The overall control system for an open-frame Remotely Operated Vehicle (ROV) is typically built from three subsystems: guidance, navigation and control (GNC). The control allocation plays a vital role in the control subsystem. Typically, open-frame underwater vehicles have p actuators (thrusters) for the motion in the horizontal plane, and the control allocation problem, in this case, is very complex and hard to visualise, because the normalised constrained control subset is a p-dimensional unit cube. The aim of this paper is to give a clear picture and a geometric interpretation of the problem and to introduce a hybrid method, based on the integration of a weighted pseudoinverse and the fixed-point method. The main idea of the hybrid method is visualised, and the deep geometric insight is provided using a “virtual” ROV in low-dimensional control spaces, including visualisation of the attainable command set, solution lines, control energy spheres and the role of pseudoinverse and fixed-point iterations. The same concepts are then extended to higher-dimensional cases, for open-frame ROV with four X-shaped (vectored) horizontal thrusters, which is one of the most common thruster configurations for commercial ROVs. The proposed hybrid method has been developed, integrated into a generic fault-tolerant ROV control system and evaluated in virtual and real-world environments off the west coast of Ireland using observation-class ROV Latis and work-class ROV Étaín.
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