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

TL;DR

This paper develops a finite-horizon LQR control method for quadrotors on the Lie group $SE_2(3)$, leveraging geometric linearization and differential flatness, showing improved robustness and performance over conventional approaches.

Contribution

It introduces a novel LQR control framework on $SE_2(3)$ for quadrotors using invariant error linearization and flatness, enhancing robustness and initial error handling.

Findings

Robustness to parametric uncertainty demonstrated

Better performance with large initial errors

Offline computation of optimal gain sequence

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.