Velocity control of a wheeled inverted pendulum by partial feedback linearization

In this paper, the dynamic model of a wheeled inverted pendulum (e.g. Segway (2003), Quasimoro (Salerno and Angeles, 2003), Joe (Grasser et al., 2002)) is analyzed from a controllability and feedback linearizability point of view. First, a dynamic model of this underactuated system is derived with respect to the wheel motor torques as inputs while taking the nonholonomic no-slip constraints into considerations. This model is compared with the previous models derived for similar systems. The strong accessibility condition is checked and the maximum relative degree of the system is found. Based on this result, a partial feedback linearization of the system is obtained and the internal dynamics equations are isolated. The resulting equations are then used to design a two-level controller for tracking vehicle orientation and heading speed set-points, while controlling the vehicle pitch within a specified range. Simulation results are provided to show the efficacy of the controller.