Dynamic model and balancing control for two-wheeled self-balancing mobile robot on the slopes

This paper studies the balance control of two-wheeled self-balancing robot on the slope. The dynamic model was first established using Lagrange method, which was proved correct by the simulation results of its zero-state response and zero-input response. A set of balance equations were then obtained from the kinetic model, and the Lyapunov method was carried out to estimate its stability and controllability. Finally, the robot´s linear model in the equilibrium position was obtained. The linear quadratic optimal regulator was designed to control its attitude and speed. The simulation results show that the two-wheeled self-balancing robot in the slope situations can keep balance without displacement.