Nonlinear control of the underactuated hovercraft using the Derivative-free nonlinear Kalman filter

The paper proposes a nonlinear control approach for the underactuated hovercraft model based on differential flatness theory and using a new nonlinear state vector and disturbances estimation method under the name of Derivative-free nonlinear Kalman Filter. It is proven that the sixth order nonlinear model of the hovercraft is a differentially flat one. It is shown that this model cannot be subjected to static feedback linearization, however it admits dynamic feedback linearization which means that the system´s state vector is extended by including as additional state variables the control inputs and their derivatives. Next, using the differential flatness properties it is also proven that this model can be subjected to input-output linearization and can be transformed to an equivalent canonical (Brunovsky) form. Based on this latter description the design of a state feedback controller is carried out enabling accurate maneuvering and trajectory tracking. Additional problems that are solved in the design of this feedback control scheme are the estimation of the nonmeasurable state variables in the hovercraft´s model and the compensation of modeling uncertainties and external perturbations affecting vessel. To this end, the application of the Derivative-free nonlinear Kalman Filter is proposed. This nonlinear filter consists of the Kalman Filter´s recursion on the linearized equivalent of the vessel and of an inverse nonlinear transformation based on the differential flatness features of the system which enables to compute state estimates for the state variables of the initial nonlinear model. The redesign of the filter as a disturbance observer makes possible the estimation and compensation of additive perturbation terms affecting the hovercraft´s model. The efficiency of the proposed nonlinear control and state estimation scheme is confirmed through simulation experiments.