{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T21:22:05Z","timestamp":1769721725611,"version":"3.49.0"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T00:00:00Z","timestamp":1722470400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T00:00:00Z","timestamp":1722470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U21B6001"],"award-info":[{"award-number":["U21B6001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"China Post-doctoral Science Foundation","award":["2022M713006"],"award-info":[{"award-number":["2022M713006"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Intell Robot Syst"],"DOI":"10.1007\/s10846-024-02151-x","type":"journal-article","created":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T16:02:14Z","timestamp":1722528134000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Novel Method of 3D Lyapunov Guidance Vector Field to Avoid Intercepting Satellite Based on Reinforcement Learning"],"prefix":"10.1007","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4252-9880","authenticated-orcid":false,"given":"Yunfei","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7117-9760","authenticated-orcid":false,"given":"Honglun","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3821-443X","authenticated-orcid":false,"given":"Menghua","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1286-8846","authenticated-orcid":false,"given":"Yiheng","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7843-5459","authenticated-orcid":false,"given":"Jianfa","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,8,1]]},"reference":[{"issue":"1","key":"2151_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cja.2013.07.042","volume":"27","author":"YZ Luo","year":"2014","unstructured":"Luo, Y.Z., Zhang, J., Tang, G.J.: Survey of Orbital Dynamics and Control of Space Rendezvous. Chin. J. Aeronaut. 27(1), 1\u201311 (2014)","journal-title":"Chin. J. Aeronaut."},{"key":"2151_CR2","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1016\/j.actaastro.2018.06.036","volume":"151","author":"S Le May","year":"2018","unstructured":"Le May, S., Gehly, S., Carter, B.A., et al.: Space debris collision probability analysis for proposed global broadband constellations. Acta Astronautica 151, 445\u2013455 (2018)","journal-title":"Acta Astronautica"},{"key":"2151_CR3","doi-asserted-by":"publisher","first-page":"34237","DOI":"10.1109\/ACCESS.2018.2817648","volume":"6","author":"Z Wu","year":"2018","unstructured":"Wu, Z., Li, J., Zuo, J., et al.: Path planning of UAVs based on collision probability and Kalman filter. IEEE Access 6, 34237\u201334245 (2018)","journal-title":"IEEE Access"},{"key":"2151_CR4","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1016\/j.asoc.2019.01.036","volume":"77","author":"U Orozco-Rosas","year":"2019","unstructured":"Orozco-Rosas, U., Montiel, O., Sep\u00falveda, R.: Mobile robot path planning using membrane evolutionary artificial potential field. Appl. Soft Comput. 77, 236\u2013251 (2019)","journal-title":"Appl. Soft Comput."},{"issue":"2","key":"2151_CR5","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1515\/fca-2021-0019","volume":"24","author":"JF Duh\u00e9","year":"2021","unstructured":"Duh\u00e9, J.F., Victor, S., Melchior, P.: Contributions on artificial potential field method for effective obstacle avoidance. Fract. Calc. Appl. Anal. 24(2), 421\u2013446 (2021)","journal-title":"Fract. Calc. Appl. Anal."},{"issue":"2","key":"2151_CR6","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/s42064-021-0119-8","volume":"6","author":"C Wen","year":"2022","unstructured":"Wen, C., Qiao, D.: Calculating collision probability for long-term satellite encounters through the reachable domain method. Astrodynamics 6(2), 141\u2013159 (2022)","journal-title":"Astrodynamics"},{"issue":"9","key":"2151_CR7","doi-asserted-by":"publisher","first-page":"3846","DOI":"10.1016\/j.asr.2021.07.023","volume":"68","author":"R Yan","year":"2021","unstructured":"Yan, R., Gong, J., Liu, S., et al.: Gaussian sum reapproximation applied to the probability of collision calculations. Adv. Space Res. 68(9), 3846\u20133858 (2021)","journal-title":"Adv. Space Res."},{"issue":"1","key":"2151_CR8","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1177\/027836498600500106","volume":"5","author":"O Khatib","year":"1986","unstructured":"Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Robot. Res. 5(1), 90\u201398 (1986)","journal-title":"Int. J. Robot. Res."},{"issue":"4","key":"2151_CR9","doi-asserted-by":"publisher","first-page":"1163","DOI":"10.1016\/j.cja.2015.06.014","volume":"28","author":"P Yao","year":"2015","unstructured":"Yao, P., Wang, H., Su, Z.: UAV feasible path planning based on disturbed fluid and trajectory propagation. Chin. J. Aeronaut. 28(4), 1163\u20131177 (2015)","journal-title":"Chin. J. Aeronaut."},{"issue":"1","key":"2151_CR10","doi-asserted-by":"publisher","first-page":"1479","DOI":"10.1109\/JSYST.2019.2917786","volume":"14","author":"J Wu","year":"2019","unstructured":"Wu, J., Wang, H., Li, N., et al.: Formation obstacle avoidance: A fluid-based solution. IEEE Syst. J. 14(1), 1479\u20131490 (2019)","journal-title":"IEEE Syst. J."},{"key":"2151_CR11","doi-asserted-by":"crossref","unstructured":"Harinarayana, T., Krishnan, S.V., Hota, S., et al.: A Lyapunov guidance vector field based continuous curvature path generation for waypoint following of UAVs. In: 2021 International Conference on Unmanned Aircraft Systems (ICUAS), pp. 498\u2013506. IEEE (2021)","DOI":"10.1109\/ICUAS51884.2021.9476722"},{"key":"2151_CR12","doi-asserted-by":"publisher","first-page":"124797","DOI":"10.1109\/ACCESS.2019.2932998","volume":"7","author":"S Sun","year":"2019","unstructured":"Sun, S., Wang, H., Liu, J., et al.: Fast Lyapunov vector field guidance for standoff target tracking based on offline search. IEEE Access 7, 124797\u2013124808 (2019)","journal-title":"IEEE Access"},{"key":"2151_CR13","doi-asserted-by":"crossref","unstructured":"Rezende, A.M.C, Gon\u00e7alves, V.M, Raffo, G.V, et al.: Robust fixed-wing UAV guidance with circulating artificial vector fields. In: 2018 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 5892\u20135899. IEEE (2018)","DOI":"10.1109\/IROS.2018.8594371"},{"key":"2151_CR14","unstructured":"Schulman, J., Wolski, F., Dhariwal, P., et al.: Proximal policy optimization algorithms. arXiv. https:\/\/arxiv.org\/abs\/1707.06347 (2017). Accessed 20 July 2017"},{"key":"2151_CR15","unstructured":"Schulman, J., Levine, S., Abbeel, P., et al.: Trust region policy optimization. In: 32nd International Conference on Machine Learning (ICML 2015), pp. 1889\u20131897. International Machine Learning Society (2015)"},{"key":"2151_CR16","unstructured":"Fujimoto, S., Hoof, H., Meger, D.: Addressing function approximation error in actorcritic methods. In: 35th International Conference on Machine Learning (ICML 2018), pp. 2587\u20132601. International Machine Learning Society (2018)"},{"key":"2151_CR17","unstructured":"Lillicrap, T.P., Hunt, J.J., Pritzel, A., et al.: Continuous control with deep reinforcement learning. arXiv. https:\/\/arxiv.org\/abs\/1509.02971 (2015). Accessed 9 Sept 2015"},{"key":"2151_CR18","doi-asserted-by":"crossref","unstructured":"Wang, Y., Wang, H., Wen, J., et al.: Obstacle avoidance of UAV based on neural networks and interfered fluid dynamical system. In: Proceedings of 2020 3rd International Conference on Unmanned Systems (ICUS), pp. 1066\u20131071. IEEE (2020)","DOI":"10.1109\/ICUS50048.2020.9274988"},{"key":"2151_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2022.107760","volume":"161","author":"O Dogru","year":"2022","unstructured":"Dogru, O., Velswamy, K., Ibrahim, F., et al.: Reinforcement learning approach to autonomous PID tuning. Comput. Chem. Eng. 161, 107760 (2022)","journal-title":"Comput. Chem. Eng."},{"key":"2151_CR20","unstructured":"Ng, A.Y., Harada, D., Russell, S.: Policy invariance under reward transformations: Theory and application to reward shaping. In: 16th International Conference on Machine Learning (ICML 99), pp. 278\u2013287. Machine Learning, Proceedings (1999)"},{"key":"2151_CR21","unstructured":"Andrychowicz, M., Wolski, F., Ray, A., et al.: Hindsight experience replay. In: Advances in Neural Information Processing Systems 30 - Proceedings of the 2017 Conference, pp. 5049\u20135059. Neural information processing systems foundation (2017)"},{"key":"2151_CR22","unstructured":"Mnih, V., Badia, A.P., Mirza, M., et al.: Asynchronous methods for deep reinforcement learning.\u00a0In: 33rd International Conference on Machine Learning (ICML 2016), pp.\u00a02850\u20132869. International Machine Learning Society (2016)"},{"key":"2151_CR23","unstructured":"Schulman, J., Moritz, P., Levine, S., et al.: High-dimensional continuous control using generalized advantage estimation. arXiv. https:\/\/arxiv.org\/abs\/1506.02438 (2015). Accessed 8 June 2015"},{"key":"2151_CR24","unstructured":"Haarnoja, T., Zhou, A., Hartikainen, K., et al.: Soft actor-critic algorithms and applications. arXiv. https:\/\/arxiv.org\/abs\/1812.05905 (2018). Accessed 13 Dec 2018"},{"key":"2151_CR25","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/j.chemolab.2015.08.020","volume":"149","author":"F. Marini","year":"2015","unstructured":"Marini, F., Walczak, B., et al.: Particle swarm optimization (PSO). A tutorial. Chemometr. Intell. Lab.\u00a0 149, 153\u2013165 (2015)","journal-title":"Chemometr. Intell. Lab.\u00a0"},{"issue":"2","key":"2151_CR26","doi-asserted-by":"publisher","first-page":"866","DOI":"10.1109\/TAES.2014.140022","volume":"51","author":"ZM Kassas","year":"2015","unstructured":"Kassas, Z.M., Humphreys, T.E.: Receding horizon trajectory optimization in opportunistic navigation environments. IEEE Trans. Aerosp. Electron. Syst. 51(2), 866\u2013877 (2015)","journal-title":"IEEE Trans. Aerosp. Electron. Syst."}],"container-title":["Journal of Intelligent & Robotic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-024-02151-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10846-024-02151-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-024-02151-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T13:13:18Z","timestamp":1727356398000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10846-024-02151-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,1]]},"references-count":26,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["2151"],"URL":"https:\/\/doi.org\/10.1007\/s10846-024-02151-x","relation":{},"ISSN":["1573-0409"],"issn-type":[{"value":"1573-0409","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,1]]},"assertion":[{"value":"22 August 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 July 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 August 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics Approval"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to Participate"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for Publication"}},{"value":"The authors declare no conflict of interest.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}],"article-number":"113"}}