{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T08:57:10Z","timestamp":1770454630337,"version":"3.49.0"},"reference-count":43,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,2,27]],"date-time":"2019-02-27T00:00:00Z","timestamp":1551225600000},"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>Information gathering (IG) algorithms aim to intelligently select a mobile sensor actions required to efficiently obtain an accurate reconstruction of a physical process, such as an occupancy map, or a magnetic field. Many recent works have proposed algorithms for IG that employ Gaussian processes (GPs) as underlying model of the process. However, most algorithms discretize the state space, which makes them computationally intractable for robotic systems with complex dynamics. Moreover, they are not suited for online information gathering tasks as they assume prior knowledge about GP parameters. This paper presents a novel approach that tackles the two aforementioned issues. Specifically, our approach includes two intertwined steps: (i) a Rapidly-Exploring Random Tree (RRT) search that allows a robot to identify unvisited locations, and to learn the GP parameters, and (ii) an RRT*-based informative path planning that guides the robot towards those locations by maximizing the information gathered while minimizing path cost. The combination of the two steps allows an online realization of the algorithm, while eliminating the need for discretization. We demonstrate that our proposed algorithm outperforms state-of-the-art both in simulations, and in a lab experiment in which a ground-based robot explores the magnetic field intensity within an indoor environment populated with obstacles.<\/jats:p>","DOI":"10.3390\/s19051016","type":"journal-article","created":{"date-parts":[[2019,2,27]],"date-time":"2019-02-27T11:41:03Z","timestamp":1551267663000},"page":"1016","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Robotic Active Information Gathering for Spatial Field Reconstruction with Rapidly-Exploring Random Trees and Online Learning of Gaussian Processes"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5219-6533","authenticated-orcid":false,"given":"Alberto","family":"Viseras","sequence":"first","affiliation":[{"name":"German Aerospace Centre (DLR), Oberpfaffenhofen, 82234 We\u00dfling, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6065-6453","authenticated-orcid":false,"given":"Dmitriy","family":"Shutin","sequence":"additional","affiliation":[{"name":"German Aerospace Centre (DLR), Oberpfaffenhofen, 82234 We\u00dfling, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4927-8647","authenticated-orcid":false,"given":"Luis","family":"Merino","sequence":"additional","affiliation":[{"name":"School of Engineering, Universidad Pablo de Olavide (UPO), 41013 Seville, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Marchant, R., and Ramos, F. (2012, January 7\u201312). Bayesian optimisation for intelligent environmental monitoring. Proceedings of the 2012 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Vilamoura, Portugal.","DOI":"10.1109\/IROS.2012.6385653"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Viseras, A., Wiedemann, T., Manss, C., Magel, L., Mueller, J., Shutin, D., and Merino, L. (2016, January 16\u201321). Decentralized multi-agent exploration with online-learning of Gaussian processes. Proceedings of the 2016 IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden.","DOI":"10.1109\/ICRA.2016.7487617"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rasmussen, C.E., and Williams, C.K. (2005). Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning), The MIT Press.","DOI":"10.7551\/mitpress\/3206.001.0001"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Merino, L., Caballero, F., and Ollero, A. (2010, January 18\u201322). Active Sensing for Range-Only Mapping using Multiple Hypothesis. Proceedings of the 2010 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Taipei, Taiwan.","DOI":"10.1109\/IROS.2010.5650442"},{"key":"ref_5","unstructured":"Ouyang, R., Low, K.H., Chen, J., and Jaillet, P. (2014, January 5\u20139). Multi-robot active sensing of non-stationary Gaussian process-based environmental phenomena. Proceedings of the 2014 International Conference on Autonomous Agents and Multi-Agent Systems, Paris, France."},{"key":"ref_6","unstructured":"Singh, A., Krause, A., and Kaiser, W.J. (2009, January 14\u201317). Nonmyopic Adaptive Informative Path Planning for Multiple Robots. Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence, Pasadena, CA, USA."},{"key":"ref_7","unstructured":"Low, K.H., Dolan, J.M., and Khosla, P. (2008, January 12\u201316). Adaptive multi-robot wide-area exploration and mapping. Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems, Estoril, Portugal."},{"key":"ref_8","unstructured":"Meliou, A., Krause, A., Guestrin, C., and Hellerstein, J.M. (2007, January 22\u201326). Nonmyopic informative path planning in spatio-temporal models. Proceedings of the 22nd National Conference on Artificial Intelligence, Vancouver, BC, Canada."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Viseras Ruiz, A., and Olariu, C. (2015, January 26\u201330). A General Algorithm for Exploration with Gaussian Processes in Complex, Unknown Environments. Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA.","DOI":"10.1109\/ICRA.2015.7139667"},{"key":"ref_10","unstructured":"Klyubin, A.S., Polani, D., and Nehaniv, C.L. (2005, January 2\u20135). Empowerment: A universal agent-centric measure of control. Proceedings of the 2005 IEEE Congress on Evolutionary Computation, Edinburgh, UK."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Levine, D.S. (2010). Information-Rich Path Planning Under General Constraints Using Rapidly-Exploring Random Trees. [Ph.D. Thesis, Massachusetts Institute of Technology].","DOI":"10.2514\/6.2010-3360"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1375","DOI":"10.1177\/0278364914526288","article-title":"On mutual information-based control of range sensing robots for mapping applications","volume":"33","author":"Julian","year":"2014","journal-title":"Int. J. Robot. Res."},{"key":"ref_13","first-page":"235","article-title":"Near-optimal sensor placements in Gaussian processes: Theory, efficient algorithms and empirical studies","volume":"9","author":"Krause","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Krause, A., and Guestrin, C. (2007, January 20\u201324). Nonmyopic active learning of gaussian processes: An exploration-exploitation approach. Proceedings of the 24th International Conference on Machine Learning, Corvalis, OR, USA.","DOI":"10.1145\/1273496.1273553"},{"key":"ref_15","unstructured":"Yamauchi, B. (1997, January 10\u201311). A frontier-based approach for autonomous exploration. Proceedings of the 1997 IEEE International Symposium on Computational Intelligence in Robotics and Automation, Monterey, CA, USA."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Viseras, A., Shutin, D., and Merino, L. (2017, January 24\u201328). Online information gathering using sampling-based planners and GPs: An information theoretic approach. Proceedings of the 2017 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, BC, Canada.","DOI":"10.1109\/IROS.2017.8202147"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Leahy, K.J., Aksaray, D., and Belta, C. (2017, January 24\u201326). Informative Path Planning under Temporal Logic Constraints with Performance Guarantees. Proceedings of the 2017 American Control Conference (ACC), Seattle, WA, USA.","DOI":"10.23919\/ACC.2017.7963223"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Cliff, O.M., Fitch, R., Sukkarieh, S., Saunders, D.L., and Heinsohn, R. (2015, January 13\u201317). Online localization of radio-tagged wildlife with an autonomous aerial robot system. Proceedings of the Robotics: Science and Systems, Rome, Italy.","DOI":"10.15607\/RSS.2015.XI.042"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Miller, L.M., and Murphey, T.D. (2015, January 24\u201328). Optimal Planning for Target Localization and Coverage Using Range Sensing. Proceedings of the 2015 IEEE International Conference on Automation Science and Engineering (CASE), Gothenburg, Sweden.","DOI":"10.1109\/CoASE.2015.7294129"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1177\/0278364914553683","article-title":"Learning to soar: Resource-constrained exploration in reinforcement learning","volume":"34","author":"Chung","year":"2015","journal-title":"Int. J. Robot. Res."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"MacDonald, R.A., and Smith, S.L. (2018). Active Sensing for Motion Planning in Uncertain Environments via Mutual Information Policies. Int. J. Robot. Res.","DOI":"10.1177\/0278364918772024"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s10514-017-9668-3","article-title":"Gaussian Processes Autonomous Mapping and Exploration for Range-Sensing Mobile Robots","volume":"42","author":"Dissanayake","year":"2018","journal-title":"Auton. Robots"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1002\/rob.21722","article-title":"Adaptive Continuous-Space Informative Path Planning for Online Environmental Monitoring","volume":"34","author":"Hitz","year":"2017","journal-title":"J. Field Robot."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Popovi\u0107, M., Hitz, G., Nieto, J., Sa, I., Siegwart, R., and Galceran, E. (June, January 29). Online Informative Path Planning for Active Classification Using UAVs. Proceedings of the 2017 IEEE International Conference on Robotics and Automation (ICRA), Singapore.","DOI":"10.1109\/ICRA.2017.7989676"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1271","DOI":"10.1177\/0278364914533443","article-title":"Sampling-based robotic information gathering algorithms","volume":"33","author":"Hollinger","year":"2014","journal-title":"Int. J. Robot. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1007\/s10514-015-9515-3","article-title":"Real-time path planning for long-term information gathering with an aerial glider","volume":"40","author":"Nguyen","year":"2016","journal-title":"Auton. Robots"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1613\/jair.2674","article-title":"Efficient informative sensing using multiple robots","volume":"34","author":"Singh","year":"2009","journal-title":"J. Artif. Intell. Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1177\/02783640122067453","article-title":"Randomized kinodynamic planning","volume":"20","author":"LaValle","year":"2001","journal-title":"Int. J. Robot. Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1177\/0278364911406761","article-title":"Sampling-based algorithms for optimal motion planning","volume":"30","author":"Karaman","year":"2011","journal-title":"Int. J. Robot. Res."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Bry, A., and Roy, N. (2011, January 9\u201313). Rapidly-exploring random belief trees for motion planning under uncertainty. Proceedings of the 2011 IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China.","DOI":"10.1109\/ICRA.2011.5980508"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1080\/01691864.2013.756386","article-title":"A Gaussian process-based RRT planner for the exploration of an unknown and cluttered environment with a UAV","volume":"27","author":"Yang","year":"2013","journal-title":"Adv. Robot."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Lan, X., and Schwager, M. (2013, January 6\u201310). Planning periodic persistent monitoring trajectories for sensing robots in gaussian random fields. Proceedings of the 2013 IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany.","DOI":"10.1109\/ICRA.2013.6630905"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1002\/rob.20309","article-title":"Gaussian process modeling of large-scale terrain","volume":"26","author":"Vasudevan","year":"2009","journal-title":"J. Field Robot."},{"key":"ref_34","unstructured":"Stranders, R., Farinelli, A., Rogers, A., and Jennings, N.R. (2009, January 11\u201317). Decentralised coordination of mobile sensors using the max-sum algorithm. Proceedings of the 21st International Jont Conference on Artifical Intelligence, Pasadena, CA, USA."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1109\/TWC.2015.2481879","article-title":"Spatial wireless channel prediction under location uncertainty","volume":"15","author":"Muppirisetty","year":"2016","journal-title":"IEEE Transa. Wirel. Commun."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Charrow, B., Liu, S., Kumar, V., and Michael, N. (2015, January 26\u201330). Information-theoretic mapping using cauchy-schwarz quadratic mutual information. Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA.","DOI":"10.1109\/ICRA.2015.7139865"},{"key":"ref_37","unstructured":"Ma, K., Ma, Z., Liu, L., and Sukhatme, G.S. (2016, January 7\u20139). Multi-Robot Informative and Adaptive Planning for Persistent Environmental Monitoring. Proceedings of the 13th International Symposium on Distributed Autonomous Robotic Systems, DARS, London, UK."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Behnke, S., Sheh, R., Sar\u0131el, S., and Lee, D.D. (2017). Searching Objects in Known Environments: Empowering Simple Heuristic Strategies. RoboCup 2016: Robot World Cup XX, Springer International Publishing.","DOI":"10.1007\/978-3-319-68792-6"},{"key":"ref_39","unstructured":"Godsil, C., and Royle, G.F. (2013). Algebraic Graph Theory, Springer Science & Business Media."},{"key":"ref_40","unstructured":"Cover, T.M., and Thomas, J.A. (2012). Elements of Information Theory, John Wiley & Sons."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1109\/LRA.2016.2521406","article-title":"Optimal Placement for a Limited-Support Binary Sensor","volume":"1","author":"Doucette","year":"2016","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_42","unstructured":"(2015). pyGPs\u2014A Package for Gaussian Processes Regression and Classification. J. Mach. Learn. Res., 16, 2611\u20132616."},{"key":"ref_43","unstructured":"Quigley, M., Gerkey, B., Conley, K., Faust, J., Foote, T., Leibs, J., Berger, E., Wheeler, R., and Ng, A. (2019, February 22). ROS: An open-source Robot Operating System. Available online: http:\/\/www.willowgarage.com\/sites\/default\/files\/icraoss09-ROS.pdf."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/5\/1016\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:35:12Z","timestamp":1760186112000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/5\/1016"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,27]]},"references-count":43,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["s19051016"],"URL":"https:\/\/doi.org\/10.3390\/s19051016","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,27]]}}}