不正確な確率動力学下での行動不確実性を等角非ホロノミックLie群で定量化する
Lies We Can Trust: Quantifying Action Uncertainty with Inaccurate Stochastic Dynamics through Conformalized Nonholonomic Lie Groups
Lie群の対称性を考慮した等角予測により、不正確な動力学モデルでも行動後のシステム構成を指定確率で含む予測集合を構築する手法を提案し、SE(2)ロボットで検証した。
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著者: Luís Marques, Maani Ghaffari, Dmitry Berenson
分類: cs.RO, cs.SY, eess.SY
原文アブストラクト
We propose Conformal Lie-group Action Prediction Sets (CLAPS), a symmetry-aware conformal prediction-based algorithm that constructs, for a given action, a set guaranteed to contain the resulting system configuration at a user-defined probability. Our assurance holds under both aleatoric and epistemic uncertainty, non-asymptotically, and does not require strong assumptions about the true system dynamics, the uncertainty sources, or the quality of the approximate dynamics model. Typically, uncertainty quantification is tackled by making strong assumptions about the error distribution or magnitude, or by relying on uncalibrated uncertainty estimates - i.e., with no link to frequentist probabilities - which are insufficient for safe control. Recently, conformal prediction has emerged as a statistical framework capable of providing distribution-free probabilistic guarantees on test-time prediction accuracy. While current conformal methods treat robots as Euclidean points, many systems have non-Euclidean configurations, e.g., some mobile robots have SE(2). In this work, we rigorously analyze configuration errors using Lie groups, extending previous Euclidean Space theoretical guarantees to SE(2). Our experiments on a simulated JetBot, and on a real MBot, suggest that by considering the configuration space's structure, our symmetry-informed nonconformity score leads to more volume-efficient prediction regions which represent the underlying uncertainty better than existing approaches.
