A Lyapunov controller for self-balancing two-wheeled vehicles

SUMMARY Segway is a self-balancing motorized two-wheeled vehicle which is able to carry the human body. The main issue in design of such a vehicle is to choose a stable control system capable of keeping the rider close to the upright position over smooth and non-smooth surfaces. This work extends the research previously performed by the authors for design of a controller, using the feedback linearization technique, to increase the stability of a two-wheeled vehicle carrying human. This paper investigates the design and validation of a controller for an inertial mobile vehicle using the Lyapunov's feedback control design technique. The system equations of motion are derived followed by finding the Lyapunov function required to design the controller. Owing to the discontinuity, originating from a sign function in the control law, the proposed control system is discontinuous. Therefore, the existence, continuity, and uniqueness of the solution are proven utilizing the Filippov's solution. Afterwards, the asymptotic stability of the control system is proven using the extensions of Lyapunov's stability theory to nonsmooth systems, and LaSalle's invariant set theorem. Finally, the effectiveness of the proposed control system is validated using simulation studies. Results confirm that the controller keeps the system stable while provides good position tracking responses.