Finite-Horizon LQR Control of Quadrotors on $SE_2(3)$
Mitchell R. Cohen, Khairi Abdulrahim, James Richard Forbes
Abstract
This letter considers optimal control of a quadrotor unmanned aerial vehicles (UAV) using the discrete-time, finite-horizon, linear quadratic regulator (LQR). The state of a quadrotor UAV is represented as an element of the matrix Lie group of double direct isometries, SE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (3). The nonlinear system is linearized using a left-invariant error about a reference trajectory, leading to an optimal gain sequence that can be calculated offline. The reference trajectory is calculated using the differentially flat properties of the quadrotor. Monte-Carlo simulations demonstrate robustness of the proposed control scheme to parametric uncertainty, state-estimation error, and initial error. Additionally, when compared to an LQR controller that uses a conventional error definition, the proposed controller demonstrates better performance when initial errors are large.
BibTeX
@inproceedings{ral2020_finitehorizonlqr,
title = {Finite-Horizon LQR Control of Quadrotors on $SE_2(3)$},
author = {Mitchell R. Cohen and Khairi Abdulrahim and James Richard Forbes},
booktitle = {RA-L 2020},
year = {2020}
}