Optimization and numerical approaches for autonomous vehicles path following problem

Abstract

This study presents and evaluates three steering angle selection methods formulated for path following tasks. The methods determine the steering angle input through numerical integration of the vehicle equations of motion over a finite prediction horizon, divided into small time subintervals. The first approach introduces classical Nelder-Mead optimization algorithm when the steering angle is defined by minimizing a cost functional which is trajectory-tracking error. In the second and third cases the minimization of the cost functional is obtained by applying the following numerical methods: Newton iteration and bisection. The methods are applicable to vehicle dynamics models of varying complexity. Presented methods have been evaluated using planar (3 degrees of freedom — DoF) and spatial (10-DoF) vehicle models. Simulation results demonstrate that proposed approaches achieve trajectory-tracking accuracy comparable to those reported in literature. The bisection-based method provides balance between accuracy and computational efficiency, enabling reliable steering angle computation for trajectories with varying curvature and non-uniform speed profiles. A key advantage of the proposed numerical methods is their ability to incorporate nonlinear vehicle dynamics while significantly reducing the computational effort compared to conventional optimization-based approaches