Closing ranks in vehicle formations based on rigidity

In this paper, a systematic way of maintaining rigidity in case of vehicle removals in formations for coordinating mobile autonomous vehicles with limited communication/sensing links is presented. The main concern is the minimal rearrangement of links in such a way that the links that have not been removed are preserved as they are, and the minimum number of new links are created in the formation to maintain rigidity. The problem is solved by the tools used in the Henneberg method. This method gives us provably rigid formations with the minimum number of links. The proposed framework meets this challenge for removed vehicles with any number of links in both 2 and 3-space. The same problem is also considered for the minimal Delaunay edge formations, which is a special class of the formations created by the Henneberg method with some geometrical properties.