The problem addressed in this paper is to achieve robust motion control of the inertia wheel pendulum (IWP). Specifically, trajectory tracking control of the pendulum of the IWP under the assumption of uncertain model is discussed. Two new robust algorithms are introduced whose design departs from a model-based input-output linearization controller. Then, the control problem is firstly solved by means of an adaptive neural network-based controller and secondly by an adaptive regressor-based controller. For both controllers, rigorous analysis of the respective closed-loop system is given, where Barbalat's lemma is used to conclude asymptotic convergence of the pendulum tracking error. In addition, the wheel velocity and adaptive extension signals are shown to be bounded. An extensive real-time experimental study validates the introduced theory, where the performance of a classical linear PID controller and the two new adaptive schemes are compared.