A synthesized integral sliding mode controller for an underactuated unicycle

In this paper we present a synthesized integral sliding mode controller (ISMC) that can stabilize an underactuated unicycle system. The unicycle consists of a wheel and a saddle that is modeled as an inverse pendulum. The only driving force is the torque applied to the shaft of the wheel, hence it is underactuated. Based on a linear approximation model, a linear controller using LQR method is designed. The control error bound achieved by the linear controller is derived for the unicycle. Next, the matched system nonlinearity of the unicycle is compensated, hence the error bound is reduced. The proposed synthesized ISMC consists of the linear controller, nonlinear compensation, a switching term, and an integral sliding surface. The synthesized ISMC can effectively reject the matched disturbance, and minimize the influence from unmatched disturbances, thus yielding a further reduced error bound.