Robust dynamic positioning of autonomous surface vessels with tube-based model predictive control

Abstract

This paper proposes two robust dynamic positioning (DP) approaches for autonomous surface vessels when full states are measurable and when only partial states are available with measurement errors. High fidelity nonlinear hydrodynamics are considered which are approximated as linear models in the local area of DP setpoint. The linearization errors are seen as bounded unmodeled dynamics and are accommodated in the tube-based model predictive control (MPC) together with environmental disturbances. The tube-based MPC controller contains all the possible uncertain trajectories in a tube that is based on a precomputed robust positive invariant set and a nominal trajectory solved online. The total controller consists of a feedforward part compensating the predicted environmental forces, a nominal part guiding the vessel towards and stabilizing it at the origin, and an affine feedback part bounding the uncertain vessel trajectory within the tube. Furthermore, an output feedback robust DP controller is proposed by utilizing a simple Luenberger observer to estimate the system states when full states are not available. The resultant estimation and measurement errors are also incorporated in the tube-based MPC. Simulation results show that the proposed full state and output feedback robust DP controllers can achieve the DP goals within system constraints.