American Journal of Aerospace Engineering

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Adapting SE (3) Nonlinear Geometric Method to Control Single-Tri Rotors with Integrator

Received: 04 October 2018    Accepted: 18 October 2018    Published: 21 November 2018
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Abstract

This paper presents a new method for controlling tri rotor-type unmanned aerial vehicles (UAV) adapted from the SE (3) nonlinear geometric method for quadrotor-type UAV. Like its predecessor, the control strategy for single tri rotors is realized in a hierarchical architecture, containing both attitude controller and position controller. As a basis, the mathematical dynamics of the tri rotor is given in form of rotation matrix that ensures the algorithm is independent from any specific representation, such as Euler angle or quaternion. Assumption about primary thrust component is made to decouple the equations of the controllers to find an appropriate reference target for the attitude controller. An integral action is proposed to alleviate the steady-state error that arises from incorrect modelling due to simplification. This is justified by a Lyapunov function that also yields additional conditions for parameter gains setup. Output of the controller includes desired torque components, as well as total thrust magnitude. It is from this point that divergence from the original method for quadrotors becomes prominent. A numerical solver is introduced to yield the desired motors’ angular speed and tail servo angle. Some numerical examples implemented on MATLAB/Simulink illustrate that the controller is able to correct steady-state error and gives quick response, just like its quadrotor-type counterpart.

DOI 10.11648/j.ajae.20180502.14
Published in American Journal of Aerospace Engineering (Volume 5, Issue 2, December 2018)
Page(s) 96-105
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Tri Rotor, Geometric, Nonlinear, Control, SE (3), SO (3).

References
[1] F. Nex and F. Remondino, “UAV for 3D mapping applications: a review,” Applied Geomatics, vol. 6, no. 1, pp. 1–15, Aug. 2013.
[2] I. Colomina and P. Molina, “Unmanned aerial systems for photogrammetry and remote sensing: A review,” ISPRS Journal of Photogrammetry and Remote Sensing, vol. 92, pp. 79–97, 2014.
[3] P. Liu, A. Y. Chen, Y.-N. Huang, J.-Y. Han, J.-S. Lai, S.-C. Kang, T.-H. Wu, M.-C. Wen, and M.-H. Tsai, “A review of rotorcraft Unmanned Aerial Vehicle (UAV) developments and applications in civil engineering,” Smart Structures and Systems, vol. 13, no. 6, pp. 1065–1094, 2014.
[4] J. Escareno, A. Sanchez, O. Garcia, and R. Lozano, “Triple tilting rotor mini-UAV: Modeling and embedded control of the attitude,” 2008 American Control Conference, 2008.
[5] S. Salazar-Cruz and R. Lozano, “Stabilization and nonlinear control for a novel trirotor mini-aircraft,” Proceedings of the 2005 IEEE International Conference on Robotics and Automation.
[6] D.-W. Yoo, H.-D. Oh, D.-Y. Won, and M.-J. Tahk, “Dynamic Modeling and Stabilization Techniques for Tri-Rotor Unmanned Aerial Vehicles,” International Journal of Aeronautical and Space Sciences, vol. 11, no. 3, pp. 167–174, 2010.
[7] J.-S. Chiou, H.-K. Tran, and S.-T. Peng, “Attitude Control of a Single Tilt Tri-Rotor UAV System: Dynamic Modeling and Each Channels Nonlinear Controllers Design,” Mathematical Problems in Engineering, vol. 2013, pp. 1–6, 2013.
[8] Z. Ali, D. Wang, and M. Aamir, “Fuzzy-Based Hybrid Control Algorithm for the Stabilization of a Tri-Rotor UAV,” Sensors, vol. 16, no. 5, p. 652, Sep. 2016.
[9] F. K. Yeh, C. W. Huang, J. J. Huang, “Adaptive fuzzy sliding-mode control for a mini-UAV with propellers”, SICE Annual Conference (SICE), 2011 Proceedings of, pp. 645-650, 2011.
[10] A. Kulhare, A. B. Chowdhury, and G. Raina, “A back-stepping control strategy for the Tri-rotor UAV,” 2012 24th Chinese Control and Decision Conference (CCDC), 2012.
[11] M. K. Mohamed and A. Lanzon, “Design and control of novel tri-rotor UAV,” Proceedings of 2012 UKACC International Conference on Control, 2012.
[12] T. Lee, M. Leok, and N. H. Mcclamroch, “Geometric tracking control of a quadrotor UAV on SE (3),” 49th IEEE Conference on Decision and Control (CDC), 2010.
[13] T. Fernando, J. Chandiramani, T. Lee, and H. Gutierrez, “Robust adaptive geometric tracking controls on SO (3) with an application to the attitude dynamics of a quadrotor UAV,” IEEE Conference on Decision and Control and European Control Conference, 2011.
[14] T. D. Hoang, “Application and simulation of nonlinear geometric control for Quadrotor UAVs,” Graduation Thesis – Ho Chi Minh City University of Technology, 2018.
[15] T. D. Hoang, “An experiment with integration in deriving Lyapunov candidate based on integral back-stepping technique,” unpublished.
Author Information
  • Department of Aerospace Engineering, Ho Chi Minh City University of Technology – VNU-HCM, Ho Chi Minh City, Vietnam

  • Department of Aerospace Engineering, Ho Chi Minh City University of Technology – VNU-HCM, Ho Chi Minh City, Vietnam

  • Department of Mathematical Sciences, School of Sciences, RMIT University, Melbourne, Australia

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  • APA Style

    Dinh-Thinh Hoang, Thi-Hong-Hieu Le, Ngoc-Hien Nguyen. (2018). Adapting SE (3) Nonlinear Geometric Method to Control Single-Tri Rotors with Integrator. American Journal of Aerospace Engineering, 5(2), 96-105. https://doi.org/10.11648/j.ajae.20180502.14

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    ACS Style

    Dinh-Thinh Hoang; Thi-Hong-Hieu Le; Ngoc-Hien Nguyen. Adapting SE (3) Nonlinear Geometric Method to Control Single-Tri Rotors with Integrator. Am. J. Aerosp. Eng. 2018, 5(2), 96-105. doi: 10.11648/j.ajae.20180502.14

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    AMA Style

    Dinh-Thinh Hoang, Thi-Hong-Hieu Le, Ngoc-Hien Nguyen. Adapting SE (3) Nonlinear Geometric Method to Control Single-Tri Rotors with Integrator. Am J Aerosp Eng. 2018;5(2):96-105. doi: 10.11648/j.ajae.20180502.14

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  • @article{10.11648/j.ajae.20180502.14,
      author = {Dinh-Thinh Hoang and Thi-Hong-Hieu Le and Ngoc-Hien Nguyen},
      title = {Adapting SE (3) Nonlinear Geometric Method to Control Single-Tri Rotors with Integrator},
      journal = {American Journal of Aerospace Engineering},
      volume = {5},
      number = {2},
      pages = {96-105},
      doi = {10.11648/j.ajae.20180502.14},
      url = {https://doi.org/10.11648/j.ajae.20180502.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajae.20180502.14},
      abstract = {This paper presents a new method for controlling tri rotor-type unmanned aerial vehicles (UAV) adapted from the SE (3) nonlinear geometric method for quadrotor-type UAV. Like its predecessor, the control strategy for single tri rotors is realized in a hierarchical architecture, containing both attitude controller and position controller. As a basis, the mathematical dynamics of the tri rotor is given in form of rotation matrix that ensures the algorithm is independent from any specific representation, such as Euler angle or quaternion. Assumption about primary thrust component is made to decouple the equations of the controllers to find an appropriate reference target for the attitude controller. An integral action is proposed to alleviate the steady-state error that arises from incorrect modelling due to simplification. This is justified by a Lyapunov function that also yields additional conditions for parameter gains setup. Output of the controller includes desired torque components, as well as total thrust magnitude. It is from this point that divergence from the original method for quadrotors becomes prominent. A numerical solver is introduced to yield the desired motors’ angular speed and tail servo angle. Some numerical examples implemented on MATLAB/Simulink illustrate that the controller is able to correct steady-state error and gives quick response, just like its quadrotor-type counterpart.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - Adapting SE (3) Nonlinear Geometric Method to Control Single-Tri Rotors with Integrator
    AU  - Dinh-Thinh Hoang
    AU  - Thi-Hong-Hieu Le
    AU  - Ngoc-Hien Nguyen
    Y1  - 2018/11/21
    PY  - 2018
    N1  - https://doi.org/10.11648/j.ajae.20180502.14
    DO  - 10.11648/j.ajae.20180502.14
    T2  - American Journal of Aerospace Engineering
    JF  - American Journal of Aerospace Engineering
    JO  - American Journal of Aerospace Engineering
    SP  - 96
    EP  - 105
    PB  - Science Publishing Group
    SN  - 2376-4821
    UR  - https://doi.org/10.11648/j.ajae.20180502.14
    AB  - This paper presents a new method for controlling tri rotor-type unmanned aerial vehicles (UAV) adapted from the SE (3) nonlinear geometric method for quadrotor-type UAV. Like its predecessor, the control strategy for single tri rotors is realized in a hierarchical architecture, containing both attitude controller and position controller. As a basis, the mathematical dynamics of the tri rotor is given in form of rotation matrix that ensures the algorithm is independent from any specific representation, such as Euler angle or quaternion. Assumption about primary thrust component is made to decouple the equations of the controllers to find an appropriate reference target for the attitude controller. An integral action is proposed to alleviate the steady-state error that arises from incorrect modelling due to simplification. This is justified by a Lyapunov function that also yields additional conditions for parameter gains setup. Output of the controller includes desired torque components, as well as total thrust magnitude. It is from this point that divergence from the original method for quadrotors becomes prominent. A numerical solver is introduced to yield the desired motors’ angular speed and tail servo angle. Some numerical examples implemented on MATLAB/Simulink illustrate that the controller is able to correct steady-state error and gives quick response, just like its quadrotor-type counterpart.
    VL  - 5
    IS  - 2
    ER  - 

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