The goal of this paper is to show how geometric control theory can be used to design efficient trajectories for an autonomous underwater vehicle descending into a basin, as well as performing its recovery after experiencing an actuator failure. The underwater vehicle is modeled as a forced affine connection control system, and the control strategies are developed through the use of integral curves of rank one and kinematic reductions. Such a method is particularly efficient in case of actuator failure and it provides a constructive way to design trajectories for the new under-actuated system. A typical scenario of basin descent is presented, control signals are computed to realize the desired trajectories and some simulations are provided
In this paper, we present a control strategy design technique for an autonomous underwater vehicle based on solutions to the motion planning problem derived from differential geometric methods. The motion planning problem is motivated by the practical application of surveying the hull of a ship for implications of harbor and port security. In recent years, engineers and researchers have been collaborating on automating ship hull inspections by employing autonomous vehicles. Despite the progresses made, human intervention is still necessary at this stage. To increase the functionality of these autonomous systems, we focus on developing model-based control strategies for the survey missions around challenging regions, such as the bulbous bow region of a ship. Recent advances in differential geometry have given rise to the field of geometric control theory. This has proven to be an effective framework for control strategy design for mechanical systems, and has recently been extended to applications for underwater vehicles. Advantages of geometric control theory include the exploitation of symmetries and nonlinearities inherent to the system.
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