Modeling of wheeled inverted pendulum systems

In this paper, the modeling of wheeled inverted pendulum systems is revisited. Such mobile robots are widely used in research and education to explore and exemplify the control of inherently unstable, under-actuated systems. But despite of the numerous studies in this field, many authors apparently fail to derive the model equations adequately as shown by means of the dynamical model of a planar wheel-rod system. Focussing on the correct handling of the driving torque, the model is developed using both Newtonian and Lagrangian mechanics approaches. Finally, the resulting nonlinear model is compared against a model commonly found in literature by numerical simulation. This paper does not only highlight a widespread misconception in modeling mechanical systems, namely the difference between applied and reaction forces and torques, respectively, but suggests a demonstrative way of teaching this particular issue in both undergraduate and graduate courses on engineering mechanics.