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.
Similar content being viewed by others
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 dam** 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
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)
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)
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)
Frew, E.W., Argrow, B.: Embedded reasoning for atmospheric science using unmanned aircraft systems. In: Proceedings of the 2010 AAAI spring symposium series (2010)
Askari, A., Mortazavi, M., Talebi, H.A.: UAV formation control via the virtual structure approach. J. Aerosp. Eng. 28(1), 04014047 (2015)
Su, Z., Wang, H., Yao, P., et al.: Back-step** based anti-disturbance flight controller with preview methodology for autonomous aerial refueling. Aerosp. Sci. Technol. 61, 95–108 (2017)
Wu, J., Wang, H., Li, N., et al.: Path planning for solar-powered UAV in urban environment. Neurocomputing 275, 2055–2065 (2018)
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)
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)
Ratnoo, A., Sujit, P.B., Kothari, M.: Adaptive optimal path following for high wind flights. IFAC Proc. 44(1), 12985–12990 (2011)
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)
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)
Rysdyk, R.: Unmanned aerial vehicle path following for target observation in wind. J. Guid. Control Dyn. 29(5), 1092–1100 (2006)
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)
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)
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)
Han, J.: From PID to active disturbance rejection control. IEEE Trans. Ind. Elect. 56(3), 900–906 (2009)
Mokhtari, M.R., Braham, A.C., Cherki, B.: Extended state observer based control for coaxial-rotor UAV. ISA Trans. 61, 1–14 (2016)
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)
Ma, D., **a, 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)
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)
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)
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)
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)
Boussaïd, I., Lepagnot, J., Siarry, P.: A survey on optimization metaheuristics. Inform. Sci. 237, 82–117 (2013)
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)
Fong, S., Deb, S., Chaudhary, A.: A review of metaheuristics in robotics. Comput. Elect. Eng. 43, 278–291 (2015)
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)
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)
**ang, X., Yu, C., Zhang, Q.: Robust fuzzy 3D path following for autonomous underwater vehicle subject to uncertainties. Comput. Oper. Res. 84, 165–177 (2017)
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)
Ramli, N., Mohamad, D.: A comparative analysis of centroid methods in ranking fuzzy numbers. Eur. J. Sci. Res. 28(3), 492–501 (2009)
Dryden, H.L.: A review of the statistical theory of turbulence. Quart. Appl. Math. 1(1), 7–42 (1943)
Funding
This work was supported by the National Natural Science Foundation of China [Grant Numbers 72001173].
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no relevant financial or non-financial interests to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-022-07450-2