A gain-scheduling optimal fuzzy logic controller design for unicycle

In this paper we propose a new fuzzy logic controller (FLC) for unicycle control. The FLC design integrates the linear quadratic regulator (LQR) and the gain-scheduling approach. By comparing FLC with the LQR designed around an operating point, the FLC coefficients can be easily tuned in a systematic way. The new FLC design aims at achieving three objectives: overcoming the difficulty in tuning the FLC coefficients, making full use of degrees of freedom in LQR design with weighting matrices, and applying gain scheduling to FLC by associating LQR weighting matrices with the variation of the operating point. The new FLC is applied to a unicycle that consists of a wheel and a saddle. Only one actuator is used to generate a torque on the wheel, and the saddle is treated as an inverse pendulum. We first study the dynamic characteristics of the unicycle, that is essentially an under-actuated mechanism, by applying input-output feedback linearization. It is shown that the zero dynamics of the unicycle is an unstable equilibrium, and full state feedback is indispensable. Next the FLC with full state feedback is designed such that the unicycle can reach any given position or setpoint while keeping the saddle stable. Through comprehensive simulation-based investigations, the effectiveness of the proposed FLC is validated, and the FLC shows superior performance than the LQR.