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.