High-Precision Force Tracking Under Uncertainty: A Fuzzy-Adaptive Sliding-Mode Impedance Control Approach

Achieving high-precision force tracking in robotic physical interaction remains challenging in the presence of environmental and dynamic model uncertainties. Conventional impedance control strategies often exhibit excessive force overshoot at contact onset and persistent steady-state errors under uncertain or time-varying interaction conditions. To overcome these limitations, this paper proposes a fuzzy-adaptive sliding-mode impedance control approach. During the initial contact phase, a tracking differentiator (TD) is employed to generate a smooth and dynamically feasible force reference, effectively suppressing impulsive force transients without requiring explicit contact detection. Furthermore, a fuzzy-logic-modulated adaptive law is developed to adjust online the adaptation gains of the impedance controller, thereby asymptotically eliminating steady-state tracking errors while preserving Lyapunov stability. In addition, a composite PD–suboptimal sliding-mode control law is embedded within the impedance loop to enhance robustness against external disturbances while ensuring continuous, chattering-free control action. The proposed architecture requires no prior knowledge of environmental stiffness and is provably robust to model inaccuracies and unstructured disturbance. Simulation and experimental results conducted on a 6-DOF robotic manipulator demonstrate that, under realistic uncertain contact scenarios and in comparison with three benchmark methods, the proposed approach reduces overshoot by 26%, shortens settling time by 30%, and decreases steady-state error by 48%.