Skip to main content
Log in

Image-based finite-time visual servoing of a quadrotor for tracking a moving target

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper proposes an image-based visual servoing control method for a moving target of a quadrotor UAV (QUAV). Firstly, the dynamic image model with moving target parameters is established based on the image moment features in the virtual camera plane. For the unpredictability of the moving target in space, we use a high-order differentiator to estimate the state parameters of the moving target. In order to solve the problem of image depth information caused by a monocular camera, we derive a nonlinear finite-time linear velocity observer from the virtual image plane, which can not only estimate the linear velocity information of QUAV but also avoid the measurement of image depth. Based on the above information, we design the global finite-time controller and use Lyapunov theory to prove the finite-time stability of the system. Finally, the numerical simulations verify the convergence of the proposed control scheme, and the ROS gazebo simulations demonstrate the improved performance of the proposed control scheme in tracking error.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Data availability

All data are available upon request at the authors’ email address.

References

  1. Shao, X., Wang, L., Li, J., Liu, J.: High-order eso based output feedback dynamic surface control for quadrotors under position constraints and uncertainties. Aerosp. Sci. Technol. 89, 288–298 (2019)

    Article  Google Scholar 

  2. Guerreiro, B.J., Silvestre, C., Cunha, R., Cabecinhas, D.: Lidar-based control of autonomous rotorcraft for the inspection of pierlike structures. IEEE Trans. Control Syst. Technol. 26(4), 1430–1438 (2017)

    Article  Google Scholar 

  3. Guerrero-Sánchez, M.E., Mercado-Ravell, D.A., Lozano, R., García-Beltrán, C.D.: Swing-attenuation for a quadrotor transporting a cable-suspended payload. ISA Trans. 68, 433–449 (2017)

    Article  Google Scholar 

  4. Tomic, T., Schmid, K., Lutz, P., Domel, A., Kassecker, M., Mair, E., Grixa, I.L., Ruess, F., Suppa, M., Burschka, D.: Toward a fully autonomous uav: research platform for indoor and outdoor urban search and rescue. IEEE Robot. Autom. Mag. 19(3), 46–56 (2012)

    Article  Google Scholar 

  5. Sani, M.F., Shoaran, M., Karimian, G.: Automatic landing of a low-cost quadrotor using monocular vision and Kalman filter in gps-denied environments. Turk. J. Electr. Eng. Comput. Sci. 27(3), 1821–1838 (2019)

  6. Chen, J., Liu, T., Shen, S.: Tracking a moving target in cluttered environments using a quadrotor. In: 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 446–453. IEEE (2016)

  7. Beyeler, A., Zufferey, J.-C., Floreano, D.: Vision-based control of near-obstacle flight. Auton. Robot. 27(3), 201–219 (2009)

    Article  Google Scholar 

  8. Chaumette, F., Hutchinson, S.: Visual servo control. i. Basic approaches. IEEE Roboti. Autom. Mag. 13(4), 82–90 (2006)

    Article  Google Scholar 

  9. Guenard, N., Hamel, T., Mahony, R.: A practical visual servo control for an unmanned aerial vehicle. IEEE Trans. Rob. 24(2), 331–340 (2008)

    Article  Google Scholar 

  10. Yesildirek, A., Imran, B.: Nonlinear control of quadrotor using multi lyapunov functions. In: 2014 American Control Conference, pp. 3844–3849. IEEE (2014)

  11. Lee, D., Lim, H., Kim, H.J., Kim, Y., Seong, K.J.: Adaptive image-based visual servoing for an underactuated quadrotor system. J. Guid. Control. Dyn. 35(4), 1335–1353 (2012)

    Article  Google Scholar 

  12. Chaumette, F.: Image moments: a general and useful set of features for visual servoing. IEEE Trans. Rob. 20(4), 713–723 (2004). https://doi.org/10.1109/TRO.2004.829463

    Article  Google Scholar 

  13. Tahri, O., Chaumette, F.: Point-based and region-based image moments for visual servoing of planar objects. IEEE Trans. Robot. 21(6), 1116–1127 (2005). https://doi.org/10.1109/TRO.2005.853500

    Article  Google Scholar 

  14. Jabbari, H., Oriolo, G., Bolandi, H.: An adaptive scheme for image-based visual servoing of an underactuated uav. Int. J. Robot. Autom. 29(1), 92–104 (2014)

    Google Scholar 

  15. Xie, H., Lynch, A.F.: State transformation-based dynamic visual servoing for an unmanned aerial vehicle. Int. J. Control 89(5), 892–908 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  16. Asl, H.J., Yoon, J.: Adaptive vision-based control of an unmanned aerial vehicle without linear velocity measurements. ISA Trans. 65, 296–306 (2016)

    Article  Google Scholar 

  17. Zheng, D., Wang, H., Wang, J., Chen, S., Chen, W., Liang, X.: Image-based visual servoing of a quadrotor using virtual camera approach. IEEE/ASME Trans. Mechatron. 22(2), 972–982 (2016)

    Article  Google Scholar 

  18. Shirzadeh, M., Amirkhani, A., Jalali, A., Mosavi, M.R.: An indirect adaptive neural control of a visual-based quadrotor robot for pursuing a moving target. ISA Trans. 59, 290–302 (2015)

    Article  Google Scholar 

  19. Shirzadeh, M., Asl, H.J., Amirkhani, A., Jalali, A.A.: Vision-based control of a quadrotor utilizing artificial neural networks for tracking of moving targets. Eng. Appl. Artif. Intell. 58, 34–48 (2017)

    Article  Google Scholar 

  20. Liu, N., Shao, X.: Desired compensation rise-based ibvs control of quadrotors for tracking a moving target. Nonlinear Dyn. 95(4), 2605–2624 (2019)

    Article  Google Scholar 

  21. Cao, Z., Chen, X., Yu, Y., Yu, J., Liu, X., Zhou, C., Tan, M.: Image dynamics-based visual servoing for quadrotors tracking a target with a nonlinear trajectory observer. IEEE Trans. Syst. Man Cybern. Syst. 50(1), 376–384 (2017)

    Article  Google Scholar 

  22. Arif, A., Wang, H., Liu, Z., Castañeda, H., Wang, Y.: Adaptive visual servo control law for finite-time tracking to land quadrotor on moving platform using virtual reticle algorithm. Robot. Auton. Syst. 141, 103764 (2021)

    Article  Google Scholar 

  23. Alexis, K., Nikolakopoulos, G., Tzes, A.: Experimental constrained optimal attitude control of a quadrotor subject to wind disturbances. Int. J. Control Autom. Syst. 12(6), 1289–1302 (2014)

    Article  MATH  Google Scholar 

  24. Tian, B., Liu, L., Lu, H., Zuo, Z., Zong, Q., Zhang, Y.: Multivariable finite time attitude control for quadrotor uav: theory and experimentation. IEEE Trans. Industr. Electron. 65(3), 2567–2577 (2017)

    Article  Google Scholar 

  25. Harshavarthini, S., Sakthivel, R., Ahn, C.K.: Finite-time reliable attitude tracking control design for nonlinear quadrotor model with actuator faults. Nonlinear Dyn. 96(4), 2681–2692 (2019)

    Article  MATH  Google Scholar 

  26. Gajbhiye, S., Cabecinhas, D., Silvestre, C., Cunha, R.: Geometric finite-time inner-outer loop trajectory tracking control strategy for quadrotor slung-load transportation. Nonlinear Dyn. 107(3), 2291–2308 (2022)

    Article  Google Scholar 

  27. Zhu, W., Du, H., Cheng, Y., Chu, Z.: Hovering control for quadrotor aircraft based on finite-time control algorithm. Nonlinear Dyn. 88(4), 2359–2369 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhao, G., Chen, G., Chen, J., Hua, C.: Finite-time control for image-based visual servoing of a quadrotor using nonsingular fast terminal sliding mode. Int. J. Control Autom. Syst. 18(9), 2337–2348 (2020)

    Article  Google Scholar 

  29. Cabecinhas, D., Cunha, R., Silvestre, C.: A globally stabilizing path following controller for rotorcraft with wind disturbance rejection. IEEE Trans. Control Syst. Technol. 23(2), 708–714 (2014)

    Article  Google Scholar 

  30. Islam, S., Liu, P.X., El Saddik, A.: Robust control of four-rotor unmanned aerial vehicle with disturbance uncertainty. IEEE Trans. Industr. Electron. 62(3), 1563–1571 (2014)

    Article  Google Scholar 

  31. Amirkhani, A., Shirzadeh, M., Papageorgiou, E.I., Mosavi, M.R.: Visual-based quadrotor control by means of fuzzy cognitive maps. ISA Trans. 60, 128–142 (2016)

    Article  Google Scholar 

  32. Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control. Optim. 38(3), 751–766 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  33. Huang, X., Lin, W., Yang, B.: Global finite-time stabilization of a class of uncertain nonlinear systems. Automatica 41(5), 881–888 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  34. Qian, C., Lin, W.: Non-lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Syst. Control Lett. 42(3), 185–200 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  35. Han, J., Wang, W.: Nonlinear tracking-differentiator (in chinese). J. Syst. Sci. Math. Sci. 14(2), 177–183 (1994)

    MATH  Google Scholar 

  36. Na, J., Ren, X., Herrmann, G., Qiao, Z.: Adaptive neural dynamic surface control for servo systems with unknown dead-zone. Control. Eng. Pract. 19(11), 1328–1343 (2011)

    Article  Google Scholar 

  37. Chen, Q., Ren, X., Na, J., Zheng, D.: Adaptive robust finite-time neural control of uncertain pmsm servo system with nonlinear dead zone. Neural Comput. Appl. 28(12), 3725–3736 (2017)

    Article  Google Scholar 

  38. Amovlab: Prometheus autonomous UAV opensource project. https://github.com/amov-lab/Prometheus (2019)

Download references

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to thank the National Natural Science Foundation of China under Grant [52275003] and Grant [U1813220], in part by the Fundamental Research Funds for the Central Universities under Grant [buctrc202105] for their support in this research.

Author information

Authors and Affiliations

Authors

Contributions

WH involved in writing—original draft, validation and software. LY involved in writing—review and editing, and supervision.

Corresponding author

Correspondence to Liang Yuan.

Ethics declarations

Conflict of interest

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Code availability

Custom code is available upon request at Liang Yuan email address.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, W., Yuan, L. Image-based finite-time visual servoing of a quadrotor for tracking a moving target. Nonlinear Dyn 111, 5307–5328 (2023). https://doi.org/10.1007/s11071-022-08107-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-022-08107-w

Keywords

Navigation