{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T05:59:18Z","timestamp":1774936758785,"version":"3.50.1"},"reference-count":23,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2022,11,27]],"date-time":"2022-11-27T00:00:00Z","timestamp":1669507200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fundamental Research Funds for the Central Universities","award":["2021ZY88"],"award-info":[{"award-number":["2021ZY88"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["62202054"],"award-info":[{"award-number":["62202054"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["62002022"],"award-info":[{"award-number":["62002022"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["32071775"],"award-info":[{"award-number":["32071775"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021ZY88"],"award-info":[{"award-number":["2021ZY88"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62202054"],"award-info":[{"award-number":["62202054"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62002022"],"award-info":[{"award-number":["62002022"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["32071775"],"award-info":[{"award-number":["32071775"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper considers a laser-powered unmanned aerial vehicle (UAV)-enabled wireless power transfer (WPT) system. In the system, a UAV is dispatched as an energy transmitter to replenish energy for battery-limited sensors in a wireless rechargeable sensor network (WRSN) by transferring radio frequency (RF) signals, and a mobile unmanned vehicle (MUV)-loaded laser transmitter travels on a fixed path to charge the on-board energy-limited UAV when it arrives just below the UAV. Based on the system, we investigate the trajectory optimization of laser-charged UAVs for charging WRSNs (TOLC problem), which aims to optimize the flight trajectories of a UAV and the travel plans of an MUV cooperatively to minimize the total working time of the UAV so that the energy of every sensor is greater than or equal to the threshold. Then, we prove that the problem is NP-hard. To solve the TOLC problem, we first propose the weighted centered minimum coverage (WCMC) algorithm to cluster the sensors and compute the weighted center of each cluster. Based on the WCMC algorithm, we propose the TOLC algorithm (TOLCA) to design the detailed flight trajectory of a UAV and the travel plans of an MUV, which consists of the flight trajectory of a UAV, the hovering points of a UAV with the corresponding hovering times used for the charging sensors, the hovering points of a UAV with the corresponding hovering times used for replenishing energy itself, and the hovering times of a UAV waiting for an MUV. Numerical results are provided to verify that the suggested strategy provides an effective method for supplying wireless rechargeable sensor networks with sustainable energy.<\/jats:p>","DOI":"10.3390\/s22239215","type":"journal-article","created":{"date-parts":[[2022,11,28]],"date-time":"2022-11-28T08:13:09Z","timestamp":1669623189000},"page":"9215","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Trajectory Optimization of Laser-Charged UAVs for Charging Wireless Rechargeable Sensor Networks"],"prefix":"10.3390","volume":"22","author":[{"given":"Ning","family":"Liu","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, Beijing Forestry University, Beijing 100083, China"},{"name":"Engineering Research Center for Forestry-Oriented Intelligent Information Processing of National Forestry and Grassland Administration, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1363-0581","authenticated-orcid":false,"given":"Chuanwen","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Beijing Forestry University, Beijing 100083, China"},{"name":"Engineering Research Center for Forestry-Oriented Intelligent Information Processing of National Forestry and Grassland Administration, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jia","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Beijing Forestry University, Beijing 100083, China"},{"name":"Engineering Research Center for Forestry-Oriented Intelligent Information Processing of National Forestry and Grassland Administration, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Hong","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Beijing Forestry University, Beijing 100083, China"},{"name":"Engineering Research Center for Forestry-Oriented Intelligent Information Processing of National Forestry and Grassland Administration, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhibo","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Beijing Forestry University, Beijing 100083, China"},{"name":"Engineering Research Center for Forestry-Oriented Intelligent Information Processing of National Forestry and Grassland Administration, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,27]]},"reference":[{"key":"ref_1","first-page":"162","article-title":"Fine-grained trajectory optimization of multiple UAVs for efficient data gathering from WSNs","volume":"29","author":"Luo","year":"2020","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/TGCN.2017.2767203","article-title":"Resource allocation for energy harvesting-powered d2d communication underlaying uav-assisted networks","volume":"2","author":"Wang","year":"2017","journal-title":"IEEE Trans. Green Communications Netw."},{"key":"ref_3","unstructured":"Jie, X., Yong, Z., and Rui, Z. (2017, January 4\u20138). Uav-enabled wireless power transfer: Trajectory design and energy region characterization. Proceedings of the 2017 IEEE Globecom Workshops (GC Wkshps), Singapore."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ku, S., Jung, S., and Lee, C. (2019, January 23\u201326). Uav trajectory design based on reinforcement learning for wireless power transfer. Proceedings of the 2019 34th International Technical Conference on Circuits\/Systems, Computers and Communications (ITC-CSCC), JeJu, Korea.","DOI":"10.1109\/ITC-CSCC.2019.8793294"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wu, Y., Qiu, L., and Xu, J. (2018, January 28\u201331). Uav-enabled wireless power transfer with directional antenna: A two-user case (invited paper). Proceedings of the 2018 15th International Symposium on Wireless Communication Systems (ISWCS), Lisbon, Portugal.","DOI":"10.1109\/ISWCS.2018.8491102"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5674","DOI":"10.1109\/TCOMM.2019.2911294","article-title":"Optimal 1d trajectory design for uav-enabled multiuser wireless power transfer","volume":"67","author":"Hu","year":"2019","journal-title":"IEEE Trans. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Yang, T., Hu, Y., Yuan, X., and Mathar, R. (2019, January 15\u201318). Genetic algorithm based uav trajectory design in wireless power transfer systems. Proceedings of the 2019 IEEE Wireless Communications and Networking Conference (WCNC), Marrakesh, Morocco.","DOI":"10.1109\/WCNC.2019.8885987"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1109\/TWC.2020.3030773","article-title":"Trajectory design for uav-enabled multiuser wireless power transfer with nonlinear energy harvesting","volume":"20","author":"Yuan","year":"2020","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3081","DOI":"10.1109\/JSAC.2021.3088682","article-title":"Joint design of uav trajectory and directional antenna orientation in uav-enabled wireless power transfer networks","volume":"39","author":"Yuan","year":"2021","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"9265","DOI":"10.1109\/TVT.2020.2972133","article-title":"Joint 3d trajectory design and time allocation for uav-enabled wireless power transfer networks","volume":"69","author":"Feng","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"12883","DOI":"10.1109\/TVT.2020.3015246","article-title":"Uav-enabled wireless power transfer with base station charging and uav power consumption","volume":"69","author":"Yan","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/s10846-011-9616-y","article-title":"Automatic battery replacement system for uavs: Analysis and design","volume":"65","author":"Suzuki","year":"2012","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"10902","DOI":"10.1109\/JIOT.2019.2943147","article-title":"Rechargeable multi-uav aided seamless coverage for qos-guaranteed iot networks","volume":"6","author":"Li","year":"2019","journal-title":"IEEE Internet Things J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"10209","DOI":"10.1109\/JIOT.2021.3051370","article-title":"Energy-efficient uav-enabled data collection via wireless charging: A reinforcement learning approach","volume":"8","author":"Fu","year":"2021","journal-title":"IEEE Internet Things J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"8083","DOI":"10.1109\/TWC.2020.3019097","article-title":"Wireless-powered edge computing with cooperative uav: Task, time scheduling and trajectory design","volume":"19","author":"Hu","year":"2020","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wang, Y., Zhang, L., Min, M., Guo, C., Sharma, V., and Han, Z. (2020, January 7\u201311). Privacy-aware wireless power transfer for aerial computation offloading via colonel blotto game. Proceedings of the 2020 IEEE Globecom Workshops (GC Wkshps), Taipei, Taiwan.","DOI":"10.1109\/GCWkshps50303.2020.9367493"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1109\/TCOMM.2021.3124950","article-title":"Efficient aerial data collection with cooperative trajectory planning for large-scale wireless sensor networks","volume":"70","author":"Zhu","year":"2021","journal-title":"IEEE Trans. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5092","DOI":"10.1109\/TWC.2018.2838134","article-title":"Uav-enabled wireless power transfer: Trajectory design and energy optimization","volume":"17","author":"Xu","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/MWC.2016.7462482","article-title":"On feasibility of 5G-grade dedicated RF charging technology for wireless-powered wearables","volume":"23","author":"Galinina","year":"2016","journal-title":"IEEE Wirel. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3853","DOI":"10.1109\/JIOT.2018.2851070","article-title":"Distributed laser charging: A wireless power transfer approach","volume":"5","author":"Zhang","year":"2018","journal-title":"IEEE Internet Things J."},{"key":"ref_21","first-page":"69","article-title":"The pseudocenter and pseudoradius of a point set","volume":"2","author":"Lu","year":"1986","journal-title":"Math Pract. Theory"},{"key":"ref_22","first-page":"16","article-title":"An algorithm and a core set result for the weighted euclidean one-center problem","volume":"21","author":"Alper","year":"2009","journal-title":"Informs J. Comput."},{"key":"ref_23","first-page":"160","article-title":"Genetic algorithms for the traveling salesman problem. Genetic algorithms for the traveling salesman problem","volume":"160","author":"Grefenstette","year":"1985","journal-title":"Proc. First Int. Conf. Genet. Algorithms Their Appl."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/23\/9215\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:27:39Z","timestamp":1760146059000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/23\/9215"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,27]]},"references-count":23,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["s22239215"],"URL":"https:\/\/doi.org\/10.3390\/s22239215","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,27]]}}}