Gain-Scheduled Sliding Mode Control with Time-Delay Estimation for a Cable-Driven Joint of an Underwater Manipulator

Using cable transmission in underwater manipulators helps to reduce the mass and rotational inertia of distal moving components, but the control performance of cable-driven joints is affected by flexible cable transmission, equivalent joint-side friction, hydrodynamic effects, and external disturbances. This paper proposes a control method combining time-delay estimation (TDE) with gain-scheduled sliding mode control (GSMC) for a cable-driven joint of an underwater manipulator. TDE uses delayed control-input and joint-acceleration data to estimate and compensate for the lumped dynamic term in the equivalent joint model online. GSMC employs a composite sliding surface and an error-dependent gain-scheduling mechanism to suppress trajectory-tracking errors in the presence of the TDE estimation residual. In joint-level MATLAB/Simulink R2024b simulations, smooth-step, sinusoidal-trajectory-tracking, and ablation results under predefined combined-uncertainty conditions, together with the results of 50 paired Monte Carlo runs, show that TDE-GSMC achieves the lowest major tracking-error indices among the four methods for the smooth-step and 0.35Hz sinusoidal trajectories and also yields the lowest mean tracking error and 95th percentile of the disturbance peak in the Monte Carlo simulations; the ablation results further characterize the performance differences among the tested controller configurations.