T EP S : Drive assistant torque [N·m] • K t : Motor torque constant [N·m/A] • T d : Driver torque [N·m] • T f : Friction torque [N·m] 0018-9545 (c)

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We propose a new approach for virtual lane prediction. The main contribution of the proposed method is that the predicted virtual lane can be substituted for lane detection using a camera sensor when the camera image processing fails to detect the lane. The proposed method generates the predicted virtual lane using the relative movement between a vehicle and a lane. To predict the lane, a third-order polynomial function of the longitudinal distance is used as a lane model. Each coefficient of the lane polynomial function at the next sampling time is geometrically calculated using the relative movement of a vehicle, the lanes, the longitudinal velocity and the yaw of the vehicle at the present time. Then, the predictive virtual lane at the next sampling time is obtained without the lane information from the camera sensor at the next sampling time. The proposed method is simple enough that it is suitable for real implementation. The performance of the proposed method was evaluated via experiments with a test vehicle.