Backing control problem of a mobile robot with multiple trailers: fuzzy modeling and LMI-based design

The paper presents backing control of computer simulated mobile robots with multiple trailers by fuzzy modeling and control. We deal with two kinds of mobile robots: a mobile robot with five trailers and a mobile robot with ten trailers. To design fuzzy controllers, nonlinear models of the mobile robots with multiple trailers are represented by Takagi-Sugeno fuzzy models (TS fuzzy model). Before making TS fuzzy models, we simplify the nonlinear dynamics of the mobile robots. Under an assumption, TS fuzzy models are made from the simplified nonlinear models. The so-called parallel distributed compensation (PDC) is employed to design fuzzy controllers from the TS fuzzy models. Next, we derive a stability condition based on the Lyapunov approach. The stability condition of the designed fuzzy control system is cast in terms of linear matrix inequalities (LMI´s) since it is reduced to a problem of finding a common Lyapunov function for a set of Lyapunov inequalities. Convex optimization techniques based on LMI´s are utilized to solve the problem of finding stable feedback gains and a common Lyapunov function for the designed fuzzy control system. The simulation results show the effects of the fuzzy modeling, the controller design via the PDC, and the stability analysis based on LMIs