Dynamic control of a unicycle robot with double flywheels using linear quadratic regulator and linear matrix inequality

Abstract

Unicycle robot is a highly nonlinear system that has less number of points of contact with the floor. Accordingly, it represents a special topic for researchers to study the stability and the balancing control. This work considers the motion control of the unicycle robot with double flywheels since this construction raises issues such as highly instability on the roll, the pitch and the yaw directions. Chantarachit et al. [1] have proposed a dynamic model of a unicycle robot with double flywheels where they used a linear quadratic regulator in order to stabilize the current model. Hence, based on this model, we shall investigate the gain matrix using the LMI algorithm and compare the results with the LQR control method which is already designed by [1]. The below figures show a comparison between two linear controllers which are the LQR approach and the LMI approach. The aim of this work is to prove the effectiveness and the robustness of LMI. Figure 2 shows that the gain found by the LMI method is able to stabilize the model within [0 ; 12] s. Hence, it is considered more effective and robust over the gain found by the LQR method. As a perspective, a proper unicycle system model will be introduced and designed in order to achieve the main objective which is the stability control by formulating this model mathematically, then studying the stability by using the linear, nonlinear and intelligent control algorithm.