Improving Trajectory Tracking of Differential Wheeled Mobile Robots With Enhanced GWO-Optimized Back-Stepping and FOPID Controllers

Improving trajectory tracking of differential wheeled mobile robots (DWMRs) is crucial for enhancing their effectiveness in various applications, such as autonomous cleaning, mowing, and leader-following scenarios. These scenarios often involve navigating complex, nonlinear paths, requiring advanced control strategies for improved performance. This work presents a novel integration of a Backstepping Controller (BSC) and a Fractional-Order Proportional-Integral-Derivative (FOPID) controller within a cascade closed-loop structure for DWMRs. The proposed BSC-FOPID controller addresses velocity saturations and nonlinearities, ensuring system stability and precise trajectory tracking. A key contribution is the enhanced Grey Wolf Optimization (GWO) strategy, termed GWO-SMA, which integrates GWO with the Slime Mould Algorithm (SMA). By leveraging opposition space and optimum cache concepts, the GWO-SMA improves fitness optimization in each iteration, enhancing both exploration and exploitation efficiency. This hybrid approach optimizes controller parameters using a multi-metric cost function that incorporates Integral Absolute Error (IAE) and Integral Squared Error (ISE) to minimize steady-state error and enhance responsiveness to larger deviations. Simulations demonstrate the superior performance of the proposed GWO-SMA algorithm compared to existing optimization techniques, such as Particle Swarm Optimization (PSO), Gazelle Optimization Algorithm (GOA), and its individual components, GWO and SMA, which have shown strong performance in recent literature for optimizing PID-type controllers. Additionally, simulation results using three distinct reference paths-lemniscate, square, and cloverleaf—demonstrate that the GWO-SMA-optimized BSC-FOPID controller outperforms both Adaptive Dynamic Compensation Control (ADCC) and the BSC-PID controller in position and posture tracking accuracy. Specifically, the BSC-FOPID controller achieves significant improvements, including average reductions of 55.65% in ISE and 38.25% in IAE for position control, as well as 62.12% and 38.95% improvements in ISE and IAE for posture control, respectively. These improvements highlight the controller’s enhanced responsiveness and smoother error convergence, particularly during maneuvers involving sharp curves.