The mobile inverted pendulum (MIP) is a mechanical system that presents multiple control challenges. In particular, two objectives, namely desired position control and stabilization of the unstable pendulum-like central body, need to be simultaneously met. In this brief, we propose a novel smooth time-invariant controller to achieve the twin objectives. A feature of the controller design is that it readily extends to achieve waypoint tracking, another interesting task for mobile platforms. To validate the theory developed, an MIP has been indigenously designed and fabricated. Extensive experiments on the MIP have been performed. It has been observed that the system accomplishes position stabilization as well as waypoint tracking with negligible error.