{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T02:56:29Z","timestamp":1771556189118,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T00:00:00Z","timestamp":1700092800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Mobile multi-robot systems are well suited for gas leak localization in challenging environments. They offer inherent advantages such as redundancy, scalability, and resilience to hazardous environments, all while enabling autonomous operation, which is key to efficient swarm exploration. To efficiently localize gas sources using concentration measurements, robots need to seek out informative sampling locations. For this, domain knowledge needs to be incorporated into their exploration strategy. We achieve this by means of partial differential equations incorporated into a probabilistic gas dispersion model that is used to generate a spatial uncertainty map of process parameters. Previously, we presented a potential-field-control approach for navigation based on this map. We build upon this work by considering a more realistic gas dispersion model, now taking into account the mechanism of advection, and dynamics of the gas concentration field. The proposed extension is evaluated through extensive simulations. We find that introducing fluctuations in the wind direction makes source localization a fundamentally harder problem to solve. Nevertheless, the proposed approach can recover the gas source distribution and compete with a systematic sampling strategy. The estimator we present in this work is able to robustly recover source candidates within only a few seconds. Larger swarms are able to reduce total uncertainty faster. Our findings emphasize the applicability and robustness of robotic swarm exploration in dynamic and challenging environments for tasks such as gas source localization.<\/jats:p>","DOI":"10.3390\/s23229232","type":"journal-article","created":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T00:49:47Z","timestamp":1700182187000},"page":"9232","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Exploration and Gas Source Localization in Advection\u2013Diffusion Processes with Potential-Field-Controlled Robotic Swarms"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4561-9769","authenticated-orcid":false,"given":"Patrick","family":"Hinsen","sequence":"first","affiliation":[{"name":"Institute of Communications and Navigation, German Aerospace Center (DLR), 82234 Wessling, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1740-8841","authenticated-orcid":false,"given":"Thomas","family":"Wiedemann","sequence":"additional","affiliation":[{"name":"Institute of Communications and Navigation, German Aerospace Center (DLR), 82234 Wessling, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6065-6453","authenticated-orcid":false,"given":"Dmitriy","family":"Shutin","sequence":"additional","affiliation":[{"name":"Institute of Communications and Navigation, German Aerospace Center (DLR), 82234 Wessling, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0217-9326","authenticated-orcid":false,"given":"Achim J.","family":"Lilienthal","sequence":"additional","affiliation":[{"name":"Chair of Perception for Intelligent Systems, School of Computation, Information and Technology (CIT), Technical University of Munich (TUM), 80992 Munich, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1002\/rob.22109","article-title":"Gas source localization and mapping with mobile robots: A review","volume":"39","author":"Francis","year":"2022","journal-title":"J. Field Robot."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2302","DOI":"10.1109\/TCYB.2014.2306291","article-title":"Optimal Swarm Formation for Odor Plume Finding","volume":"44","author":"Marjovi","year":"2014","journal-title":"IEEE Trans. Cybern."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Neumann, P.P., Hirschberger, P., and Bartholmai, M. (November, January 31). Flying Ant Robot\u2013Aerial Chemical Trail Detection and Localization. Proceedings of the 2021 IEEE Sensors, Sydney, Australia.","DOI":"10.1109\/SENSORS47087.2021.9639857"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Soares, J.M., Aguiar, A.P., Pascoal, A.M., and Martinoli, A. (2015, January 26\u201330). A distributed formation-based odor source localization algorithm\u2014Design, implementation, and wind tunnel evaluation. Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA.","DOI":"10.1109\/ICRA.2015.7139436"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wiedemann, T., Schaab, M., Gomez, J.M., Shutin, D., Scheibe, M., and Lilienthal, A.J. (June, January 29). Gas Source Localization Based on Binary Sensing with a UAV. Proceedings of the 2022 IEEE International Symposium on Olfaction and Electronic Nose (ISOEN), Aveiro, Portugal.","DOI":"10.1109\/ISOEN54820.2022.9789553"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3163","DOI":"10.1109\/JSEN.2012.2208740","article-title":"Chemical sensing in robotic applications: A review","volume":"12","author":"Ishida","year":"2012","journal-title":"IEEE Sens. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1163\/1568553041738103","article-title":"Experimental analysis of gas-sensitive Braitenberg vehicles","volume":"18","author":"Lilienthal","year":"2004","journal-title":"Adv. Robot."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3319","DOI":"10.1109\/ROBOT.2004.1308766","article-title":"A robotic platform for testing moth-inspired plume tracking strategies","volume":"Volume 4","author":"Rutkowski","year":"2004","journal-title":"Proceedings of the IEEE International Conference on Robotics and Automation, 2004, ICRA \u201904"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.robot.2018.11.014","article-title":"Odor source localization algorithms on mobile robots: A review and future outlook","volume":"112","author":"Chen","year":"2019","journal-title":"Robot. Auton. Syst."},{"key":"ref_10","unstructured":"Marjovi, A., and Marques, L. (June, January 31). Multi-robot odor distribution mapping in realistic time-variant conditions. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Hong Kong, China."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"938","DOI":"10.1002\/tee.23364","article-title":"Recent Progress and Trend of Robot Odor Source Localization","volume":"16","author":"Jing","year":"2021","journal-title":"IEEJ Trans. Electr. Electron. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.inffus.2016.11.010","article-title":"A review of source term estimation methods for atmospheric dispersion events using static or mobile sensors","volume":"36","author":"Hutchinson","year":"2017","journal-title":"Inf. Fusion"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1007\/s10458-017-9375-7","article-title":"Multi-agent exploration of spatial dynamical processes under sparsity constraints","volume":"32","author":"Wiedemann","year":"2018","journal-title":"Auton. Agents Multi-Agent Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1038\/nature05464","article-title":"\u2019Infotaxis\u2019 as a strategy for searching without gradients","volume":"445","author":"Vergassola","year":"2007","journal-title":"Nature"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Dai, X.Y., Wang, J.Y., and Meng, Q.H. (2019, January 27\u201330). An Infotaxis-based Odor Source Searching Strategy for a Mobile Robot Equipped with a TDLAS Gas Sensor. Proceedings of the 2019 Chinese Control Conference (CCC), Guangzhou, China.","DOI":"10.23919\/ChiCC.2019.8866581"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.inffus.2017.10.009","article-title":"Entrotaxis as a strategy for autonomous search and source reconstruction in turbulent conditions","volume":"42","author":"Hutchinson","year":"2018","journal-title":"Inf. Fusion"},{"key":"ref_17","unstructured":"Tardioli, D., Matell\u00e1n, V., Heredia, G., Silva, M.F., and Marques, L. (2022, January 23\u201325). Potential Field Based Swarm Exploration of Processes Governed by Partial Differential Equations. Proceedings of the ROBOT2022: Fifth Iberian Robotics Conference, Zaragoza, Spain."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Schwab, A., Littek, F., and Lunze, J. (July, January 29). Experimental Evaluation of a Novel Approach to Cooperative Control of Multiple Robots with Artificial Potential Fields. Proceedings of the 2021 European Control Conference (ECC), Delft, The Netherlands.","DOI":"10.23919\/ECC54610.2021.9654958"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1177\/027836498600500106","article-title":"Real-Time Obstacle Avoidance for Manipulators and Mobile Robots","volume":"5","author":"Khatib","year":"1986","journal-title":"Intl. J. Robot. Res."},{"key":"ref_20","unstructured":"Koditschek, D. (1989). The Robotics Review, MIT Press."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1109\/MRA.2012.2184671","article-title":"Autonomous Gas-Sensitive Microdrone: Wind Vector Estimation and Gas Distribution Mapping","volume":"19","author":"Neumann","year":"2012","journal-title":"IEEE Robot. Autom. Mag."},{"key":"ref_22","unstructured":"Strang, G. (2007). Computational Science and Engineering, Wellesley-Cambridge Press."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3297","DOI":"10.1016\/j.ijheatmasstransfer.2009.02.002","article-title":"Analytical solution of the advection\u2013diffusion transport equation using a change-of-variable and integral transform technique","volume":"52","author":"Pimentel","year":"2009","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wiedemann, T., Lilienthal, A.J., and Shutin, D. (2019). Analysis of model mismatch effects for a model-based gas source localization strategy incorporating advection knowledge. Sensors, 19.","DOI":"10.3390\/s19030520"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1109\/70.163777","article-title":"Exact robot navigation using artificial potential functions","volume":"8","author":"Rimon","year":"1992","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"S117","DOI":"10.1088\/0026-1394\/45\/6\/S17","article-title":"The Ornstein\u2013Uhlenbeck process as a model of a low pass filtered white noise","volume":"45","author":"Bibbona","year":"2008","journal-title":"Metrologia"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/22\/9232\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:24:18Z","timestamp":1760131458000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/22\/9232"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,16]]},"references-count":26,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["s23229232"],"URL":"https:\/\/doi.org\/10.3390\/s23229232","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,16]]}}}