{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,28]],"date-time":"2026-06-28T18:33:48Z","timestamp":1782671628161,"version":"3.54.5"},"reference-count":21,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T00:00:00Z","timestamp":1745452800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Capacity Building Program of Municipal Universities of Shanghai","award":["20040501400"],"award-info":[{"award-number":["20040501400"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In view of the double pendulum characteristics of cranes in actual production, simply equating them to single pendulum characteristics and ignoring the mass of the hook will lead to significant errors in the oscillation frequency. To tackle this issue, an input-shaping double pendulum anti-sway control method based on phase plane trajectory planning is proposed. This method generates the required acceleration signal by designing an input shaper and calculates the acceleration switching time and amplitude of the trolley according to the phase plane swing angle and the physical constraints of the system. Through this strategy, it is ensured that the speed of the trolley and the swing angle of the load are always kept within the constraint range so that the trolley can reach the target position accurately. The comparative analysis of numerical simulation and existing control methods shows that the proposed control method can significantly reduce the swing angle amplitude and enable the system to enter the swing angle stable state faster. Numerical simulation and physical experiments show the effectiveness of the control method.<\/jats:p>","DOI":"10.3390\/a18050246","type":"journal-article","created":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T09:26:58Z","timestamp":1745486818000},"page":"246","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Phase Plane Trajectory Planning for Double Pendulum Crane Anti-Sway Control"],"prefix":"10.3390","volume":"18","author":[{"given":"Kai","family":"Zhang","sequence":"first","affiliation":[{"name":"Institute of Logistics Science and Engineering, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0411-8762","authenticated-orcid":false,"given":"Wangqing","family":"Niu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Transport Industry of Marine Technology and Control Engineering, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kailun","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Automation Engineering, Shanghai University of Electric Power, Shanghai 200090, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6193","DOI":"10.1109\/TIE.2021.3088356","article-title":"Online Anti-swing Trajectory Planning for a Practical Rubber Tire Container Gantry Crane","volume":"69","author":"Lu","year":"2022","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"103954","DOI":"10.1016\/j.autcon.2021.103954","article-title":"Swing Suppression Control in Tower Cranes with Time-Varying Rope Length Using Real-Time Modified Trajectory Planning","volume":"132","author":"Tian","year":"2021","journal-title":"Autom. Constr."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/s11071-022-07851-3","article-title":"Fixed-time observer-based back-stepping controller design for tower cranes with mismatched disturbance","volume":"111","author":"Xia","year":"2023","journal-title":"Nonlinear Dyn."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2182","DOI":"10.1109\/TASE.2020.3015870","article-title":"Disturbance-Compensation-Based Continuous Sliding Mode Control for Overhead Cranes With Disturbances","volume":"17","author":"Wu","year":"2020","journal-title":"IEEE Trans. Autom. Sci. 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Mechatron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1007\/s40430-023-04236-4","article-title":"Research on accurate motion control of cable crane based on variable structure sliding mode","volume":"45","author":"Tong","year":"2023","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/j.ymssp.2019.04.046","article-title":"Model-independent PD-SMC method with payload swing suppression for 3D overhead crane systems","volume":"129","author":"Zhang","year":"2019","journal-title":"Mech. Syst. 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Appl."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/5\/246\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:20:56Z","timestamp":1760030456000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/5\/246"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,24]]},"references-count":21,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["a18050246"],"URL":"https:\/\/doi.org\/10.3390\/a18050246","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,24]]}}}