{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:07:49Z","timestamp":1787321269451,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>In this paper, we investigate nonuniform coverage of a planar region by a network of autonomous, mobile agents. We derive centralized nonuniform coverage control laws from uniform coverage algorithms using cartograms, transformations that map nonuniform metrics to a near Euclidean metric. We also investigate time-varying coverage metrics and the design of control algorithms to cover regions with slowly varying, nonuniform metrics. Our results are applicable to the design of mobile sensor networks, notably when the coverage metric varies as data is collected such as in the case of an information metric. The results apply also to the study of animal groups foraging for food that is nonuniformly distributed and possibly changing.<\/jats:p>","DOI":"10.1137\/070681120","type":"journal-article","created":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T23:04:59Z","timestamp":1234393499000},"page":"351-372","source":"Crossref","is-referenced-by-count":61,"title":["Nonuniform Coverage and Cartograms"],"prefix":"10.1137","volume":"48","author":[{"given":"Francois","family":"Lekien","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Naomi Ehrich","family":"Leonard","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"R1","unstructured":"J.P. Aubin,\n                      Applied Functional Analysis\n                      , Pure Appl. Math. (N.Y.), Wiley-Interscience, New York, 2000."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.2307\/5108"},{"key":"R3","first-page":"559","volume":"23","author":"Bretherton F. P.","year":"1976","journal-title":"-73, Deep-Sea Res."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012903428652"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1109\/TRA.2004.824698"},{"key":"R6","unstructured":"B. Daya Reddy,\n                      Introductory Functional Analysis\n                      , Springer-Verlag, New York, 1997."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01601953"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2004.840301"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0400280101"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.74.016117"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1142\/S0219525905000397"},{"key":"R12","unstructured":"M. W. Hirsch and S. Smale,\n                      Differential Equations, Dynamical Systems and Linear Algebra\n                      , Academic Press, New York, 1974."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1029\/2006JC003984"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1029\/2004JC002323"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2006.887295"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.02.010"},{"key":"R17","unstructured":"W. Li and C. G. Cassandras,\n                      Distributed cooperative coverage control of sensor networks\n                      , in Proceedings of the 44th IEEE Conference on Decision and Control, 2005, pp. 2542\u20132547."},{"key":"R18","doi-asserted-by":"crossref","unstructured":"S. Poduri and G. S. Sukhatme,\n                      Constrained coverage for mobile sensor networks\n                      , in Proceedings of the IEEE International Conference on Robotics and Automation, 2004, pp. 165\u2013172.","DOI":"10.1109\/ROBOT.2004.1307146"},{"key":"R19","unstructured":"W. Rudin,\n                      Principles of Mathematical Analysis\n                      , McGraw\u2013Hill, New York, 1976."},{"key":"R20","unstructured":"D. W. Stephens and J. R. Krebs,\n                      Foraging Theory\n                      , Princeton University Press, Princeton, NJ, 1986."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070681120","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:09:45Z","timestamp":1787317785000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070681120"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/070681120"],"URL":"https:\/\/doi.org\/10.1137\/070681120","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}