Modelling of LQR and Fuzzy-LQR Controllers for Stabilisation of Multi-link Robotic System (Robogymnast)

This study applies a Linear Quadratic Regulator, LQR and a fuzzy logic linear quadratic regulator controller to stabilize a 3-link robot gymnast (Robogymnast) system. This system mimics manoeuvres in human acrobatics in which a person who is hanging by their hands from a high bar attempt to swing into a handstand posture while holding onto the bar. This imitation involves a secure attachment of the hand parts of the Robogymnast to a ball-bearing-mounted high bar capable of free rotation. The paper considers issues in controlling swing-up with this 3-link, underactuated system, as well as linearising the system’s mathematical model, examining approaches using Largran’s equation to determine the system’s state space. A Fuzzy-LQR controller was selected for system implementation in order to identify the extent of stabilization of responses. In addition, MATLAB Simulink was used to simulate the system to demonstrate outcomes for variables including overshoot, rising, and settling times. The main aim of the study is to examine the application of linear quadratic regulator /fuzzy logic controllers to the robotic gymnast.