{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T15:37:29Z","timestamp":1785512249573,"version":"3.56.0"},"reference-count":50,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,6,23]],"date-time":"2020-06-23T00:00:00Z","timestamp":1592870400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Education, Republic of Korea","award":["10039673, 10079961"],"award-info":[{"award-number":["10039673, 10079961"]}]},{"DOI":"10.13039\/501100003052","name":"Ministry of Trade, Industry and Energy","doi-asserted-by":"publisher","award":["N0001992"],"award-info":[{"award-number":["N0001992"]}],"id":[{"id":"10.13039\/501100003052","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004085","name":"Ministry of Education, Science and Technology","doi-asserted-by":"publisher","award":["2011-0017495"],"award-info":[{"award-number":["2011-0017495"]}],"id":[{"id":"10.13039\/501100004085","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In automated parking systems, a path planner generates a path to reach the vacant parking space detected by a perception system. To generate a safe parking path, accurate detection performance is required. However, the perception system always includes perception uncertainty, such as detection errors due to sensor noise and imperfect algorithms. If the parking path planner generates the parking path under uncertainty, problems may arise that cause the vehicle to collide due to the automated parking system. To avoid these problems, it is a challenging problem to generate the parking path from the erroneous parking space. To solve this conundrum, it is important to estimate the perception uncertainty and adapt the detection error in the planning process. This paper proposes a robust parking path planning that combines an error-adaptive sampling of generating possible path candidates with a utility-based method of making an optimal decision under uncertainty. By integrating the sampling-based method and the utility-based method, the proposed algorithm continuously generates an adaptable path considering the detection errors. As a result, the proposed algorithm ensures that the vehicle is safely located in the true position and orientation of the parking space under perception uncertainty.<\/jats:p>","DOI":"10.3390\/s20123560","type":"journal-article","created":{"date-parts":[[2020,6,24]],"date-time":"2020-06-24T07:14:19Z","timestamp":1592982859000},"page":"3560","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Robust Parking Path Planning with Error-Adaptive Sampling under Perception Uncertainty"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8278-5742","authenticated-orcid":false,"given":"Seongjin","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Automotive Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7195-3349","authenticated-orcid":false,"given":"Wonteak","family":"Lim","sequence":"additional","affiliation":[{"name":"Department of Automotive Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3505-6675","authenticated-orcid":false,"given":"Myoungho","family":"Sunwoo","sequence":"additional","affiliation":[{"name":"Department of Automotive Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,23]]},"reference":[{"key":"ref_1","first-page":"349","article-title":"Directional-DBSCAN: Parking-slot detection using a clustering method in around-view monitoring system","volume":"457","author":"Lee","year":"2016","journal-title":"IEEE Intell. Veh. Symp. Proc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"823","DOI":"10.4028\/www.scientific.net\/AMM.437.823","article-title":"Image-based parking guiding using Ackermann steering geometry","volume":"437","author":"Tseng","year":"2013","journal-title":"Appl. Mech. Mater."},{"key":"ref_3","unstructured":"Hamada, K., Hu, Z., Fan, M., and Chen, H. (July, January 28). Surround view based parking lot detection and tracking. Proceedings of the IEEE Intelligent Vehicles Symposium (IV), Seoul, Korea."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5687","DOI":"10.1109\/TIE.2016.2558480","article-title":"Automatic Parking Space Detection and Tracking for Underground and Indoor Environments","volume":"63","author":"Suhr","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_5","unstructured":"Park, W.J., Kim, B.S., Seo, D.E., Kim, D.S., and Lee, K.H. (2008, January 4\u20136). Parking space detection using ultrasonic sensor in parking assistance system. Proceedings of the IEEE Intelligent Vehicles Symposium, Eindhoven, The Netherlands."},{"key":"ref_6","first-page":"55","article-title":"Smart Parking System (SPS) architecture using ultrasonic detector","volume":"6","author":"Kianpisheh","year":"2012","journal-title":"Int. J. Softw. Eng. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s12239-010-0050-0","article-title":"Low cost design of parallel parking assist system based on an ultrasonic sensor","volume":"11","author":"Jeong","year":"2010","journal-title":"Int. J. Automot. Technol."},{"key":"ref_8","unstructured":"Satonaka, H., Okuda, M., Hayasaka, S., Endo, T., Tanaka, Y., and Yoshida, T. (2006, January 8\u201312). Development of parking space detection using an ultrasonic sensor. Proceedings of the 13th World Congress, London, UK."},{"key":"ref_9","unstructured":"Hsieh, M.F., and \u00d6zguner, \u00dc. (2008, January 4\u20136). A parking algorithm for an autonomous vehicle. Proceedings of the IEEE Intelligent Vehicles Symposium, Eindhoven, The Netherlands."},{"key":"ref_10","first-page":"298","article-title":"Turning Standard Line (TSL) Based Path Planning Algorithm for Narrow Parking Lots","volume":"1","author":"Lim","year":"2015","journal-title":"SAE Tech. Pap."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.robot.2008.03.009","article-title":"A Bezier curve based path planning in a multi-agent robot soccer system without violating the acceleration limits","volume":"57","author":"Jolly","year":"2009","journal-title":"Rob. Autom. Syst."},{"key":"ref_12","unstructured":"Yoon, J., and Crane, C.D. (2011, January 26\u201329). Path planning for unmanned ground vehicle in urban parking area. Proceedings of the 11th International Conference on Control, Automation and Systems, Gyeonggi-do, Korea."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Han, L., and Do, Q.H. (2011, January 9\u201313). Unified path planner for parking an autonomous vehicle based on RRT. Proceedings of the IEEE International Conference on Robotics and Automation, Shanghai, China.","DOI":"10.1109\/ICRA.2011.5980105"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1177\/0278364909359210","article-title":"Path planning for autonomous vehicles in unknown semi-structured environments","volume":"29","author":"Dolgov","year":"2010","journal-title":"Int. J. Rob. Res."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Sakaeta, K., Oda, T., Nonaka, K., and Sekiguchi, K. (2015, January 21\u201323). Model predictive parking control with on-line path generations and multiple switching motions. Proceedings of the IEEE Conference on Control Applications (CCA), Sydney, Australia.","DOI":"10.1109\/CCA.2015.7320716"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.knosys.2015.04.016","article-title":"A unified motion planning method for parking an autonomous vehicle in the presence of irregularly placed obstacles","volume":"86","author":"Li","year":"2015","journal-title":"Knowl. Based Syst."},{"key":"ref_17","unstructured":"Kobayashi, T., and Majima, S. (2001, January 25\u201328). Real-time optimization control for parking a vehicle automatically. Proceedings of the IEEE International Vehicle Electronics Conference, Tottori, Japan."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.robot.2016.02.004","article-title":"Optimisation based path planning for car parking in narrow environments","volume":"79","author":"Zips","year":"2016","journal-title":"Rob. Autom. Syst."},{"key":"ref_19","unstructured":"Yamamoto, M., Hayashi, Y., and Mohri, A. (2005, January 19\u201321). Garage parking planning and control of car-like robot using a real time optimization method. Proceedings of the IEEE International Symposium on Assembly and Task Planning: From Nano to Macro Assembly and Manufacturing, Montreal, QC, Canada."},{"key":"ref_20","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 IEEE international conference on robotics and automation, Shanghai, China.","DOI":"10.1109\/ICRA.2011.5980508"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"291","DOI":"10.7551\/mitpress\/9123.003.0041","article-title":"Belief space planning assuming maximum likelihood observations","volume":"6","author":"Platt","year":"2011","journal-title":"Robot. Sci. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1177\/0278364911406562","article-title":"LQG-MP: Optimized path planning for robots with motion uncertainty and imperfect state information","volume":"30","author":"Abbeel","year":"2011","journal-title":"Int. J. Rob. Res."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Patil, S., Van Den Berg, J., and Alterovitz, R. (2012, January 14\u201318). Estimating probability of collision for safe motion planning under Gaussian motion and sensing uncertainty. Proceedings of the IEEE International Conference on Robotics and Automation, Saint Paul, MN, USA.","DOI":"10.1109\/ICRA.2012.6224727"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1109\/TSMCB.2010.2098438","article-title":"Generalized sampling-based motion planners","volume":"41","author":"Chakravorty","year":"2011","journal-title":"IEEE Trans. Syst. Man Cybern. Part B Cybern."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5902","DOI":"10.3182\/20110828-6-IT-1002.02184","article-title":"Belief space planning for linear, Gaussian systems in uncertain environments","volume":"44","author":"Vitus","year":"2011","journal-title":"IFAC Proc. Vol."},{"key":"ref_26","unstructured":"Missiuro, P.E., and Roy, N. (2006, January 15\u201319). Adapting probabilistic roadmaps to handle uncertain maps. Proceedings of the IEEE International Conference on Robotics and Automation, Orlando, FL, USA."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Blackmore, L., Li, H., and Williams, B. (2006, January 14\u201316). A probabilistic approach to optimal robust path planning with obstacles. Proceedings of the American Control Conference, Minneapolis, MN, USA.","DOI":"10.1109\/ACC.2006.1656653"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1080","DOI":"10.1109\/TRO.2011.2161160","article-title":"Chance-constrained optimal path planning with obstacles","volume":"27","author":"Blackmore","year":"2011","journal-title":"IEEE Trans. Rob."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Burns, B., and Brock, O. (2007, January 10\u201314). Sampling-based motion planning with sensing uncertainty. Proceedings of the IEEE International Conference on Robotics and Automation, Roma, Italy.","DOI":"10.1109\/ROBOT.2007.363984"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Burns, B., and Brock, O. (2007, January 10\u201314). Single-query motion planning with utility-guided random trees. Proceedings of the IEEE International Conference on Robotics and Automation, Roma, Italy.","DOI":"10.1109\/ROBOT.2007.363983"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"580","DOI":"10.2514\/1.12919","article-title":"Real-time planning for multiple autonomous vehicles in dynamic uncertain environments","volume":"1","author":"Pongpunwattana","year":"2004","journal-title":"J. Aerosp. Comput. Inf. Commun."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Im, G., Kim, M., and Park, J. (2019). Parking line based SLAM approach using AVM\/LiDAR sensor fusion for rapid and accurate loop closing and parking space detection. Sensors, 19.","DOI":"10.3390\/s19214811"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"241","DOI":"10.5194\/isprs-archives-XLII-2-W7-241-2017","article-title":"Automatic parking of self-driving car based on LiDAR","volume":"42","author":"Lee","year":"2017","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3377","DOI":"10.1109\/TITS.2015.2450738","article-title":"Precise Localization of an Autonomous Car Based on Probabilistic Noise Models of Road Surface Marker Features Using Multiple Cameras","volume":"16","author":"Jo","year":"2015","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1177\/027836498600500304","article-title":"Toward Efficient Trajectory Planning: The Path-Velocity Decomposition","volume":"5","author":"Kant","year":"1986","journal-title":"Int. J. Rob. Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1006\/gmip.1998.0464","article-title":"Polynomial\/Rational Approximation of Minkowski Sum Boundary Curves","volume":"60","author":"Lee","year":"1998","journal-title":"Graph. Model. Image Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"163","DOI":"10.2307\/3439089","article-title":"An Introduction to Bernoullian Utility Theory: I. Utility Functions","volume":"69","author":"Jensen","year":"1967","journal-title":"Swed. J. Econ."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Kochenderfer, M.J. (2015). Decision Making Under Uncertainty: Theory and Application, MIT Press. [1st ed.].","DOI":"10.7551\/mitpress\/10187.001.0001"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s00138-018-0986-z","article-title":"Semantic segmentation-based parking space detection with standalone around view monitoring system","volume":"30","author":"Jang","year":"2019","journal-title":"Mach. Vis. Appl."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Akai, N., Morales, L.Y., Yamaguchi, T., Takeuchi, E., Yoshihara, Y., Okuda, H., Suzuki, T., and Ninomiya, Y. (2017, January 16\u201319). Autonomous driving based on accurate localization using multilayer LiDAR and dead reckoning. Proceedings of the 20th International Conference on Intelligent Transportation Systems (ITSC), Yokohama, Japan.","DOI":"10.1109\/ITSC.2017.8317797"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1109\/JOE.2017.2769838","article-title":"A Low-Cost Dead Reckoning Navigation System for an AUV Using a Robust AHRS: Design and Experimental Analysis","volume":"43","author":"Sabet","year":"2017","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1080\/00423110802018297","article-title":"MPC-based yaw and lateral stabilisation via active front steering and braking","volume":"46","author":"Falcone","year":"2008","journal-title":"Veh. Syst. Dyn."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Gao, Y., Lin, T., Borrelli, F., Tseng, E., and Hrovat, D. (2010, January 12\u201315). Predictive control of autonomous ground vehicles with obstacle avoidance on slippery roads. Proceedings of the Dynamic Systems and Control Conference, Cambridge, MA, USA.","DOI":"10.1115\/DSCC2010-4263"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Gray, A., Gao, Y., Lin, T., Hedrick, J.K., Tseng, H.E., and Borrelli, F. (2012, January 27\u201329). Predictive control for agile semi-autonomous ground vehicles using motion primitives. Proceedings of the American Control Conference (ACC), Montreal, QC, Canada.","DOI":"10.1109\/ACC.2012.6315303"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/978-3-642-13408-1_6","article-title":"Experimental study of an optimal-control- based framework for trajectory planning, threat assessment, and semi-autonomous control of passenger vehicles in hazard avoidance scenarios","volume":"62","author":"Howard","year":"2010","journal-title":"Field and Service Robotics"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1109\/TCST.2010.2049203","article-title":"Model predictive multi-objective vehicular adaptive cruise control","volume":"19","author":"Li","year":"2010","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.1109\/TVT.2004.833625","article-title":"Model predictive control of transitional maneuvers for adaptive cruise control vehicles","volume":"53","author":"Bageshwar","year":"2004","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_48","unstructured":"Quigley, M., Gerkey, B., Conley, K., Faust, J., Foote, T., Leibs, J., Berger, E., Wheeler, R., and Ng, A. (,  2009). ROS: An Open- Source Robot Operating System. Proceedings of the ICRA Workshop on Open Source Software, Available online: https:\/\/www.willowgarage.com\/sites\/default\/files\/icraoss09-ROS.pdf."},{"key":"ref_49","unstructured":"Kraft, D. (2020, June 23). A Software Package for Sequential Quadratic Programming. Available online: http:\/\/www.opengrey.eu\/item\/display\/10068\/147127."},{"key":"ref_50","unstructured":"Johnson, S.G. (2020, June 23). The NLopt Nonlinear-Optimization Package. Available online: http:\/\/github.com\/stevengj\/nlopt."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/12\/3560\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:41:56Z","timestamp":1760175716000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/12\/3560"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,23]]},"references-count":50,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["s20123560"],"URL":"https:\/\/doi.org\/10.3390\/s20123560","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,23]]}}}