離散曲面上のロボット学習：理論と応用
Robot Learning on Discrete Surfaces: Theory and Applications
多面体メッシュ上でロボット学習を直接行うための離散リーマン幾何学フレームワークを提案し、DMP・ガウス過程・リーマニアンフローマッチングに適用して実機検証した。
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著者: Matteo Dalle Vedove, Fares J. Abu-Dakka, Luigi Palopoli, Daniele Fontanelli, Matteo Saveriano
分類: cs.RO
原文アブストラクト
All the objects composing our world are enclosed within surfaces. Yet, most robot learning and motion generation frameworks treat surfaces as constraints ignoring their intrinsic geometry. This gap is acute for polyhedral meshes--the standard output of CAD and 3D reconstruction--whose discrete geometric structure remains unexploited. In this paper, we propose a unified discrete Riemannian framework that enables robot learning directly on polyhedral surface meshes. Using discrete differential geometry, we define logarithmic and exponential maps, parallel transport, and ambient-space projections that remain well-defined across faces, edges, and vertices. We instantiate the framework in three learning paradigms: (i) Dynamic Movement Primitives (DMPs), an improved exponential-map computation and a fixed-tangent-cone forcing-term encoding with parallel transport yield better cross-surface generalisation and stability over prior mesh-based approaches. (ii) Gaussian Process (GP), a geodesic-based kernel with practical admissibility control, enables regression at arbitrary mesh locations without smoothness assumptions. (iii) Riemannian Flow Matching (RFM), mesh-native operators improve generative quality over spectral baselines while reducing training time. The framework is validated in simulation against state-of-the-art methods and demonstrated on two real-robot scenarios: generalising user-drawn trajectories across different surfaces and planning polishing motions on RGB-D-reconstructed surfaces.