任意のリーマン多様体上の時間場を学習するためのリーマン・スプラット回帰モデル
Riemannian Splat Regression Models for Learning Time Fields on Arbitrary Riemannian Manifolds
リーマン多様体上で関数を学習するため、ラップドガウス分布によるスプラット回帰モデルを提案し、到着時間場の学習に適用して精度とモデルサイズを比較した。
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著者: Anastasios Manganaris, Rohit Banerjee, Gokul Prabhakaran, Ahmed H. Qureshi
分類: cs.RO
原文アブストラクト
Motion planning on arbitrary Riemannian manifolds is an important and difficult problem that frustrates typical planning methods for Euclidean spaces. In particular, motion planning methods that approximate optimal time-to-go functions with neural networks, e.g., Neural Time Fields (NTFields), cannot be directly applied without using ad-hoc coordinate projections into higher dimensions. Using these methods directly without such projections is desirable, as it promises to provide the lowest-possible-runtime method for obtaining optimal plans on high-dimensional manifolds while using minimal model capacity. In this work, we develop a model that requires no coordinate projection and can learn arbitrary functions on Riemannian manifolds by combining splat regression models with splats defined by wrapped Gaussian distributions. We successfully apply this model for learning arrival time fields on several Riemannian manifolds, and we compare the accuracy and model size of this approach with multi-layer perceptrons adapted to work on each manifold individually.