Finite-Horizon LQR Control of Quadrotors on $SE_2(3)$
Abstract
This paper 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, . 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.
Keywords
Cite
@article{arxiv.2105.13935,
title = {Finite-Horizon LQR Control of Quadrotors on $SE_2(3)$},
author = {Mitchell R. Cohen and Khairi Abdulrahim and James Richard Forbes},
journal= {arXiv preprint arXiv:2105.13935},
year = {2021}
}
Comments
Published in IEEE Robotics and Automation Letters and presented at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)