# Finite-Horizon LQR Control of Quadrotors on SE2(3)

arXiv: https://arxiv.org/abs/2105.13935 · HTML: https://mlsanity.com/paper/2105.13935/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2021.

## Built on by (most cited first, 2 of 2)

- [Landing with the Score: Riemannian Optimization through Denoising](https://mlsanity.com/paper/2509.23357/) (2025)
- [Can Euclidean Symmetry be Leveraged in Reinforcement Learning and Planning?](https://mlsanity.com/paper/2307.08226/) (2023)

## Abstract (arXiv)

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, SE2(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.