Trajectory Design and Tracking Control for Nonlinear Underactuated Wheeled Inverted Pendulum

An underactuated wheeled inverted pendulum (UWIP) is a nonlinear mechanical system that has two degrees of freedom and has only one control input. The motion planning problem for this nonlinear system is difficult to solve because of the existence of an uncontrollable manifold in the configuration space. In this paper, we present a method of designing motion trajectory for this underactuated system. The design of trajectory is based on the dynamic properties of the UWIP system. Furthermore, the tracking control of the UWIP for the constructed trajectory is also studied. A tracking control law is designed by using quadratic optimal control theory. Numerical simulation results verify the effectiveness of the presented theoretical results.