Control of Unmanned Ground Vehicles with Fractional Derivative

Abstract

This study investigates the control problem of a well-established unmanned ground vehicle (UGV) model formulated within the framework of conformable fractional calculus, with particular emphasis on both local and global stability analyses. To demonstrate the effectiveness and robustness of the proposed control strategies, we begin by conducting comprehensive numerical simulations that illustrate the vehicle's behavior under local stability conditions. Subsequently, we extend our analysis to the global domain, where the theoretical results are validated through detailed simulations confirming the system's convergence properties across a wide range of initial states. Furthermore, to clearly distinguish between local and global stability regimes, additional simulations are performed using randomly selected initial conditions—often located significantly far from the equilibrium point. These results highlight the remarkable performance of the proposed nonlinear controllers in ensuring global asymptotic stability. As anticipated, the designed control laws maintain excellent stability characteristics irrespective of the initial configuration, thereby confirming their suitability for practical implementations in real-world UGV navigation and control tasks.