{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T22:34:24Z","timestamp":1781822064697,"version":"3.54.5"},"reference-count":35,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2020,12,16]],"date-time":"2020-12-16T00:00:00Z","timestamp":1608076800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation of China Joint Fund Project","award":["U1864205"],"award-info":[{"award-number":["U1864205"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The traditional potential field-based path planning is likely to generate unexpected path by strictly following the minimum potential field, especially in the driving scenarios with multiple obstacles closely distributed. A hybrid path planning is proposed to avoid the unsatisfying path generation and to improve the performance of autonomous driving by combining the potential field with the sigmoid curve. The repulsive and attractive potential fields are redesigned by considering the safety and the feasibility. Based on the objective of the shortest path generation, the optimized trajectory is obtained to improve the vehicle stability and driving safety by considering the constraints of collision avoidance and vehicle dynamics. The effectiveness is examined by simulations in multiobstacle dynamic and static scenarios. The simulation results indicate that the proposed method shows better performance on vehicle stability and ride comfortability than that of the traditional potential field-based method in all the examined scenarios during the autonomous driving.<\/jats:p>","DOI":"10.3390\/s20247197","type":"journal-article","created":{"date-parts":[[2020,12,16]],"date-time":"2020-12-16T09:21:15Z","timestamp":1608110475000},"page":"7197","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Hybrid Path Planning Combining Potential Field with Sigmoid Curve for Autonomous Driving"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4441-1704","authenticated-orcid":false,"given":"Bing","family":"Lu","sequence":"first","affiliation":[{"name":"National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2874-1858","authenticated-orcid":false,"given":"Hongwen","family":"He","sequence":"additional","affiliation":[{"name":"National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huilong","family":"Yu","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Mechatronics Engineering, Waterloo University, Waterloo, ON N2L 3G1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hong","family":"Wang","sequence":"additional","affiliation":[{"name":"Tsinghua Intelligent Vehicle Design and Safety Research Institute, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7889-4695","authenticated-orcid":false,"given":"Guofa","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Man","family":"Shi","sequence":"additional","affiliation":[{"name":"National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dongpu","family":"Cao","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Mechatronics Engineering, Waterloo University, Waterloo, ON N2L 3G1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1109\/70.163777","article-title":"Exact robot navigation using artificial potential functions","volume":"8","author":"Rimon","year":"1992","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIE.2015.2504042","article-title":"Distributed formation control of nonholonomic vehicles subject to velocity constraints","volume":"63","author":"Yu","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/TVT.2019.2945934","article-title":"A Novel Local Motion Planning Framework for Autonomous Vehicles Based on Resistance Network and Model Predictive Control","volume":"69","author":"Huang","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3313","DOI":"10.1109\/TITS.2018.2873921","article-title":"Crash mitigation in motion planning for autonomous vehicles","volume":"20","author":"Wang","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1109\/TITS.2015.2498841","article-title":"A review of motion planning techniques for automated vehicles","volume":"17","author":"Nashashibi","year":"2016","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Anderson, S.J., Karumanchi, S.B., and Iagnemma, K. (2012, January 3\u20137). Constraint-based planning and control for safe, semi-autonomous operation of vehicles. Proceedings of the 2012 IEEE Intelligent Vehicles Symposium, Alcala de Henares, Spain.","DOI":"10.1109\/IVS.2012.6232153"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1109\/TSMCA.2003.812599","article-title":"A fast path planning by path graph optimization","volume":"33","author":"Hwang","year":"2003","journal-title":"IEEE Trans. Syst. Man Cybern. Part A Syst. Hum."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ziegler, J., Werling, M., and Schr\u00f6der, J. (2008, January 4\u20136). Navigating car-like robots in unstructured environments using an obstacle sensitive cost function. Proceedings of the 2008 IEEE Intelligent Vehicles Symposium, Eindhoven, The Netherlands.","DOI":"10.1109\/IVS.2008.4621302"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ziegler, J., and Stiller, C. (2009, January 11\u201315). Spatiotemporal state lattices for fast trajectory planning in dynamic on-road driving scenarios. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems, St. Louis, MO, USA.","DOI":"10.1109\/IROS.2009.5354448"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2568","DOI":"10.1109\/TMECH.2018.2821767","article-title":"A fast and efficient double-tree RRT*-like sampling-based planner applying on mobile robotic systems","volume":"23","author":"Chen","year":"2018","journal-title":"IEEE\/Asme Trans. Mechatron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1109\/70.508439","article-title":"Probabilistic roadmaps for path planning in high-dimensional configuration spaces","volume":"12","author":"Kavraki","year":"1996","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"32800","DOI":"10.1109\/ACCESS.2018.2845448","article-title":"Hybrid trajectory planning for autonomous driving in highly constrained environments","volume":"6","author":"Zhang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2182","DOI":"10.1109\/TCST.2017.2739706","article-title":"Spline-based motion planning for autonomous guided vehicles in a dynamic environment","volume":"26","author":"Mercy","year":"2018","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1109\/TRO.2013.2283928","article-title":"Real-time approximation of clothoids with bounded error for path planning applications","volume":"30","author":"Brezak","year":"2014","journal-title":"IEEE Trans. Robot."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1109\/TMECH.2015.2493980","article-title":"Real-Time Trajectory Planning for Autonomous Urban Driving: Framework, Algorithms, and Verifications","volume":"21","author":"Li","year":"2016","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_16","unstructured":"Narendra, K.S. (1986). The Potential Field Approach And Operational Space Formulation In Robot Control. Adaptive and Learning Systems: Theory and Applications, Springer."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"952","DOI":"10.1109\/TVT.2016.2555853","article-title":"Path planning and tracking for vehicle collision avoidance based on model predictive control with multiconstraints","volume":"66","author":"Ji","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1109\/TITS.2016.2604240","article-title":"A potential field-based model predictive path-planning controller for autonomous road vehicles","volume":"18","author":"Rasekhipour","year":"2017","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Krogh, B.H., and Thorpe, C.E. (1986, January 7\u201310). Integrated path planning and dynamic steering control for autonomous vehicles. Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, CA, USA.","DOI":"10.1109\/ROBOT.1986.1087444"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.ymssp.2019.01.040","article-title":"Shared control with a novel dynamic authority allocation strategy based on game theory and driving safety field","volume":"124","author":"Li","year":"2019","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_21","unstructured":"Park, D.H., Hoffmann, H., Pastor, P., and Schaal, S. (2008, January 1\u20133). Movement reproduction and obstacle avoidance with dynamic movement primitives and potential fields. Proceedings of the IEEE-RAS International Conference on Humanoid Robots, Daejeon, Korea."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"102820","DOI":"10.1016\/j.trc.2020.102820","article-title":"Risk assessment based collision avoidance decision-making for autonomous vehicles in multi-scenarios","volume":"122","author":"Li","year":"2021","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Lee, J., Nam, Y., and Hong, S. (2010, January 7\u201310). Random force based algorithm for local minima escape of potential field method. Proceedings of the 2010 11th International Conference on Control Automation Robotics and Vision, Singapore.","DOI":"10.1109\/ICARCV.2010.5707422"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"8889","DOI":"10.1109\/TIE.2019.2945295","article-title":"Deep learning approaches on pedestrian detection in hazy weather","volume":"67","author":"Li","year":"2020","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5177","DOI":"10.1016\/j.eswa.2015.02.033","article-title":"Path planning for mobile robots using bacterial potential field for avoiding static and dynamic obstacles","volume":"42","author":"Montiel","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.robot.2016.04.007","article-title":"A novel potential field method for path planning of mobile robots by adapting animal motion attributes","volume":"82","author":"Szayer","year":"2016","journal-title":"Robot. Auton. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1109\/70.127236","article-title":"A potential field approach to path planning","volume":"8","author":"Hwang","year":"1992","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1109\/TITS.2015.2477355","article-title":"Randomized bidirectional B-spline parameterization motion planning","volume":"17","author":"Elbanhawi","year":"2016","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Resende, P., and Nashashibi, F. (2010, January 19\u201322). Real-time dynamic trajectory planning for highly automated driving in highways. Proceedings of the International IEEE Conference on Intelligent Transportation Systems, Funchal, Portugal.","DOI":"10.1109\/ITSC.2010.5625194"},{"key":"ref_30","unstructured":"Finney, D.J. (1952). Probit Analysis: A Statistical Treatment of the Sigmoid Response Curve, Cambridge University Press."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"5932","DOI":"10.1016\/j.eswa.2015.03.022","article-title":"Trajectory planning and tracking control for autonomous lane change maneuver based on the cooperative vehicle infrastructure system","volume":"42","author":"You","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.ymssp.2017.04.041","article-title":"Kalman filter-based tracking of moving objects using linear ultrasonic sensor array for road vehicles","volume":"98","author":"Li","year":"2017","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1177\/0278364915625345","article-title":"Efficient collision checking in sampling-based motion planning via safety certificates","volume":"35","author":"Bialkowski","year":"2016","journal-title":"Int. J. Robot. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1080\/00423114.2016.1267368","article-title":"Integrated chassis control for a three-axle electric bus with distributed driving motors and active rear steering system","volume":"55","author":"Liu","year":"2017","journal-title":"Veh. Syst. Dyn."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2031","DOI":"10.1109\/TMECH.2018.2862924","article-title":"Reconfigurable Integrated Stability Control for Four- and Three-wheeled Urban Vehicles With Flexible Combinations of Actuation Systems","volume":"23","author":"Ataei","year":"2018","journal-title":"IEEE\/ASME Trans. Mechatron."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/24\/7197\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:45:38Z","timestamp":1760179538000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/24\/7197"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,16]]},"references-count":35,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["s20247197"],"URL":"https:\/\/doi.org\/10.3390\/s20247197","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,16]]}}}