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This article describes the types of sensing and control architectures that are needed to maintain the shape of a formation, while the formation moves as a cohesive whole. It details how some aspects of a formation architecture can be described using graphs. It addresses operations with formations, including merging, splitting and closing ranks, which is the task of repairing a formation when one or more agents are lost. It identifies rules for assigning edges between two meta-agents in order that the combination be capable of maintaining cohesive motion.

In this paper, we study the construction and transformation of 2-D persistent graphs. Persistence is a generalization to directed graphs of the undirected notion of rigidity. Both notions are currently being used in various studies on coordination and control of autonomous multiagent formations. In the context of mobile autonomous agent formations, persistence characterizes the efficacy of a directed formation structure with unilateral distance constraints seeking to preserve the shape of the formation. Analogously to the powerful results about Henneberg sequences in minimal rigidity theory, we propose different types of directed graph operations allowing one to sequentially build any minimally persistent graph (i.e., persistent graph with a minimal number of edges for a given number of vertices), each intermediate graph being also minimally persistent. We also consider the more generic problem of obtaining one minimally persistent graph from another, which corresponds to the online reorganization of the sensing and control architecture of an autonomous agent formation. We prove that we can obtain any minimally persistent formation from any other one by a sequence of elementary local operations such that minimal persistence is preserved throughout the reorganization process. Finally, we briefly explore how such transformations can be performed in a decentralized way. [ABSTRACT FROM AUTHOR]