This study investigated the design of an Adaptive Fractional Order Sliding Mode Control (AFOSMC) for stabilizing a flexible bicycle robot using a reaction wheel that depends chiefly on an adaptive mechanism to estimate unknown or time-varying system parameters online. The system’s inherently unstable roll dynamics pose a significant challenge, requiring precise control to maintain an upright posture. The proposed strategy combines a fractional-order sliding mode algorithm, known for its smooth control and robustness, with an adaptive mechanism. It effectively eliminates the need for their prior knowledge and prevents the excessive control chattering caused by overestimation. High-fidelity simulation results under realistic multi-source disturbance conditions, including wind perturbations, road irregularities, parameter uncertainties, and impulsive effects, demonstrate that the proposed AFOSMC consistently outperforms conventional sliding mode approaches. The method achieves up to 64% improvement in tracking accuracy, 62.5% reduction in maximum absolute error, and 84.4% reduction in chattering index, while maintaining smooth control behavior. These results highlight the effectiveness of the proposed framework in stabilizing highly unstable and disturbance-sensitive systems. The findings provide practical insights into the design of robust control strategies for underactuated robotic platforms, with potential applications in autonomous mobility, assistive robotics, and intelligent transportation systems.
Pham et al. (Mon,) studied this question.