{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T16:20:36Z","timestamp":1761582036006,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2020,12,3]],"date-time":"2020-12-03T00:00:00Z","timestamp":1606953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Grant 51309058"],"award-info":[{"award-number":["Grant 51309058"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005046","name":"Natural Science Foundation of Heilongjiang Province","doi-asserted-by":"publisher","award":["Grant E2017015"],"award-info":[{"award-number":["Grant E2017015"]}],"id":[{"id":"10.13039\/501100005046","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Mapping and localization of mobile robots in an unknown environment are essential for most high-level operations like autonomous navigation or exploration. This paper presents a novel approach for combining estimated trajectories, namely curvefusion. The robot used in the experiments is equipped with a horizontally mounted 2D profiler, a constantly spinning 3D laser scanner and a GPS module. The proposed algorithm first combines trajectories from different sensors to optimize poses of the planar three degrees of freedom (DoF) trajectory, which is then fed into continuous-time simultaneous localization and mapping (SLAM) to further improve the trajectory. While state-of-the-art multi-sensor fusion methods mainly focus on probabilistic methods, our approach instead adopts a deformation-based method to optimize poses. To this end, a similarity metric for curved shapes is introduced into the robotics community to fuse the estimated trajectories. Additionally, a shape-based point correspondence estimation method is applied to the multi-sensor time calibration. Experiments show that the proposed fusion method can achieve relatively better accuracy, even if the error of the trajectory before fusion is large, which demonstrates that our method can still maintain a certain degree of accuracy in an environment where typical pose estimation methods have poor performance. In addition, the proposed time-calibration method also achieves high accuracy in estimating point correspondences.<\/jats:p>","DOI":"10.3390\/s20236918","type":"journal-article","created":{"date-parts":[[2020,12,3]],"date-time":"2020-12-03T11:15:43Z","timestamp":1606994143000},"page":"6918","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Curvefusion\u2014A Method for Combining Estimated Trajectories with Applications to SLAM and Time-Calibration"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-7940-7844","authenticated-orcid":false,"given":"Shitong","family":"Du","sequence":"first","affiliation":[{"name":"College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"Informatics VII: Robotics and Telematics, Julius-Maximilians-University W\u00fcrzburg, Am Hubland, 97074 W\u00fcrzburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Helge A.","family":"Lauterbach","sequence":"additional","affiliation":[{"name":"Informatics VII: Robotics and Telematics, Julius-Maximilians-University W\u00fcrzburg, Am Hubland, 97074 W\u00fcrzburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuyou","family":"Li","sequence":"additional","affiliation":[{"name":"College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0001-7068-1604","authenticated-orcid":false,"given":"Girum G.","family":"Demisse","sequence":"additional","affiliation":[{"name":"Faculty of Sciences, Technology and Communication, University of Luxembourg, 4, rue Alphonse Weicker, L-2721 Luxembourg"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-1363-4913","authenticated-orcid":false,"given":"Dorit","family":"Borrmann","sequence":"additional","affiliation":[{"name":"Informatics VII: Robotics and Telematics, Julius-Maximilians-University W\u00fcrzburg, Am Hubland, 97074 W\u00fcrzburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0003-3870-783X","authenticated-orcid":false,"given":"Andreas","family":"N\u00fcchter","sequence":"additional","affiliation":[{"name":"Informatics VII: Robotics and Telematics, Julius-Maximilians-University W\u00fcrzburg, Am Hubland, 97074 W\u00fcrzburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1109\/TMECH.2006.882988","article-title":"A Low-Order DGPS-Based Vehicle Positioning System Under Urban Environment","volume":"11","author":"Huang","year":"2006","journal-title":"IEEE ASME Trans. Mechatron."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1002\/rob.21732","article-title":"Autonomous aerial navigation using monocular visual inertial fusion","volume":"35","author":"Lin","year":"2018","journal-title":"J. Field Robot."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Pinies, P., Lupton, T., Sukkarieh, S., and Tardos, J.D. (2007, January 10\u201314). Inertial aiding of inverse depth SLAM using a monocular camera. Proceedings of the 2007 IEEE International Conference on Robotics and Automation, Roma, Italy.","DOI":"10.1109\/ROBOT.2007.363895"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Tong, C., and Barfoot, T. (2013, January 6\u201310). Gaussian process gaussnewton for 3d laser-based visual odometry. Proceedings of the IEEE International Conference on Robotics and Automation, Karlsruhe, Germany.","DOI":"10.1109\/ICRA.2013.6631321"},{"key":"ref_5","unstructured":"Segal, A., Haehnel, D., and Thrun, S. (July, January 28). Generalized-ICP. Proceedings of the Robotics: Science and Systems, Seattle, WA, USA."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Magnusson, M., Vaskevicius, N., Stoyanov, T., Pathak, K., and Birk, A. (2015, January 26\u201330). Beyond Points: Evaluating Recent 3D Scan-Matching Algorithms. Proceedings of the 2015 IEEE International Conference on Robotics and Automation, Seattle, WA, USA.","DOI":"10.1109\/ICRA.2015.7139703"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2942","DOI":"10.1109\/LRA.2018.2848308","article-title":"Integrating Deep Semantic Segmentation into 3D Point Cloud Registration","volume":"3","author":"Zaganidis","year":"2018","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Liu, H., Ye, Q., Wang, H., Chen, L., and Yang, J. (2019). A Precise and Robust Segmentation-Based Lidar Localization System for Automated Urban Driving. Remote. Sens., 11.","DOI":"10.3390\/rs11111348"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1016\/j.ymssp.2017.07.051","article-title":"An innovative information fusion method with adaptive Kalman filter for integrated INS\/GPS navigation of autonomous vehicles","volume":"100","author":"Liu","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Liu, S., Tsai, G., Hu, H., Chu, C.C., and Zheng, F. (2018, January 21\u201325). PIRVS: An Advanced Visual-Inertial SLAM System with Flexible Sensor Fusion and Hardware Co-Design. Proceedings of the 2018 IEEE International Conference on Robotics and Automation, Brisbane, Australia.","DOI":"10.1109\/ICRA.2018.8460672"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Bloesch, M., Omari, S., Hutter, M., and Siegwart, R. (October, January 28). Robust visual inertial odometry using a direct EKF-based approach. Proceedings of the 2015 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Hamburg, Germany.","DOI":"10.1109\/IROS.2015.7353389"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1017\/S037346331400054X","article-title":"A LiDAR-Aided Indoor Navigation System for UGVs","volume":"68","author":"Liu","year":"2015","journal-title":"J. Navig."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2015","DOI":"10.1109\/TMECH.2016.2547905","article-title":"Robust Relative Navigation by Integration of ICP and Adaptive Kalman Filter Using Laser Scanner and IMU","volume":"21","author":"Aghili","year":"2016","journal-title":"IEEE ASME Trans. Mechatron."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Bry, A., Bachrach, A., and Roy, N. (2012, January 14\u201318). State estimation for aggressive flight in gpsdenied environments using onboard sensing. Proceedings of the IEEE International Conference on Robotics and Automation, Saint Paul, MN, USA.","DOI":"10.1109\/ICRA.2012.6225295"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1002\/rob.21506","article-title":"Autonomous vision-based microair vehicle for indoor and outdoor navigation","volume":"31","author":"Schmid","year":"2014","journal-title":"J. Field Robot."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1109\/MRA.2006.1678144","article-title":"Simultaneous localization and mapping (SLAM): Part I the essential algorithms","volume":"13","author":"Bailey","year":"2006","journal-title":"IEEE Robot. Autom. Mag."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1109\/MITS.2010.939925","article-title":"A Tutorial on GraphBased SLAM","volume":"2","author":"Grisetti","year":"2010","journal-title":"IEEE Intell. Transp. Syst. Mag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1177\/0278364913491297","article-title":"Vision meets robotics: The KITTI dataset","volume":"32","author":"Geiger","year":"2013","journal-title":"Int. J. Robot. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1177\/0278364913507326","article-title":"The Malaga urban dataset: High-rate stereo and LiDAR in a realistic urban scenario","volume":"33","year":"2014","journal-title":"Int. J. Robot. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"13753","DOI":"10.3390\/rs71013753","article-title":"Evaluation of a Backpack-Mounted 3D Mobile Scanning System","volume":"7","author":"Lauterbach","year":"2015","journal-title":"Remote. Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1338","DOI":"10.1109\/TPAMI.2017.2711607","article-title":"Deformation Based Curved Shape Representation","volume":"40","author":"Demisse","year":"2017","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2236","DOI":"10.1109\/TMECH.2015.2506041","article-title":"Sensor fusion for robotic workspace state estimation","volume":"21","author":"Olofsson","year":"2016","journal-title":"IEEE ASME Trans. Mechatron."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1109\/TMECH.2014.2298247","article-title":"A Simple and Parallel Algorithm for Real-Time Robot Localization by Fusing Monocular Vision and Odometry\/AHRS Sensors","volume":"19","author":"Wang","year":"2014","journal-title":"IEEE ASME Trans. Mechatron."},{"key":"ref_24","unstructured":"(2020, July 30). Riegl. Available online: https:\/\/2.zoppoz.workers.dev:443\/https\/www.riegl.com."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Olson, E. (2010, January 18\u201322). A Passive Solution to the Sensor Synchronization Problem. Proceedings of the 2010 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan.","DOI":"10.1109\/IROS.2010.5650579"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Hu, H., Wu, J., and Xiong, Z. (2018, January 9\u201312). A Soft Time Synchronization Framework for Multi-Sensors in Autonomous Localization and Navigation. Proceedings of the 2018 IEEE\/ASME International Conference on Advanced Intelligent Mechatronics, Auckland, New Zealand.","DOI":"10.1109\/AIM.2018.8452384"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1109\/TRO.2006.889486","article-title":"Improved Techniques for Grid Mapping With Rao-Blackwellized Particle Filters","volume":"23","author":"Grisetti","year":"2007","journal-title":"IEEE Trans. Robot."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Kohlbrecher, S., von Stryk, O., Meyer, J., and Klingauf, U. (November, January 31). A flexible and scalable SLAM system with full 3D motion estimation. Proceedings of the 2011 IEEE International Symposium on Safety, Security, and Rescue Robotics, Kyoto, Japan.","DOI":"10.1109\/SSRR.2011.6106777"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1109\/TRO.2015.2463671","article-title":"ORB-SLAM: A Versatile and Accurate Monocular SLAM System","volume":"31","author":"Montiel","year":"2015","journal-title":"IEEE Trans. Robot."},{"key":"ref_30","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, Berkeley, CA, USA.","DOI":"10.15607\/RSS.2014.X.007"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1094","DOI":"10.1109\/TRO.2008.2004636","article-title":"Large-Scale SLAM Building Conditionally Independent Local Maps: Application to Monocular Vision","volume":"24","author":"Pinies","year":"2008","journal-title":"IEEE Trans. Robot."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Chen, C., Zhu, H., Li, M., and You, S. (2018). A Review of Visual-Inertial Simultaneous Localization and Mapping from Filtering-Based and Optimization-Based Perspectives. Robotics, 7.","DOI":"10.3390\/robotics7030045"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1177\/0278364914554813","article-title":"Keyframe-based visual\u2013inertial odometry using nonlinear optimization","volume":"34","author":"Leutenegger","year":"2015","journal-title":"Int. J. Robot. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2063","DOI":"10.1142\/S0218127405013307","article-title":"The CNN paradigm: Shapes and complexity","volume":"15","author":"Arena","year":"2005","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1697","DOI":"10.1177\/0278364916669237","article-title":"ElasticFusion: Real-time dense SLAM and light source estimation","volume":"35","author":"Whelan","year":"2016","journal-title":"Int. J. Robot. Res."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Puri, P., Jia, D., and Kaess, M. (2017, January 24\u201328). GravityFusion: Real-time Dense Mapping without Pose Graph using Deformation and Orientation. Proceedings of the 2017 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Vancouver, BC, Canada.","DOI":"10.1109\/IROS.2017.8206559"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Park, C., Moghadam, P., Kim, S., and Elfes, A. (2018, January 21\u201325). Elastic LiDAR Fusion: Dense Map-Centric Continuous-Time SLAM. Proceedings of the 2018 IEEE International Conference on Robotics and Automation, Brisbane, Australia.","DOI":"10.1109\/ICRA.2018.8462915"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Demisse, G.G., Aouada, D., and Ottersten, B. (July, January 26). Similarity Metric For Curved Shapes in Euclidean Space. Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.545"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"5871","DOI":"10.3390\/rs5115871","article-title":"Algorithmic solutions for computing precise maximum likelihood 3D point clouds from mobile laser scanning platforms","volume":"5","author":"Elseberg","year":"2013","journal-title":"Remote. Sens."},{"key":"ref_40","unstructured":"(2020, July 30). Google. Available online: https:\/\/2.zoppoz.workers.dev:443\/https\/www.google.com\/maps."},{"key":"ref_41","unstructured":"N\u00fcchter, A., and Lingemann, K. (2020, July 30). 6D SLAM Software. Available online: https:\/\/2.zoppoz.workers.dev:443\/http\/slam6d.sourceforge.net\/."},{"key":"ref_42","unstructured":"Girardeau-Montaut, D. (2020, July 30). CloudCompare 3D Point Cloud and Mesh Processing Software. Available online: https:\/\/2.zoppoz.workers.dev:443\/http\/www.cloudcompare.org\/."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Lauterbach, H.A., and N\u00fcchter, A. (2018, January 6\u20138). Preliminary Results on Instantaneous UAV-Based 3D Mapping for Rescue Applications. Proceedings of the 16th IEEE International Symposium on Safety, Security, and Rescue Robotics, Philadelphia, PA, USA.","DOI":"10.1109\/SSRR.2018.8468625"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.mdpi.com\/1424-8220\/20\/23\/6918\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:41:06Z","timestamp":1760179266000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.mdpi.com\/1424-8220\/20\/23\/6918"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,3]]},"references-count":43,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["s20236918"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/s20236918","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,12,3]]}}}