Comparison of Time-Varying Stabilizing Strategies for a Kinematic Car Model: Numerical Simulations

This paper addresses the kinematic model of a front-wheel-driven car with two control inputs. We develop a family of time-varying feedback laws that incorporate oscillating signals to stabilize the equilibrium of this model. Our contribution encompasses three control design strategies: designing for the original vector fields, employing a nilpotent approximation, and implementing a simplified scheme through component-wise matrix inversion. We simulate the trajectory behaviors for these strategies under classical solutions of the closed-loop system and under sampling-based solutions. Numerical simulations are conducted to provide a comparative analysis of the stabilization algorithms presented.