トルク制限付き単振り子に対するLQR制御器の吸引領域の解析的推定
Analytic Estimation of Region of Attraction of an LQR Controller for Torque Limited Simple Pendulum
トルク制限付き単振り子の線形常微分方程式の解析解に基づき、LQR制御器の吸引領域を高速に推定する手法を提案し、シミュレーションと実機実験で有効性を示した。
著者: Lukas Gross, Lasse Maywald, Shivesh Kumar, Frank Kirchner, Christoph Lüth
分類: cs.RO
原文アブストラクト
Linear-quadratic regulators (LQR) are a well known and widely used tool in control theory for both linear and nonlinear dynamics. For nonlinear problems, an LQR-based controller is usually only locally viable, thus, raising the problem of estimating the region of attraction (ROA). The need for good ROA estimations becomes especially pressing for underactuated systems, as a failure of controls might lead to unsafe and unrecoverable system states. Known approaches based on optimization or sampling, while working well, might be too slow in time critical applications and are hard to verify formally. In this work, we propose a novel approach to estimate the ROA based on the analytic solutions to linear ODEs for the torque limited simple pendulum. In simulation and physical experiments, we compared our approach to a Lyapunov-sampling baseline approach and found that our approach was faster to compute, while yielding ROA estimations of similar phase space area.
