Equation of motion of a Wheeled Inverted Pendulum on an irregular terrain

In this research, an equation of motion of a WIP (Wheeled Inverted Pendulum) running on an irregular terrain such as the inclined road is derived. The WIP becomes a popular platform for mobile robots which should be running on not only regular pavement but also irregular terrain. In order for the WIP to run on those roads there requires a robust controller which can be achieved from a fine equation of motion. This paper derives a planar (2D) equation of motion of the WIP based on Newton-Euler equation and equilibrium point changes of it with respect to those inclined roads. The changes mean that the reference point should be changed with respect to the inclined road conditions.