## Control of Underactuated Marine Vehicles in the Presence of Environmental Disturbances

##### Doctoral thesis

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http://hdl.handle.net/11250/2432755##### Issue date

2016##### Metadata

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##### Abstract

This thesis presents several topics on the subject of controlling underactuated marine vessels and the rejection of environmental disturbances.
To address disturbances caused by waves, an observer is introduced for the wave encounter frequency. To estimate the wave encounter frequency we utilise an estimator intended to estimate the frequency of sinusoidal signals. The estimator is used to estimate the frequency of motion signals of the ship which are directly related to the wave encounter frequency and are sinusoidal in nature, e.g. the roll angle and pitch angle of the ship. Consequently, no model of the ship is required. The frequency estimator is equipped with a gain-switching mechanism to assure good performance in situations of high and low excitation. It is shown that when applied to sinusoidal signals with a time-varying, amplitude the frequency estimation error of the filter equipped with a gain switching-mechanism is globally exponentially stable. The theoretical results are verified using experimental data. The frequency estimator is applied to data from several towing tank tests and data gathered during an Atlantic passage of a container ship. To assess the performance of the filter, the frequency estimate is compared to the peak of a frequency spectrum of the data that is created using fast Fourier transform frequency spectral analysis.
The next part of the thesis is concerned with multi-agent control strategies of marine vessels. In this part results are presented to achieve coordinated pathfollowing of underactuated marine vehicles in the presence of unknown constant ocean currents. Both marine surface vessels and autonomous underwater vehicles are considered. The vehicles are individually guided to the path using an integral line-of-sight guidance law to reject the ocean current disturbances. To achieve coordination, the vehicles communicate their along-path distance. The along-path distance is used in a decentralised coordination law to achieve the desired along-path distances between the vehicles. The theoretical results are verified using numerical simulations and experimental results with three autonomous underwater vehicles.
A coordinated control strategy based on leader-follower synchronisation is also presented for underactuated marine surface vessels. This strategy is based on a constant bearing guidance algorithm from the marine system literature. First we show that the guidance algorithm is semi-globally exponentially stable and give explicit bounds on the solution. We then analyse the synchronisation properties using the constant bearing guidance when it is used on curved trajectories rather then the straight lines it is designed for. From an analysis of the guidance in closed loop with a heading and velocity controller we show that on curved trajectories the synchronisation errors between leader and follower are integral input-to-state stable when the sway velocity is considered as a disturbance input to the synchronisation error dynamics. The theoretical results are verified using numerical simulations.
The third part first presents two strategies to follow curved paths in the presence of unknown constant ocean currents. In both strategies the paths are parametrised by a path variable that is used to propagate a path-tangential reference frame. In one strategy the frame is propagated to makes sure the vessel stays on the normal of the path tangential reference frame. This results in a singularity in the update law and make the strategy only usable locally. In the other strategy a parametrisation is used that is globally valid. An appropriate guidance law is defined for both parametrisations. The controllers use the input from the guidance law and from an ocean current observer to reject the ocean current and converge to the path. The closed-system with the controllers and observer is analysed and it is shown that the path-following errors are globally asymptotically stable. The theoretical results are verified using numerical simulations.
A novel curved path-following strategy that does not require parametrisation of the path is also presented in the third part of the thesis. This strategy is based on principles from geometric control and hierarchical control design. In this strategy the path is defined implicitly as a manifold of the state space. It is shown that using three geometric objects, i.e. the normal to the path, the tangent to the path, and the curvature of the path, we can define controllers that make the manifold that describes the path asymptotically stable. The theoretical results are verified using numerical simulation. This work does not consider environmental disturbances.