Lateral Control for Autonomous Vehicles: A Robust Bounded Back-Stepping Technique

In this paper, we propose a conceptually different backstepping approach to solve the global asymptotic stabilization problem for a class of nonlinear input-coupled systems with parameter uncertainties and both state and input constraints. This approach avoids both input-decoupling transformations and the cancellation of time derivatives of virtual control functions— steps that are typically required in conventional backstepping-based control designs for input-coupled systems. As a by-product, it broadens the applicability of existing backstepping techniques and significantly reduces the computational burden— a major obstacle for real-time implementation of these methods. The proposed approach relies on an innovative combination of control tools, including non-quadratic Lyapunov-like analysis, the concept of Input-to-State Stability (ISS), and the Invariance Principle, enabling the construction of a control law without quadratic (smooth) control Lyapunov functions— an advantage over standard Lyapunov-based designs, where constructing such functions is challenging in the presence of input constraints. Applied to the nonlinear lateral dynamics of autonomous vehicles, particularly in lane-keeping scenarios, it solves the lateral control and trajectory tracking problem, effectively addresses key limitations of standard backstepping designs, and demonstrates clear advantages over a representative existing method— proving its potential practical applicability in real-world control applications within dynamic and complex driving environments, such as lane-changing scenarios.