A multi-robot formation composed of autonomous agents may need to maintain an overall rigid shape for tasks such as collective transport of an object. To distribute control, we construct leader-follow formations in the plane that are persistent: designated "leader" robots control the movement of the entire formation, while the remaining "follower" robots maintain directed local links sensing data to other robots in such a way that the entire formation retains its overall shape. In this paper, we present an approach based on rigidity theory for constructing persistent leader-follower formations with redundancy; specified robots may experience sensor link failure without losing the persistence of the formation. Within this model, we consider the impact of special positions due to certain geometric conditions and provide simulation results confirming the expected behavior.
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