以$SE_2美元(3)对四罗德者控制Fiite-Horizon LQR (Finite-Horizon LQR Control of Quadrotors on $SE_2(3)$)

from arxiv, Published in IEEE Robotics and Automation Letters and presented at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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.

翻译：本文考虑使用离散时间、有限高度轨道、线性二次调节器(LQR)来最佳控制赤道无人驾驶飞行器(UAV),四角轨道无人驾驶飞行器的状况作为基质 Lie 一组双直直偏异体($SE_2(3)美元)的一个要素。非线性系统使用参考轨迹的左偏差错误线性化,从而得出最佳收益序列,可以离线计算。参考轨迹是利用四角轨道的差异平面特性计算的。蒙特卡洛模拟显示,拟议的控制办法对于参数不确定性、状态估计错误和初始错误具有很强性能。此外,与使用常规误差定义的LQR控制器相比,拟议的控制器在初始误差较大时表现得更好。