Polynomial Controller for Bicycle Robot based on Nonlinear Descriptor System

Most researches on balance control of the bicycle robots are for the situation that the bicycle robot is with constant forward velocity and constant feedback gain, but are not appropriate to be employed for time varying forward velocity situation. In this paper, the nonlinear Euler-Lagrange model of the bicycle robot and the simplified nonlinear descriptor state space model are firstly deduced. A polynomial controller, rather than a constant gain feedback one, is proposed, which constituting the nonlinear closed-loop descriptor system. The sufficient condition on examining the stability of closed-loop system, together with one alternative method on designing a polynomial controller utilizing the SOSTool, are then proposed. By this work, the polynomial controller is broadened to be applied on nonlinear descriptor system, and on the balance and forward control of bicycle robot with time varying forward velocity. One numerical example shows the capacity of the control scheme proposed in this paper.