{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T08:22:30Z","timestamp":1774858950971,"version":"3.50.1"},"reference-count":65,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T00:00:00Z","timestamp":1769472000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T00:00:00Z","timestamp":1770768000000},"content-version":"vor","delay-in-days":15,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Intell Robot Syst"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>One barrier to persistent operations in systems of unmanned aerial vehicles (UAVs) served by logistics support stations is the need for methods to manage and efficiently schedule system resources. This paper presents a scheduling framework for UAV systems served by battery charging and battery replacement stations. We extend existing Petri net models for these systems to prevent unwanted resource overlap and impose a resource pairing rule to facilitate cyclic operation. Based on this rule, an extended Petri net that explicitly models the interactions of specific resources is derived. The detailed nature of the extended Petri net allows for the creation of linear programs that capture the structure of the net and generate optimal cyclic resource schedules. These cyclic schedules enable the persistent orchestration of tasks for UAV and logistics support stations. Computational complexity of the linear programs is explored.<\/jats:p>","DOI":"10.1007\/s10846-026-02352-6","type":"journal-article","created":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T14:15:17Z","timestamp":1769523317000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Cyclic Resource Scheduling in Systems of UAVs and Logistics Support Stations via Petri Nets and Linear Programming"],"prefix":"10.1007","volume":"112","author":[{"given":"Mirza E.","family":"Neebraz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ammar","family":"Altaweel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7773-000X","authenticated-orcid":false,"given":"James R.","family":"Morrison","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,1,27]]},"reference":[{"key":"2352_CR1","doi-asserted-by":"publisher","unstructured":"Zhou, M., Wu, N.: System Modeling and Control with Resource-Oriented Petri Nets. CRC Press, (2010). https:\/\/doi.org\/10.1080\/00207543.2010.515415","DOI":"10.1080\/00207543.2010.515415"},{"key":"2352_CR2","doi-asserted-by":"publisher","unstructured":"Hillier, F. S., Lieberman, G. J.: Introduction to Operations Research. McGraw-Hill, (2015). https:\/\/doi.org\/10.2307\/2345190","DOI":"10.2307\/2345190"},{"key":"2352_CR3","doi-asserted-by":"publisher","unstructured":"Lv, L., Zheng, C., Zhang, L., Shan, C., Tian, Z., Du, X., Guizani, M.: Contract and Lyapunov optimization-based load scheduling and energy management for UAV charging stations. IEEE Trans. Green Commun. Netw., 5 (3), 1381\u20131394, (2021). https:\/\/doi.org\/10.1109\/TGCN.2021.3085561","DOI":"10.1109\/TGCN.2021.3085561"},{"key":"2352_CR4","doi-asserted-by":"publisher","unstructured":"Halder, S., Ghosal, A., Conti, M.: Dynamic super round-based distributed task scheduling for UAV networks. IEEE Trans. Wirel. Commun., 22 (2), 1014\u20131028, (2022). https:\/\/doi.org\/10.1109\/TWC.2022.3200366","DOI":"10.1109\/TWC.2022.3200366"},{"issue":"6","key":"2352_CR5","first-page":"16098","volume":"35","author":"H Kang","year":"2022","unstructured":"Kang, H., Kwon, T., Park, J., Morrison, J.R.: Learning NP-hard multi-agent assignment planning using GNN: Inference on a random graph and provable auction-fitted Q-learning. NeurIPS 35(6), 16098\u201316109 (2022)","journal-title":"NeurIPS"},{"key":"2352_CR6","doi-asserted-by":"publisher","unstructured":"Khochare, A., Sorbelli, F. B., Simmhan, Y., Das, S. K.: Improved algorithms for co-scheduling of edge analytics and routes for UAV fleet missions. IEEE\/ACM Trans. Netw., 32 (1), 17\u201333, (2023). https:\/\/doi.org\/10.1109\/TNET.2023.3277810","DOI":"10.1109\/TNET.2023.3277810"},{"key":"2352_CR7","doi-asserted-by":"publisher","unstructured":"Emami, Y., Wei, B., Li, K., Ni, W., Tovar, E.: Joint communication scheduling and velocity control in multi-UAV-assisted sensor networks: A deep reinforcement learning approach. IEEE Trans. Veh. Technol., 70 (10), 10986\u201310998, (2021). https:\/\/doi.org\/10.1109\/TVT.2021.3110801","DOI":"10.1109\/TVT.2021.3110801"},{"key":"2352_CR8","doi-asserted-by":"publisher","unstructured":"Liu, W., Li, D., Liang, T., Zhang, T., Lin, Z., Dhahir, N. A.: Joint trajectory and scheduling optimization for age of synchronization minimization in UAV-assisted networks with random updates. IEEE Trans. Commun., 71 (11), 6633\u20136646, (2023). https:\/\/doi.org\/10.1109\/TCOMM.2023.3297198","DOI":"10.1109\/TCOMM.2023.3297198"},{"key":"2352_CR9","doi-asserted-by":"publisher","unstructured":"Bian, Y., Hu, J., Zhang, P., Wang, S., Wang, Y., Cong, J., Fu, C.: Joint trajectory control, power control and collection schedule in UAV-assisted anti-jamming wireless data collection with imperfect CSI. IEEE Commun. Lett., 28 (12), 2839\u20132843, (2024). https:\/\/doi.org\/10.1109\/LCOMM.2024.3488178","DOI":"10.1109\/LCOMM.2024.3488178"},{"key":"2352_CR10","doi-asserted-by":"publisher","unstructured":"Betalo, M. L., Leng, S., Abishu, H. N., Dharejo, F. A., Seid, A. M., Erbad, A., Naqvi, R. A., Zhou, L., Guizani, M.: Multi-agent deep reinforcement learning-based task scheduling and resource sharing for O-RAN-empowered multi-UAV-assisted wireless sensor networks. IEEE Trans. Veh. Technol., 73 (7), 9247\u20139261, (2023). https:\/\/doi.org\/10.1109\/TVT.2023.3330661","DOI":"10.1109\/TVT.2023.3330661"},{"key":"2352_CR11","doi-asserted-by":"publisher","unstructured":"Arribas, E., Cholvi, V., Mancuso, V.: Optimizing UAV resupply scheduling for heterogeneous and persistent aerial service. IEEE Trans. Robot., 39 (4), 2639\u20132653, (2023). https:\/\/doi.org\/10.1109\/TRO.2023.3263077","DOI":"10.1109\/TRO.2023.3263077"},{"key":"2352_CR12","doi-asserted-by":"publisher","unstructured":"Jung, S., Yun, W. J., Shin, M., Kim, J., Kim, J. H.: Orchestrated scheduling and multi-agent deep reinforcement learning for cloud-assisted multi-UAV charging systems. IEEE Trans. Veh. Technol., 70 (6), 5362\u20135377, (2021). https:\/\/doi.org\/10.1109\/TVT.2021.3062418","DOI":"10.1109\/TVT.2021.3062418"},{"key":"2352_CR13","doi-asserted-by":"publisher","unstructured":"Ma, Y., Niu, Y., Han, Z., Ai, B., Li, K., Zhong, Z., Wang, N.: Robust transmission scheduling for UAV-assisted millimeter-wave train-ground communication system. IEEE Trans. Veh. Technol., 71 (11), 11741\u201311755, (2022). https:\/\/doi.org\/10.1109\/TVT.2022.3192033","DOI":"10.1109\/TVT.2022.3192033"},{"key":"2352_CR14","doi-asserted-by":"publisher","unstructured":"Wang, Y., Niu, Y., Wu, H., Mao, S., Ai, B., Zhong, Z., Wang, N.: Scheduling of UAV-assisted millimeter wave communications for high-speed railway. IEEE Trans. Veh. Technol., 71 (8), 8756\u20138767, (2022). https:\/\/doi.org\/10.1109\/TVT.2022.3176855","DOI":"10.1109\/TVT.2022.3176855"},{"key":"2352_CR15","doi-asserted-by":"publisher","unstructured":"Tian, J., Wang, D., Zhang, H., Wu, D.: Service satisfaction-oriented task offloading and UAV scheduling in UAV-enabled MEC networks. IEEE Trans. Wirel. Commun., 22 (12), 8949\u20138964, (2023). https:\/\/doi.org\/10.1109\/TWC.2023.3267330","DOI":"10.1109\/TWC.2023.3267330"},{"key":"2352_CR16","doi-asserted-by":"publisher","unstructured":"Nishi, T., Maeno, R.: Petri net modeling and decomposition method for solving production scheduling problems. J. Adv. Mech. Design, Syst., Manuf., 1 (2), 262\u2013271, (2007). https:\/\/doi.org\/10.1299\/jamdsm.1.262","DOI":"10.1299\/jamdsm.1.262"},{"key":"2352_CR17","doi-asserted-by":"publisher","unstructured":"Sun, T. H., Cheng, C. W., Fu, L. C.: A Petri net based approach to modeling and scheduling for an FMS and a Case Study. IEEE Trans. Ind. Electron., 41 (6), 593\u2013601, (1994). https:\/\/doi.org\/10.1109\/41.334576","DOI":"10.1109\/41.334576"},{"key":"2352_CR18","doi-asserted-by":"publisher","unstructured":"Zhou, M., Jeng, M. D.: Modeling, analysis, simulation, scheduling, and control of semiconductor manufacturing systems: A Petri net approach. IEEE Trans. Semicond. Manuf., 11 (3), 333\u2013357, (1998). https:\/\/doi.org\/10.1109\/66.705370","DOI":"10.1109\/66.705370"},{"key":"2352_CR19","doi-asserted-by":"publisher","unstructured":"Camurri, A., Franchi, P., Gandolfo, F., Zaccaria, R.: Petri net based process scheduling: A model of the control system of flexible manufacturing systems. J. Intell. Robot. Syst., 8 (1), 99\u2013123, (1993). https:\/\/doi.org\/10.1007\/BF01258642","DOI":"10.1007\/BF01258642"},{"key":"2352_CR20","doi-asserted-by":"publisher","unstructured":"Chen, J. H., Fu, L. C.: Petri-net and GA-based approach to modeling, scheduling, and performance evaluation for wafer fabrication. IEEE Trans. Robot. Automat. 17, 619\u2013636, (2011). https:\/\/doi.org\/10.1109\/70.964663","DOI":"10.1109\/70.964663"},{"key":"2352_CR21","doi-asserted-by":"publisher","unstructured":"Tuncel, G., Bayhan, G. M.: Applications of Petri nets in production scheduling: A review. Int. J. Adv. Manuf. Technol., 34 (7), 762\u2013773, (2007). https:\/\/doi.org\/10.1007\/s00170-006-0640-1","DOI":"10.1007\/s00170-006-0640-1"},{"key":"2352_CR22","doi-asserted-by":"publisher","unstructured":"Lee, D. Y., Dicesare. F.: Scheduling flexible manufacturing systems using Petri nets and heuristic search. IEEE Trans. Robot. Autom., 10 (2), 123\u2013132, (1994). https:\/\/doi.org\/10.1109\/70.282537","DOI":"10.1109\/70.282537"},{"key":"2352_CR23","doi-asserted-by":"publisher","unstructured":"Xiong, P. C., Fan, Y. S., Zhou, M.: A Petri net approach to analysis and composition of web services. IEEE Trans. Syst., Man, Cybern. - Part A: Syst., Hum., 40 (2), 376\u2013387, (2010). https:\/\/doi.org\/10.1109\/TSMCA.2009.2037018","DOI":"10.1109\/TSMCA.2009.2037018"},{"key":"2352_CR24","doi-asserted-by":"publisher","unstructured":"Yao, L., Dong, P., Zheng, T., Zhang, H., Du, X., Guizani, M.: Network security analyzing and modeling based on Petri net and attack tree for SDN. International Conference on Computing, Networking and Communications (ICNC), pp. 1\u20135. (2016) https:\/\/doi.org\/10.1109\/ICCNC.2016.7440631","DOI":"10.1109\/ICCNC.2016.7440631"},{"key":"2352_CR25","doi-asserted-by":"publisher","unstructured":"Ahson, S.: Petri net models of fuzzy neural networks. IEEE Trans. Syst., Man, Cybern., 25 (6), 926\u2013932, (1995). https:\/\/doi.org\/10.1109\/21.384255","DOI":"10.1109\/21.384255"},{"key":"2352_CR26","doi-asserted-by":"publisher","unstructured":"Kemper, F. P., Suzuki, K. A. O., Morrison, J. R.: UAV consumable replenishment: Design concepts for automated service stations. J. Intell. Robot. Syst., 61 (1), 369\u2013397, (2011). https:\/\/doi.org\/10.1007\/s10846-010-9502-z","DOI":"10.1007\/s10846-010-9502-z"},{"key":"2352_CR27","doi-asserted-by":"publisher","unstructured":"Suzuki, K. A. O., Kemper, F. P., Morrison, J. R.: Automatic battery replacement system for UAVs: Analysis and design. J. Intell. Robot. Syst., 65 (1), 563\u2013586, (2012). https:\/\/doi.org\/10.1007\/s10846-011-9616-y","DOI":"10.1007\/s10846-011-9616-y"},{"key":"2352_CR28","doi-asserted-by":"publisher","unstructured":"Neebraz, M. E., Altaweel, A., Morrison, J. R.: Persistent drone light shows: Petri net models, performance evaluation and resource requirements. IEEE International Conference on Artificial Intelligence, Blockchain and Internet of Things (AIBThings), pp. 1\u20137. (2023) https:\/\/doi.org\/10.1109\/AIBThings58340.2023.10292450","DOI":"10.1109\/AIBThings58340.2023.10292450"},{"key":"2352_CR29","doi-asserted-by":"publisher","unstructured":"Park, H., Lee, B. H. Y., Morrison, J. R.: Persistent UAV security presence service: Architecture and prototype implementation. International Conference on Unmanned Aircraft Systems (ICUAS), pp. 1800\u20131807. (2017) https:\/\/doi.org\/10.1109\/ICUAS.2017.7991422","DOI":"10.1109\/ICUAS.2017.7991422"},{"key":"2352_CR30","doi-asserted-by":"publisher","unstructured":"Baccelli, F., Cohen, G., Olsder, G. J., Quadrat, J. P.: Synchronization and Linearity. New York Wiley, 1, (1992). https:\/\/doi.org\/10.1057\/JORS.1994.15","DOI":"10.1057\/JORS.1994.15"},{"key":"2352_CR31","doi-asserted-by":"publisher","unstructured":"Zhang, S. W., Wu, N. Q., Li, Z. W., Qu, T., Li, C. D.: Petri net-based approach to short-term scheduling of crude oil operations with less tank requirement. Inf. Sci., 417, 247\u2013261, (2017). https:\/\/doi.org\/10.1016\/j.ins.2017.07.009","DOI":"10.1016\/j.ins.2017.07.009"},{"key":"2352_CR32","doi-asserted-by":"publisher","unstructured":"Huang, B., Zhou, M., Lu, X. S.: Abusorrah, A. Scheduling of resource allocation systems with timed Petri nets: A survey. ACM Comput. Surveys, 55 (11), 1\u201327, (2023). https:\/\/doi.org\/10.1145\/357032","DOI":"10.1145\/357032"},{"key":"2352_CR33","doi-asserted-by":"publisher","unstructured":"Aalst, W. V. D.: Petri net based scheduling. OR Spectr., 18 219\u2013229, (1996). https:\/\/doi.org\/10.1007\/BF01540160","DOI":"10.1007\/BF01540160"},{"key":"2352_CR34","doi-asserted-by":"publisher","unstructured":"Wu, J. S., Liu, C. C., Liou, K. L., Chu, R. F.: A Petri net algorithm for scheduling of generic restoration actions. IEEE Trans. Power Syst., 12 (1), 69\u201376, (1997). https:\/\/doi.org\/10.1109\/9780470545607.ch71","DOI":"10.1109\/9780470545607.ch71"},{"key":"2352_CR35","doi-asserted-by":"publisher","unstructured":"Davidrajuh, R. Activity-oriented Petri net for scheduling of resources. IEEE International Conference on Systems, Man, and Cybernetics (IEEE SMC), pp. 1201\u20131206. (2012) https:\/\/doi.org\/10.1109\/ICSMC.2012.6377895","DOI":"10.1109\/ICSMC.2012.6377895"},{"key":"2352_CR36","doi-asserted-by":"publisher","unstructured":"Lefebvre, D.: Near-optimal scheduling for Petri net models with forbidden markings. IEEE Trans. Autom. Control, 63 (8), 2550\u20132557, (2018). https:\/\/doi.org\/10.1109\/TAC.2017.2767827","DOI":"10.1109\/TAC.2017.2767827"},{"key":"2352_CR37","unstructured":"Gu, T., Bahri, P., Cai, G.: Timed Petri-net based formulation and an algorithm for the optimal scheduling of batch plants. Int. J. Appl. Math. Comput. Sci., 13 (4), 527\u2013536, (2003). http:\/\/matwbn.icm.edu.pl\/ksiazki\/amc\/amc13\/amc13410.pdf"},{"key":"2352_CR38","doi-asserted-by":"publisher","unstructured":"Hong, Y., Jung, S., Kim, S., Cha, J.: Multi-UAV routing with priority using mixed integer linear programming. Proceedings of the 20th International Conference on Control, Automation and Systems, pp. 699\u2013702. (2020) https:\/\/doi.org\/10.23919\/ICCAS50221.2020.9268329","DOI":"10.23919\/ICCAS50221.2020.9268329"},{"key":"2352_CR39","doi-asserted-by":"publisher","unstructured":"Song, B. D., Park, K., Kim, J.: Persistent UAV delivery logistics: MILP formulation and efficient heuristic. Comput. Ind. Eng., 120, 418\u2013428, (2018). https:\/\/doi.org\/10.1016\/j.cie.2018.05.013","DOI":"10.1016\/j.cie.2018.05.013"},{"key":"2352_CR40","doi-asserted-by":"publisher","unstructured":"Lee, S., Morrison, J. R.: Decision support scheduling for maritime search and rescue planning with a system of UAVs and fuel service stations. Proceed IEEE Int. Conf. Unmanned Aircraft Syst., pp. 1168\u20131177. (2015) https:\/\/doi.org\/10.1109\/ICUAS.2015.7152409","DOI":"10.1109\/ICUAS.2015.7152409"},{"key":"2352_CR41","doi-asserted-by":"publisher","unstructured":"Chircop, P. A., Surendonk, T. J., Briel, M. V. D., Walsh, T.: A column generation approach for the scheduling of patrol boats to provide complete patrol coverage. Proceed. 20th Int. Congress Model. Simul. pp. 1\u20136. (2013) https:\/\/doi.org\/10.36334\/modsim.2013.Keynote.chircop","DOI":"10.36334\/modsim.2013.Keynote.chircop"},{"key":"2352_CR42","doi-asserted-by":"publisher","unstructured":"Kim, J., Morrison, J. R. On the concerted design and scheduling of multiple resources for persistent UAV operations. J. Intell. Robotic Syst., 74 (1\u20132), 479\u2013498, (2013). https:\/\/doi.org\/10.1109\/ICUAS.2013.6564780","DOI":"10.1109\/ICUAS.2013.6564780"},{"key":"2352_CR43","doi-asserted-by":"publisher","unstructured":"Jeong, H. Y., Song, B. D.: Optimization of urban logistics with multi-modal systems: A comprehensive study of the airship-vehicle routing problem. Transp. Res. Part E: Logist. Transp. Rev., 204, 1\u201324, (2025). https:\/\/doi.org\/10.1016\/j.tre.2025.104415","DOI":"10.1016\/j.tre.2025.104415"},{"key":"2352_CR44","doi-asserted-by":"publisher","unstructured":"H. Park, H., Morrison, J. R.: System design and resource analysis for persistent robotic presence with multiple refueling stations. IEEE Int. Conf. Unmanned Aircraft Syst. (ICUAS), pp. 622\u2013629. (2019) https:\/\/doi.org\/10.1109\/ICUAS.2019.8797808","DOI":"10.1109\/ICUAS.2019.8797808"},{"key":"2352_CR45","doi-asserted-by":"publisher","unstructured":"Kim, W., Yu, T. S., Lee, T. E.: Integrated scheduling of a dual-armed cluster tool for maximizing steady schedule patterns. IEEE Trans. Syst., Man, Cybern. Syst., 51 (12), 7282\u20137294, (2021). https:\/\/doi.org\/10.1109\/TSMC.2020.2978486","DOI":"10.1109\/TSMC.2020.2978486"},{"key":"2352_CR46","doi-asserted-by":"publisher","unstructured":"Zhu, Q. H., Zhou, M., Qiao, Y., Wu, N. Q.: Petri net modeling and scheduling of a close-down process for time-constrained single-arm cluster tools. IEEE Trans. Syst., Man, Cybern., Syst., 48 (3), 389\u2013400, (2018). https:\/\/doi.org\/10.1109\/TSMC.2016.2598303","DOI":"10.1109\/TSMC.2016.2598303"},{"key":"2352_CR47","doi-asserted-by":"publisher","unstructured":"Bharat, S., Kumar, R., Singh, V. P.: Reinforcement learning in robotic applications: A comprehensive survey. Artif. Intell. Rev., 55 (2), 945\u2013990, (2022). https:\/\/doi.org\/10.1007\/s10462-021-09997-9","DOI":"10.1007\/s10462-021-09997-9"},{"key":"2352_CR48","doi-asserted-by":"publisher","unstructured":"Monika, R., Popowniak, N., Lazarowska, A.: A survey of machine learning approaches for mobile robot control. Robotics, 13 (1), 1\u201312, (2024). https:\/\/doi.org\/10.3390\/robotics13010012","DOI":"10.3390\/robotics13010012"},{"key":"2352_CR49","doi-asserted-by":"publisher","unstructured":"Tang, C., Abbatematteo, B., Hu, J., Chandra, R., Mart\u00edn-Mart\u00edn, R., Stone, P.: Deep reinforcement learning for robotics: A survey of real-world successes. Proceed. AAAI Conf. Artif. Intell. 39 (27), 28694\u201328698, April. (2025) https:\/\/doi.org\/10.1609\/aaai.v39i27.35095","DOI":"10.1609\/aaai.v39i27.35095"},{"key":"2352_CR50","doi-asserted-by":"crossref","unstructured":"Chen, L., Jin, Z., Shao, K., Wang, G., He, S., Stojanovic, V., Bahri, P. A., Wang, H.: Adaptive integral terminal sliding mode control of unmanned bicycle via ELM and barrier function. Robotica, 42 (8), 2635\u20132657, (2024). https:\/\/doi.org\/10.1017\/S0263574724000997","DOI":"10.1017\/S0263574724000997"},{"key":"2352_CR51","doi-asserted-by":"publisher","unstructured":"Song, X., Wu, C., Song, S., Stojanovic, V., Tejado, In\u00e9s.: Fuzzy wavelet neural adaptive finite-time self-triggered fault-tolerant control for a quadrotor unmanned aerial vehicle with scheduled performance. Eng. Appl. Artif. Intell., 131, 107832, (2024). https:\/\/doi.org\/10.1016\/j.engappai.2023.107832","DOI":"10.1016\/j.engappai.2023.107832"},{"key":"2352_CR52","doi-asserted-by":"publisher","unstructured":"Song, X., Wu, C., Stojanovic, V., Song, S.: 1 bit encoding-decoding-based event-triggered fixed-time adaptive control for unmanned surface vehicle with guaranteed tracking performance. Control Eng. Pract., 135, 105513, (2023). https:\/\/doi.org\/10.1016\/j.conengprac.2023.105513","DOI":"10.1016\/j.conengprac.2023.105513"},{"key":"2352_CR53","doi-asserted-by":"publisher","unstructured":"Gu, W., Zhao, J., Rizzo, A.: Learning uncertainties online for quadrotor flight control: A comparative study. J. Intell. Robot. Syst., 111 (3), 1\u201320, (2025). https:\/\/doi.org\/10.1007\/s10846-025-02305-5","DOI":"10.1007\/s10846-025-02305-5"},{"key":"2352_CR54","doi-asserted-by":"publisher","unstructured":"Mon, B. F., Hayajneh, M., Ali, N. A., Ullah, F., Warafy, A. A., Saeed, N.: Machine learning for autonomous navigation and collision avoidance in UAVs. IEEE 16th Int. Conf. Comput. Intell. Commun. Netw. (CICN), pp. 381\u2013388. (2024) https:\/\/doi.org\/10.1109\/CICN63059.2024.10847476","DOI":"10.1109\/CICN63059.2024.10847476"},{"key":"2352_CR55","doi-asserted-by":"publisher","unstructured":"Liu, C., Zeng, Q., Duan, H., Zhou, M., Lu, F., Cheng, J.: E-net modeling and analysis of emergency response processes constrained by resources and uncertain durations. IEEE Trans. Syst. Man Cybern. Syst., 45 (1), 84\u201396, (2015). https:\/\/doi.org\/10.1109\/TSMC.2014.2330555","DOI":"10.1109\/TSMC.2014.2330555"},{"key":"2352_CR56","doi-asserted-by":"publisher","unstructured":"Fedorova, A., Beliautsou, V., Zimmermann, A.: Colored Petri net modelling and evaluation of drone inspection methods for distribution networks. Sensors, 22 (9), 1\u201320, (2022). https:\/\/doi.org\/10.3390\/s22093418","DOI":"10.3390\/s22093418"},{"key":"2352_CR57","doi-asserted-by":"publisher","unstructured":"Wang, X., Guo, Y., Lu, N., He, P.: UAV cluster behavior modeling based on spatial-temporal hybrid Petri net. Appl. Sci., 13 (2), 1\u201316, (2023). https:\/\/doi.org\/10.3390\/app13020762","DOI":"10.3390\/app13020762"},{"key":"2352_CR58","doi-asserted-by":"publisher","unstructured":"Qin, H., Ding, W., Xu, L., Ruan, C.: Petri-net-based charging scheduling optimization in rechargeable sensor networks. Sensors, 24 (19), 1\u201326, (2024). https:\/\/doi.org\/10.3390\/s24196316","DOI":"10.3390\/s24196316"},{"key":"2352_CR59","doi-asserted-by":"publisher","unstructured":"Lins, L., Nascimento, E., Dantas, J., Araujo, J., Maciel, P.: Stochastic Petri nets for drone surveillance: Modeling availability and reliability. Proceed. 13th Latin-Am. Symp. Depend. Secure Comput. pp. 65\u201377. (2024) https:\/\/doi.org\/10.1145\/3697090.369709","DOI":"10.1145\/3697090.369709"},{"key":"2352_CR60","doi-asserted-by":"publisher","unstructured":"Li, B., Li, Z., Wu, W., Zhou, M.: Petri net modeling and deadlock-free scheduling of attachable heterogeneous AGV systems. pp. 1\u201317. (2025) https:\/\/doi.org\/10.48550\/arXiv.2508.00724, arXiv:2508.00724","DOI":"10.48550\/arXiv.2508.00724"},{"key":"2352_CR61","doi-asserted-by":"publisher","unstructured":"Kim, J. H., Lee, T. H., Lee, H. Y., Park, D. B.: Scheduling analysis of timed-constrained dual-armed cluster tools. IEEE Trans. Semicond. Manuf., 16 (3), 521\u2013534, (2003). https:\/\/doi.org\/10.1109\/TSM.2003.815203","DOI":"10.1109\/TSM.2003.815203"},{"key":"2352_CR62","doi-asserted-by":"publisher","unstructured":"Altaweel, A., Neebraz, M. E., Morrison, J. R.: Resource schedules for persistent UAV systems with logistics replenishment platforms: Petri net models and LP formulation. International Conference on Unmanned Aircraft Systems (ICUAS), pp. 488\u2013495. (2024) https:\/\/doi.org\/10.1109\/ICUAS60882.2024.10557077","DOI":"10.1109\/ICUAS60882.2024.10557077"},{"key":"2352_CR63","doi-asserted-by":"publisher","unstructured":"Murata, T.: Petri nets: Properties, analysis and applications. Proc. IEEE, 77 (4), 541\u2013580, (1989). https:\/\/doi.org\/10.1109\/5.24143","DOI":"10.1109\/5.24143"},{"key":"2352_CR64","doi-asserted-by":"publisher","unstructured":"Pinedo, M. L.: Scheduling Theory, Algorithms, and Systems. Springer Cham, (2022). https:\/\/doi.org\/10.1007\/978-3-031-05921-6","DOI":"10.1007\/978-3-031-05921-6"},{"key":"2352_CR65","doi-asserted-by":"publisher","unstructured":"Vaidya, P. M.: Speeding-up linear programming using fast matrix multiplication. 30th annual symposium on foundations of computer science, pp. 332\u2013337. (1989) https:\/\/doi.org\/10.1109\/SFCS.1989.63499","DOI":"10.1109\/SFCS.1989.63499"}],"container-title":["Journal of Intelligent &amp; Robotic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10846-026-02352-6","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-026-02352-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-026-02352-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T07:39:56Z","timestamp":1774856396000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10846-026-02352-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,27]]},"references-count":65,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["2352"],"URL":"https:\/\/doi.org\/10.1007\/s10846-026-02352-6","relation":{},"ISSN":["1573-0409"],"issn-type":[{"value":"1573-0409","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,27]]},"assertion":[{"value":"26 November 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 January 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 January 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}},{"value":"As our research consists solely of mathematical modeling and computational studies, no human or animal subjects were involved. No approvals or oversight were required.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}},{"value":"Not applicable to our research.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to Participate"}},{"value":"As no human research participants were a part of the research, no consent is required. The authors have given their consent to publish the paper.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for Publication"}}],"article-number":"18"}}