Stabilisation of infinitesimally rigid formations of multi-robot networks


This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. This article considers the design of a formation control for multivehicle systems that uses only local information. The control is derived from a potential function based on an undirected infinitesimally rigid graph that specifies the target formation. A potential function is obtained from the graph, from which a gradient control is derived. Under this controller the target formation becomes a manifold of equilibria for the multivehicle system. It is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold. A complete study of the stability of the regular polygon formation is presented and results for directed graphs are presented as well. Finally, the controller is validated experimentally. 1. Introduction This article considers distributed control of systems of agents that are interconnected dynamically or have a common objective, and where control is local, with the possible exception of high-level intermittent centralised supervision. Undoubtedly these kinds of systems will become more and more prevalent as embedded hardware evolves. An interesting example and area of ongoing research is the control of a group of autonomous mobile robots, ideally without centralised control or a global coordinate system, so that they work cooperatively to accomplish a common goal. The aims of such research are to achieve systems that are scalable, modular, and robust. These goals are similar to those of sensor networks – networks of inexpensive devices with computing, communications, and sensing capabilities. Such devices are currently commercially available and include products like the Intel Mote. A natural extension of sensor networks would be to add simple actuators to the sensors to make them mobile, and then to adapt the network configuration to optimise network coverage. If global coordinates are known and there is an omniscient supervisor, …

DOI: 10.1080/00207170802108441

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@article{Krick2009StabilisationOI, title={Stabilisation of infinitesimally rigid formations of multi-robot networks}, author={Laura Krick and Mireille E. Broucke and Bruce A. Francis}, journal={Int. J. Control}, year={2009}, volume={82}, pages={423-439} }