Development and Control of the Stick Robot Using Three Reaction Wheels

A prototype of a stick robot with three reaction wheels is developed. Its balancing control is proposed in this paper. The stick robot is an inverted pendulum system using three reaction wheels as actuators. The robot can maintain itself at the upright position by applying appropriate motions of the three reaction wheels. A mechanical design, electrical circuit design, and control algorithm design are all required to build and balance the stick robot. The Linear Quadratic Regulator (LQR) is proposed to balance the robot. This control method attempts to minimize the cost related to the robot's states and control energy. This paper illustrates the dynamic model of the stick robot that has coupling effects between axes and can be used to describe the robot's behavior in terms of dynamics equation. From both simulations and experiments, the stick robot is able to stand on its own at the upright position. The angle in the x-direction has an error band of 0.1343 degree. It has a 0.2-second settling time. It also has 0.0011 degrees and 0.0335 degrees for mean square error and root mean squared error. The angle in the y-direction has an error band of 0.1186 degree. It has 0.14 second settle time and a mean square error of 0.0008 degree. It also has a root mean squared error equal to 0.0278 degrees. The results show an effective control performance of the proposed LQR.