Regular virtual tube for cooperative transportation of a payload by multiple quadrotors

doi:10.23919/JSEE.2025.000076

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (4): 1068-1076.doi: 10.23919/JSEE.2025.000076

• CONTROL THEORY AND APPLICATION • Previous Articles

Regular virtual tube for cooperative transportation of a payload by multiple quadrotors

Jiacheng TANG(), Zixiao YANG(), Lei ZHANG(), Tianjiang HU(), Bo ZHU()

School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518107, China

Received:2024-03-01 Online:2025-08-18 Published:2025-09-04
Contact: Bo ZHU E-mail:tangjch5@mail2.sysu.edu.cn;yangzx53@mail2.sysu.edu.cn;zhanglei87@mail2.sysu.edu.cn;hutj3@mail.sysu.edu.cn;zhubo5@mail.sysu.edu.cn
About author:
TANG Jiacheng was born in 1997. He received his first B.E. degree in mathematics and applied mathematics and the second B.E. degree in electrical engineering and automation from Hubei University of Science and Technology, China, in 2019, M.S. degree in control theory and control engineering from Hohai University, China, in 2022. He is currently working toward his Ph.D. degree with the Machine Intelligence and Collective Robotics Lab, Sun Yat-sen University, Shenzhen, China. His main research interests include coordinated transport, robotics swarms and related application. E-mail: tangjch5@mail2.sysu.edu.cn

YANG Zixiao was born in 1999. He received his B.E. degree in aeronautical and astronautical engineering from University of Electronic Science and Technology of China in 2022. He is currently working towards his M.S. degree with the Machine Intelligence and Collective Robotics Lab, Sun Yat-sen University, Shenzhen, China. His main research interests include robust control of the quadrotor unmanned aerial vehicle-slung load system. E-mail: yangzx53@mail2.sysu.edu.cn

ZHANG Lei was born in 1989. He received his B.E. degree in mechanical engineering from Southwest Jiaotong University, China, in 2013, M.S. degree in the Department of Aeronautics and Astronautics from University of Electronic Science and Technology of China in 2018. He is currently working toward his Ph.D. degree with the Machine Intelligence and Collective Robotics Lab, Sun Yat-sen University, Shenzhen, China. His main research interests include control theory, disturbance rejection control, swarm robots, and related application. E-mail: zhanglei87@mail2.sysu.edu.cn

HU Tianjiang was born in 1979. He received his B.E. and Ph.D. degrees in automatic control and robotics, both from the National University of Defense Technology, Changsha, China. He was a joint Ph.D. candidate of Nanyang Technological University Singapore, financially supported by the Chinese Scholarship Council. He is currently a full professor with Sun Yat-sen University, China, where he has been serving as the founder of the Machine Intelligence and Collective Robotics Lab and Vice Dean of School of Artificial Intelligence. His main research interests include collective behaviors, swarm robotics, cooperative perception and control for autonomous systems, and artificial intelligence for computer science (AI4CS) particularly. E-mail: hutj3@mail.sysu.edu.cn

ZHU Bo was born in 1982. He received his B.E. and Ph.D. degrees from Beihang University, Beijing, China, in 2004 and 2010, respectively. He is an associate professor and Ph.D. supervisor with the School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou, China. His research interests include disturbance rejection techniques, autonomous, dependable and affordable (ADA) control of swarm systems, and related applications. E-mail: zhubo5@mail.sysu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (62373386; 61973327).

Abstract

Abstract:

How multi-unmanned aerial vehicles (UAVs) carrying a payload pass an obstacle-dense environment is practically important. Up to now, there have been few results on safe motion planning for the multi-UAVs cooperative transportation system (CTS) to pass through such an environment. The problem is challenging because it is difficult to analyze and explicitly take into account the swing motion of the payload in planning. In this paper, a modeling method of virtual tube is proposed by fusing the advantages of the existing modeling algorithm for regular virtual tube and the expansion environment method. The proposed method can not only generate a safe and smooth tube for UAVs, but also ensure the payload stays away from the dense obstacles. Simulation results show the effectiveness of the method and the safety of the planned tube.

Key words: virtual tube, multi-unmanned aerial vehicles (UAVs), motion planning, cooperative transportation system, expansion environment, anti swing

Jiacheng TANG, Zixiao YANG, Lei ZHANG, Tianjiang HU, Bo ZHU. Regular virtual tube for cooperative transportation of a payload by multiple quadrotors[J]. Journal of Systems Engineering and Electronics, 2025, 36(4): 1068-1076.

Figures/Tables 15

Fig 1

Fig 2

Fig 3

Fig 4

Fig 5

Fig 6

Fig 7

Fig 8

Fig 9

Fig 10

Fig 11

Fig 12

Fig 13

Table 1

Table 2

References 38

1	YU W, ZHU B, WANG X H, et al Enhanced affine formation maneuver control using historical velocity command (HVC). IEEE Robotics and Automation Letters, 2023, 8 (11): 7186- 7193. doi: 10.1109/LRA.2023.3316079
2	YU W, YI P, ZHU B, et al Enhanced affine formation maneuver control using historical acceleration command. International Journal of Robust and Nonlinear Control, 2023, 33 (18): 11458- 11480. doi: 10.1002/rnc.6953
3	WANG F K, HUANG J L, LOW K H, et al AGDS: adaptive goal-directed strategy for swarm drones flying through unknown environments. Complex and Intelligent Systems, 2023, 9 (2): 2065- 2080. doi: 10.1007/s40747-022-00900-9
4	KE C X, CAI K Y, QUAN Q Analysis of a uniform passive fault-tolerant control method for multicopters. Journal of Systems Engineering and Electronics, 2024, 35 (6): 1574- 1582.
5	MAO P D, FU R, QUAN Q Optimal virtual tube planning and control for swarm robotics. The International Journal of Robotics Research, 2024, 43 (5): 602- 627. doi: 10.1177/02783649231210012
6	QUAN Q, GAO Y, BAI C G Distributed control for a robotic swarm to pass through a curve virtual tube. Robotics and Autonomous Systems, 2023, 162, 104368. doi: 10.1016/j.robot.2023.104368
7	HAO N D, MOHAMED B, RAFARALAHY H, et al. Formation of leader follower quadrotors in cluttered environment. Proc. of the American Control Conference, 2016: 6477−6482.
8	GAO Y, BAI C G, QUAN Q Distributed control for a multiagent system to pass through a connected quadrangle virtual tube. IEEE Trans. on Control of Network Systems, 2022, 10 (2): 693- 705.
9	WANG X Y, SUN S J, XIAO F, et al Dynamic event-triggered formation control of second-order nonholonomic systems. Journal of Systems Engineering and Electronics, 2023, 34 (2): 501- 514. doi: 10.23919/JSEE.2023.000049
10	QUAN L, YIN L J, ZHANG T R, et al Robust and efficient trajectory planning for formation flight in dense environments. IEEE Trans. on Robotics, 2023, 39 (6): 4785- 4804. doi: 10.1109/TRO.2023.3301295
11	LUIS C E, SCHOELLIG A P Trajectory generation for multiagent point-to-point transitions via distributed model predictive control. IEEE Robotics and Automation Letters, 2019, 4 (2): 375- 382. doi: 10.1109/LRA.2018.2890572
12	PARK J, KIM J, JANG I, et al. Efficient multi-agent trajectory planning with feasibility guarantee using relative bernstein polynomial. Proc. of the IEEE International Conference on Robotics and Automation, 2020: 434−440.
13	GKOULETSOS D, IANNELLI A, HUDOBA D B M, et al Decentralized trajectory optimization for multi-agent ergodic exploration. IEEE Robotics and Automation Letters, 2021, 6 (4): 6329- 6336. doi: 10.1109/LRA.2021.3094242
14	ZHOU X, ZHU J C, ZHOU H Y, et al. Ego-swarm: a fully autonomous and decentralized quadrotor swarm system in cluttered environments. Proc. of the IEEE International Conference on Robotics and Automation, 2021: 4101−4107.
15	MADRIDANO A, AL-KAFF A, MARTÍN D, et al Trajectory planning for multi-robot systems: methods and applications. Expert Systems with Applications, 2021, 173, 114660. doi: 10.1016/j.eswa.2021.114660
16	HOU J L, ZHOU X, GAN Z X, et al Enhanced decentralized autonomous aerial robot teams with group planning. IEEE Robotics and Automation Letters, 2022, 7 (4): 9240- 9247. doi: 10.1109/LRA.2022.3191037
17	CHEN M, FRAZZOLI E, HSU D, et al. POMDP-lite for robust robot planning under uncertainty. Proc. of the IEEE International Conference on Robotics and Automation, 2016: 5427−5433.
18	WANG L, AMES A D, EGERSTEDT M Safety barrier certificates for collisions-free multirobot systems. IEEE Trans. on Robotics, 2017, 33 (3): 661- 674.
19	PAN Z H, ZHANG C X, XIA Y Q, et al An improved artificial potential field method for path planning and formation control of the multi-UAV systems. IEEE Trans. on Circuits and Systems II-Express Briefs, 2021, 69 (3): 1129- 1133.
20	QUAN Q, FU R, LI M X, et al Practical distributed control for VTOL UAVs to pass a virtual tube. IEEE Trans. on Intelligent Vehicles, 2021, 7 (2): 342- 353.
21	MAO P D, QUAN Q. Making robotics swarm flow more smoothly: a regular virtual tube model. Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 2022: 4498−4504.
22	GAO Y, BAI C G, ZHANG L, et al Multi-UAV cooperative target encirclement within an annular virtual tube. Aerospace Science and Technology, 2022, 128, 107800. doi: 10.1016/j.ast.2022.107800
23	YU X, ZHOU X B, ZHANG Y M Collision-free trajectory generation and tracking for UAVs using Markov decision process in a cluttered environment. Journal of Intelligent and Robotic Systems, 2019, 93 (1/2): 17- 32. doi: 10.1007/s10846-018-0802-z
24	YU X, ZHOU X B, ZHANG Y M. Collision-free trajectory generation for UAVs using Markov decision process. Proc. of the International Conference on Unmanned Aircraft Systems, 2017: 56−61.
25	WANG B, ZHANG Y M, ZHANG W Integrated path planning and trajectory tracking control for quadrotor UAVs with obstacle avoidance in the presence of environmental and systematic uncertainties: theory and experiment. Aerospace Science and Technology, 2022, 120, 107277. doi: 10.1016/j.ast.2021.107277
26	CEN H J, LI B, ACARMAN T, et al. Optimization-based maneuver planning for a tractor-trailer vehicle in complex environments using safe travel corridors. Proc. of the IEEE Intelligent Vehicles Symposium, 2021: 974−979.
27	LI R C, YANG Q K, ZHAO W P, et al. Collision-free trajectory generation for multiple UAVs with sensing constraints. Proc. of the 40th Chinese Control Conference, 2021: 5592−5597.
28	BOUABDALLAH S, MURRIERI P, SIEGWART R. Design and control of an indoor micro quadrotor. Proc. of the IEEE International Conference on Robotics and Automation, 2004: 4393−4398.
29	LABBADI M, CHERKAOUI M Adaptive fractional-order nonsingular fast terminal sliding mode based robust tracking control of quadrotor UAV with Gaussian random disturbances and uncertainties. IEEE Trans. on Aerospace and Electronic Systems, 2021, 57 (4): 2265- 2277. doi: 10.1109/TAES.2021.3053109
30	DOAKHAN M, KABGANIAN M, AZIMI A. Robust adaptive control for formation-based cooperative transportation of a payload by multi quadrotors. European Journal of Control, 2023, 69: 100763.
31	ZHANG Z, JIANG J, WU J, et al Efficient and optimal penetration path planning for stealth unmanned aerial vehicle using minimal radar cross-section tactics and modified A-Star algorithm. ISA Transactions, 2023, 134, 42- 57. doi: 10.1016/j.isatra.2022.07.032
32	SUN N, FANG Y C, ZHANG Y D, et al A novel kinematic coupling-based trajectory planning method for overhead cranes. IEEE/ASME Trans. on Mechatronics, 2012, 17 (1): 166- 173. doi: 10.1109/TMECH.2010.2103085
33	SREENATH K, MICHAEL N, KUMAR V. Trajectory generation and control of a quadrotor with a cable-suspended load a differentially-flat hybrid system. Proc. of the IEEE International Conference on Robotics and Automation, 2013: 4888−4895.
34	SREENATH K, LEE T, KUMAR V. Geometric control and differential flatness of a quadrotor UAV with a cable-suspended load. Proc. of the IEEE Conference on Decision and Control, 2013: 2269−2274.
35	SATHYAN A, MA O, COHEN K Genetic fuzzy methodology for decentralized cooperative UAVs to transport a shared payload. Drones, 2023, 7 (2): 103. doi: 10.3390/drones7020103
36	JIANG Q M, KUMAR V Determination and stability analysis of equilibrium configurations of objects suspended from multiple aerial robots. Journal of Mechanisms and Robotics−Transactions of the ASME, 2012, 4 (2): 021005. doi: 10.1115/1.4005588
37	JIANG Q M, KUMAR V The inverse kinematics of cooperative transport with multiple aerial robots. IEEE Trans. on Robotics, 2013, 29 (1): 136- 145. doi: 10.1109/TRO.2012.2218991
38	LI B, ACARMAN T, PENG X Y. Maneuver planning for automatic parking with safe travel corridors: a numerical optimal control approach. Proc. of the European Control Conference, 2020: 1993−1998.

Parameter	Value
$ {m_l} $	10
$ {\psi _{\max }} $/(°)	$ {30} $
$ {r_a} $	0.4
$ {r_s} $	0.2
$ {\lambda _{\max }} $	10
$ k $	150
$ c $	200

Tube model	${v_{m,i}} $=5 m/s		${v_{m,i}} $=10 m/s		${v_{m,i}} $=20 m/s
Tube model	NC	AD	NC	AD	NC	AD
A*	0	26.66	0	25.08	47	25.29
RVT	315	25.51	156	25.36	79	25.33
RVT-EE	0	30.80	0	31.12	0	30.89

[1]	Yan GAO, Chenggang BAI, Quan QUAN. A survey on passing-through control of multi-robot systems in cluttered environments [J]. Journal of Systems Engineering and Electronics, 2025, 36(4): 1037-1056.
[2]	Delong WU, Hao FANG, Yiren HAO, Aobo WANG. Outdoor navigation of millimeter-wave radar quadrotors based on optimal virtual tube [J]. Journal of Systems Engineering and Electronics, 2025, 36(4): 1057-1067.
[3]	Lu DONG, Zichen HE, Chunwei SONG, Changyin SUN. A review of mobile robot motion planning methods: from classical motion planning workflows to reinforcement learning-based architectures [J]. Journal of Systems Engineering and Electronics, 2023, 34(2): 439-459.

Regular virtual tube for cooperative transportation of a payload by multiple quadrotors

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

Share this article

Figures/Tables 15

References 38

Related Articles 3

Recommended Articles

Metrics

Comments