制御アフィン系のデータ駆動バッチ状態推定のためのKoopman線形化
Koopman Linearization for Data-Driven Batch State Estimation of Control-Affine Systems
制御アフィン系をRKHSに持ち上げて双線形化し、学習したモデル行列からテスト時に線形時変系としてバッチ状態推定を行うモデルフリー手法KoopSEを提案。移動ロボットのUWBと車輪オドメトリによる自己位置推定で、モデル未知ながら標準RTSスムーザより高精度・高整合を達成。
著者: Zi Cong Guo, Vassili Korotkine, James R. Forbes, Timothy D. Barfoot
分類: cs.RO
原文アブストラクト
We present the Koopman State Estimator (KoopSE), a framework for model-free batch state estimation of control-affine systems that makes no linearization assumptions, requires no problem-specific feature selections, and has an inference computational cost that is independent of the number of training points. We lift the original nonlinear system into a higher-dimensional Reproducing Kernel Hilbert Space (RKHS), where the system becomes bilinear. The time-invariant model matrices can be learned by solving a least-squares problem on training trajectories. At test time, the system is algebraically manipulated into a linear time-varying system, where standard batch linear state estimation techniques can be used to efficiently compute state means and covariances. Random Fourier Features (RFF) are used to combine the computational efficiency of Koopman-based methods and the generality of kernel-embedding methods. KoopSE is validated experimentally on a localization task involving a mobile robot equipped with ultra-wideband receivers and wheel odometry. KoopSE estimates are more accurate and consistent than the standard model-based extended Rauch-Tung-Striebel (RTS) smoother, despite KoopSE having no prior knowledge of the system's motion or measurement models.
