A modified dynamical formulation for two-wheeled self-balancing robots

Two-wheeled self-balancing robot, moving on a horizontal plane, may be presented by a set of highly coupled nonlinear differential equations. In the recent literatures and in the commonly used two-wheeled self-balancing robots, the control algorithms are designed based on the mathematical models with simplified structure. In these models, a nonlinear coupling term is usually neglected, whereas it has significant effects on the dynamic behavior of the system. In this paper, the mathematical representation of two-wheeled self-balancing robots, including this new term, is derived using both Kane's and Lagrangian methods. The significant effect of the new term on the response of the system is shown by presenting the behavior of the system under different conditions and by comparing it with the system models when this term is neglected. Then sliding-mode control techniques are used to derive the controllers. 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.