Unmanned Aerial Vehicle Formation Control Based on Prescribed-time Consensus Theory

doi:10.12382/bgxb.2024.0863

Abstract

Abstract:

Unmanned aerial vehicle (UAV) formation can execute complex collective tasks and reduce the risk and operation difficulty of a single UAV. A distributed formation compound control method with the leader-follower structure is designed based on the prescribed-time stability theory and multi-agent consensus theory for the control of UAV swarm formation in three-dimensional scene.Firstly,a multi-UAVs kinematic model is established by analyzing the relationship between the actual input and the equivalent control.In order to enhance the robustness of UAVs against external disturbances,a prescribed-time convergent extended state observer is designed to achieve online estimation of disturbance based on active disturbance rejection control theory.Furthermore,considering that only the followers connecting to the leader can access the leader's state information,a prescribed-time convergent distributed estimator is introduced to rapidly estimate the leader's state.On this basis,a prescribed-time convergent consensus formation control algorithm is proposed combined with the outputs of the observer and the estimator,and the prescribed-time stability of closed-loop system is proved by Lyapunov theory.The simulated results validate the effectiveness of the proposed method.The research results show that the proposed control method can achieve the stable cooperative control of UAV formation within a preset time in the presence of external disturbances.

Key words: unmanned aerial vehicle, formation control, prescribed-time stability, extended state observer, distributed estimator, multi-agent consensus theory

CLC Number:

TJ301

LI Junhui, WANG Wei, WANG Yuchen, JI Yi. Unmanned Aerial Vehicle Formation Control Based on Prescribed-time Consensus Theory[J]. Acta Armamentarii, 2025, 46(8): 240863-.

Figures/Tables 8

References 28

[1]	曾照洋, 彭文胜, 李云凯, 等. 智能无人机集群可靠性技术内涵、发展及挑战[J]. 兵工学报, 2025, 46(3):240322. doi: 10.12382/bgxb.2024.0322
	ZENG Z Y, PENG W S, LI Y K, et al. Technical connotation,development and challenges of intelligent drone swarm reliability[J]. Acta Armamentarii, 2025, 46(3):240322. (in Chinese)
[2]	ZHAO Y, GAO K, HUANG P F, et al. Specified-time affine formation maneuver control of multiagent systems over directed networks[J]. IEEE Transactions on Automatic Control, 2024, 69(3):1936-1943.
[3]	TEKIN R, ERER K S. Three-dimensional formation guidance with rigidly connected virtual leaders[J]. Journal of Guidance,Control,and Dynamics, 2021, 44(6):1229-1236.
[4]	潘无为, 姜大鹏, 庞永杰, 等. 人工势场和虚拟结构相结合的多水下机器人编队控制[J]. 兵工学报, 2017, 38(2):326-334. doi: 10.3969/j.issn.1000-1093.2017.02.017
	PAN W W, JIANG D P, PANG Y J, et al. A multi-AUV formation algorithm combining artificial potential field and virtual structure[J]. Acta Armamentarii, 2017, 38(2):326-334. (in Chinese)
[5]	ZOU Y, MENG Z Y. Leader-follower formation control of multiple vertical takeoff and landing UAVs:distributed estimator design and accurate trajectory tracking[C]// Proceedings of the 2017 13rd IEEE International Conference on Control & Automation. Ohrid,Macedonia: IEEE, 2017:764-769.
[6]	邹尧, 孟子阳. 垂直起降飞行器的自适应集群编队飞行控制[J]. 中国科学:技术科学, 2020, 50(4):369-379.
	ZOU Y, MENG Z Y. Adaptive formation control of multiple vertical takeoff and landing UAVs[J]. Scientia Sinica(Technologica), 2020, 50(4):369-379. (in Chinese)
[7]	张清瑞, 刘赟韵, 孙慧杰, 等. 固定翼无人机紧密编队的鲁棒协同跟踪控制[J]. 航空学报, 2024, 45(1):629233. doi: 10.7527/S1000-6893.2023.29233
	ZHANG Q R, LIU Y Y, SUN H J, et al. Robust cooperative tracking control for close formation of fixed-wing unmanned aerial vehicles[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(1):629233. (in Chinese)
[8]	DING Z T. Consensus disturbance rejection with disturbance observers[J]. IEEE Transactions on Industrial Electronics, 2015, 62(9):5829-5837.
[9]	BHAT S P, BERNSTEIN D S. Finite-time stability of continuous autonomous systems[J]. SIAM Journal on Control and Optimization, 2000, 38(3):751-766.
[10]	POLYAKOV A. Nonlinear feedback design for fixed-time stabilization of linear control systems[J]. IEEE Transactions on Automatic Control, 2011, 57(8):2106-2110.
[11]	SONG Y D, WANG Y J, HOLLOWAY J, et al. Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time[J]. Automatica, 2017, 83:243-251.
[12]	DU H B, ZHU W W, WEN G H, et al. Finite-time formation control for a group of quadrotor aircraft[J]. Aerospace Science and Technology, 2017, 69:609-616.
[13]	LIU B J, LI A J, GUO Y, et al. Adaptive distributed finite-time formation control for multi-UAVs under input saturation without collisions[J]. Aerospace Science and Technology, 2022, 120:107252.
[14]	ZUO Z Y, TIE L. Distributed robust finite-time nonlinear consensus protocols for multi-agent systems[J]. International Journal of Systems Science, 2016, 47(6):1366-1375.
[15]	CHENG W L, ZHANG K, JIANG B. Continuous fixed-time fault-tolerant formation control for heterogeneous multiagent systems under fixed and switching topologies[J]. IEEE Transactions on Vehicular Technology, 2022, 72(2):1545-1558.
[16]	MIAO Q Y, ZHANG K, JIANG B. Fixed-time collision-free fault-tolerant formation control of multi-UAVs under actuator faults[J]. IEEE Transactions on Cybernetics, 2024, 54(6):3679-3691.
[17]	NING B D, HAN Q L, ZUO Z. Practical fixed-time consensus for integrator-type multi-agent systems:a time base generator approach[J]. Automatica, 2019, 105:406-414.
[18]	PAL A K, KAMAL S, NAGAR S K, et al. Design of controllers with arbitrary convergence time[J]. Automatica, 2020, 112:108710.
[19]	马骥, 陈向勇, 温广辉, 等. 随机切换拓扑下无人机集群预设时间跟踪控制[J]. 航空学报, 2024, 45(增刊1):730793.
	MA J, CHEN X Y, WEN G H, et al. Predefined time tracking control of unmanned aerial vehicles nder stochastic switched topologies[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(S1):730793. (in Chinese)
[20]	DING T F, GE M F, XIONG C, et al. Prescribed-time formation tracking of second-order multi-agent networks with directed graphs[J]. Automatica, 2023, 152:110997.
[21]	REN W, BEARD R W. Distributed consensus in multi-vehicle cooperative control[M]. Berlin,Germany: Springer, 2008.
[22]	RÍOS H, TEEL A R. A hybrid fixed-time observer for state estimation of linear systems[J]. Automatica, 2018, 87:103-112.
[23]	ZHANG H W, LI Z K, QU Z H, et al. On constructing Lyapunov functions for multi-agent systems[J]. Automatica, 2015, 58:39-42.
[24]	WANG Y J, YUAN Y, LIU J G. Finite-time leader-following output consensus for multi-agent systems via extended state observer[J]. Automatica, 2021, 124:109133.
[25]	REN Y H, ZHOU W N, LI Z W, et al. Prescribed-time cluster lag consensus control for second-order non-linear leader-following multiagent systems[J]. ISA Transactions, 2021, 109:49-60. doi: 10.1016/j.isatra.2020.09.012 pmid: 33051052
[26]	LÜ J X, JU X Z, JING L, et al. Adaptive predefined-time observer design for generalized strict-feedback second-order systems under perturbations[J]. International Journal of Robust and Nonlinear Control, 2023, 33(1):311-335.
[27]	CHANG L, HAN Q L, GE X H, et al. On designing distributed prescribed finite-time observers for strict-feedback nonlinear systems[J]. IEEE Transactions on Cybernetics, 2019, 51(9):4695-4706.
[28]	CRUZ-ZAVALA E, MORENO J A. Levant's arbitrary-order exact differentiator:a Lyapunov approach[J]. IEEE Transactions on Automatic Control, 2018, 64(7):3034-3039.

参数	无人机1	无人机2	无人机3	无人机4
位置跟踪误差/m	0.0001	0.0027	0.0058	0.0092
速度跟踪误差/(m·s^-1)	0.0011	0.0027	0.0734	0.0966
位置估计误差/m	3.1×10^-16	1.5×10^-14	1.3×10^-5	2.2×10^-5
速度估计误差/(m·s^-1)	1.9×10^-13	6.2×10^-7	3.1×10^-5	5.0×10^-5
加速度估计误差/(m·s^-2)	0	0	0	0
T_u扰动估计误差	0.3529	0.1912	0.0367	0.2274
5T_u扰动估计误差	0.0170	0.0087	0.0182	0.0638

参数	无人机1	无人机2	无人机3	无人机4
位置跟踪误差/m	0.0001	0.0027	0.0058	0.0092
速度跟踪误差/(m·s^-1)	0.0011	0.0027	0.0734	0.0966
位置估计误差/m	3.1×10^-16	1.5×10^-14	1.3×10^-5	2.2×10^-5
速度估计误差/(m·s^-1)	1.9×10^-13	6.2×10^-7	3.1×10^-5	5.0×10^-5
加速度估计误差/(m·s^-2)	0	0	0	0
T_u扰动估计误差	0.3529	0.1912	0.0367	0.2274
5T_u扰动估计误差	0.0170	0.0087	0.0182	0.0638

参数	无人机1	无人机2	无人机3	无人机4
位置跟踪误差/m	0.0082	0.0082	0.0058	0.0074
速度跟踪误差/(m·s^-1)	0.0020	0.0068	0.0160	0.0294
位置估计误差/m	7.6×10^-7	1.2×10^-5	0.0165	0.0267
速度估计误差/(m·s^-1)	3.8×10^-6	5.5×10^-5	0.0124	0.0201
加速度估计误差/(m·s^-2)	2.9×10^-5	4.5×10^-4	0.0099	0.0160
T_u扰动估计误差	0.1343	0.0189	0.0241	0.0272
5T_u扰动估计误差	0.0092	0.0162	0.0137	0.0390

参数	无人机1	无人机2	无人机3	无人机4
位置跟踪误差/m	0.0082	0.0082	0.0058	0.0074
速度跟踪误差/(m·s^-1)	0.0020	0.0068	0.0160	0.0294
位置估计误差/m	7.6×10^-7	1.2×10^-5	0.0165	0.0267
速度估计误差/(m·s^-1)	3.8×10^-6	5.5×10^-5	0.0124	0.0201
加速度估计误差/(m·s^-2)	2.9×10^-5	4.5×10^-4	0.0099	0.0160
T_u扰动估计误差	0.1343	0.0189	0.0241	0.0272
5T_u扰动估计误差	0.0092	0.0162	0.0137	0.0390

参数	无人机1	无人机2	无人机3	无人机4
位置跟踪误差/m	0.0231	0.1059	0.1881	0.2698
速度跟踪误差/(m·s^-1)	0.0158	0.0807	0.0613	0.1214
位置估计误差/m	0.0024	0.0208	0.3798	0.6132
速度估计误差/(m·s^-1)	0.0020	0.0138	0.0967	0.1545
加速度估计误差/(m·s^-2)	2.3×10^-16	9.6×10^-15	1.4×10^-6	2.1×10^-6