Two-layer formation-containment fault-tolerant control of fixed-wing UAV swarm for dynamic target tracking

doi:10.23919/JSEE.2023.000153

Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (6): 1375-1396.doi: 10.23919/JSEE.2023.000153

• AUTONOMOUS DECISION AND COOPERATIVE CONTROL OF UAV SWARMS • Previous Articles Next Articles

Two-layer formation-containment fault-tolerant control of fixed-wing UAV swarm for dynamic target tracking

Boyu QIN¹^,²(), Dong ZHANG¹^,²^,*(), Shuo TANG¹^,²(), Yang XU³()

¹ School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China
² Shaanxi Aerospace Flight Vehicle Design Key Laboratory, Xi’an 710072, China
³ School of Civil Aviation, Northwestern Polytechnical University, Xi’an 710072, China

Received:2023-06-11 Online:2023-12-18 Published:2023-12-29
Contact: Dong ZHANG E-mail:byqin@mail.nwpu.edu.cn;zhangdong@nwpu.edu.cn;stang@nwpu.edu.cn;yang.xu@nwpu.edu.cn
About author:
QIN Boyu was born in 2000. He received his B.S. degree from Northwestern Polytechnical University, China in 2021. He currently pursues his Ph.D. degree at the School of Astronautics, Northwestern Polytechnical University, China. His research interests include cooperative planning, guidance and control of the intelligent flight vehicle swarm. E-mail: byqin@mail.nwpu.edu.cn

ZHANG Dong was born in 1986. He received his Ph.D. degree from the School of Astronautics, Northwestern Polytechnical University, Xi ’an, China, in 2013. He is currently an associate professor and doctoral supervisor of Northwestern Polytechnical University. He is also a visiting professor of the Key Laboratory of Complex System Control and Intelligent Collaborative Technology. His research interests include dynamic modeling and control of aerospace vehicles, high-speed aircraft swarms combat mission planning, and collaborative guidance and control. E-mail: zhangdong@nwpu.edu.cn

TANG Shuo was born in 1963. He received his B.S., M.S., and Ph.D. degrees from Northwestern Polytechnical University, Xi’an, China, in 1982, 1985, and 1988, respectively. He is currently a professor with the School of Astronautics, Northwestern Polytechnical University, Xi’an. His current research interests include aerospace vehicle design, flight dynamics, flight simulation, and virtual prototype technology. E-mail: stang@nwpu.edu.cn

XU Yang was born in 1987. He received his Ph.D. degree from Xiamen University, Xiamen, China, in 2019. He has been a visiting Ph.D. student at National University of Singapore from 2016 to 2018, and a research fellow at Westlake University from 2019 to 2020. Now, he is an associate professor in School of Civil Aviation, Northwestern Polytechnical University. His research interests include control theory and application of multiple robotic systems. E-mail: yang.xu@nwpu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (61933010) and the Natural Science Basic Research Plan in Shaanxi Province of China (2023-JC-QN-0733).

Abstract

Abstract:

This paper tackles the formation-containment control problem of fixed-wing unmanned aerial vehicle (UAV) swarm with model uncertainties for dynamic target tracking in three-dimensional space in the faulty case of UAVs ’ actuator and sensor. The fixed-wing UAV swarm under consideration is organized as a “multi-leader-multi-follower” structure, in which only several leaders can obtain the dynamic target information while others only receive the neighbors’ information through the communication network. To simultaneously realize the formation, containment, and dynamic target tracking, a two-layer control framework is adopted to decouple the problem into two subproblems: reference trajectory generation and trajectory tracking. In the upper layer, a distributed finite-time estimator (DFTE) is proposed to generate each UAV ’s reference trajectory in accordance with the control objective. Subsequently, a distributed composite robust fault-tolerant trajectory tracking controller is developed in the lower layer, where a novel adaptive extended super-twisting (AESTW) algorithm with a finite-time extended state observer (FTESO) is involved in solving the robust trajectory tracking control problem under model uncertainties, actuator, and sensor faults. The proposed controller simultaneously guarantees rapidness and enhances the system ’s robustness with fewer chattering effects. Finally, corresponding simulations are carried out to demonstrate the effectiveness and competitiveness of the proposed two-layer fault-tolerant cooperative control scheme.

Key words: fixed-wing unmanned aerial vehicle (UAV) swarm, two-layer control, formation-containment, dynamic target tracking

Boyu QIN, Dong ZHANG, Shuo TANG, Yang XU. Two-layer formation-containment fault-tolerant control of fixed-wing UAV swarm for dynamic target tracking[J]. Journal of Systems Engineering and Electronics, 2023, 34(6): 1375-1396.

Figures/Tables 19

Table 1

Fig 1

Fig 2

Fig 3

Fig 4

Table 2

Table 3

Table 4

Fig 5

Fig 6

Fig 7

Fig 8

Fig 9

Fig 11

Fig 12

Fig 13

Fig 10

Fig 14

Fig 15

References 57

1	MEI J, REN W, SONG Y D A unified framework for adaptive leaderless consensus of uncertain multi-agent systems under directed graphs. IEEE Trans. on Automatic Control, 2021, 66 (12): 6179- 6186. doi: 10.1109/TAC.2021.3062594
2	SUN Q, CHEN J C, SHI Y Integral-type event-triggered model predictive control of nonlinear systems with additive disturbance. IEEE Trans. on Cybernetics, 2021, 51 (12): 5921- 5929. doi: 10.1109/TCYB.2019.2963141
3	RUAN Z W, YANG Q M, GE S S, et al Adaptive fuzzy fault tolerant control of uncertain MIMO nonlinear systems with output constraints and unknown control directions. IEEE Trans. on Fuzzy Systems, 2022, 30 (5): 1224- 1238. doi: 10.1109/TFUZZ.2021.3055336
4	XU Y, LUO D L, LI D Y, et al Target-enclosing affine formation control of two-layer networked spacecraft with collision avoidance. Chinese Journal of Aeronautics, 2019, 32 (12): 2679- 2693. doi: 10.1016/j.cja.2019.04.016
5	LIN W Distributed UAV formation control using differential game approach. Aerospace Science and Technology, 2014, 35, 54- 62. doi: 10.1016/j.ast.2014.02.004
6	WANG J A, XIN M Integrated optimal formation control of multiple unmanned aerial vehicles. IEEE Trans. on Control Systems Technology, 2013, 21 (5): 1731- 1744. doi: 10.1109/TCST.2012.2218815
7	XU Y, LUO D L, YOU Y C, et al New advances in multiple autonomous aerial robots formation control technology. Science China-Technological Sciences, 2019, 62 (10): 1871- 1872. doi: 10.1007/s11431-018-9457-9
8	ZHANG Q R, LIU H H T Robust nonlinear close formation control of multiple fixed-wing aircraft. Journal of Guidance, Control, and Dynamics, 2021, 44 (3): 572- 586. doi: 10.2514/1.G004592
9	XU Y, LI D, LUO D L, et al Two-layer distributed hybrid affine formation control of networked Euler-Lagrange systems. Journal of the Franklin Institute, 2019, 356 (4): 2172- 2197. doi: 10.1016/j.jfranklin.2018.11.029
10	LI Z K, WEN G H, DUAN Z S, et al Designing fully distributed consensus protocols for linear multi-agent systems with directed graphs. IEEE Trans. on Automatic Control, 2015, 60 (4): 1152- 1157. doi: 10.1109/TAC.2014.2350391
11	NI J K, SHI P Adaptive neural network fixed-time leader-follower consensus for multi-agent systems with constraints and disturbances. IEEE Trans. on Cybernetics, 2021, 51 (4): 1835- 1848. doi: 10.1109/TCYB.2020.2967995
12	WANG Q, DONG X W, YU J L, et al Predefined finite-time output containment of nonlinear multi-agent systems with leaders of unknown inputs. IEEE Trans. on Circuits Systems I-Regular Papers, 2021, 68 (8): 3436- 3448. doi: 10.1109/TCSI.2021.3083612
13	WANG X K, LIU Z H, CONG Y R, et al Miniature fixed-wing UAV swarms: review and outlook. Acta Aeronautica et Astronautica Sinica, 2020, 41 (4): 23732.
14	LIAN F, TEO R, WANG J L, et al Distributed formation and reconfiguration control of VTOL UAVs. IEEE Trans. on Control Systems Technology, 2017, 25 (1): 270- 277. doi: 10.1109/TCST.2016.2547952
15	CAI Z H, WANG L H, ZHAO J, et al Virtual target guidance-based distributed model predictive control for formation control of multiple UAVs. Chinese Journal of Aeronautics, 2020, 33 (3): 1037- 1056. doi: 10.1016/j.cja.2019.07.016
16	ZHAO J, SUN J M, CAI Z H, et al Distributed coordinated control scheme of UAV swarm based on heterogeneous roles. Chinese Journal of Aeronautics, 2022, 35 (1): 81- 97. doi: 10.1016/j.cja.2021.01.014
17	LUO Q N, DUAN H B Distributed UAV flocking control based on homing pigeon hierarchical strategies. Aerospace Science and Technology, 2017, 70, 2570264.
18	QIU H X, DUAN H B Multiple UAV distributed close formation control based on in-flight leadership hierarchies of pigeon flocks. Aerospace Science and Technology, 2017, 70, 471- 486. doi: 10.1016/j.ast.2017.08.030
19	DONG X W, LI Q D, REN Z, et al Formation-containment control for high-order linear time-invariant multi-agent systems with time delays. Journal of the Franklin Institute, 2015, 352 (9): 3564- 3584. doi: 10.1016/j.jfranklin.2015.05.008
20	LI C J, CHEN L M, GUO Y N, et al Formation-containment control for networked Euler-Lagrange systems with input saturation. Nonlinear Dynamics, 2018, 91 (2): 1307- 1320. doi: 10.1007/s11071-017-3946-7
21	CHEN L M, LI C J, MEI J, et al Adaptive cooperative formation-containment control for networked Euler-Lagrange systems without using relative velocity information. IET Control Theory and Applications, 2017, 11 (9): 1450- 1458. doi: 10.1049/iet-cta.2016.1185
22	ZHAI D, AN L W, DONG J X, et al Output feedback adaptive sensor failure compensation for a class of parametric strict feedback systems. Automatica, 2018, 97, 48- 57. doi: 10.1016/j.automatica.2018.07.014
23	HU Q L, XIAO B, ZHANG Y M Fault-tolerant attitude control for spacecraft under loss of actuator effectiveness. Journal of Guidance, Control, and Dynamics, 2011, 34 (3): 927- 932. doi: 10.2514/1.49095
24	YU X, LI P, ZHANG Y M The design of fixed-time observer and finite-time fault-tolerant control for hypersonic gliding vehicles. IEEE Trans. on Industrial Electronics, 2018, 65 (5): 4135- 4144. doi: 10.1109/TIE.2017.2772192
25	MA H, LIANG H J, ZHOU Q, et al Adaptive dynamic surface control design for uncertain nonlinear strict-feedback systems with unknown control direction and disturbances. IEEE Trans. on System, Man and Cybernetics System, 2019, 49 (3): 506- 515. doi: 10.1109/TSMC.2018.2855170
26	CUI Y W, LI A J, MENG X F A fault-tolerant control method for distributed flight control system facing wing damage. Journal of Systems Engineering and Electronics, 2021, 32 (5): 1041- 1052. doi: 10.23919/JSEE.2021.000089
27	PAN C W, LIU X, CHEN Y, et al Finite-time fault-tolerant control of teleoperating cyber physical system against faults. Journal of Systems Engineering and Electronics, 2023, 34 (2): 469- 478. doi: 10.23919/JSEE.2023.000044
28	MALIKA S, WANG F Y, LIU Z X, et al Distributed fuzzy fault-tolerant consensus of leader-follower multi-agent systems with mismatched uncertainties. Journal of Systems Engineering and Electronics, 2021, 32 (5): 1031- 1040. doi: 10.23919/JSEE.2021.000088
29	MAZARE M, TAGHIZADEH M, GHAF-GHANBARI P Pitch actuator fault-tolerant control of wind turbines based on time delay control and disturbance observer. Ocean Engineering, 2021, 238, 109724. doi: 10.1016/j.oceaneng.2021.109724
30	MAZARE M, TAGHIZADEH M Uncertainty estimator-based dual layer adaptive fault-tolerant control for wind turbines. Renewable Energy, 2022, 188, 545- 560. doi: 10.1016/j.renene.2022.02.030
31	YU Z Q, ZHANG Y M, JIANG B, et al A review on fault-tolerant cooperative control of multiple unmanned aerial vehicles. Chinese Journal of Aeronautics, 2022, 35 (1): 1- 18. doi: 10.1016/j.cja.2021.04.022
32	LIU C, JIANG B, PATTON R J, et al Integrated fault-tolerant control for close formation flight. IEEE Trans. on Aerospace Electronics and System, 2020, 56 (2): 839- 852. doi: 10.1109/TAES.2019.2920221
33	KAMEL M A, GHAMRY K A, ZHANG Y M Real-time fault-tolerant cooperative control of multiple UAVs-UGVs in the presence of actuator faults. Journal of Intelligent & Robotic Systems, 2017, 88 (2/4): 469- 480.
34	YANG H L, JIANG B, YANG H, et al Synchronization of multiple 3-DOF helicopters under actuator faults and saturations with prescribed performance. ISA Transactions, 2018, 75, 118- 126. doi: 10.1016/j.isatra.2018.02.009
35	YU Z Q, ZHANG Y M, JIANG B, et al Decentralized fractional-order backstepping fault-tolerant control of multi-UAVs against actuator faults and wind effects. Aerospace Science and Technology, 2020, 104, 105939. doi: 10.1016/j.ast.2020.105939
36	YU Z Q, ZHANG Y M, JIANG B, et al Fractional-order adaptive fault-tolerant synchronization tracking control of networked fixed-wing UAVs against actuator-sensor faults via intelligent learning mechanism. IEEE Trans. on Neural Networks and Learning Systems, 2021, 32 (12): 5539- 5553. doi: 10.1109/TNNLS.2021.3059933
37	YU Z Q, ZHANG Y M, JIANG B, et al Distributed adaptive fault-tolerant close formation flight control of multiple trailing fixed-wing UAVs. ISA Transactions, 2020, 106, 181- 199. doi: 10.1016/j.isatra.2020.07.005
38	YU Z Q, LIU Z X, ZHANG Y M, et al Distributed finite-time fault-tolerant containment control for multiple unmanned aerial vehicles. IEEE Trans. on Neural Networks and Learning Systems, 2020, 31 (6): 2077- 2091. doi: 10.1109/TNNLS.2019.2927887
39	XIANG X B, LIU C, SU H S, et al On decentralized adaptive full-order sliding mode control of multiple UAVs. ISA Transactions, 2017, 71, 196- 205. doi: 10.1016/j.isatra.2017.09.008
40	LI D Y, ZHANG W, HE W, et al Two-layer distributed formation-containment control of multiple Euler-Lagrange systems by output feedback. IEEE Trans. on Cybernetics, 2019, 49 (2): 675- 687. doi: 10.1109/TCYB.2017.2786318
41	YU D, GE S S, LI D Y, et al Finite-horizon robust formation-containment control of multi-agent networks with unknown dynamics. Neurocomputing, 2021, 458, 403- 415. doi: 10.1016/j.neucom.2021.01.063
42	ZHENG W M, XU Y, LUO D L. Distributed hierarchical formation-containment control of multi quadrotors system. Journal of Beijing University of Aeronautics and Astronautics,2022. DOI: 10.13700/j.bh.1001-5965.2022.0506. (in Chinese)
43	LEVANT A Higher-order sliding modes differentiation and output-feedback control. International Journal of Control, 2003, 76 (9/10): 924- 941. doi: 10.1080/0020717031000099029
44	NAGESH I, EDWARDS C A multivariable super-twisting sliding mode approach. Automatica, 2014, 50 (3): 984- 988. doi: 10.1016/j.automatica.2013.12.032
45	ANDERSON J D. Fundamentals of aerodynamics, McGraw-Hill series in aeronautical and aerospace engineering. 6th ed. New York: McGraw-Hill Education, 2017.
46	AC 120-28D. Criteria for approval of category Ⅲ weather minima for takeoff, landing, and rollout. Washington: U. S. Department of Transportation and Federal Aviation Administration, 1999.
47	BOSKOVIC J D, BERGSTROM S E, MEHRA R K Robust integrated flight control design under failures, damage, and state-dependent disturbances. Journal of Guidance, Control, and Dynamics, 2005, 28 (5): 902- 917. doi: 10.2514/1.11272
48	ZHANG L L, YANG G H Observer-based fuzzy adaptive sensor fault compensation for uncertain nonlinear strict-feedback systems. IEEE Trans. on Fuzzy Systems, 2018, 26 (4): 2301- 2310. doi: 10.1109/TFUZZ.2017.2772879
49	XU B Robust adaptive neural control of flexible hypersonic flight vehicle with dead-zone input nonlinearity. Nonlinear Dynamics, 2015, 80 (3): 1509- 1520. doi: 10.1007/s11071-015-1958-8
50	XU Y, LUO D L, LI D Y, et al Affine formation control for heterogeneous multi-agent systems with directed interaction networks. Neurocomputing, 2019, 330, 104- 115. doi: 10.1016/j.neucom.2018.11.023
51	LI W Q, XIE L H, ZHANG J F Containment control of leader-following multi-agent systems with Markovian switching network topologies and measurement noises. Automatica, 2015, 51, 263- 267. doi: 10.1016/j.automatica.2014.10.070
52	MENG Z Y, REN W, YOU Z Distributed finite-time attitude containment control for multiple rigid bodies. Automatica, 2010, 46 (12): 2092- 2099. doi: 10.1016/j.automatica.2010.09.005
53	BHAT S P, BERNSTEIN D S Finite-time stability of continuous autonomous systems. SIAM Journal on Control Optimization, 2000, 38 (3): 751- 766. doi: 10.1137/S0363012997321358
54	SUN C, HU G Q, XIE L H, et al Robust finite-time connectivity preserving coordination of second-order multi-agent systems. Automatica, 2018, 89, 21- 27. doi: 10.1016/j.automatica.2017.11.020
55	ZHANG W Q, DONG C Y, RAN M P, et al Fully distributed time-varying formation tracking control for multiple quadrotor vehicles via finite-time convergent extended state observer. Chinese Journal of Aeronautics, 2020, 33 (11): 2907- 2920. doi: 10.1016/j.cja.2020.03.004
56	HAN J Q From PID to active disturbance rejection control. IEEE Trans. on Industrial and Electronics, 2009, 56 (3): 900- 906. doi: 10.1109/TIE.2008.2011621
57	K HASSAN K. Nonlinear systems. 3rd ed. New Jersey: Prentice Hall, 2002.

Nomenclature	Interpretation
${{\boldsymbol{I}}_n}$	Identity matrix with n dimensions
${\rm{diag}}\{ \cdot \}$	Diagonal matrix
$ {\lambda _{\max }}( \cdot ),{\lambda _{\min }}( \cdot ) $	Maximum and minimum eigenvalues
$\left\| \cdot \right\|,{\left\\| \cdot \right\\|_p}$	Absolute value, p-norm
${{\rm{sgn}}} ( \cdot ),{\text{si} }{ {\text{g} }^\alpha }( \cdot )$	Signum function, notation of ${{\rm{sgn}}} ( \cdot ){\left\| \cdot \right\|^\alpha }$
$ \otimes $	Kronecker product
${\boldsymbol{L}}$	Laplacian matrix
${x_i},{y_i},{z_i}$	Position coordinates of UAV i
${V_i},{\theta _i},{\psi _i}$	Velocity, path angle, and heading angle of UAV i
${T_i},{\alpha _i},{\phi _i}$	Thrust, angle of attack, and banking angle of UAV i
${u_{ix}},{u_{iy}},{u_{iz}}$	Virtual control input of UAV i
${{\boldsymbol{\eta }}_{ai}},{{\boldsymbol{b}}_{ai}}$	Execution effectiveness, bias of UAV i’s actuator
${{\boldsymbol{\eta }}_{mi}},{{\boldsymbol{b}}_{mi}}$	Measurement effectiveness, bias of UAV i’s angle sensor
${{\boldsymbol{d}}_i}$	Integrated disturbance and its observed value of UAV i
$ {{\boldsymbol{\tilde p}}_i},{{\boldsymbol{\tilde q}}_i} $	Reference position and velocity of UAV i generated by DFTE
${{\boldsymbol{\hat p}}_i},{{\boldsymbol{\hat q}}_i},{{\boldsymbol{\hat d}}_i}$	Position, velocity, and integrated disturbance of UAV i observed by FTESO
$ {{\boldsymbol{s}}_i},{\varpi _i} $	Sliding mode variables

Parameter	Value
$m/{\rm{kg}}$	1.5
$g/{\text{ (m} } \cdot { {\text{s} }^{ - 2} }{\text{)} }$	9.81
$\rho/ ({\rm{kg}} \cdot {{\rm{m}}^{ - 3} })$	1.225
${C_{D0}}$	0.05
${C_{L0}}$	0.06
$C_L^\alpha/ (^\circ )$	0.4
$S/{ {\text{m} }^2}$	0.06
${l_b}/{\rm{m} }$	0.6
${l_c}/{\rm{m} }$	0.15

Fault component	Fault signal	0 s < t < 60 s	60 s < t < 120 s	t > 120 s
Actuator fault	η_a,i1	1	0.3e^{−1.5(t − 60)} + 0.7	0.3e^{−1.5(t − 60)} + 0.7
	η_a,i2	1	0.25e^{−1.5(t − 60)} + 0.75	0.25e^{−1.5(t − 60)} + 0.75
	η_a,i3	1	0.25e^{−1.5(t − 60)} + 0.75	0.25e^{−1.5(t − 60)} + 0.75
	b_a,i1	0	−5(1 − e^{−1.5(t − 60)})	−5(1 − e^{−1.5(t − 60)})
	b_a,i2	0	0.5(1 − e^{−1.5(t − 60)})	0.5(1 − e^{−1.5(t − 60)})
	b_a,i3	0	5(1 − e^{−1.5(t − 60)})	5(1 − e^{−1.5(t − 60)})
Sensor fault	η_m,i1	1	1	0.2e^{−(t − 120)} + 0.8
	η_m,i2	1	1	0.2e^{−(t − 120)} + 0.8
	b_m,i1	0	0	5(1 − e^{−(t − 120)})
	b_m,i2	0	0	5(1 − e^{−(t − 120)})

Scenario	Signal	Parameter	Value
Planar formation	Maneuver trajectory of the dynamic target	x_0/m	600sin(0.05t − π / 2) + 8t
		y₀ /m	0
		z₀ /m	600cos(0.05t − π / 2) − 8t + 1500
		v_x0/(m·s⁻¹)	30cos(0.05t − π / 2) + 8
		v_y0/(m·s⁻¹)	0
		v_z0 /(m·s⁻¹)	−30sin(0.05t − π / 2) − 8
	The desired formation function (For UAV 1 to UAV 8)	h_xi /m	400cos(0.02t + π / 2)
		h_yi /m	50
		h_zi /m	400sin(0.02t + π / 2)
Cubic formation	Maneuver trajectory of the dynamic target	x₀ /m	1500sin(0.02t −π / 6)
		y₀/m	50 + t
		z₀/m	1500cos(0.02t − π / 6)
		v_x0/(m·s⁻¹)	30cos(0.02t − π / 6)
		v_y0/(m·s⁻¹)	1
		v_z0/(m·s⁻¹)	−30sin(0.05t − π / 6)
	The desired formation function (For UAV 1 to UAV 8)	h_xi /m	500cos[0.02t +(2i − 1)π / 4]
		h_yi /m	25 (i = 1,2,3,4); −25 (i = 5,6,7,8)
		h_zi /m	500sin[0.02t +(2i − 1)π / 4]

Two-layer formation-containment fault-tolerant control of fixed-wing UAV swarm for dynamic target tracking

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

Share this article

Figures/Tables 19

References 57

Related Articles 0

Recommended Articles

Metrics

Comments