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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
Authors
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
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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.
Keywords
Tri Rotor, Geometric, Nonlinear, Control, SE (3), SO (3).
Dinh-Thinh Hoang, Thi-Hong-Hieu Le, Ngoc-Hien Nguyen, 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. doi: 10.11648/j.ajae.20180502.14
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