In a surface vehicle ride, the passenger’s comfort is desirable, ensuring safety under various tight constraints. To consider this requirement, this article has proposed a lateral control for autonomous vehicle considering the lateral offset error constraints. A reduced-order dynamics of the vehicle has been considered for improving and easy implementation of backstepping. A nonlinear control has been developed by utilizing the Time-varying Asymmetric Barrier Lyapunov Function via the Active Disturbance Rejection Control (ADRC) approach. The Extended State Observer, a component of applied ADRC, estimates all unknown system states as well as the unknown disturbance. The desired trajectories (smooth and non-smooth) based on the yaw rate profile have been synthesized to test the performance of the vehicle. Simulation results are presented to show the effectiveness of the proposed closed-loop control strategy. The vehicle performance has been compared using the proposed method, the conventional Quadratic Lyapunov Function and Symmetric Barrier Lyapunov Function based control. The proposed control provides a smoother control signal, small tracking error and robustness in presence of hard road constraints for smooth/non-smooth vehicle motion.