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arXiv · 2105.13935

Finite-Horizon LQR Control of Quadrotors on $SE_2(3)$

Mitchell R. Cohen·Khairi Abdulrahim·James Richard Forbes
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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, $SE_2(3)$. 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.

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Mitchell R. Cohen, Khairi Abdulrahim, James Richard Forbes. 2021-05-28. Finite-Horizon LQR Control of Quadrotors on $SE_2(3)$. https://doi.org/10.1109/lra.2020.3010214

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