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Path following control for miniature fixed-wing unmanned aerial vehicles under uncertainties and disturbances: a two-layered framework

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Abstract

This study presents a solution to the path following control problem for miniature fixed-wing unmanned aerial vehicles (MAVs) in the presence of inaccuracy modeling parameters and environmental disturbances. We introduce a two-layered framework to combine the guidance level with the control level. A modified vector field-based path following methodology is proposed in the kinematics phase to track a Dubins path with a straight line and circular segments. Subsequently, a proportional integral derivative (PID) controller based on feedback linearization and gain scheduling techniques are designed such that the MAV can reject nonlinear dynamics, system uncertainties, and disturbances using a robust fuzzy control scheme. Eventually, using a comparison test with control effort and track error as assessment metrics, the practicality of the framework and the outperformance of the proposed algorithm are well demonstrated.

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Data availability

The datasets generated and/or analyzed in this study are available from the corresponding author on request.

Abbreviations

3D:

Three-dimensional

UAS:

Unmanned aerial system

UAV:

Unmanned aerial vehicle

MAV:

Miniature fixed wing unmanned aerial vehicle

AD:

Airflow disturbance

LQR:

Linear quadratic regulator

PID:

Proportional-integral-derivation

VF:

Vector fields

NB:

Negative large

NS:

Negative small

NLGL:

Nonlinear guidance law

PLOS:

Pursuit with line of sight

\({\scriptstyle{F}^i}\) :

Inertial coordinate system

\({\scriptstyle{F}^b}\) :

Body coordinate system

\({\scriptstyle{F}^g}\) :

Path coordinate system

\({{\mathbf{F}}^p}\) :

Path error coordinate system

\({\left( {{{\dot p}_n},{{\dot p}_e},{{\dot p}_d}} \right)^{\text{T}}}\) :

Location vector of the MAV in \({\scriptstyle{F}^i}\)

\({\left( {u,v,w} \right)^{\text{T}}}\) :

Velocity vector of the MAV in \({\scriptstyle{F}^b}\)

\(\ell ({u_F},{u_T})\), \(\ell ({v_F},{v_T})\), \(\ell ({w_F},{w_T})\) :

Control forces on MAV

\(\ell ({p_F},{p_T})\),\(\ell ({q_F},{q_T})\), \(\ell ({r_F},{r_T})\) :

Control torques on MAV

\({n_{11}}\)−\({n_{66}}\) :

Hydrodynamic derivatives of MAV’s model

\({d_{11}}\)−\({d_{66}}\) :

Hydrodynamic damping effects on MAV

\({F_l}\) :

Magnitude of the lift force on MAV

\(v\) :

Magnitude of the velocity of MAV

\(R\) :

Instantaneous turning radius of the MAV

\({\mathbf{q}}\) :

Direction of \({\scriptstyle{P}_{{\text{sl}}}}\left( {{\mathbf{r}},{\mathbf{q}}} \right)\)

\({\chi_q}\) :

Heading angle of \({\scriptstyle{P}_{{\text{sl}}}}\left( {{\mathbf{r}},{\mathbf{q}}} \right)\)

\({{\mathbf{e}}_p}\) :

The path error in \({{\mathbf{F}}^p}\)

\({\mathbf{c}} = {\left( {{c_n},{c_e},{c_d}} \right)^T}\) :

Center location of \({\scriptstyle{P}_{{\text{arc}}}}\)

\(\lambda \) :

Rotation direction of \({\scriptstyle{P}_{{\text{arc}}}}\)

\(d\) :

Distance between \({\mathbf{c}}\) and MAV’s center of mass

\({k_{{\text{orbit}}}}\) :

Constant related to \({\scriptstyle{P}_{{\text{arc}}}}\)

\({d_\chi }\) :

Type of system disturbance

\({h_{{\text{hold}}}}\), \({h_{{\text{takeoff}}}}\) :

Altitude control command

\({V_a}\) :

Airspeed of MAV

\(\xi \) :

Comprehensive score of algorithm

\(\Gamma \) :

Weight value

\(\Delta {k_{p*}}({e_*}{\dot e_*})\), \(\Delta {k_{i*}}({e_*}{\dot e_*})\), \(\Delta {k_{d*}}({e_*}{\dot e_*})\) :

Adaptive incremental gains \(\Delta {k_{i*}}({e_*}{\dot e_*})\)

\({\mathbf{P}}\) :

Instructive trajectory

\(p\) :

Virtual reference point

\({{\varvec{\upvarepsilon}}} = {\left\{ {{x_g},{y_g},{z_g}} \right\}^{\text{T}}}\) :

Path following error in \({\scriptstyle{F}^g}\)

\({x_g}\) :

Directional-track error

\({y_g}\) :

Lateral-track error

\({z_g}\) :

Altitudinal-track error

\([{x_p},{y_p},{z_p}]\) :

Instructive path

\(\left[ {\chi ,{h_d},{v_a}} \right]\) :

Heading, altitude, and velocity command

\(\dot \chi \) :

Change rate of heading angle

\(\omega \) :

Magnitude of heading angular velocity of MAV

\({\scriptstyle{P}_{{\text{sl}}}}\left( {{\mathbf{r}},{\mathbf{q}}} \right)\) :

Straight-line path

\({\mathbf{r}}\) :

Starting point of \({\scriptstyle{P}_{{\text{sl}}}}\left( {{\mathbf{r}},{\mathbf{q}}} \right)\)

\(\left( {{q_n},{q_e},{q_d}} \right)\) :

Components in north, east, and down directions

\(\scriptstyle{R}_i^P\) :

Conversion matrix

\({k_{{\text{path}}}}\) :

Constant related to curvature of \({\scriptstyle{P}_{{\text{sl}}}}\left( {{\mathbf{r}},{\mathbf{q}}} \right)\)

\({\scriptstyle{P}_{{\text{arc}}}}\) :

Arc path

\(\rho \) :

Radius of \({\scriptstyle{P}_{{\text{arc}}}}\)

\({h^c}\) :

Altitude command to track \({\scriptstyle{P}_{{\text{arc}}}}\)

\(\varphi \) :

Phase angle of \({\scriptstyle{P}_{{\text{arc}}}}\)

\({k_\rho }\) :

Constant adjustment parameter

\({k_{p_\phi }}\), \({k_{i_\phi }}\), \({k_{d_\phi }}\) :

Parameters of PID controller

\({{\mathbf{e}}_{{\text{con}}}}\) :

Path following error in \({\scriptstyle{F}^i}\)

\(Tc\) :

Total control consumption

\(Te\) :

Total error

\(\bar Tc\), \(\bar Te\) :

Mean value of \(Tc\), \(Te\)

References

  1. Maza, I., Caballero, F., Capitán, J., et al.: Experimental results in multi-UAV coordination for disaster management and civil security applications. J. Intell. Robot. Syst. 61(1), 563–585 (2011)

    Article  Google Scholar 

  2. Schmale Iii, D.G., Dingus, B.R., Reinholtz, C.: Development and application of an autonomous unmanned aerial vehicle for precise aerobiological sampling above agricultural fields. J. Field Robot. 25(3), 133–147 (2008)

    Article  Google Scholar 

  3. Sujit, P.B., Kingston, D., Beard, R.: Cooperative forest fire monitoring using multiple UAVs. In: Proceedings of the 2007 46th IEEE conference on decision and control. IEEE, pp 4875–4880 (2007)

  4. Frew, E.W., Argrow, B.: Embedded reasoning for atmospheric science using unmanned aircraft systems. In: Proceedings of the 2010 AAAI spring symposium series (2010)

  5. Askari, A., Mortazavi, M., Talebi, H.A.: UAV formation control via the virtual structure approach. J. Aerosp. Eng. 28(1), 04014047 (2015)

    Article  Google Scholar 

  6. Su, Z., Wang, H., Yao, P., et al.: Back-stepping based anti-disturbance flight controller with preview methodology for autonomous aerial refueling. Aerosp. Sci. Technol. 61, 95–108 (2017)

    Article  Google Scholar 

  7. Wu, J., Wang, H., Li, N., et al.: Path planning for solar-powered UAV in urban environment. Neurocomputing 275, 2055–2065 (2018)

    Article  Google Scholar 

  8. Muniraj, D., Palframan, M.C., Guthrie, K.T., et al.: Path-following control of small fixed-wing unmanned aircraft systems with H∞ type performance. Control Eng. Pract. 67, 76–91 (2017)

    Article  Google Scholar 

  9. Wang, B., Dong, X., Chen, B.M.: Cascaded control of 3D path following for an unmanned helicopter. In: Proceedings of the 2010 IEEE conference on cybernetics and intelligent systems. IEEE, pp 70–75 (2010)

  10. Ratnoo, A., Sujit, P.B., Kothari, M.: Adaptive optimal path following for high wind flights. IFAC Proc. 44(1), 12985–12990 (2011)

    Google Scholar 

  11. Healey, A.J., Lienard, D.: Multivariable sliding mode control for autonomous diving and steering of unmanned underwater vehicles. IEEE J. Ocean. Eng. 18(3), 327–339 (1993)

    Article  Google Scholar 

  12. Li, Z., Sun, J., Oh, S.: Design, analysis and experimental validation of a robust nonlinear path following controller for marine surface vessels. Automatica 45(7), 1649–1658 (2009)

    Article  MathSciNet  Google Scholar 

  13. Rysdyk, R.: Unmanned aerial vehicle path following for target observation in wind. J. Guid. Control Dyn. 29(5), 1092–1100 (2006)

    Article  Google Scholar 

  14. Hota, S., Ghose, D.: A modified Dubins method for optimal path planning of a miniature air vehicle converging to a straight line path. In: Proceedings of the American control conference. IEEE, pp 2397–2402 (2009)

  15. Nelson, D.R., Barber, D.B., McLain, T.W., et al.: Vector field path following for miniature air vehicles. IEEE Trans. Robot. 23(3), 519–529 (2007)

    Article  Google Scholar 

  16. Sujit, P.B., Saripalli, S., Sousa, J.B.: Unmanned aerial vehicle path following: A survey and analysis of algorithms for fixed-wing unmanned aerial vehicless. IEEE Control Syst. Mag. 34(1), 42–59 (2014)

    Article  MathSciNet  Google Scholar 

  17. Han, J.: From PID to active disturbance rejection control. IEEE Trans. Ind. Elect. 56(3), 900–906 (2009)

    Article  Google Scholar 

  18. Mokhtari, M.R., Braham, A.C., Cherki, B.: Extended state observer based control for coaxial-rotor UAV. ISA Trans. 61, 1–14 (2016)

    Article  Google Scholar 

  19. Shao, X., Wang, H., Zhang, H.P.: Enhanced trajectory linearization control based advanced guidance and control for hypersonic re-entry vehicle with multiple disturbances. Aerosp. Sci. Technol. 46, 523–536 (2015)

    Article  Google Scholar 

  20. Ma, D., Xia, Y., Li, T., et al.: Active disturbance rejection and predictive control strategy for a quadrotor helicopter. IET Control Theory Appl. 10(17), 2213–2222 (2016)

    Article  MathSciNet  Google Scholar 

  21. Son, Y.I., Kim, I.H., Choi, D.S., et al.: Robust cascade control of electric motor drives using dual reduced-order PI observer. IEEE Trans. Ind. Elect. 62(6), 3672–3682 (2014)

    Google Scholar 

  22. Kim, S.K.: Offset-free one-step ahead state predictor for power electronic applications using robust proportional–integral observer. IEEE Trans. Ind. Elect. 63(3), 1763–1770 (2015)

    Article  Google Scholar 

  23. Zhu, D., Hua, X., Sun, B.: A neurodynamics control strategy for real-time tracking control of autonomous underwater vehicles. J. Navig. 67(1), 113–127 (2014)

    Article  Google Scholar 

  24. Edison, E., Shima, T.: Integrated task assignment and path optimization for cooperating uninhabited aerial vehicles using genetic algorithms. Comput. Oper. Res. 38(1), 340–356 (2011)

    Article  MathSciNet  Google Scholar 

  25. Boussaïd, I., Lepagnot, J., Siarry, P.: A survey on optimization metaheuristics. Inform. Sci. 237, 82–117 (2013)

    Article  MathSciNet  Google Scholar 

  26. Kar, S., Das, S., Ghosh, P.K.: Applications of neuro fuzzy systems: a brief review and future outline. Appl. Soft Comput. 15, 243–259 (2014)

    Article  Google Scholar 

  27. Fong, S., Deb, S., Chaudhary, A.: A review of metaheuristics in robotics. Comput. Elect. Eng. 43, 278–291 (2015)

    Article  Google Scholar 

  28. Sáez, D., Cortés, C.E., Núñez, A.: Hybrid adaptive predictive control for the multi-vehicle dynamic pick-up and delivery problem based on genetic algorithms and fuzzy clustering. Comput. Oper. Res. 35(11), 3412–3438 (2008)

    Article  Google Scholar 

  29. Khodayari, M.H., Balochian, S.: Modeling and control of autonomous underwater vehicle (AUV) in heading and depth attitude via self-adaptive fuzzy PID controller. J. Mar. Sci. Technol. 20(3), 559–578 (2015)

    Article  Google Scholar 

  30. Xiang, X., Yu, C., Zhang, Q.: Robust fuzzy 3D path following for autonomous underwater vehicle subject to uncertainties. Comput. Oper. Res. 84, 165–177 (2017)

    Article  MathSciNet  Google Scholar 

  31. Labbadi, M., Cherkaoui, M.: Adaptive fractional-order nonsingular fast terminal sliding mode based robust tracking control of quadrotor UAV with Gaussian random disturbances and uncertainties. IEEE Trans. Aerosp. Elect. Syst. 57(4), 2265–2277 (2021)

    Article  Google Scholar 

  32. Ramli, N., Mohamad, D.: A comparative analysis of centroid methods in ranking fuzzy numbers. Eur. J. Sci. Res. 28(3), 492–501 (2009)

    Google Scholar 

  33. Dryden, H.L.: A review of the statistical theory of turbulence. Quart. Appl. Math. 1(1), 7–42 (1943)

    Article  MathSciNet  Google Scholar 

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Funding

This work was supported by the National Natural Science Foundation of China [Grant Numbers 72001173].

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Authors and Affiliations

  1. School of Astronautics, Northwestern Polytechnical University, 127 Youyi West Road, Xian, 710072, ShaanXi, China

    Weinan Wu, Yao Wang, Chunlin Gong & Dan Ma

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  1. Weinan Wu
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  2. Yao Wang
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Correspondence to Chunlin Gong.

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Wu, W., Wang, Y., Gong, C. et al. Path following control for miniature fixed-wing unmanned aerial vehicles under uncertainties and disturbances: a two-layered framework. Nonlinear Dyn 108, 3761–3781 (2022). https://doi.org/10.1007/s11071-022-07450-2

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