データ駆動型不確かさ下における確率的可到達集合の凸近似の微調整
Fine-Tuned Convex Approximations of Probabilistic Reachable Sets under Data-driven Uncertainties
FFTで高速化したカーネル密度推定により不確かさをモデル化し、混合整数非線形計画法とヒューリスティックアルゴリズムで確率的可到達集合を最適な凸多角形で近似する手法を提案した。
著者: Pengcheng Wu, Sonia Martinez, Jun Chen
分類: cs.RO
原文アブストラクト
This paper proposes a mechanism to fine-tune convex approximations of probabilistic reachable sets (PRS) of uncertain dynamic systems. We consider the case of unbounded uncertainties, for which it may be impossible to find a bounded reachable set of the system. Instead, we turn to find a PRS that bounds system states with high confidence. Our data-driven approach builds on a kernel density estimator (KDE) accelerated by a fast Fourier transform (FFT), which is customized to model the uncertainties and obtain the PRS efficiently. However, the non-convex shape of the PRS can make it impractical for subsequent optimal designs. Motivated by this, we formulate a mixed integer nonlinear programming (MINLP) problem whose solution result is an optimal $n$ sided convex polygon that approximates the PRS. Leveraging this formulation, we propose a heuristic algorithm to find this convex set efficiently while ensuring accuracy. The algorithm is tested on comprehensive case studies that demonstrate its near-optimality, accuracy, efficiency, and robustness. The benefits of this work pave the way for promising applications to safety-critical, real-time motion planning of uncertain dynamic systems.
