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Bio-Design and Manufacturing  2022 Vol.5 No.5 P.558~566

10.1631/jzus.2004.0558


Graph rigidity and localization of multi-robot formations


Author(s):  ZHANG Fan

Affiliation(s):  General Robotics Automation Sensing and Perception Laboratory, University of Pennsylvania, Philadelphia, PA 19104, USA

Corresponding email(s):   zhangfan@grasp.cis.upenn.edu

Key Words:  Cooperative localization, Graph rigidity, Multi-robot formation


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ZHANG Fan. Graph rigidity and localization of multi-robot formations[J]. Journal of Zhejiang University Science D, 2022, 5(5): 558~566.

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Abstract: 
This paper provides theoretical foundation for the problem of localization in multi-robot formations. Sufficient and necessary conditions for completely localizing a formation of mobile robots/vehicles in SE(2) based on distributed sensor networks and graph rigidity are proposed. A method for estimating the quality of localizations via a linearized weighted least-squares algorithm is presented, which considers incomplete and noisy sensory information. The approach in this paper had been implemented in a multi-robot system of five car-like robots equipped with omni-directional cameras and IEEE 802.11b wireless network.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[3] Desai, A., Kumar, V., Ostrowski, J., 2001. A Theoretical Framework for Modeling and Controlling Formation of Mobile Robot. IEEE Transactions on Robotics and Automations.

[4] Eren, T., Belhumeur P.N., Anderson B.D.O., Morse, A.S., 2002. A Framework for Maintaining Formations based on Rigidity.Proceedings of the IFAC Congress, p.2752-2757.

[5] Eren, T., Goldenberg, D., Whiteley, W., Yang, Y.R., Morse, A.S., Anderson, B.D.O., Belhumeur, P.N., 2004. Rigidity and Randomness in Network Localization. Proc. of the IEEE INFOCOM Conference, Hong Kong.

[6] Howard, A., Matari, M., Sukhatme, C., 2002. Team Localization: A Maximum Likelihood Approach. Technical Report IRIS-01-415, Institute for Robotics and Intelligent Systems Technical Report, University of Southern California.

[7] Laman, G., 1970. On graphs and rigidity of plane skeletal structures.Journal of Engineering Mathematics,4:331-340.

[8] Olfati-Saber, R., Murray, R.M., 2002. Graph Rigidity and Distributed Formation Stabilization of Multi-vehicle systems. Proc. of the 41st IEEE Conf. on Decision and Control, Las Vegas, NV.

[9] Pappas, G.J., Tabuada P., Lima, P., 2001. Feasible Formations of Multi-agent Systems. Proceedings of the American Control Conference, Arlington, Virginia.

[10] Roth, B., 1982. Rigidity and flexible frameworks.The American Mathematical Monthly,88:6-21.

[11] Roumeliotis, S., Bekey, G., 2000. Collective Localization: A Distributed Kalman Filter Approach to Localization of Groups of Mobile Robots. Proc. of the IEEE Intl. Conf. on Robotics and Automation, San Francisco, p.2958-2965.

[12] Spletzer, J., Taylor, C.J., 2003. Dynamic sensor planning and control for optimally tracking targets.International Journal of Robotics Research,22:7-20.

[13] Whiteley, W., Tay, T., 1985. Generating isostatic frame-works.Structural Topology,11:21-69.

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