Standard dynamic model and control of a two-wheeled inverted pendulum robot on inclined planes

Recently, there has been significant attention on the dynamic model of two-wheeled inverted pendulum robots (TWIPRs) on horizontal planes, leaving an inadequacy in understanding their behavior on inclined planes. This paper aims to address this gap by establishing a standard three-degree-of-freedom (3-DOF) nonlinear model for TWIPRs on inclined planes, particularly considering the complex coupling among yaw motion, forward motion, and body balance. First, to accommodate varying incline angles, multiple coordinate systems are introduced, including one aligned with the inclined plane. Second, through the analysis of kinematics and dynamics, the Lagrangian method is employed to derive the standard model, incorporating the effects of yaw motion on potential energy, slope angles, and pitch angles. Third, a sliding mode control strategy is applied in the model to guide TWIPRs along predefined paths on inclined planes for maintaining balance. Finally, numerical simulations demonstrate the model’s effectiveness and show its superior accuracy in trajectory tracking on inclined planes compared to the previous models.