{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T08:43:47Z","timestamp":1770540227056,"version":"3.49.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,6,1]],"date-time":"2023-06-01T00:00:00Z","timestamp":1685577600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,6,19]],"date-time":"2023-06-19T00:00:00Z","timestamp":1687132800000},"content-version":"vor","delay-in-days":18,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Intell Robot Syst"],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The control problem of a multi-copter swarm, mechanically coupled through a modular lattice structure of connecting rods, is considered in this article. The system\u2019s structural elasticity is considered in deriving the system\u2019s dynamics. The devised controller is robust against the induced flexibilities, while an inherent adaptation scheme allows for the control of asymmetrical configurations and the transportation of unknown payloads. Certain optimization metrics are introduced for solving the individual agent thrust allocation problem while achieving maximum system flight time, resulting in a platform-independent control implementation. Experimental studies are offered to illustrate the efficiency of the suggested controller under typical flight conditions, increased rod elasticities and payload transportation.<\/jats:p>","DOI":"10.1007\/s10846-023-01842-1","type":"journal-article","created":{"date-parts":[[2023,6,19]],"date-time":"2023-06-19T09:02:07Z","timestamp":1687165327000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Modular Multi-Copter Structure Control for Cooperative Aerial Cargo Transportation"],"prefix":"10.1007","volume":"108","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6079-5488","authenticated-orcid":false,"given":"Dimitris","family":"Chaikalis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nikolaos","family":"Evangeliou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anthony","family":"Tzes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Farshad","family":"Khorrami","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,6,19]]},"reference":[{"key":"1842_CR1","doi-asserted-by":"publisher","first-page":"17584","DOI":"10.1109\/ACCESS.2021.3053654","volume":"9","author":"K Gkountas","year":"2021","unstructured":"Gkountas, K., Tzes, A.: Leader\/follower force control of aerial manipulators. IEEE Access 9, 17584\u201317595 (2021)","journal-title":"IEEE Access"},{"key":"1842_CR2","doi-asserted-by":"crossref","unstructured":"Preiss, J.A., Honig, W., Sukhatme, G.S., Ayanian, N.: Crazyswarm: a large nano-quadcopter swarm. In: 2017 IEEE International Conference on Robotics and Automation (ICRA), Marina Bay Sands, Singapore , pp.\u00a03299\u20133304 (2017)","DOI":"10.1109\/ICRA.2017.7989376"},{"key":"1842_CR3","doi-asserted-by":"crossref","unstructured":"Chen, M., Zhou, Z., Wang, R.: Multi-rigid-body dynamics modeling and controller design for a connected UAV formation. In: 2019 IEEE 10th International Conference on Mechanical and Aerospace Engineering (ICMAE), Brussels, Belgium, pp.\u00a0187\u2013192 (2019)","DOI":"10.1109\/ICMAE.2019.8880953"},{"issue":"1","key":"1842_CR4","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/s10514-010-9205-0","volume":"30","author":"N Michael","year":"2011","unstructured":"Michael, N., Fink, J., Kumar, V.: Cooperative manipulation and transportation with aerial robots. Autonomous Robots 30(1), 73\u201386 (2011)","journal-title":"Autonomous Robots"},{"issue":"1","key":"1842_CR5","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1109\/TASE.2016.2605707","volume":"15","author":"H Lee","year":"2016","unstructured":"Lee, H., Kim, H., Kim, H.J.: Planning and control for collision-free cooperative aerial transportation. IEEE Transactions on Automation Science and Engineering 15(1), 189\u2013201 (2016)","journal-title":"IEEE Transactions on Automation Science and Engineering"},{"issue":"3","key":"1842_CR6","doi-asserted-by":"publisher","first-page":"1635","DOI":"10.1007\/s10846-020-01213-0","volume":"100","author":"F Pierri","year":"2020","unstructured":"Pierri, F., Nigro, M., Muscio, G., Caccavale, F.: Cooperative manipulation of an unknown object via omnidirectional unmanned aerial vehicles. Journal of Intelligent & Robotic Systems 100(3), 1635\u20131649 (2020)","journal-title":"Journal of Intelligent & Robotic Systems"},{"key":"1842_CR7","doi-asserted-by":"crossref","unstructured":"Lee, H., Kim, H., Kim, H.J.: Path planning and control of multiple aerial manipulators for a cooperative transportation. In: 2015 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany, pp.\u00a02386\u20132391 (2015)","DOI":"10.1109\/IROS.2015.7353700"},{"issue":"4","key":"1842_CR8","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1109\/MRA.2018.2852789","volume":"25","author":"A Ollero","year":"2018","unstructured":"Ollero, A., Heredia, G., Franchi, A., Antonelli, G., Kondak, K., Sanfeliu, A., Viguria, A., Martinez-de Dios, J.R., Pierri, F., Cort\u00e9s, J., et al.: The AEROARMS project: aerial robots with advanced manipulation capabilities for inspection and maintenance. IEEE Robotics & Automation Magazine 25(4), 12\u201323 (2018)","journal-title":"IEEE Robotics & Automation Magazine"},{"issue":"3","key":"1842_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10846-021-01457-4","volume":"103","author":"C Masone","year":"2021","unstructured":"Masone, C., Stegagno, P.: Shared control of an aerial cooperative transportation system with a cable-suspended payload. Journal of Intelligent & Robotic Systems 103(3), 1\u201329 (2021)","journal-title":"Journal of Intelligent & Robotic Systems"},{"issue":"2","key":"1842_CR10","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1109\/LCSYS.2019.2924413","volume":"4","author":"E Rossi","year":"2019","unstructured":"Rossi, E., Tognon, M., Carli, R., Schenato, L., Cort\u00e9s, J., Franchi, A.: Cooperative aerial load transportation via sampled communication. IEEE Control Systems Letters 4(2), 277\u2013282 (2019)","journal-title":"IEEE Control Systems Letters"},{"key":"1842_CR11","doi-asserted-by":"publisher","first-page":"1085","DOI":"10.1007\/s10846-020-01212-1","volume":"100","author":"K Umemoto","year":"2020","unstructured":"Umemoto, K., Endo, T., Matsuno, F.: Dynamic cooperative transportation control using friction forces of $$n$$ multi-rotor unmanned aerial vehicles. Journal of Intelligent & Robotic Systems 100, 1085\u20131095 (2020)","journal-title":"Journal of Intelligent & Robotic Systems"},{"issue":"6","key":"1842_CR12","doi-asserted-by":"publisher","first-page":"908","DOI":"10.1016\/j.mechatronics.2010.08.003","volume":"21","author":"R Oung","year":"2011","unstructured":"Oung, R., D\u2019Andrea, R.: The distributed flight array. Mechatronics 21(6), 908\u2013917 (2011)","journal-title":"Mechatronics"},{"issue":"2","key":"1842_CR13","doi-asserted-by":"publisher","first-page":"458","DOI":"10.1109\/TRO.2019.2954679","volume":"36","author":"B Mu","year":"2019","unstructured":"Mu, B., Chirarattananon, P.: Universal flying objects: modular multirotor system for flight of rigid objects. IEEE Transactions on Robotics 36(2), 458\u2013471 (2019)","journal-title":"IEEE Transactions on Robotics"},{"key":"1842_CR14","doi-asserted-by":"crossref","unstructured":"Saldana, D., Gabrich, B., Li, G., Yim, M., Kumar, V.: Modquad: the flying modular structure that self-assembles in midair. In: 2018 IEEE International Conference on Robotics and Automation (ICRA), Brisbane, Australia, pp.\u00a0691\u2013698 (2018)","DOI":"10.1109\/ICRA.2018.8461014"},{"key":"1842_CR15","doi-asserted-by":"crossref","unstructured":"Gabrich, B., Li, G., Yim, M.: ModQuad-DoF: a novel yaw actuation for modular quadrotors. In: 2020 IEEE International Conference on Robotics and Automation (ICRA), pp.\u00a08267\u20138273 (2020). IEEE","DOI":"10.1109\/ICRA40945.2020.9196735"},{"key":"1842_CR16","doi-asserted-by":"crossref","unstructured":"Mor\u00edin, D.G., Araujo, J., Tayamon, S., Andersson, L.A.: Autonomous cooperative flight of rigidly attached quadcopters. In: 2019 IEEE International Conference on Robotics and Automation (ICRA), Montreal, Canada, pp.\u00a05309\u20135315 (2019)","DOI":"10.1109\/ICRA.2019.8794266"},{"key":"1842_CR17","doi-asserted-by":"crossref","unstructured":"Oishi, K., Jimbo, T.: Autonomous cooperative transportation system involving multi-aerial robots with variable attachment mechanism. In: 2021 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 6322\u20136328 (2021). IEEE","DOI":"10.1109\/IROS51168.2021.9636145"},{"issue":"4","key":"1842_CR18","doi-asserted-by":"publisher","first-page":"8094","DOI":"10.1109\/LRA.2021.3103637","volume":"6","author":"Y Su","year":"2021","unstructured":"Su, Y., Yu, P., Gerber, M.J., Ruan, L., Tsao, T.-C.: Nullspace-based control allocation of overactuated uav platforms. IEEE Robotics and Automation Letters 6(4), 8094\u20138101 (2021)","journal-title":"IEEE Robotics and Automation Letters"},{"issue":"3","key":"1842_CR19","doi-asserted-by":"publisher","first-page":"167","DOI":"10.5139\/IJASS.2010.11.3.167","volume":"11","author":"D-W Yoo","year":"2010","unstructured":"Yoo, D.-W., Oh, H.-D., Won, D.-Y., Tahk, M.-J.: Dynamic modeling and stabilization techniques for tri-rotor unmanned aerial vehicles. International Journal of Aeronautical and Space Sciences 11(3), 167\u2013174 (2010)","journal-title":"International Journal of Aeronautical and Space Sciences"},{"key":"1842_CR20","unstructured":"Abara, D.N.: Modelling, control and construction of tricopter unmanned aerial vehicles. PhD thesis, The University of Manchester, UK (2022)"},{"key":"1842_CR21","doi-asserted-by":"crossref","unstructured":"Chaikalis, D., Evangeliou, N., Tzes, A., Khorrami, F.: Adaptive control of coupled-multicopter systems. In: 2022 International Conference on Unmanned Aircraft Systems (ICUAS), pp.\u00a01375\u20131380 . IEEE (2022)","DOI":"10.1109\/ICUAS54217.2022.9836081"},{"key":"1842_CR22","doi-asserted-by":"crossref","unstructured":"Siciliano, B., Khatib, O., Kr\u00f6ger, T.: Springer Handbook of Robotics vol. 200. Springer, (2008)","DOI":"10.1007\/978-3-540-30301-5"},{"issue":"5","key":"1842_CR23","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1109\/9.135504","volume":"37","author":"O Morgul","year":"1992","unstructured":"Morgul, O.: Dynamic boundary control of an Euler-Bernoulli beam. IEEE Transactions on automatic control 37(5), 639\u2013642 (1992)","journal-title":"IEEE Transactions on automatic control"},{"issue":"1","key":"1842_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10846-020-01265-2","volume":"101","author":"L Martins","year":"2021","unstructured":"Martins, L., Cardeira, C., Oliveira, P.: Feedback linearization with zero dynamics stabilization for quadrotor control. Journal of Intelligent & Robotic Systems 101(1), 1\u201317 (2021)","journal-title":"Journal of Intelligent & Robotic Systems"},{"key":"1842_CR25","unstructured":"Krstic, M., Kokotovic, P.V., Kanellakopoulos, I.: Nonlinear and Adaptive Control Design. John Wiley & Sons, Inc., (1995)"},{"key":"1842_CR26","doi-asserted-by":"crossref","unstructured":"Achtelik, M., Doth, K.-M., Gurdan, D., Stumpf, J.: Design of a multi rotor MAV with regard to efficiency, dynamics and redundancy. In: AIAA Guidance, Navigation, and Control Conference, Minneapolis, Minnesota, p.\u00a04779 (2012)","DOI":"10.2514\/6.2012-4779"},{"key":"1842_CR27","doi-asserted-by":"publisher","first-page":"58383","DOI":"10.1109\/ACCESS.2018.2875040","volume":"6","author":"HV Abeywickrama","year":"2018","unstructured":"Abeywickrama, H.V., Jayawickrama, B.A., He, Y., Dutkiewicz, E.: Comprehensive energy consumption model for unmanned aerial vehicles, based on empirical studies of battery performance. IEEE Access 6, 58383\u201358394 (2018)","journal-title":"IEEE Access"},{"key":"1842_CR28","doi-asserted-by":"crossref","unstructured":"Mellinger, D., Shomin, M., Michael, N., Kumar, V.: Cooperative grasping and transport using multiple quadrotors. In: Distributed Autonomous Robotic Systems, pp. 545\u2013558. Springer, New York (2013)","DOI":"10.1007\/978-3-642-32723-0_39"},{"issue":"2","key":"1842_CR29","doi-asserted-by":"publisher","first-page":"2953","DOI":"10.1109\/LRA.2022.3145063","volume":"7","author":"L Bauersfeld","year":"2022","unstructured":"Bauersfeld, L., Scaramuzza, D.: Range, endurance, and optimal speed estimates for multicopters. IEEE Robotics and Automation Letters 7(2), 2953\u20132960 (2022)","journal-title":"IEEE Robotics and Automation Letters"},{"issue":"9","key":"1842_CR30","doi-asserted-by":"publisher","first-page":"2221","DOI":"10.3390\/en11092221","volume":"11","author":"M-H Hwang","year":"2018","unstructured":"Hwang, M.-H., Cha, H.-R., Jung, S.Y.: Practical endurance estimation for minimizing energy consumption of multirotor unmanned aerial vehicles. Energies 11(9), 2221 (2018)","journal-title":"Energies"},{"key":"1842_CR31","doi-asserted-by":"crossref","unstructured":"Ravat, A.K., Dhawan, A., Tiwari, M.: LMI and YALMIP: modeling and optimization toolbox in matlab. In: Advances in VLSI, Communication, and Signal Processing, pp. 507\u2013515. Springer, New York (2021)","DOI":"10.1007\/978-981-15-6840-4_41"},{"key":"1842_CR32","unstructured":"ApS, M.:Mosek optimization toolbox for matlab. User\u2019s Guide and Reference Manual, Version 4 (2019)"},{"key":"1842_CR33","doi-asserted-by":"crossref","unstructured":"Giernacki, W., Skwierczy\u0144ski, M., Witwicki, W., Wro\u0144ski, P., Kozierski, P.: Crazyflie 2.0 quadrotor as a platform for research and education in robotics and control engineering. In: 22nd International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 37\u201342 (2017). IEEE","DOI":"10.1109\/MMAR.2017.8046794"},{"key":"1842_CR34","doi-asserted-by":"crossref","unstructured":"H\u00f6nig, W., Ayanian, N.: Flying multiple UAVs using ROS. In: Robot Operating System (ROS), pp. 83\u2013118. Springer, New York (2017)","DOI":"10.1007\/978-3-319-54927-9_3"},{"key":"1842_CR35","doi-asserted-by":"crossref","unstructured":"Lynen, S., Achtelik, M.W., Weiss, S., Chli, M., Siegwart, R.: A robust and modular multi-sensor fusion approach applied to MAV navigation. In: 2013 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan, pp.\u00a03923\u20133929 (2013)","DOI":"10.1109\/IROS.2013.6696917"},{"key":"1842_CR36","unstructured":"Bouabdallah, S., Siegwart, R.: Backstepping and sliding-mode techniques applied to an indoor micro quadrotor. In: Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain, pp.\u00a02247\u20132252 (2005)"}],"container-title":["Journal of Intelligent &amp; Robotic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-023-01842-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10846-023-01842-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-023-01842-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,22]],"date-time":"2024-10-22T15:18:24Z","timestamp":1729610304000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10846-023-01842-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["1842"],"URL":"https:\/\/doi.org\/10.1007\/s10846-023-01842-1","relation":{},"ISSN":["0921-0296","1573-0409"],"issn-type":[{"value":"0921-0296","type":"print"},{"value":"1573-0409","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6]]},"assertion":[{"value":"11 October 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 February 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 June 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declaration"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest"}},{"value":"No ethical approval is required for publishing his research.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical standard"}}],"article-number":"31"}}