Research on Trajectory Generation Method for Multi-Objective Optimization of Thrust Vector Vehicle in Constrained Space

Yongjie Shu , Wei Wei , Mingkai Ding , Yunyi Wang , Xubo Zhao , Jianfeng Liu

Drones Auton. Veh. ›› 2026, Vol. 3 ›› Issue (2) : 10013

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Drones Auton. Veh. ›› 2026, Vol. 3 ›› Issue (2) :10013 DOI: 10.70322/dav.2026.10013
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Research on Trajectory Generation Method for Multi-Objective Optimization of Thrust Vector Vehicle in Constrained Space
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Abstract

Thrust-vectoring UAVs can realize decoupling of position and attitude compared with conventional quadrotors due to the ability to change thrust direction, and are used to perform various complex indoor and outdoor missions. However, existing trajectory generation frameworks are mostly for quadrotors with fixed thrust direction and a coplanar surface, and do not consider the dynamics of thrust-vectoring UAVs. To address this, this paper proposes a multi-objective trajectory generation method for thrust-vectoring UAVs in constraint space. By parametrically modeling the constraint space, the method considers the effects of environmental boundary constraints and platform dynamics characteristics on the collision constraints and motion decoupling of the trajectory, and comprehensively optimizes the trajectory’s indicators of stability, speed, and safety to plan the states and input actions of the flight trajectory. Meanwhile, a trajectory generation evaluation system is proposed, given that compared with the conventional quadratic objective function, the proposed method is effective in reducing the attitude change of the trajectory, improving the rapidity and safety, in which LθL_{\theta}Lθ​ and LriskL_{r i s k}Lrisk​ are reduced by 70.4% and 19.1%, respectively. Meanwhile, by comparing with the conventional quadrotor, the advantages of the thrust-vectoring in decoupling motion are quantified, especially in reducing the attitude change during flight, the pitch angle of the generated trajectory is reduced from ±30° to within ±20° degrees, which exerts the motion decoupling advantages of the thrust-vectoring.

Keywords

Constraint space / Thrust vector vehicle / Trajectory generation / Multi-objective optimization

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Yongjie Shu, Wei Wei, Mingkai Ding, Yunyi Wang, Xubo Zhao, Jianfeng Liu. Research on Trajectory Generation Method for Multi-Objective Optimization of Thrust Vector Vehicle in Constrained Space. Drones Auton. Veh., 2026, 3 (2) : 10013 DOI:10.70322/dav.2026.10013

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Statement of the Use of Generative AI and AI-Assisted Technologies in the Writing Process

During the preparation of this manuscript, the authors used ChatGPT for language polishing. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the published article.

Author Contributions

Y.S.: Software, Formal analysis, Writing—Original Draft. W.W.: Conceptualization, Methodology, Supervision, Resources. M.D.: Investigation, Writing—Review & Editing. Y.W.: Investigation, Validation. X.Z.: Data Curation. J.L.: Investigation.

Ethics Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data supporting the findings of this study are available from the corresponding author upon reasonable request.

Funding

This research received no external funding. The APC was funded by the Beijing Natural Science Foundation (3244036), the National Key Research and Development Program of China (2020YFC1512500), the Shandong Postdoctoral Innovation Project (SDCX-ZG-202303052), and the General Program of the Chongqing Natural Science Foundation (CSTB2022NSCQ-MSX1101).

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References

[1]

Wei W, Shu Y, Liu J, Dong L, Jia L, Wang J, et al. Research on a hierarchical feature-based contour extraction method for spatial complex truss-like structures in aerial images. Eng. Appl. Artif. Intell. 2024, 127, 107313. DOI:10.1016/j.engappai.2023.107313

[2]

Brescianini D, D’Andrea R. Tilt-Prioritized Quadrocopter Attitude Control. IEEE Trans. Control Syst. Technol. 2020, 28, 376-387. DOI:10.1109/TCST.2018.2873224

[3]

Wei W, Shu Y, Ke Z, Fan K, Dong L. Study on Roll Oscillation Phenomenon and Controller Design of Deflection-based Flying Vehicles. In Proceedings of the 2023 10th International Conference on Dependable Systems and Their Applications (DSA), Tokyo, Japan, 10-11 August 2023; pp. 800-809. DOI:10.1109/DSA59317.2023.00113

[4]

Bamert S, Cathomen R, Gorlo N, Käppeli G, Müller MS, Reinhart T, et al. Geranos: A Novel Tilted-Rotors Aerial Robot for the Transportation of Poles. IEEE Robot. Autom. Mag. 2024, 31, 66-77. DOI:10.1109/MRA.2023.3348306

[5]

Dong X, Cui Y, Xiang J, Li D, Tu Z. An Efficient Trajectory Generation for Bi-copter Flight in Tight Space. arXiv 2024, arXiv:2406.00671. DOI:10.48550/arXiv.2406.00671

[6]

Rashad R, Goerres J, Aarts R, Engelen JBC, Stramigioli S. Fully Actuated Multirotor UAVs: A Literature Review. IEEE Robot. Autom. Mag. 2020, 27, 97-107. DOI:10.1109/MRA.2019.2955964

[7]

Hamandi M, Usai F, Sablé Q, Staub N, Tognon M, Franchi A. Design of multirotor aerial vehicles: A taxonomy based on input allocation. Int. J. Robot. Res. 2021, 40, 1015-1044. DOI:10.1177/02783649211025998

[8]

Hameed SW, Imanberdiyev N, Camci E, Yau W-Y, Feroskhan M. Bio-inspired classification and evolution of multirotor Micro Aerial Vehicles (MAVs): A comprehensive review. Robot. Auton. Syst. 2024, 182, 104802. DOI:10.1016/j.robot.2024.104802

[9]

Park S, Lee J, Ahn J, Kim M, Her J, Yang G-H, et al. ODAR: Aerial Manipulation Platform Enabling Omnidirectional Wrench Generation. IEEE/ASME Trans. Mechatron. 2018, 23, 1907-1918. DOI:10.1109/TMECH.2018.2848255

[10]

Allenspach M, Bodie K, Brunner M, Rinsoz L, Taylor Z, Kamel M, et al. Design and optimal control of a tiltrotor micro-aerial vehicle for efficient omnidirectional flight. Int. J. Robot. Res. 2020, 39, 1305-1325. DOI:10.1177/0278364920943654

[11]

Hamandi M, Ali AM, Evangeliou N, Chaikalis D, Tzes A, Kyriakopoulos K, et al. Mechatronic Design of an Omnidirectional Octorotor UAV. In Proceedings of the 2024 10th International Conference on Automation, Robotics and Applications (ICARA), Athens, Greece, 22-24 February 2024; pp. 300-304. DOI:10.1109/ICARA60736.2024.10553043

[12]

Iriarte I, Otaola E, Culla D, Iglesias I, Lasa J, Sierra B. Modeling and control of an overactuated aerial vehicle with four tiltable quadrotors attached by means of passive universal joints. In Proceedings of the 2020 International Conference on Unmanned Aircraft Systems (ICUAS), Athens, Greece, 1-4 September 2020; pp. 1748-1756. DOI:10.1109/ICUAS48674.2020.9213848

[13]

Shi C, Wang K, Yu Y. Expandable Fully Actuated Aerial Vehicle Assembly: Geometric Control Adapted from an Existing Flight Controller and Real-World Prototype Implementation. Drones 2022, 6, 272. DOI:10.3390/drones6100272

[14]

Qin Y, Chen N, Cai Y, Xu W, Zhang F, Zhang F. Gemini II: Design, Modeling, and Control of a Compact Yet Efficient Servoless Bi-copter. IEEE/ASME Trans. Mechatron. 2022, 27, 4304-4315. DOI:10.1109/TMECH.2022.3153587

[15]

Sakaguchi A, Takimoto T, Ushio T. A Novel Quadcopter with A Tilting Frame using Parallel Link Mechanism. In Proceedings of the 2019 International Conference on Unmanned Aircraft Systems (ICUAS), Atlanta, GA, USA, 11-14 June 2019; pp. 674-683. DOI:10.1109/ICUAS.2019.8797934

[16]

Zheng P, Tan X, Kocer BB, Yang E, Kovac M. TiltDrone: A Fully-Actuated Tilting Quadrotor Platform. IEEE Robot. Autom. Lett. 2020, 5, 6845-6852. DOI:10.1109/LRA.2020.3010460

[17]

Ryll M, Bicego D, Giurato M, Lovera M, Franchi A, Hexarotor AM, et al. Control and Experimental Validation. IEEE/ASME Trans. Mechatron. 2022, 27, 1244-1255. DOI:10.1109/TMECH.2021.3099197

[18]

Kamel M, Verling S, Elkhatib O, Sprecher C, Wulkop P, Taylor Z, et al. The Voliro Omniorientational Hexacopter: An Agile and Maneuverable Tiltable-Rotor Aerial Vehicle. IEEE Robot. Autom. Mag. 2018, 25, 34-44. DOI:10.1109/MRA.2018.2866758

[19]

Cuniato E, Geckeler C, Brunner M, Strübin D, Bähler E, Ospelt F, et al. Design and Control of a Micro Overactuated Aerial Robot with an Origami Delta Manipulator. In Proceedings of the 2023 IEEE International Conference on Robotics and Automation (ICRA), London, UK, 29 May-2 June 2023; pp. 5352-5358. DOI:10.1109/ICRA48891.2023.10161060

[20]

Yang Y, Yu X, Li Z, Basin MV. A New Overactuated Multirotor: Prototype Design, Dynamics Modeling, and Control. IEEE Trans. Ind. Electron. 2024, 71, 9449-9459. DOI:10.1109/TIE.2023.3314924

[21]

Zhou X, Wang Z, Ye H, Xu C, Gao F. EGO-Planner: An ESDF-Free Gradient-Based Local Planner for Quadrotors. IEEE Robot. Autom. Lett. 2021, 6, 478-485. DOI:10.1109/LRA.2020.3047728

[22]

Zhou B, Pan J, Gao F, Shen S. RAPTOR: Robust and Perception-aware Trajectory Replanning for Quadrotor Fast Flight. IEEE Trans. Robot. 2021, 37, 1992-2009. DOI:10.1109/TRO.2021.3071527

[23]

Zhou B, Gao F, Wang L, Liu C, Shen S. Robust and Efficient Quadrotor Trajectory Generation for Fast Autonomous Flight. IEEE Robot. Autom. Lett. 2019, 4, 3529-3536. DOI:10.1109/LRA.2019.2927938

[24]

Han Z, Wang Z, Pan N, Lin Y, Xu C, Gao F. Fast-Racing: An Open-Source Strong Baseline for SE(3) Planning in Autonomous Drone Racing. IEEE Robot. Autom. Lett. 2021, 6, 8631-8638. DOI:10.1109/LRA.2021.3113976

[25]

Selin M, Tiger M, Duberg D, Heintz F, Jensfelt P. Efficient Autonomous Exploration Planning of Large-Scale 3-D Environments. IEEE Robot. Autom. Lett. 2019, 4, 1699-1706. DOI:10.1109/LRA.2019.2897343

[26]

Liu P, Shen Y, Liu Y, Quan F, Wang C, Chen H. Generating 6-D Trajectories for Omnidirectional Multirotor Aerial Vehicles in Cluttered Environments. IEEE Robot. Autom. Lett. 2024, 9, 8818-8825. DOI:10.1109/LRA.2024.3448135

[27]

Liu P, Quan F, Liu Y, Chen H. Collision-Free 6-DoF Trajectory Generation for Omnidirectional Multi-rotor Aerial Vehicle. arXiv 2022, arXiv:2209.06764. DOI:10.48550/arXiv.2209.06764

[28]

Liu K, Ma L, Zhou H, Li S, Zhang K, Huang D, et al. Optimal Time Trajectory Generation and Tracking Control for Over-actuated Multirotors with Large-angle Maneuvering Capability. IEEE Robot. Autom. Lett. 2022, 7, 8339-8346. DOI:10.1109/LRA.2022.3187260

[29]

Hamandi M, Al-Ali I, Seneviratne L, Franchi A, Zweiri Y. Full-Pose Trajectory Tracking of Overactuated Multi-Rotor Aerial Vehicles with Limited Actuation Abilities. IEEE Robot. Autom. Lett. 2023, 8, 4951-4958. DOI:10.1109/LRA.2023.3290422

[30]

Hachem M, Miquel T, Bronz M, Roos C. Trajectory Optimization for Fully Actuated Hexacopters: Enhancing Maneuverability and Applications. 2023. Available online: https://enac.hal.science/hal-04396701 (accessed on 27 March 2025).

[31]

Su Y, Li J, Jiao Z, Wang M, Chu C, Li H, et al. Sequential Manipulation Planning for Over-Actuated UAMs. In Proceedings of the 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Detroit, MI, USA, 1-5 October 2023.

[32]

Su Y, Zhang J, Jiao Z, Li H, Wang M, Liu H. Real-time Dynamic-consistent Motion Planning for Over-actuated UAVs. In Proceedings of the 2024 IEEE International Conference on Robotics and Automation (ICRA), Yokohama, Japan, 13-17 May 2024; pp. 11789-11795. DOI:10.1109/ICRA57147.2024.10610236

[33]

Allenspach M, Laasch S, Lawrance N, Tognon M, Siegwart R. Mixed Reality Human-Robot Interface to Generate and Visualize 6DoF Trajectories:Application to Omnidirectional Aerial Vehicles. In Proceedings of the 2023 International Conference on Unmanned Aircraft Systems (ICUAS), Warsaw, Poland, 6-9 June 2023; pp. 395-400. DOI:10.1109/ICUAS57906.2023.10156523

[34]

Mandralis I, Sihite E, Ramezani A, Gharib M. Minimum Time Trajectory Generation for Bounding Flight: Combining Posture Control and Thrust Vectoring. In Proceedings of the 2023 European Control Conference (ECC), Bucharest, Romania, 13-16 June 2023; pp. 1-7. DOI:10.23919/ECC57647.2023.10178360

[35]

Liu K, Zheng J. UAV Trajectory Optimization for Time-Constrained Data Collection in UAV-Enabled Environmental Monitoring Systems. IEEE Internet Things J. 2022, 9, 24300-24314. DOI:10.1109/JIOT.2022.3189214

[36]

Memos VA, Psannis KE. Optimized UAV-based data collection from MWSNs. ICT Express 2023, 9, 29-33. DOI:10.1016/j.icte.2022.10.003

[37]

Cui J, Ding Z, Deng Y, Nallanathan A, Hanzo L. Adaptive UAV-Trajectory Optimization Under Quality of Service Constraints: A Model-Free Solution. IEEE Access 2020, 8, 112253-112265. DOI:10.1109/ACCESS.2020.3001752

[38]

Shu Y, Dong L, Liu J, Liu C, Wei W. Overview of Terrain Traversability Evaluation for Autonomous Robots. J. Field Robot. 2024, 42, 1724-1765. DOI:10.1002/rob.22461

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