Quadrotors suspended water containers may be used for fire-fighting services. Unfortunately, the complicated dynamics in this type of system degrade the flight safety because of coupling effects among the quadrotor attitude, container swing, and liquid sloshing. However, few effects have been directed at the attitude-pendulum-sloshing dynamics in this type of aerial cranes. A novel planar model of a quadrotor carrying a liquid tank under dual-hoist mechanisms is presented. The model includes vehicle-attitude dynamics, load-swing dynamics, and fluid-sloshing dynamics. Resulting from the model, a new method is proposed to control coupled oscillations among the vehicle attitude, load swing, and fluid sloshing. Numerous simulations on the nonlinear model demonstrate that the control method can reduce the undesirable oscillations, stabilize the quadrotor’s attitude, and reject the external disturbances. The theoretical findings may also extend to the three-dimensional dynamics of quadrotors slung liquid tanks, and other types of aerial vehicles transporting liquid containers including helicopters or tiltrotors.
DongWDingYYangL, et al.An efficient approach for stability analysis and parameter tuning in delayed feedback control of a flying robot carrying a suspended load. J Dyn Syst Meas Control2019; 141(8): 081015.
2.
GodboleARSubbaraoK. Nonlinear control of unmanned aerial vehicles with cable suspended payloads. Aerosp Sci Technol2019; 93: 105299.
3.
YuGCabecinhasDCunhaR, et al.Nonlinear backstepping control of a quadrotor-slung load system. IEEE/ASME Trans Mechatron2019; 24(5): 2304–2315.
4.
BinXWangSYangS. Nonlinear adaptive control for an unmanned aerial payload transportation system: theory and experimental validation. Nonlinear Dyn2019; 98: 1745–1760.
5.
LiangXFangYSunN, et al.Adaptive nonlinear hierarchical control for a rotorcraft transporting a cable-suspended payload. IEEE Trans Syst Man, Cybern Syst2021; 51: 4171–4182. DOI: 10.1109/TSMC.2019.2931812.
6.
BarikbinBFakharianA. Trajectory tracking for quadcopter UAV transporting cable-suspended payload in wind presence. Trans Inst Meas Control2019; 41(5): 1243–1255.
7.
QianLLiuH. Path following control of a quadcopter UAV with a cable suspended payload under wind disturbances. IEEE Trans Ind Electron2019; 67(3): 2021–2029.
8.
CabecinhasDCunhaRSilvestreC. A trajectory tracking control law for a quadrotor with slung load. Automatica2019; 106: 384–389.
9.
OgunbodedeOYoshinagaRSinghT. Vibration Control of Unmanned Aerial Vehicle with Suspended Load Using the Concept of Differential Flatness. Philadelphia, USA: American Control Conference, 2019, pp. 4268–4273.
10.
FieldingSNahonM. Input Shaped Trajectory Generation and Controller Design for a Quadrotor-Slung Load System. Atlanta, USA: International Conference on Unmanned Aircraft Systems, 2019, pp. 162–170.
11.
de MoraisMLopezAMartinsJ, et al.Equivalent mechanical model of rectangular container attached to a pendulum compared to experimental data and analytical solution. J Braz Soc Mech Sci Eng2020; 42: 143.
12.
AlshayaAAlghanimK. Command shaping for sloshing suppression of a suspended liquid container. J Dyn Syst Meas Control2020; 142: 121003.
13.
KhorshidEAl-FadhliA. Optimal command shaping design for a liquid slosh suppression in overhead crane systems. J Dyn Syst Meas Control2021; 143: 021005.
GoudarziMDaneshP. Numerical investigation of a vertically baffled rectangular tank under seismic excitation. J Fluids Struct2016; 61: 450–460.
16.
HasheminejadSMohammadiMJamalpoorA. Hydroelastic modeling and active control of transient sloshing in a three dimensional rectangular floating roof tank. J Sound Vib2020; 470: 115146.
17.
YanoKTerashimaK. Robust liquid container transfer control for complete sloshing suppression. IEEE Trans Control Syst Technol2001; 9(3): 483–493.
18.
Sira-RamirezHFliessM. A Flatness Based Generalized PI Control Approach to Liquid Sloshing Regulation in a Moving Container. Anchorage, AK, USA: American Control Conference, 2002, pp. 2909–2914.
ThakarPTrivediPBandyopadhyayB, et al.A new nonlinear control for asymptotic stabilization of a class of underactuated systems: an implementation to slosh-container problem. IEEE/ASME Trans Mechatron2017; 22(2): 1082–1092.
21.
KonopkaMDe RoseFStrauchH, et al.Active slosh control and damping – Simulation and experiment. Acta Astronautica2020; 158: 89–102.
22.
CoulterNMoncayoH. Comparison of optimal and bioinspired adaptive control laws for spacecraft sloshing dynamics. J Spacecr Rockets2020; 57(1): 12–32.
23.
NavabiMDavoodiAReyhanogluM. Optimum fuzzy sliding mode control of fuel sloshing in a spacecraft using PSO algorithm. Acta Astronautica2020; 167: 331–342.
24.
Al-MashhadaniM. Modeling and adaptive robust wavelet control for a liquid container system under slosh and uncertainty. Meas Control2020; 53(9–10): 1643–1653.
25.
NavabiMDavoodiAReyhanogluM. Modeling and control of a nonlinear coupled spacecraft-fuel system. Acta Astronautica2019; 162: 436–446.
26.
PridgenBBaiKSinghoseW. Shaping container motion for multimode and robust slosh suppression. J Spacecr Rockets2013; 50(2): 440–448.
27.
YueBZhuL. Hybrid control of liquid-filled spacecraft maneuvers by dynamic inversion and input shaping. AIAA J2014; 52(3): 618–626.
28.
ZangQHuangJ. Dynamics and control of three-dimensional slosh in a moving rectangular liquid container undergoing planar excitations. IEEE Trans Ind Electron2015; 62(4): 2309–2318.
29.
ZangQHuangJLiangZ. Slosh suppression for infinite modes in a moving liquid container. IEEE/ASME Trans Mechatron2015; 20(1): 217–225.
30.
HuangJZhaoX. Control of three-dimensional nonlinear slosh in moving rectangular containers. Trans ASME - J Dyn Syst Meas Control2018; 140(8): 081016.
31.
XingBHuangJ. Control of pendulum-sloshing dynamics in suspended liquid containers. IEEE Trans Ind Electron2021; 68(6): 5146–5154.
32.
SayyaadiHSoltaniA. Modeling and control for cooperative transport of a slung fluid container using quadrotors. Chin J Aeronaut2018; 31(2): 262–272.
33.
WangZQiJWuC, et al.Control of Quadrotor Slung Load System Based on Double ADRC, Chinese Control Conference. China: Shenyang, 2020, pp. 6810–6815.
34.
GengJLangelaanJ. Implementation and Demonstration of Coordinated Transport of a Slung Load by a Team of Rotorcraft. San Diego, CA: AIAA Scitech Forum, 2019, pp. 1–19.
35.
AbdelmaksoudSMailahMAbdallahA. Control strategies and novel techniques for autonomous rotorcraft unmanned aerial vehicles: a review. IEEE Access2020; 8: 195142–195169.
36.
NavabiMDavoodiAMirzaeiH. Trajectory tracking of under-actuated quadcopter using Lyapunov-based optimum adaptive controller. Proc Inst Mech Eng G: J Aerosp Eng2022; 236(1): 202–215, doi:10.1177/09544100211010852, https://doi.org/10.1177/09544100211010852.
37.
DhadekarDTaloleS. Robust fault-tolerant flight control of quadrotor against faults in multiple motors. Proc Inst Mech Eng Part G: J Aerosp Eng2021; 235(16): 2504–2516, doi:10.1177/0954410021999547, https://doi.org/10.1177/0954410021999547.
38.
ZahedMFieldsT. Evaluation of pilot and quadcopter performance from open-loop mission-oriented flight testing. Proc Inst Mech Eng Part G: J Aerosp Eng2021; 235(13): 1817–1830, doi:10.1177/0954410020985987, https://doi.org/10.1177/0954410020985987.
39.
ChenASunMWangZ, et al. Attitude trajectory tracking of quadrotor UAV using super-twisting observer-based adaptive controller. Proc Inst Mech Eng Part G: J Aerosp Eng2021; 235(10): 1146–1157, doi:10.1177/0954410020966476, https://doi.org/10.1177/0954410020966476.
40.
WuYLiHSuX. A path planning model of a tiltrotor for approaching an aircraft carrier during landing. Proc Inst Mech Eng Part G: J Aerosp Eng2021; 235(16): 2392–2406, doi:10.1177/0954410021996491, https://doi.org/10.1177/0954410021996491.
41.
DuanDWangZLiJ, et al. Stabilization control for unmanned helicopter-slung load system based on active disturbance rejection control and improved sliding mode control. Proc Inst Mech Eng Part G: J Aerosp Eng2021; 235(13): 1803–1816, doi:10.1177/0954410020985157, https://doi.org/10.1177/0954410020985157.
42.
KaneTLikinsPLevinsonD. Spacecraft Dynamics. ]Ithaca, NY, USA: The Internet-First University Press, 2005.
43.
TylerJ. Characteristics of model-following systems as synthesized by optimal control. IEEE Trans Automat Contr1964; 9(4): 485–498.
44.
AdamsCPotterJSinghoseW. Input-shaping and model-following control of a helicopter carrying a suspended load. J Guid Control Dyn2015; 38(1): 94–105.
