LQR motion control and analysis of a prototype spherical robot

This article presents the results of a study on a prototype of spherical rolling robot and proposed a linear quadratic regulator controller to stabilize the system. The dynamic model of this spherical rolling robot has been presented with 2-DOF pendulum located inside a spherical shell and considered as a plate-ball system. The motion of the system is generated with a servo motor for left and right direction and a DC motor for forward and backward motion. Dynamic equations of the system are derived based on Euler-Lagrange method. Controlling a spherical robot is a challenging problem till today due to its nature of kinematics and highly nonlinear dynamics. Accordingly, a mid loop linear quadratic regulator (LQR) has been designed using full-state feedback to control the spherical robot. Simulation and experimental test have been carried out to show the effectiveness of the proposed controller.