{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:24:12Z","timestamp":1772119452668,"version":"3.50.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T00:00:00Z","timestamp":1763769600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T00:00:00Z","timestamp":1763769600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100014013","name":"UK Research and Innovation","doi-asserted-by":"publisher","award":["10038941"],"award-info":[{"award-number":["10038941"]}],"id":[{"id":"10.13039\/100014013","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100019180","name":"HORIZON EUROPE European Research Council","doi-asserted-by":"publisher","award":["101070918"],"award-info":[{"award-number":["101070918"]}],"id":[{"id":"10.13039\/100019180","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Auton Robot"],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Building a distributed spatial awareness within a swarm of locally sensing and communicating robots enables new swarm algorithms. We use local observations by robots of each other and Gaussian belief propagation message passing combined with continuous swarm movement to build a global and distributed swarm-centric frame of reference. With low bandwidth and computation requirements, this shared reference frame allows new swarm algorithms. We characterise the system in simulation and demonstrate two example algorithms, then demonstrate reliable performance on real robots with imperfect sensing.<\/jats:p>","DOI":"10.1007\/s10514-025-10228-1","type":"journal-article","created":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T10:33:01Z","timestamp":1763807581000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Distributed spatial awareness for robot swarms"],"prefix":"10.1007","volume":"49","author":[{"given":"Simon","family":"Jones","sequence":"first","affiliation":[]},{"given":"Sabine","family":"Hauert","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,11,22]]},"reference":[{"key":"10228_CR1","unstructured":"Agarwal, S., Mierle, K., & Team, T. C. S. (2023). Ceres solver. https:\/\/github.com\/ceres-solver\/ceres-solver"},{"key":"10228_CR2","doi-asserted-by":"crossref","unstructured":"Bickson, D., Shental, O., & Dolev, D. (2008). Distributed Kalman filter via Gaussian belief propagation. In: 2008 46th annual allerton conference on communication, control, and computing (pp. 628\u2013635).","DOI":"10.1109\/ALLERTON.2008.4797617"},{"key":"10228_CR3","doi-asserted-by":"publisher","first-page":"59","DOI":"10.3389\/frobt.2019.00059","volume":"6","author":"M Birattari","year":"2019","unstructured":"Birattari, M., Ligot, A., Bozhinoski, D., Brambilla, M., Francesca, G., Garattoni, L., & St\u00fctzle, T. (2019). Automatic off-line design of robot swarms: A manifesto. Frontiers in Robotics and AI, 6, 59. https:\/\/doi.org\/10.3389\/frobt.2019.00059","journal-title":"Frontiers in Robotics and AI"},{"issue":"4","key":"10228_CR4","doi-asserted-by":"publisher","first-page":"3386","DOI":"10.1109\/LRA.2019.2926961","volume":"4","author":"D Carrillo-Zapata","year":"2019","unstructured":"Carrillo-Zapata, D., Sharpe, J., Winfield, A. F. T., Giuggioli, L., & Hauert, S. (2019). Towards controllable morphogenesis in large robot swarms. IEEE Robotics and Automation Letters, 4(4), 3386\u20133393. https:\/\/doi.org\/10.1109\/LRA.2019.2926961","journal-title":"IEEE Robotics and Automation Letters"},{"key":"10228_CR5","unstructured":"Catto, E. (2009). Box2D: A 2D physics engine for games. http:\/\/box2d.org\/"},{"key":"10228_CR6","doi-asserted-by":"crossref","unstructured":"Crosscombe, M., Lawry, J., Hauert, S., Homer, M. (2017). Robust distributed decision-making in robot swarms: Exploiting a third truth state. In: T.\u00a0Maciejewski (Ed.), 2017 IEEE\/RSJ international conference on intelligent robots and systems (IROS) (pp. 4326\u20134332). Vancouver, Canada.","DOI":"10.1109\/IROS.2017.8206297"},{"key":"10228_CR7","unstructured":"Davison, A.J., & Ortiz, J. (2019). FutureMapping 2: Gaussian belief propagation for spatial AI. arXiv:1910.14139."},{"key":"10228_CR8","unstructured":"Dellaert, F., & Contributors, G. (2022). borglab\/gtsam. Georgia Tech Borg Lab. https:\/\/github.com\/borglab\/gtsam"},{"key":"10228_CR9","doi-asserted-by":"publisher","unstructured":"Dellaert, F., Kaess, M., et\u00a0al. (2017). Factor graphs for robot perception. Foundations and Trends\u00ae in Robotics, 6(1\u20132), 1\u2013139. https:\/\/doi.org\/10.1561\/2300000043","DOI":"10.1561\/2300000043"},{"issue":"1","key":"10228_CR10","first-page":"6302","volume":"18","author":"J Du","year":"2018","unstructured":"Du, J., Ma, S., Wu, Y.-C., Kar, S., & Moura, J. M. (2018). Convergence analysis of distributed inference with vector-valued gaussian belief propagation. Journal of Machine Learning Research, 18(1), 6302\u20136339. http:\/\/jmlr.org\/papers\/v18\/16-556.html.","journal-title":"Journal of Machine Learning Research"},{"key":"10228_CR11","unstructured":"Erd\u0151s, P., R\u00e9nyi, A., et\u00a0al. (1960). On the evolution of random graphs. Publications of the"},{"issue":"6","key":"10228_CR12","doi-asserted-by":"publisher","first-page":"988","DOI":"10.1109\/TAC.2003.812781","volume":"48","author":"A Jadbabaie","year":"2003","unstructured":"Jadbabaie, A., Lin, J., & Morse, A. S. (2003). Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 48(6), 988\u20131001.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10228_CR13","doi-asserted-by":"publisher","unstructured":"Jones, S., Milner, E., Sooriyabandara, M., Hauert, S. (2022). DOTS: An open testbed for industrial swarm robotic solutions. https:\/\/doi.org\/10.48550\/arXiv.2203.13809","DOI":"10.48550\/arXiv.2203.13809"},{"key":"10228_CR14","unstructured":"Jones, S., Studley, M., Hauert, S., & Winfield, A.F. (2016). Evolving behaviour trees for swarm robotics. In: R.\u00a0Gro\u00df et\u00a0al. (Eds.), 13th International symposium on distributed autonomous robotic systems (DARS 2016). London: Springer."},{"issue":"6","key":"10228_CR15","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/s11554-023-01373-w","volume":"20","author":"S Jones","year":"2023","unstructured":"Jones, S., & Hauert, S. (2023). Frappe: Fast fiducial detection on low cost hardware. Journal of Real-Time Image Processing, 20(6), 119. https:\/\/doi.org\/10.1007\/s11554-023-01373-w","journal-title":"Journal of Real-Time Image Processing"},{"issue":"11","key":"10228_CR16","doi-asserted-by":"publisher","first-page":"2000110","DOI":"10.1002\/aisy.202000110","volume":"2","author":"S Jones","year":"2020","unstructured":"Jones, S., Milner, E., Sooriyabandara, M., & Hauert, S. (2020). Distributed situational awareness in robot swarms. Advanced Intelligent Systems, 2(11), 2000110. https:\/\/doi.org\/10.1002\/aisy.202000110","journal-title":"Advanced Intelligent Systems"},{"issue":"6","key":"10228_CR17","doi-asserted-by":"publisher","first-page":"1900031","DOI":"10.1002\/aisy.201900031","volume":"1","author":"S Jones","year":"2019","unstructured":"Jones, S., Winfield, A. F., Hauert, S., & Studley, M. (2019). Onboard evolution of understandable swarm behaviors. Advanced Intelligent Systems, 1(6), 1900031. https:\/\/doi.org\/10.1002\/aisy.201900031","journal-title":"Advanced Intelligent Systems"},{"key":"10228_CR18","doi-asserted-by":"publisher","first-page":"1505","DOI":"10.1007\/s10514-018-9807-5","volume":"43","author":"G Li","year":"2019","unstructured":"Li, G., St-Onge, D., Pinciroli, C., Gasparri, A., Garone, E., & Beltrame, G. (2019). Decentralized progressive shape formation with robot swarms. Autonomous Robots, 43, 1505\u20131521. https:\/\/doi.org\/10.1007\/s10514-018-9807-5","journal-title":"Autonomous Robots"},{"issue":"14","key":"10228_CR19","doi-asserted-by":"publisher","first-page":"1743","DOI":"10.1177\/027836491037513","volume":"29","author":"W Liu","year":"2010","unstructured":"Liu, W., & Winfield, A. F. (2010). Modeling and optimization of adaptive foraging in swarm robotic systems. The International Journal of Robotics Research, 29(14), 1743\u20131760. https:\/\/doi.org\/10.1177\/027836491037513","journal-title":"The International Journal of Robotics Research"},{"key":"10228_CR20","unstructured":"Milner, E., Sooriyabandara, M., & Hauert, S. (2022b). Swarm diffusion-taxis: Transport of spatial information for cooperative gradient-based navigation. AROB-ISBC-SWARM 2022."},{"issue":"2","key":"10228_CR21","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1007\/s10015-022-00749-8","volume":"27","author":"E Milner","year":"2022","unstructured":"Milner, E., Sooriyabandara, M., & Hauert, S. (2022). Stochastic behaviours for retrieval of storage items using simulated robot swarms. Artificial Life and Robotics, 27(2), 264\u2013271. https:\/\/doi.org\/10.1007\/s10015-022-00749-8","journal-title":"Artificial Life and Robotics"},{"issue":"2","key":"10228_CR22","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1109\/TRO.2016.2523542","volume":"32","author":"E Montijano","year":"2016","unstructured":"Montijano, E., Cristofalo, E., Zhou, D., Schwager, M., & Saguees, C. (2016). Vision-based distributed formation control without an external positioning system. IEEE Transactions on Robotics, 32(2), 339\u2013351.","journal-title":"IEEE Transactions on Robotics"},{"key":"10228_CR23","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1109\/TRO.2023.3324127","volume":"40","author":"R Murai","year":"2024","unstructured":"Murai, R., Ortiz, J., Saeedi, S., Kelly, P. H., & Davison, A. J. (2024). A robot web for distributed many-device localization. IEEE Transactions on Robotics, 40, 121\u2013138. https:\/\/doi.org\/10.1109\/TRO.2023.3324127","journal-title":"IEEE Transactions on Robotics"},{"key":"10228_CR24","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/j.robot.2016.12.006","volume":"91","author":"H Oh","year":"2017","unstructured":"Oh, H., Shirazi, A. R., Sun, C., & Jin, Y. (2017). Bio-inspired self-organising multi-robot pattern formation: A review. Robotics and Autonomous Systems, 91, 83\u2013100. https:\/\/doi.org\/10.1016\/j.robot.2016.12.006","journal-title":"Robotics and Autonomous Systems"},{"issue":"1","key":"10228_CR25","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1109\/JPROC.2006.887293","volume":"95","author":"R Olfati-Saber","year":"2007","unstructured":"Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007). Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE, 95(1), 215\u2013233.","journal-title":"Proceedings of the IEEE"},{"key":"10228_CR26","unstructured":"Ortiz, J., Evans, T., & Davison, A.J. (2021). A visual introduction to Gaussian belief propagation. arXiv:2107.02308"},{"key":"10228_CR27","doi-asserted-by":"crossref","unstructured":"Ortiz, J., Pupilli, M., Leutenegger, S., & Davison, A.J. (2020). Bundle adjustment on a graph processor. In: Proceedings of the IEEE\/CVF conference on computer vision and pattern recognition (pp. 2413\u20132422).","DOI":"10.1109\/CVPR42600.2020.00249"},{"key":"10228_CR28","doi-asserted-by":"publisher","first-page":"1272","DOI":"10.1007\/s12555-018-0690-9","volume":"17","author":"Z Pan","year":"2019","unstructured":"Pan, Z., Wang, D., Deng, H., & Li, K. (2019). A virtual spring method for the multi-robot path planning and formation control. International Journal of Control, Automation and Systems, 17, 1272\u20131282. https:\/\/doi.org\/10.1007\/s12555-018-0690-9","journal-title":"International Journal of Control, Automation and Systems"},{"issue":"2","key":"10228_CR29","doi-asserted-by":"publisher","first-page":"552","DOI":"10.1109\/LRA.2022.3227858","volume":"8","author":"A Patwardhan","year":"2023","unstructured":"Patwardhan, A., Murai, R., & Davison, A. J. (2023). Distributing collaborative multi-robot planning with gaussian belief propagation. IEEE Robotics and Automation Letters, 8(2), 552\u2013559. https:\/\/doi.org\/10.1109\/LRA.2022.3227858","journal-title":"IEEE Robotics and Automation Letters"},{"key":"10228_CR30","unstructured":"Pearl, J. (1982). Reverend bayes on inference engines: A distributed hierarchical approach. In: AAAI\u201982: Proceedings of the second AAAI conference on artificial intelligence (pp. 133\u2013136). AAAI Press."},{"key":"10228_CR31","doi-asserted-by":"crossref","unstructured":"Pitonakova, L., Winfield, A., & Crowder, R. (2018). Recruitment Near Worksites Facilitates Robustness of Foraging E-puck Swarms to Global Positioning Noise. 2018 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS) (pp. 4276\u20134281).","DOI":"10.1109\/IROS.2018.8593788"},{"key":"10228_CR32","doi-asserted-by":"crossref","unstructured":"Reynolds, C.W. (1987). Flocks, herds and schools: A distributed behavioral model. ACM SIGGRAPH Computer Graphics (Vol.\u00a021, pp. 25\u201334).","DOI":"10.1145\/37402.37406"},{"key":"10228_CR33","doi-asserted-by":"crossref","unstructured":"Rubenstein, M., Ahler, C., & Nagpal, R. (2012). Kilobot: A low cost scalable robot system for collective behaviors. L.\u00a0Parker (Ed.), IEEE International Conference on Robotics and Automation (ICRA 2012) (pp. 3293\u20133298). St. Paul, MN, USA.","DOI":"10.1109\/ICRA.2012.6224638"},{"issue":"6198","key":"10228_CR34","doi-asserted-by":"publisher","first-page":"795","DOI":"10.1126\/science.1254295","volume":"345","author":"M Rubenstein","year":"2014","unstructured":"Rubenstein, M., Cornejo, A., & Nagpal, R. (2014). Programmable self-assembly in a thousand-robot swarm. Science, 345(6198), 795\u2013799. https:\/\/doi.org\/10.1126\/science.1254295","journal-title":"Science"},{"key":"10228_CR35","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/s10514-011-9225-4","volume":"30","author":"L Sabattini","year":"2011","unstructured":"Sabattini, L., Secchi, C., & Fantuzzi, C. (2011). Arbitrarily shaped formations of mobile robots: Artificial potential fields and coordinate transformation. Autonomous Robots, 30, 385\u2013397. https:\/\/doi.org\/10.1007\/s10514-011-9225-4","journal-title":"Autonomous Robots"},{"key":"10228_CR36","doi-asserted-by":"publisher","first-page":"36","DOI":"10.3389\/frobt.2020.00036","volume":"7","author":"M Schranz","year":"2020","unstructured":"Schranz, M., Umlauft, M., Sende, M., & Elmenreich, W. (2020). Swarm Robotic Behaviors and Current Applications. Frontiers in Robotics and AI, 7, 36. https:\/\/doi.org\/10.3389\/frobt.2020.00036","journal-title":"Frontiers in Robotics and AI"},{"issue":"25","key":"10228_CR37","doi-asserted-by":"publisher","first-page":"eaau9178","DOI":"10.1126\/scirobotics.aau9178","volume":"3","author":"I Slavkov","year":"2018","unstructured":"Slavkov, I., Carrillo-Zapata, D., Carranza, N., Diego, X., Jansson, F., Kaandorp, J., & Sharpe, J. (2018). Morphogenesis in robot swarms. Science Robotics, 3(25), eaau9178. https:\/\/doi.org\/10.1126\/scirobotics.aau9178","journal-title":"Science Robotics"},{"key":"10228_CR38","doi-asserted-by":"crossref","unstructured":"Soares, J.M., Navarro, I., & Martinoli, A. (2016). The khepera iv mobile robot: performance evaluation, sensory data and software toolbox. Robot 2015: second iberian robotics conference (pp. 767\u2013781).","DOI":"10.1007\/978-3-319-27146-0_59"},{"key":"10228_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2023.107501","volume":"128","author":"DH Stolfi","year":"2024","unstructured":"Stolfi, D. H., & Danoy, G. (2024). Evolutionary swarm formation: From simulations to real world robots. Engineering Applications of Artificial Intelligence, 128, Article 107501.","journal-title":"Engineering Applications of Artificial Intelligence"},{"issue":"5","key":"10228_CR40","doi-asserted-by":"publisher","first-page":"1144","DOI":"10.1109\/TSP.2015.2389755","volume":"63","author":"Q Su","year":"2015","unstructured":"Su, Q., & Wu, Y.-C. (2015). On Convergence Conditions of Gaussian Belief Propagation. IEEE Transactions on Signal Processing, 63(5), 1144\u20131155. https:\/\/doi.org\/10.1109\/TSP.2015.2389755","journal-title":"IEEE Transactions on Signal Processing"},{"issue":"1","key":"10228_CR41","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s11721-019-00176-9","volume":"14","author":"MS Talamali","year":"2020","unstructured":"Talamali, M. S., Bose, T., Haire, M., Xu, X., Marshall, J. A., & Reina, A. (2020). Sophisticated collective foraging with minimalist agents: A swarm robotics test. Swarm Intelligence, 14(1), 25\u201356. https:\/\/doi.org\/10.1007\/s11721-019-00176-9","journal-title":"Swarm Intelligence"},{"issue":"1\u20132","key":"10228_CR42","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s11721-022-00218-9","volume":"17","author":"G Tzoumas","year":"2023","unstructured":"Tzoumas, G., Pitonakova, L., Salinas, L., Scales, C., Richardson, T., & Hauert, S. (2023). Wildfire detection in large-scale environments using force-based control for swarms of UAVs. Swarm Intelligence, 17(1\u20132), 89\u2013115. https:\/\/doi.org\/10.1007\/s11721-022-00218-9","journal-title":"Swarm Intelligence"},{"key":"10228_CR43","doi-asserted-by":"publisher","first-page":"9","DOI":"10.3389\/frobt.2017.00009","volume":"4","author":"G Valentini","year":"2017","unstructured":"Valentini, G., Ferrante, E., & Dorigo, M. (2017). The Best-of-n Problem in Robot Swarms: Formalization, State of the Art, and Novel Perspectives. Frontiers in Robotics and AI, 4, 9. https:\/\/doi.org\/10.3389\/frobt.2017.00009","journal-title":"Frontiers in Robotics and AI"},{"key":"10228_CR44","doi-asserted-by":"crossref","unstructured":"Weiss, Y., & Freeman, W. (1999). Correctness of Belief Propagation in Gaussian Graphical Models of Arbitrary Topology. Advances in Neural Information Processing Systems 12 (NIPS 1999) (Vol.\u00a012).","DOI":"10.21236\/ADA603879"},{"key":"10228_CR45","doi-asserted-by":"crossref","unstructured":"Winfield, A.F. (2009). Foraging robots. Encyclopedia of Complexity and Systems Science (pp. 3682\u20133700). Springer.","DOI":"10.1007\/978-0-387-30440-3_217"}],"container-title":["Autonomous Robots"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10514-025-10228-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10514-025-10228-1","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10514-025-10228-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,24]],"date-time":"2025-12-24T08:33:04Z","timestamp":1766565184000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10514-025-10228-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,22]]},"references-count":45,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["10228"],"URL":"https:\/\/doi.org\/10.1007\/s10514-025-10228-1","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-6682240\/v1","asserted-by":"object"}]},"ISSN":["0929-5593","1573-7527"],"issn-type":[{"value":"0929-5593","type":"print"},{"value":"1573-7527","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,22]]},"assertion":[{"value":"16 May 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 August 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 October 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 November 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"41"}}