Integral Line-of-Sight Guidance and Control of Underactuated Marine Vehicles

Abstract

This dissertation presents an extensive analysis of the integral line-of-sight (ILOS) guidance method for path following tasks of underactuated marine vessels and vehicles, operating on and below the sea surface. It is shown that thanks to the embedded integral action, the guidance law makes the vessels follow straight lines in presence of environmental disturbances such as currents, wind and waves. The analysis develops linearly with a growth of complexity that spans from simple two and three dimensional (2-3D) kinematic models to full kinematic-dynamic models for surface and underwater vehicles including environmental disturbances of different nature. Furthermore, the problem of steering a vehicle against the ocean current or with the ocean current is addressed as well.

The ILOS guidance is first applied to a simple kinematic model of surface vessels that neglects the vehicle dynamics. It is shown, using simple and intuitive mathematical tools, that current compensation for underactuated surface vessels reduces to a pure vectorial sum and has one possible solution that identifies the only heading the ship can hold to compensate for the drift. The relative velocity of the vessel is kept constant and compensation is achieved through side-slipping. It is proved that path following of straight lines is obtained. A discussion involving intuitive as well as practical aspects of the ILOS law is also given. A 3D version of the same ILOS is then applied to a kinematic model of underactuated underwater vehicles, thus extending the same concepts and the same analysis to 3D.

The following step in complexity consists of including the underactuated dynamics into the Lyapunov analysis of the 2D ILOS guidance law. Disturbances in the form of constant irrotational ocean currents and constant dynamic, attitude dependent, forces are taken into account. The mathematical complexity of the analysis increases significantly compared to the pure kinematic cases, yielding explicit bounds on the guidance law gains to guarantee stability.

Next, the complete kinematic and dynamic closed loop system of the ILOS guidance law for path following purposes of underactuated surface vessels is analyzed. The actuated surge and yaw dynamics are included in the analysis and it is shown that the resulting closed loop system forms a cascade. The properties of uniform global asymptotic stability (UGAS) and uniform local exponential stability (ULES) are shown for the closed loop cascaded system. In this case disturbances in the form of irrotational ocean currents are considered only. Results from simulations and experiments are presented to support and illustrate the theoretical results where the ILOS guidance is applied to the CART vehicle for sea trials.

The possibility of extending the ILOS guidance law proposed for underactuated surface marine vehicles to fully actuated marine vehicles with saturated transverse actuators is analyzed as well. Low-speed path following of straight lines is considered and the proposed solution is inspired by practical issues faced when operating remotely operated vehicles (ROVs) at sea. As a result, a solution combining the ILOS guidance law with a nonlinear bounded sway feedback controller is designed. UGAS and ULES for the origin of the closed loop system are proved and the theoretical results are supported by simulations.

It is furthermore shown that the ILOS guidance law successfully compensates for combined kinematic and dynamic disturbances, thus further extending the previous results. To this end, a 3 degrees-of-freedom (DOFs) maneuvering model for control design purposes that includes both the kinematic and dynamic disturbing effects of currents, wind and waves is presented. The ILOS guidance method is extended with adaptation and it is analytically shown that the resulting control scheme successfully compensates for both kinds of disturbances and hence guarantees path following of underactuated surface vessels in different sea conditions with UGAS and ULES stability properties. The theoretical results are supported by simulations.

The complete kinematic and dynamic closed loop system of the 3D ILOS guidance law is analyzed as well, hence extending the developed analysis to underactuated AUVs for 3D straight-line path following applications in the presence of constant irrotational ocean currents. The closed loop stability analysis concludes UGAS and ULES and gives explicit conditions on the guidance law parameters. The proposed 3D ILOS guidance control scheme is applied to the LAUV autonomous underwater vehicle and results from simulations and sea trials are shown to support the theoretical findings.

This dissertation addresses the problem of steering a marine vessel against the ocean current or with the ocean current as well and hence two guidance laws for counter-current and co-current guidance of underactuated marine vehicles in 3-DOFs are presented. The guidance laws are based on the relation between the relative and absolute velocities and show different stability properties: local exponential stability (LES) for the first and uniform semiglobal exponential stability (USES) for the second. In both the cases the closed loop system reveals multiple stable/unstable equilibrium points, corresponding to the counter-current/co-current directions depending on the setting. Simulation results support the theoretical findings