NMPC-based Trajectory Tracking and Collison Avoidance of Underactuated Vessels with Elliptical Ship Domain*

:This paper presents a Nonlinear Model Predictive Control (NMPC) for position and velocity tracking of underactuated surface vessels of elliptical ship domains with a collision avoidance scheme. A constrained nonlinear optimization problem is formulated to minimize vessel states' deviation from a time varying reference generated by a virtual vessel over a finite horizon. Linear constraints is imposed on input force and moment to be within the physical limits. Collision avoidance is represented as separation of each pair of the elliptic disks, representing the ship domain of our vessel and each encountered one, and is formulated as nonlinear time-varying constraint over the prediction horizon. A real-time C-code is generated using the ACADO toolkit and qpOASES solver with multiple shooting technique for discretization and Gauss-Newton iteration algorithm. This algorithm is computationally efficient, thus enabling real-time implementation of the proposed technique. MATLAB simulations are used to assess the validity of the proposed technique.