Adapting SE (3) Nonlinear Geometric Method to Control Single-Tri Rotors with Integrator
American Journal of Aerospace Engineering
Volume 5, Issue 2, December 2018, Pages: 96-105
Received: Oct. 4, 2018;
Accepted: Oct. 18, 2018;
Published: Nov. 21, 2018
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Dinh-Thinh Hoang, Department of Aerospace Engineering, Ho Chi Minh City University of Technology – VNU-HCM, Ho Chi Minh City, Vietnam
Thi-Hong-Hieu Le, Department of Aerospace Engineering, Ho Chi Minh City University of Technology – VNU-HCM, Ho Chi Minh City, Vietnam
Ngoc-Hien Nguyen, Department of Mathematical Sciences, School of Sciences, RMIT University, Melbourne, Australia
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.
Adapting SE (3) Nonlinear Geometric Method to Control Single-Tri Rotors with Integrator, American Journal of Aerospace Engineering.
Vol. 5, No. 2,
2018, pp. 96-105.
F. Nex and F. Remondino, “UAV for 3D mapping applications: a review,” Applied Geomatics, vol. 6, no. 1, pp. 1–15, Aug. 2013.
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.
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.
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.
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.
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.
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.
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.
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.
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.
M. K. Mohamed and A. Lanzon, “Design and control of novel tri-rotor UAV,” Proceedings of 2012 UKACC International Conference on Control, 2012.
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.
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.
T. D. Hoang, “Application and simulation of nonlinear geometric control for Quadrotor UAVs,” Graduation Thesis – Ho Chi Minh City University of Technology, 2018.
T. D. Hoang, “An experiment with integration in deriving Lyapunov candidate based on integral back-stepping technique,” unpublished.