This paper investigates a formation control strategy for multiple quadrotor unmanned aerial vehicles (QUAVs). The formation communication topology is first modeled using graph theory, and the dynamics of an individual QUAV are derived based on the Newton–Euler formulation. A multi-QUAV formation model is then established within a leader–follower framework. To address the dual challenges of lumped internal disturbances and time-varying environmental perturbations, a control scheme integrating fast non-singular terminal sliding mode control (FNTSMC) with a radial basis function neural network (RBFNN) is proposed. The RBFNN compensates for system uncertainties in real time, while a novel continuous sliding surface is designed to ensure finite-time convergence and reduce chattering, thereby enhancing formation responsiveness. The stability of the closed-loop system is rigorously demonstrated through Lyapunov analysis. Numerical simulations verify that the proposed control strategy reduces the root mean square error (RMSE) of the overall formation tracking error by more than 90%, with the disturbance estimation error being less than 5%. It can achieve high-precision formation control under both mixed wind and rectangular wind disturbances.
SunYXiaKZouY, et al. Distributed output-feedback formation tracking control for clustered quadrotors. IEEE Trans Aerosp Electron Syst2022; 58(3): 1894–1905.
2.
NigamNBieniawskiSKrooI, et al. Control of multiple UAVs for persistent surveillance: algorithm and flight test results. IEEE Trans Control Syst Technol2012; 20(5): 1236–1251.
3.
ChenY-JChangD-KZhangC. Autonomous tracking using a swarm of UAVs: a constrained multi-agent reinforcement learning approach. IEEE Trans Vehicular Technol2020; 69(11): 13702–13717.
4.
ZhangBSunXLiuS, et al. Event-triggered adaptive fault-tolerant synchronization tracking control for multiple 6-DOF fixed-wing uavs. IEEE Trans Vehicular Technol2022; 71(1): 148–161.
5.
ChoiY-CAhnHS. Nonlinear control of quadrotor for point tracking: actual implementation and experimental tests. IEEE/ASME Trans Mechatron2015; 20(3): 1179–1192.
6.
ChenFJiangRZhangK, et al. Robust backstepping sliding mode control and observer-based fault estimation for a quadrotor UAV. IEEE Trans Ind Electron2016; 63(8): 5044–5056.
7.
WangZZouYLiuY, et al. Distributed control algorithm for leader–follower formation tracking of multiple quadrotors: theory and experiment. IEEE/ASME Trans Mechatron2021; 26(2): 1095–1105.
8.
ZhaoZRenYMuC, et al. Adaptive neural-network-based fault-tolerant control for a flexible string with composite disturbance observer and input constraints. IEEE Trans Cybern2022; 52(12): 12843–12853.
9.
WeiLChenM. Distributed DETMs-based internal collision avoidance control for UAV formation with lumped disturbances. Appl Math Comput2022; 433: 127362.
10.
LiXQinHLiL. Fixed-time formation control for AUVs with unknown actuator faults based on lumped disturbance observer. Ocean Eng2023; 269: 113495.
11.
AydemirMArıkanKB. Evaluation of the disturbance rejection performance of an aerial manipulator. J Intell Robot Syst2020; 97: 451–469.
LiangJChenYLaiN, et al. Low-complexity prescribed performance control for unmanned aerial manipulator robot system under model uncertainty and unknown disturbances. IEEE Trans Ind Inform2022; 18(7): 4632–4641.
14.
ChenYLiangJWuY, et al. Adaptive sliding-mode disturbance observer-based finite-time control for unmanned aerial manipulator with prescribed performance. IEEE Trans Cybern2023; 53(5): 3263–3276.
15.
ShenLMaoPFangQ, et al. Nonsingular global fast terminal sliding mode control with extended state observer for contact force regulation in aerial manipulator. Int J Aerosp Eng2022; 2022: 1–20.
16.
DingLYaoYMaR. Observer-based control for a cable-driven aerial manipulator under lumped disturbances. Comput Model Eng Sci2023; 135(2): 1539–1558.
17.
YangSBaiWLiT, et al. Neural-network-based formation control with collision, obstacle avoidance and connectivity maintenance for a class of second-order nonlinear multi-agent systems. Neurocomputing2021; 439: 243–255.
18.
ShojaeiK. Neural network formation control of underactuated autonomous underwater vehicles with saturating actuators. Neurocomputing2016; 194: 372–384.
19.
KuoCWTsaiCCLeeCT. Intelligent leader-following consensus formation control using recurrent neural networks for small-size unmanned helicopters. IEEE Trans Syst Man Cybern Syst2021; 51(2): 1288–1301.
20.
HartmanEJKeelerJDKowalskiJM. Layered neural networks with Gaussian hidden units as universal approximations. Neural Comput1990; 2(2): 210–215.
21.
GaoTHuangJZhouY, et al. Robust adaptive tracking control of an underactuated ship with guaranteed transient performance. Int J Syst Sci2017; 48(2): 272–279.
22.
JiaZHuZZhangW. Adaptive output-feedback control with prescribed performance for trajectory tracking of underactuated surface vessels. ISA Trans2019; 95: 18–26.
23.
ZhuGDuJ. Global robust adaptive trajectory tracking control for surface ships under input saturation. IEEE J Oceanic Eng2020; 45(2): 442–450.
24.
KaminskiWStrumilloP. Kernel orthonormalization in radial basis function neural networks. IEEE Trans Neural Netw1997; 8(5): 1177–1183.
25.
YuHReinerPDXieT, et al. An incremental design of radial basis function networks. IEEE Trans Neural Netw Learn Syst2014; 25(10): 1793–1803.
PanchapakesanCPalaniswamiMRalphD, et al. Effects of moving the center’s in an RBF network. IEEE Trans Neural Netw2002; 13(6): 1299–1307.
28.
BruzzoneLPrietoDF. A technique for the selection of kernel-function parameters in RBF neural networks for classification of remote-sensing images. IEEE Trans Geosci Remote Sens1999; 37(2): 1179–1184.
29.
MaoKZHuangGB. Neuron selection for RBF neural network classifier based on data structure preserving criterion. IEEE Trans Neural Netw2005; 16(6): 1531–1540.
30.
BorsAGPitasI. Median radial basis function neural network. IEEE Trans Neural Netw1996; 7(6): 1351–1364.
31.
XieTYuHHewlettJ, et al. Fast and efficient second-order method for training radial basis function networks. IEEE Trans Neural Netw Learn Syst2012; 23(4): 609–619.
32.
OyangYJHwangSCOuYY, et al. Data classification with radial basis function networks based on a novel kernel density estimation algorithm. IEEE Trans Neural Netw2005; 16(1): 225–236.
33.
HuJZhangHLiuH, et al. A survey on sliding mode control for networked control systems. Int J Syst Sci2021; 52(6): 1129–1147.
34.
BrogliatoBPolyakovA. Digital implementation of sliding-mode control via the implicit method: a tutorial. Int J Robust Nonlinear Control2021; 31(9): 3528–3586.
35.
GambhireSJKishoreDRLondhePS, et al. Review of sliding mode based control techniques for control system applications. Int J Dyn Control2021; 9(1): 363–378.
36.
ShtesselYPlestanFEdwardsC, et al. Adaptive sliding mode and higher order sliding-mode control techniques with applications: a survey. In: OliveiraTRFridmanLHsuL (eds.) Sliding-mode control and variable-structure systems: the state of the art. Springer International Publishing, 2023, pp. 267–305.
37.
RodriguesVHPHsuLOliveiraTR, et al. Adaptive sliding mode control with guaranteed performance based on monitoring and barrier functions. Int J Adapt Control Signal Process2022; 36(6): 1252–1271.
38.
GedefawEAAbdissaCMLemmaLN. An improved trajectory tracking control of quadcopter using a novel sliding mode control with fuzzy PID surface. PLoS One2024; 19(11): e0308997.
39.
AberaNBAbdissaCMLemmaLN. An improved nonsingular adaptive super twisting sliding mode controller for quadcopter. PLoS One2024; 19(10): e0309098.
40.
YaresheFTMadeboNWAbdissaCM, et al. Trajectory tracking of fixed-wing uav using anfis-based sliding mode controller. IEEE Access2025; 13: 61986–62003.
41.
DongHYangXGaoH, et al. Practical terminal sliding-mode control and its applications in servo systems. IEEE Trans Ind Electron2023; 70(1): 752–761.
42.
Cruz-OrtizDChairezIPoznyakA. Non-singular terminal sliding-mode control for a manipulator robot using a barrier Lyapunov function. ISA Trans2022; 121: 268–283.
43.
YangLYangJ. Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems. Int J Robust Nonlinear Control2011; 21(16): 1865–1879.
44.
ZhangHLewisFL. Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics. Automatica2012; 48(7): 1432–1439.
45.
DongWGuGYZhuX, et al. High-performance trajectory tracking control of a quadrotor with disturbance observer. Sens Actuators A Phys2014; 211: 67–77.
46.
JiRLiDMaJ. Adaptive second-order fast nonsingular terminal sliding mode control for a tilting quadcopter. In: 2022 13th Asian control conference (ASCC), 2022, pp. 403-408. IEEE.
47.
BouabdallahSMurrieriPSiegwartR. Design and control of an indoor micro quadrotor. In: IEEE international conference on robotics and automation, 2004. Proceedings. ICRA’04, 2004, vol. 5. IEEE.
48.
XiongJPanJChenG, et al. Sliding mode dual-channel disturbance rejection attitude control for a quadrotor. IEEE Trans Ind Electron2022; 69(10): 10489–10499.
49.
NarendraKSAnnaswamyAM. Persistent excitation in adaptive systems. Int J Control1987; 45: 127–160.
50.
BuiDNVan NguyenTTPhungMD. Lyapunov-based nonlinear model predictive control for attitude trajectory tracking of unmanned aerial vehicles. Int J Aeronaut Space Sci2023; 24(2): 502–513.
51.
GuoKShiPWangP, et al. Non-singular terminal sliding mode controller with nonlinear disturbance observer for robotic manipulator. Electronics2023; 12(4): 849.
52.
AhmadILiaquatMMalikFM, et al. Variants of the sliding mode control in presence of external disturbance for quadrotor. IEEE Access2020; 8: 227810–227824.
53.
WangBHWangDBAliZA, et al. An overview of various kinds of wind effects on unmanned aerial vehicle. Meas Control2019; 52(7–8): 731–739.
