{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T22:34:51Z","timestamp":1768516491467,"version":"3.49.0"},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2020,5,20]],"date-time":"2020-05-20T00:00:00Z","timestamp":1589932800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>Quadrotors are unmanned aerial vehicles with many potential applications ranging from mapping to supporting rescue operations. A key feature required for the use of these vehicles under complex conditions is a technique to analytically solve the problem of trajectory planning. Hence, this paper presents a heuristic approach for optimal path planning that the optimization strategy is based on the indirect solution of the open-loop optimal control problem. Firstly, an adequate dynamic system modeling is considered with respect to a configuration of a commercial quadrotor helicopter. The model predicts the effect of the thrust and torques induced by the four propellers on the quadrotor motion. Quadcopter dynamics is described by differential equations that have been derived by using the Newton\u2013Euler method. Then, a path planning algorithm is developed to find the optimal trajectories that meet various objective functions, such as fuel efficiency, and guarantee the flight stability and high-speed operation. Typically, the necessary condition of optimality for a constrained optimal control problem is formulated as a standard form of a two-point boundary-value problem using Pontryagin\u2019s minimum principle. One advantage of the proposed method can solve a wide range of optimal maneuvers for arbitrary initial and final states relevant to every considered cost function. In order to verify the effectiveness of the presented algorithm, several simulation and experiment studies are carried out for finding the optimal path between two points with different objective functions by using MATLAB software. The results clearly show the effect of the proposed approach on the quadrotor systems.<\/jats:p>","DOI":"10.1017\/s0263574720000247","type":"journal-article","created":{"date-parts":[[2020,5,20]],"date-time":"2020-05-20T08:32:24Z","timestamp":1589963544000},"page":"137-152","source":"Crossref","is-referenced-by-count":11,"title":["Trajectory Planning of Quadrotor Systems for Various Objective Functions"],"prefix":"10.1017","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7405-3218","authenticated-orcid":false,"given":"Hamidreza","family":"Heidari","sequence":"first","affiliation":[]},{"given":"Martin","family":"Saska","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2020,5,20]]},"reference":[{"key":"S0263574720000247_ref1","first-page":"4393","article-title":"Design and control of an indoor micro quadrotor","volume":"5","author":"Bouabdallah","year":"2004","journal-title":"IEEE Trans. Robot. Autom."},{"key":"S0263574720000247_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s10514-017-9690-5"},{"key":"S0263574720000247_ref18","unstructured":"18. Tayebi, A. and McGilvray, S. , \u201cAttitude Stabilization of a Four-Rotor Aerial Robot\u201d, In: 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), Nassau, vol. 2 (2004) pp. 1216\u20131221."},{"key":"S0263574720000247_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s10846-012-9778-2"},{"key":"S0263574720000247_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574718000218"},{"key":"S0263574720000247_ref9","unstructured":"9. Sayyaadi, H. and Soltani, A. , \u201cDecentralized polynomial trajectory generation for flight formation of quadrotors\u201d, Proc. Inst. Mech. Eng. Part K: J. Multi-Body Dyn. 231(4), 690\u2013707 (2017)."},{"key":"S0263574720000247_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s10514-012-9282-3"},{"key":"S0263574720000247_ref3","doi-asserted-by":"publisher","DOI":"10.1002\/oca.2302"},{"key":"S0263574720000247_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/s10846-012-9807-1"},{"key":"S0263574720000247_ref17","first-page":"275","article-title":"Universal path planning for an indoor drone","volume":"95","author":"Li","year":"2018","journal-title":"Appl. Math. Model."},{"key":"S0263574720000247_ref4","first-page":"325","article-title":"Path following control tuning for an autonomous unmanned quadrotor using particle swarm optimization","volume":"50","author":"Rendon","year":"2017","journal-title":"Appl. Math. Model."},{"key":"S0263574720000247_ref11","doi-asserted-by":"publisher","DOI":"10.1109\/MED.2008.4602025"},{"key":"S0263574720000247_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.measurement.2017.05.036"},{"key":"S0263574720000247_ref14","unstructured":"14. Hehn, M. and D\u2019Andrea, R. , \u201cQuadrocopter Trajectory Generation and Control\u201d, In: Proceedings of the 18th World Congress, The International Federation of Automatic Control (IFAC), Milano, Italy, vol. 44(1) (2011) pp. 1485\u20131491."},{"key":"S0263574720000247_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s10846-005-9015-3"},{"key":"S0263574720000247_ref7","unstructured":"7. Bousbaine, A. , Wu, M. H. and Poyi, G. T. , \u201cModeling and Simulation of a Quad-Rotor Helicopter\u201d, In: 6th IET International Conference on Power Electronics, Machines and Drives (PEMD 2012), Bristol (2012) pp. 1\u20136."},{"key":"S0263574720000247_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/s11044-015-9496-1"},{"key":"S0263574720000247_ref6","doi-asserted-by":"publisher","DOI":"10.7906\/indecs.14.1.9"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574720000247","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,29]],"date-time":"2021-01-29T09:05:22Z","timestamp":1611911122000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574720000247\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,20]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["S0263574720000247"],"URL":"https:\/\/doi.org\/10.1017\/s0263574720000247","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,20]]}}}