Design and simulation of spherical robot’s controlling approaches to follow a desired trajectory.

Abstract

Robots have developed greatly due to the research that focused on them, and one of these robots is the spherical robot that attracted the attention of

researchers because of its great importance in practical life. In this research, a mathematical model was found that represents the dynamics of the spherical robot, and then its dynamic equations were represented with state equations and simulate them using MATLAB Simulink.

Advanced control methodologies were also used in this research to achieve stability of the spherical robot and achieve tracking of reference positions, curved paths, circular paths, and paths in the shape of the

letter (∞). The methodologies used are:

The linear quadratic optimization controller PI_LQR, the integral

optimization controller LQI, and the optimization controller with the Fuzzy Controller and Model reference adaptive control MARC. The performance of these controllers was tested for the ideal and real case, which is the absence of frictional forces between the spherical robot and the contact plane with it, and for the presence of frictional forces whose value is proportional to the speed. , where the responses were compared for different linear speeds and frictional forces proportional to them, according to the roughness of the contact surfaces with the spherical robot.

Simulation results using MATLAB demonstrated the importance of the LQR feedback controller in achieving system stability. It also showed the superiority of the FUZZY with LQR control system compared to the PI with LQR and Integral-LQR control systems in response speed and low static error value while following a desired path without friction forces. At the same time, MARC demonstrated high performance toward frictions.