Simulation and control system design for a two-wheeled self-balancing robot via adaptive sliding mode technique using modified dynamical model

The problem of two wheeled self-balancing robot is an interesting and challenging problem in control and dynamic systems. This complexity is due to the inherent instability, nonholonomic constraints, and under-actuated mechanism. Dynamical model of two wheeled self-balancing robot can be presented by a set of highly coupled nonlinear differential equations. Authors, previously, developed the modified dynamical equations of the robot. The governed equations have some differences with the commonly used equations. The main difference is due to the existence of a nonlinear coupling term which is neglected before. In this paper we used an adaptive sliding-mode controller based on the zero dynamics theory. The controller objective is to drive the two wheeled self balancing robot to the desired path as well as to make the robot stable. By some simulations the behavior of the robot with the proposed controller is discussed. It is shown that if the nonlinear coupling term is ignored in designing the controller, the controller cannot compensate its effect. Using Lyapunov theorem and the invariant set theorem, it is proved that the errors are globally asymptotically stable.