Adaptive Gain Twisting Sliding Mode Controller Design for Flexible Manipulator Joints with Variable Stiffness

This paper proposes an adaptive gain twisting sliding-mode control (AGTSMC) strategy for trapezoidal variable-stiffness joints (TVSJs) to achieve accurate trajectory tracking under both matched and mismatched uncertainties. The TVSJ employs a compact trapezoidal leaf spring with grooved bearing followers (GBFs), enabling wide-range stiffness modulation through low-friction rolling contact. To address the strong nonlinearities and unmodeled dynamics introduced by stiffness variation, a Lyapunov-based adaptive twisting controller is developed, where the gains are automatically adjusted without conservative overestimation. A second-order sliding-mode differentiator is integrated to estimate velocity and disturbance terms in finite time using only position measurements, effectively reducing chattering. The proposed controller guarantees finite-time stability of the closed-loop system despite bounded uncertainties and measurement noise. Extensive simulations and hardware-in-the-loop experiments on a TVSJ platform validate the method. Compared with conventional sliding mode controller (CSMC), terminal sliding mode controller (TSMC), and fixed-gain twisting control (TC), the AGTSMC achieves faster convergence, lower steady-state error, and improved vibration suppression across low, high, and variable stiffness modes. Experimental results confirm that the proposed approach enhances tracking accuracy and energy efficiency while maintaining robustness under large stiffness variations.