{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T21:19:01Z","timestamp":1774991941877,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,7,25]],"date-time":"2018-07-25T00:00:00Z","timestamp":1532476800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002855","name":"Ministry of Science and Technology of the People's Republic of China","doi-asserted-by":"publisher","award":["2016YFE0202300"],"award-info":[{"award-number":["2016YFE0202300"]}],"id":[{"id":"10.13039\/501100002855","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010580","name":"Department of Science and Technology, Hubei Provincial People's Government","doi-asserted-by":"publisher","award":["2018AAA070"],"award-info":[{"award-number":["2018AAA070"]}],"id":[{"id":"10.13039\/501100010580","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003819","name":"Natural Science Foundation of Hubei Province","doi-asserted-by":"publisher","award":["2018CFA007"],"award-info":[{"award-number":["2018CFA007"]}],"id":[{"id":"10.13039\/501100003819","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In the fields of autonomous vehicles, virtual reality and three-dimensional (3D) reconstruction, 2D laser rangefinders have been widely employed for different purposes, such as localization, mapping, and simultaneous location and mapping. However, the extrinsic calibration of multiple 2D laser rangefinders is a fundamental prerequisite for guaranteeing their performance. In contrast to existing calibration methods that rely on manual procedures or suffer from low accuracy, an automatic and high-accuracy solution is proposed in this paper for the extrinsic calibration of 2D laser rangefinders. In the proposed method, a mobile sphere is used as a calibration target, thereby allowing the automatic extrapolation of a spherical center and the automatic matching of corresponding points. Based on the error analysis, a matching machine of corresponding points with a low error is established with the restriction constraint of the scan circle radius, thereby achieving the goal of high-accuracy calibration. Experiments using the Hokuyo UTM-30LX sensor show that the method can increase the extrinsic orientation accuracy to a sensor intrinsic accuracy of 10 mm without requiring manual measurements or manual correspondence among sensor data. Therefore, the calibration method in this paper is automatic, highly accurate, and highly effective, and it meets the requirements of practical applications.<\/jats:p>","DOI":"10.3390\/rs10081176","type":"journal-article","created":{"date-parts":[[2018,7,25]],"date-time":"2018-07-25T08:28:47Z","timestamp":1532507327000},"page":"1176","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Extrinsic Calibration of 2D Laser Rangefinders Based on a Mobile Sphere"],"prefix":"10.3390","volume":"10","author":[{"given":"Shoubin","family":"Chen","sequence":"first","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"},{"name":"Collaborative Innovation Center of Geospatial Technology, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingbin","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"},{"name":"Collaborative Innovation Center of Geospatial Technology, Wuhan University, Wuhan 430079, China"},{"name":"Department of Remote Sensing and Photogrammetry and the Center of Excellence in Laser Scanning Research, Finnish Geospatial Research Institute, 02430 Masala, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Teng","family":"Wu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenchao","family":"Huang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keke","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deyu","family":"Yin","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinlian","family":"Liang","sequence":"additional","affiliation":[{"name":"Department of Remote Sensing and Photogrammetry and the Center of Excellence in Laser Scanning Research, Finnish Geospatial Research Institute, 02430 Masala, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juha","family":"Hyypp\u00e4","sequence":"additional","affiliation":[{"name":"Department of Remote Sensing and Photogrammetry and the Center of Excellence in Laser Scanning Research, Finnish Geospatial Research Institute, 02430 Masala, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6683-2342","authenticated-orcid":false,"given":"Ruizhi","family":"Chen","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"},{"name":"Collaborative Innovation Center of Geospatial Technology, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,7,25]]},"reference":[{"key":"ref_1","unstructured":"(2018, April 20). Scanning Range Finder Utm-30lx Product Page. Available online: http:\/\/www.hokuyo-aut.jp\/02sensor\/07scanner\/utm_30lx.html."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Pouliot, N., Richard, P.L., and Montambault, S. (2012, January 24). Linescout power line robot: Characterization of a utm-30lx lidar system for obstacle detection. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems, Vilamoura, Portugal.","DOI":"10.1109\/IROS.2012.6385476"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Demski, P., Mikulski, M., and Koteras, R. (2013). Characterization of Hokuyo Utm-30lx Laser Range Finder for an Autonomous Mobile Robot, Springer.","DOI":"10.1007\/978-3-642-31665-4_12"},{"key":"ref_4","first-page":"385","article-title":"An integrated flexible self-calibration approach for 2d laser scanning range finders applied to the Hokuyo utm-30lx-ew","volume":"5","author":"Mader","year":"2014","journal-title":"ISPRS Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_5","unstructured":"(2018, April 20). Navvis Digitizing Indoors\u2014Navvis. Available online: http:\/\/www.navvis.com."},{"key":"ref_6","unstructured":"(2018, April 20). Google Cartographer Backpack. Available online: https:\/\/opensource.google.com\/projects\/cartographer."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Hess, W., Kohler, D., Rapp, H., and Andor, D. (2016, January 16\u201321). Real-time loop closure in 2d lidar slam. Proceedings of the IEEE International Conference on Robotics and Automation, Stockholm, Sweden.","DOI":"10.1109\/ICRA.2016.7487258"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Lehtola, V.V., Kaartinen, H., N\u00fcchter, A., Kaijaluoto, R., Kukko, A., Litkey, P., Honkavaara, E., Rosnell, T., Vaaja, M.T., and Virtanen, J.P. (2017). Comparison of the selected state-of-the-art 3d indoor scanning and point cloud generation methods. Remote Sens., 9.","DOI":"10.3390\/rs9080796"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.isprsjprs.2014.10.008","article-title":"Localization of mobile laser scanner using classical mechanics","volume":"99","author":"Lehtola","year":"2015","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhang, J., and Singh, S. (2014, January 12\u201316). Loam: Lidar odometry and mapping in real-time. Proceedings of the Robotics: Science and Systems Conference, Berkeley, CA, USA.","DOI":"10.15607\/RSS.2014.X.007"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.1177\/0278364915580683","article-title":"Extrinsic calibration of 2d laser rangefinders from perpendicular plane observations","volume":"34","author":"Arevalo","year":"2015","journal-title":"I. J. Robot. Res."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Levinson, J., Askeland, J., Becker, J., Dolson, J., Held, D., Kammel, S., Kolter, J.Z., Langer, D., Pink, O., and Pratt, V. (2011, January 5\u20139). Towards fully autonomous driving: Systems and algorithms. Proceedings of the Intelligent Vehicles Symposium, Baden-Baden, Germany.","DOI":"10.1109\/IVS.2011.5940562"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/TRO.2010.2085490","article-title":"Efficient unbiased tracking of multiple dynamic obstacles under large viewpoint changes","volume":"27","author":"Miller","year":"2011","journal-title":"IEEE Trans. Robot."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1002\/rob.20262","article-title":"A perception-driven autonomous urban vehicle","volume":"25","author":"Leonard","year":"2008","journal-title":"J. Field Robot."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1595","DOI":"10.1177\/0278364910384295","article-title":"A high-rate, heterogeneous data set from the darpa urban challenge","volume":"29","author":"Huang","year":"2010","journal-title":"Int. J. Robot. Res."},{"key":"ref_16","unstructured":"Gao, C., and Spletzer, J.R. (2010, January 3\u20137). On-line calibration of multiple lidars on a mobile vehicle platform. Proceedings of the IEEE International Conference on Robotics and Automation, Anchorage, AK, USA."},{"key":"ref_17","unstructured":"Underwood, J., Hill, A., and Scheding, S. (November, January 29). Calibration of range sensor pose on mobile platforms. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems, San Diego, CA, USA."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1016\/j.robot.2016.05.010","article-title":"Self calibration of multiple lidars and cameras on autonomous vehicles","volume":"83","author":"Pereira","year":"2016","journal-title":"Robot. Auton. Syst."},{"key":"ref_19","unstructured":"(2018, June 15). Pcl Turorials: Filtering a Pointcloud Using a Passthrough Filter. Available online: http:\/\/www.pointclouds.org\/documentation\/tutorials\/passthrough.php#passthrough."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1007\/s00371-011-0580-0","article-title":"Registration of point clouds using sample-sphere and adaptive distance restriction","volume":"27","author":"Meng","year":"2011","journal-title":"Vis. Comput."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Fischler, M.A., and Bolles, R.C. (1981). Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography, ACM.","DOI":"10.1145\/358669.358692"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1111\/j.2517-6161.1995.tb02015.x","article-title":"Assessment and propagation of model uncertainty","volume":"57","author":"Draper","year":"1995","journal-title":"J. R. Stat. Soc."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1364\/JOSAA.5.001127","article-title":"Closed-form solution of absolute orientation using unit quaternions","volume":"5","author":"Horn","year":"1987","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1109\/TPAMI.1987.4767965","article-title":"Least-squares fitting of two 3-d point sets","volume":"9","author":"Arun","year":"1987","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Barfoot, T.D. (2017). A matrix lie group approach. State Estimation for Robotics, Cambridge University Press.","DOI":"10.1017\/9781316671528"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Hassani, S. (2013). Representation of Lie Groups and Lie Algebras, Springer International Publishing.","DOI":"10.1007\/978-3-319-01195-0_30"},{"key":"ref_27","unstructured":"Varadarajan, V.S. (1974). Lie Groups, Lie Algebras, and Their Representations, Springer."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1109\/34.88573","article-title":"Least-squares estimation of transformation parameters between two point patterns","volume":"13","author":"Umeyama","year":"1991","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_29","first-page":"193","article-title":"A close-form solution of absolute orientation using unit quaternions","volume":"3","author":"Jiang","year":"2007","journal-title":"J. Zhengzhou Inst. Surv. Mapp."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/34.982886","article-title":"Icp registration using invariant features","volume":"24","author":"Sharp","year":"2002","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"34","DOI":"10.3724\/SP.J.1246.2012.00034","article-title":"Correlation of coordinate transformation parameters","volume":"3","author":"Du","year":"2012","journal-title":"Geod. Geodyn."},{"key":"ref_32","first-page":"3","article-title":"The iteration by correcting characteristic value and its application in surveying data processing","volume":"15","author":"Wang","year":"2001","journal-title":"J. Heilongjiang Inst. Technol."},{"key":"ref_33","first-page":"183","article-title":"Airborne and Terrestrial Laser Scanning","volume":"4","author":"Vosselman","year":"2010","journal-title":"International Journal of Digital Earth."},{"key":"ref_34","unstructured":"Ministry of Housing and Urban-Rural Development of the People\u2019s Republic of China (2015). Code for Design of the Residential Interior Decoration."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/8\/1176\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:14:17Z","timestamp":1760195657000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/8\/1176"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,25]]},"references-count":34,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2018,8]]}},"alternative-id":["rs10081176"],"URL":"https:\/\/doi.org\/10.3390\/rs10081176","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7,25]]}}}