This paper aims to design a one-wheeled robot as regards its pitch freedom and balance control on the one hand and to assess the application feasibility of the GM (1,1) swing estimation controller on the other. System control focuses mainly on one-wheeled robot stability, body swings in position, and speed control. Mathematical modeling and GM (1,1) prediction control are under investigation. The mathematical modeling is firstly conducted through referencing to the Newtonian mechanics and the Lagrange equation, from which the robot transfer function and state-space differential equation are derived. Next, the linear quadratic regulator is applied as the control rule at the balance point. Applying GM (1,1) to assess the robot gyro signal at a dynamic state is a discussion. Next, model reference estimation control is processed, and a mathematical model of the balance control method is completed. Finally, a simulation is conducted to verify the feasibility of the GM (1,1) estimation reference model. The linear quadratic regulator, which is credited with tenacity, can provide pitch swing and balance control of the one-wheeled robot.
