Motion Control of a Two-Wheeled Mobile Vehicle with an Inverted Pendulum

Nested saturation control design techniques are usually applied to derive a control law for a two-wheeled vehicle with an inverted pendulum. In presence of external disturbances, this control law may result in a catastrophic problem of finite escape time in the controlled system. This paper proposes control solutions to overcome the above problem. First, a disturbance observer is designed to estimate the external disturbances exponentially. Several coordinate transformations and partial-feedback linearization techniques are then derived to transform the vehicle’s dynamics into an upper-triangular form. Next, nested p-times differentiable saturation and backstepping techniques are combined to design a control law for the transformed system. Attractive features of our proposed control design include a large domain of attraction and simplicity of tuning control gains and the controller implementation. Numerical simulations illustrate the results.