AUV Control and Navigation with Differential Flatness Theory and Derivative-Free Nonlinear Kalman Filtering

Abstract

The problem of control and navigation for autonomous underwater vessels (AUVs) is solved using differential flatness theory and the Derivative-free nonlinear Kalman Filter. First, differential flatness is proven for the 6-DOF dynamic model of the AUV. This allows for transforming the AUV model into the linear canonical (Brunovsky) form and for designing a state feedback controller. Uncertainty about the parameters of the AUV’s dynamic model, as well external perturbations which affect its motion are issues that have to be taken into account in the controller’s design. To compensate for model imprecision and disturbance terms, it is proposed to use a disturbance observer which is based on the Derivative-free nonlinear Kalman Filter. The considered filtering method consists of the standard Kalman Filter recursion applied on the linearized model of the vessel and of an inverse transformation based on differential flatness theory, which enables to obtain estimates of the state variables of the initial nonlinear model of the vessel. With the use of the the Kalman Filter-based disturbance observer, simultaneous estimation of the non-measurable state variables of the AUV and of the perturbation terms that affect its dynamics is achieved. Moreover, after estimating such disturbances, their compensation is also succeeded. Simulation experiments are performed to confirm the efficiency of the proposed AUV control and estimation scheme.