Adaptive Fuzzy Sliding Mode Control with Scalar Sign Function for High-Precision Trajectory Tracking of 3-DOF Planar Robotic Manipulators

This paper presents an Adaptive Fuzzy Sliding Mode Control (AFSMC) framework for high-precision trajectory tracking of 3-degree-of-freedom (3-DOF) planar robotic manipulators, addressing critical challenges in industrial automation and
precision robotics. The proposed controller systematically integrates fuzzy logic adaptation with an enhanced supervisory layer and a novel scalar sign function implementation to overcome the inherent limitations of conventional Sliding Mode
Control (SMC), particularly chattering phenomena and sensitivity to system uncertainties. A Proportional-Integral-Derivative (PID) sliding surface architecture ensures robust tracking performance while providing theoretical guarantees for asymptotic stability through rigorous Lyapunov analysis. The supervisory fuzzy system dynamically modulates control gains in real-time based on tracking error and its derivative, enabling autonomous adaptation to varying operational conditions without requiring precise knowledge of uncertainty bounds. The implementation of a smooth scalar sign function through continued fraction expansion effectively eliminates chattering while maintaining the disturbance rejection capabilities essential for robotic applications. Comprehensive numerical simulations, conducted under realistic operating scenarios including parametric uncertainties of up to ±25%, unmodeled dynamics, external disturbances, and measurement noise, demonstrate the superior performance of the proposed AFSMC approach. Comparative evaluations
against conventional SMC and non-adaptive Fuzzy SMC (FSMC) reveal significant improvements in tracking accuracy, chattering reduction, convergence speed, and robustness to parameter variations and external disturbances. The proposed controller demonstrates particular effectiveness in precision applications such as micro-assembly, biomedical device handling, and high-speed pick-and-place operations, offering a computationally efficient solution suitable for real-time implementation. The results establish the AFSMC framework as a viable and advanced control
strategy for next-generation robotic systems requiring high precision, robust performance, and adaptive capabilities under realistic operating conditions.