Fuzzy adaptive EKF motion control for non-holonomic and underactuated cars with parametric and non-parametric uncertainties

A new fuzzy adaptive motion control system including on-line extended Kalman's filter (EKF) for wheeled underactuated cars with non-holonomic constraints on the motion is presented. The presence of parametric uncertainties in the kinematics and in the dynamics is treated using suitable differential adaptation laws. We merge adaptive control with fuzzy inference system. By using fuzzy system, the parameters of the kinematical controller are functions of the lateral, longitudinal and orientation errors of the motion. In this way we have a robust control system where the dynamics of the motion errors is with lower time response than the adaptive control without fuzzy. Also Lyapunov's stability of the motion errors is proved based on the properties of the fuzzy maps. If data from incremental encoders are employed for the feedback directly, sensor noises can damage the performance of the motion control in terms of the motion errors and of the parametric adaptation. These noises are aleatory and denote a kind of non-parametric uncertainties which perturb the nominal model of the car. Therefore an EKF is inserted in the adaptive control system to compensate for the above non-parametric uncertainties. The control algorithm efficiency is confirmed through simulation tests in Matlab environment.