Comparative Analysis of Fuzzy Membership Functions for Step and Smooth Input Tracking in a 3-Axis Robotic Manipulator

Robotic manipulators are essential in industrial and medical applications, requiring precise control to improve efficiency and reduce errors. This research looks at how well fuzzy logic controllers using Gaussian, generalized bell, triangular, and trapezoidal membership functions can handle step and smooth inputs for a robot system that is meant to move materials. Critical metrics like steady-state values, overshoot, rise time, integral absolute error (IAE), and root mean square error (RMSE) were tested using five different methods. The results showed that both the Gaussian and extended bell functions found a good balance between being stable and being responsive. This made them useful for situations with moderate to high input levels. While triangular functions displayed enhanced responsiveness, they also revealed heightened overshoot. In contrast, trapezoidal functions demonstrated significant stability at high saturation levels, although they had challenges in attaining smooth transitions. These findings highlight the necessity of choosing membership functions according to particular application needs. This study investigates the utilization of hybrid methodologies and adaptive optimization strategies to improve fuzzy control systems. These concepts offer compelling approaches to improve accuracy and resilience in dynamic robotic settings.