Finite-Horizon LQR Control of Quadrotors on $SE_2(3)$
This work addresses precise control for quadrotor UAVs, representing an incremental improvement over existing LQR methods.
The paper tackled optimal control of quadrotor UAVs by applying a finite-horizon LQR on the SE_2(3) Lie group, resulting in a controller that showed robustness to uncertainties and outperformed a conventional LQR in handling large initial errors.
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.