Decentralized Formation Control Part I: Geometric Aspects

In this paper, we develop new methods for the analysis of decentralized control systems and we apply them to formation control problems. The basic set-up consists of a system with multiple agents represented by the nodes of a directed graph whose edges represent an available communication channel for the agents. We address the question of whether the information flow defined by the graph is sufficient for the agents to accomplish a given task. Formation control is concerned with problems in which agents are required to stabilize at a given distance of other agents. In this context, the graph of a formation encodes both the information flow, as described above, and the distance constraints, by fixing the lengths of the edges. A formation is said to be rigid if it cannot be continuously deformed with the distance constraints satisfied; a formation is minimally rigid if no distance constraint can be omitted without the formation losing its rigidity. Hence, the graph underlying minim...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Mohamed-Ali Belabbas
• Keywords: CORR 2011, Distance Constraint, Education, Rigid, Rigid Formation