Control of the Uncertain Fully Flexible Link-Joint Robot Manipulators: A Free-Drift Adaptive Fractional-Order Robust Approach

This paper presents a fast and low-vibration tracking control strategy for an uncertain fully flexible link-joint (FFLJ) robot manipulator. Due to the highly underactuated nature of the system, along with the presence of uncertainties and external disturbances, a two-time-scale singular perturbation (SP) approach is adopted to decompose the system into slow and fast subsystems. To control the slow subsystem, a fractional-order fast terminal sliding mode control (FOFTSMC) is designed, ensuring rapid convergence with minimal transient and steady-state errors, which is essential for vibration suppression. Additionally, a free-drift partially adaptive super twisting reaching law is incorporated to prevent overestimation of control inputs, mitigate uncertainties and disturbances, and reduce chattering while optimizing energy efficiency. For the fast subsystem, a linear state-space representation is formulated based on the slow subsystem’s control input, explicitly considering uncertainties. An optimal proportional derivative linear quadratic regulator (PD-LQR) is then employed to regulate the fast subsystem dynamics, leading to a robust composite control scheme. A rigorous stability analysis guarantees the global asymptotic stability of both subsystems and the overall closed-loop control system. Simulation results confirm the effectiveness of the proposed strategy in handling nonlinearities, underactuation, and uncertainties. Compared to the FOFTSMC and the integer order robust fuzzy SMC (IORFSMC), the proposed free-drift adaptive FOFTSMC (AFOFTSMC) demonstrates superior performance, achieving approximately 45% and 85% improvement, respectively, in the first link tracking, and 4% and 65% improvement, respectively, in the second link tracking in terms of the integral of time multiplied by absolute error (ITAE) index. These results highlight the proposed approach’s robustness, efficiency, and capability to ensure precise trajectory tracking, vibration suppression, and chattering reduction while maintaining energy efficiency.