A hybrid Fuzzy approach of different controllers to stabilize a 3-link swinging robotic (Robogymnast)

In the research presented here, a Fuzzy logic controller is tuned for both a Linear Quadratic Regulator (LQR) and a proportional derivative (PD) controller, which are applied in stabilizing a multi-link robotic system called the Robogymnast. The Robogymnast imitates the activity of gymnast on the high bar swinging up to reach a vertical handstand, keeping the hands in contact with the bar. To replicate this, the section of the robotic system representing the hands is securely attached to the high bar via ball bearing mountings which can rotate freely. This study investigates problems of controlled upswing, using the underactuated, three-link Robogymnast system. The mathematical system modelling is linearised evaluating methods which employ Largran's equation for state-space determinations. The study employed a controller based on Fuzzy LQR [1] to implement the system and an evaluation was made of how far response was stabilised. This evaluation was repeated applying a Fuzzy PD controller, with comparisons of each controller's performance made. In the final part of the study, the system was simulated using MATLAB Simulink, examining a range of factors such as rise and settling time, as well as over and undershoot. This paper chiefly aims to evaluate Robogymnast implementation with a fuzzy logic/LQR controller.