Adaptive Sliding Mode Control with Time-Delay Error Compensation and Admittance-Based Force Tracking

This paper presents a control framework that integrates adaptive sliding mode control (ASMC), time-delay control (TDC), and admittance filtering to achieve robust force and position tracking in robot manipulators. TDC is employed to estimate unmodeled dynamics using delayed measurements, while ASMC enhances robustness by compensating for time-delay estimation (TDE) errors and mitigating chattering effects. An adaptive law incorporating a decline-rate reduction factor is introduced to explicitly regulate the decay of the adaptive gain inside the boundary layer, thereby preserving compensation capability against time-delay estimation errors and external disturbances for a longer duration while improving position tracking performance. In addition, the admittance mechanism converts force-tracking errors into position correction signals, enabling force tracking without modifying the underlying position control structure. The stability of the closed-loop system is analyzed based on Lyapunov theory, ensuring bounded tracking performance in the presence of estimation errors and uncertainties. Simulation results demonstrate that the proposed method improves position tracking accuracy—reducing the root mean square error (RMSE) from 0.0522 mm to 0.019 mm—while maintaining reliable force tracking performance.