Adaptive and fractional-order super-twisting (FO-STA) control for trajectory tracking of mobile robots with differential traction

Differential-drive mobile robots (DDMRs) are extensively used in logistics applications such as warehouse automation, last-mile delivery, and material handling owing to their simple mechanical structure and high maneuverability. Nevertheless, achieving accurate trajectory tracking remains challenging due to nonholonomic constraints, parameter uncertainties, wheel slip, and external disturbances in dynamic environments. Motivated by the inherent symmetry in the kinematic and dynamic structure of DDMRs, this paper proposes an adaptive control and a fractional-order super-twisting Algorithm (FO-STA)-based control framework for robust trajectory tracking using a dynamic model. The proposed approach adopted a dual-loop control architecture composed of an external kinematic loop and an inner dynamic loop, forming a robust control structure. The kinematic controller ensures convergence of the robot position to the desired reference trajectory, while the dynamic controller compensates for model uncertainties and external disturbances to achieve stable velocity tracking. An adaptive FO-STA mechanism was incorporated to enhance robustness against time-varying dynamics and unknown parameter variations. Both control laws were systematically derived using Lyapunov stability theory, guaranteeing closed-loop convergence and boundedness of tracking errors. Simulation results confirmed the effectiveness of the proposed strategy, demonstrating accurate trajectory tracking and strong robustness under parameter uncertainties and external disturbances, thereby validating its suitability for logistics-oriented mobile robotic systems.