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            <title xml:lang="en">Ellipsoid uncertainty tether model for collision avoidance in a fleet of Remotely Operated Vehicles</title>
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              <p>During collision avoidance, the tether of Remote Operated Vehicle (ROV) is subject to entanglement with obstacles or other ROVs' tether. This specificity renders traditional multi-robot obstacle avoidance approaches inadequate for tethered multi-robot scenarios. This paper proposes a guaranteed ellipsoid model for representing the ROV's tether and its nearby obstacles, enabling an efficient, low-computation collision avoidance method for a fleet of ROVs. The model ensures that if the ellipsoid encompassing the tether remains entirely outside the ellipsoid encompassing an obstacle, there is no risk that the tether collides with it. The approach requires only the two attachment points of the tether and its length, without needing any information about the tether's shape, dynamics, or external disturbances such as underwater currents. A collision avoidance strategy is developed based on potential field methods combined with tether length management. When multiple ROVs are involved, personalities are added to ROV to obtain different behaviors, reducing the likelihood of deadlocks during avoidance maneuvers. Simulations demonstrate the method's effectiveness across various scenarios, and its limitations are also discussed.</p>
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