Research Papers

Stability and Performance Analysis of Six-Rotor Unmanned Aerial Vehicles in Wind Disturbance

[+] Author and Article Information
Xianying Li

College of Mechanical and
Electrical Engineering,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, Jiangsu, China
e-mail: lixy@nuaa.edu.cn

Biao Zhao

College of Mechanical and
Electrical Engineering,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, Jiangsu, China
e-mail: zhaobiao@nuaa.edu.cn

Yu Yao

College of Aerospace Engineering,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, Jiangsu, China
e-mail: yy503@126.com

Hongtao Wu

College of Mechanical and
Electrical Engineering,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, Jiangsu, China
e-mail: eehtwu@nuaa.edu.cn

Yunping Liu

College of information and control,
Nanjing University of
Information Science and Technology,
Nanjing 210044, Jiangsu, China
e-mail: liuyunping@nuist.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 8, 2017; final manuscript received December 2, 2017; published online January 10, 2018. Assoc. Editor: Katrin Ellermann.

J. Comput. Nonlinear Dynam 13(3), 031005 (Jan 10, 2018) (11 pages) Paper No: CND-17-1107; doi: 10.1115/1.4038776 History: Received March 08, 2017; Revised December 02, 2017

The effect of wind disturbances on the stability of six-rotor unmanned aerial vehicles (UAVs) was investigated, exploring the various disturbances in different directions. The simulation model-based Euler–Poincare equation was established to investigate the spectra of Lyapunov exponents. Next, the value of the Lyapunov exponents was used to evaluate the stability of the systems. The results obtained show that the various speeds of rotors are optimized to keep up the stability after disturbances. In addition, the flight experiment with the hitting gust has been carried out to verify the validity and accuracy of the simulation results.

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Bai, Y. Q. , Liu, H. , Shi, Z. Y. , and Zhong, Y. S. , 2012, “Robust Flight Control of Six-Rotor Unmanned Air Vehicles,” Robot, 34(5), pp. 519–524. [CrossRef]
Deittert, M. , Richards, A. , Toomer, C. A. , and Pipe, A. , 2009, “Engineless UAV Propulsion by Dynamic Soaring,” J. Guid. Control Dyn., 32(5), pp. 1446–1457. [CrossRef]
Ramsdell, J. V. , 1978, “Wind Shear Fluctuations Downwind of Large Surface Roughness Elements,” J. Appl. Meteorol., 17(4), pp. 436–443. [CrossRef]
Neumann, P. P. , and Bartholmai, M. , 2015, “Real-Time Wind Estimation on a Micro Unmanned Aerial Vehicle Using Its Inertial Measurement Unit,” Sens. Actuators, A, 235, pp. 300–310. [CrossRef]
Ding, L. , Wu, H. T. , and Yao, Y. , 2015, “Chaotic Artificial Bee Colony Algorithm for System Identification of a Small-Scale Unmanned Helicopter,” Int. J. Aerosp. Eng., 2015, pp. 1–11. [CrossRef]
Liu, C. J. , McAree, O. , and Chen, W. H. , 2013, “Path-Following Control for Small Fixed-Wing Unmanned Aerial Vehicles Under Wind Disturbances,” Int. J. Robust Nonlinear Control, 23(15), pp. 1682–1698.
Cabecinhas, D. , Cunha, R. , and Silvestre, C. , 2015, “A Globally Stabilizing Path Following Controller for Rotorcraft With Wind Disturbance Rejection,” IEEE Trans. Control Syst. Technol., 23(2), pp. 708–714. [CrossRef]
Bambang, S. , Naoki, U. , and Shigenori, S. , 2016, “Least Square Based Sliding Mode Control for a Quad-Rotor Helicopter and Energy Saving by Chattering Reduction,” Mech. Syst. Signal Process., 66–67, pp. 769–784.
Lei, X. S. , Bai, L. , Du, Y. H. , Miao, C. X. , Chen, Y. , and Wang, T. M. , 2011, “A Small Unmanned Polar Research Aerial Vehicle Based on the Composite Control Method,” Mechatronics, 21(5), pp. 821–830. [CrossRef]
Kladis, G. P. , Economou, J. T. , Knowles, K. , Lauber, J. , and Guerra, T. M. , 2011, “Energy Conservation Based Fuzzy Tracking for Unmanned Aerial Vehicle Missions Under a Priori Known Wind Information,” Eng. Appl. Artif. Intell., 24(2), pp. 278–294. [CrossRef]
Sun, Y. , and Wu, Q. , 2012, “Stability Analysis Via the Concept of Lyapunov Exponents: A Case Study in Optimal Controlled Biped Standing,” Int. J. Control, 85(12), pp. 1952–1966. [CrossRef]
Pflimlin, J. M. , Soueres, P. , and Hamel, T. , 2007, “Position Control of a Ducted Fan VTOL UAV in Crosswind,” Int. J. Control, 80(5), pp. 666–683. [CrossRef]
Islam, S. , Liu, P. X. , and Saddik, A. , 2014, “Nonlinear Adaptive Control for Quadrotor Flying Vehicle,” Nonlinear Dyn., 78(1), pp. 117–133. [CrossRef]
Liu, Y. P. , Chen, C. , Wu, H. T. , Zhang, Y. H. , and Mei, P. , 2016, “Structural Stability Analysis and Optimization of the Quadrotor Unmanned Aerial Vehicles Via the Concept of Lyapunov Exponents,” Int. J. Adv. Manuf. Technol., 86(4), pp. 1–11.
Liu, Y. P. , Li, X. Y. , Wang, T. M. , Zhang, Y. H. , and Mei, P. , 2017, “Quantitative Stability of Quadrotor Unmanned Aerial Vehicles,” Nonlinear Dyn., 87(3), pp. 1819–1833. [CrossRef]
Dingwell, J. B. , and Marin, L. C. , 2006, “Kinematic Variability and Local Dynamic Stability of Upper Body Motions When Walking at Different Speeds,” J. Biomech., 39(3), pp. 444–452. [CrossRef] [PubMed]
Yang, C. X. , and Wu, Q. , 2006, “On Stabilization of Bipedal Robots During Disturbed Standing Using the Concept of Lyapunov Exponents,” Robotica, 24(5), pp. 621–624. [CrossRef]
Yang, C. X. , and Wu, Q. , 2010, “On Stability Analysis Via Lyapunov Exponents Calculated From a Time Series Using Nonlinear Mapping—A Case Study,” Nonlinear Dyn., 59, pp. 239–257. [CrossRef]
Yang, C. X. , and Wu, Q. , 2011, “A Robust Method on Estimation of Lyapunov Exponents From a Noisy Time Series,” Nonlinear Dyn., 64(3), pp. 279–292. [CrossRef]
Ershkov, S. V. , 2014, “New Exact Solution of Euler's Equations (Rigid Body Dynamics) in the Case of Rotation Over the Fixed Point,” Arch. Appl. Mech., 84(3), pp. 385–389. [CrossRef]
Kuznetsov, N. V. , Alexeeva, T. A. , and Leonov, G. A. , 2016, “Invariance of Lyapunov Exponents and Lyapunov Dimension for Regular and Irregular Linearizations,” Nonlinear Dyn., 85(1), pp. 195–201. [CrossRef]
Levin, G. , Przytycki, F. , and Shen, W. X. , 2016, “The Lyapunov Exponent of Holomorphic Maps,” Invent. Math., 205(2), pp. 363–382. [CrossRef]
Czolczynskia, K. , Okolewskib, A. , and Okolewska, B. B. , 2017, “Lyapunov Exponents in Discrete Modelling of a Cantilever Beam Impacting on a Moving Base,” Int. J. Nonlinear Mech., 88, pp. 74–84. [CrossRef]


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Fig. 1

Schematic evolution of an initially infinitesimal two-dimensional sphere

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Fig. 2

Schematic diagram of the six-rotor UAV

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Fig. 3

Calculation process of Lyapunov exponents

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Fig. 4

Attitude curves at the hovering stage without disturbances

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Fig. 5

Attitude curves with resultant disturbance force at the hovering stage revealing the remarkable range of variation of the roll curve and the position curve of z axis

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Fig. 6

Optimized attitude curves at the hovering stage revealing a stable system with convergent curves compared to the initial attitude curve with disturbances

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Fig. 7

Energy consumption with the disturbed system and standard state of systems revealing the consumption value of disturbed systems is higher than that of standard state of systems with delay of time

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Fig. 8

Physical map of six-rotor UAVs at the hovering stage

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Fig. 9

Variation curves of rotors speed of six-rotor UAVs encountered with the unexpected gusts between 82 to 88 s

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Fig. 10

Location curves of different axis revealing the large fluctuation position between 82 to 88 s under gust disturbances: (a) x axis, (b) y axis, and (c) z axis



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