In this paper, a simple control approach based on a region boundary technique for geometric formation of multiple Autonomous Underwater Vehicles (AUVs) is presented. The control objective is to keep each underwater vehicle at each corner of a desired geometric shape, i.e. an equilateral triangle or a square. An edge-based segmentation approach is utilized rather than specifying the minimum distance between members to ensure that each vehicle is placed exactly at the desired position in their formation. This allows each vehicle that has its own function to carry out an effective individual task, thus improving the formation's performance. The model of the ODIN vehicle is used as an example to demonstrate the proposed controller. Simulation results show the effectiveness of the controllers.
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