AI 中文总结
针对任意黎曼流形上的运动规划，提出一种无需坐标投影的样条回归模型，结合包裹高斯分布样条学习到达时间场，在多个流形上验证了其准确性与模型规模优势。
AI 中文摘要
在任意黎曼流形上的运动规划是一个重要且困难的问题，它使得典型的欧几里得空间规划方法受挫。特别是，使用神经网络（如神经时间场，NTFields）逼近最优到达时间函数的运动规划方法，若不采用临时的高维坐标投影，则无法直接应用。无需此类投影而直接使用这些方法是可取的，因为它有望以最小的模型容量，在流形上获得最优规划的同时，提供最低运行时间的方法。在本工作中，我们开发了一种无需坐标投影的模型，通过将样条回归模型与由包裹高斯分布定义的样条相结合，能够在黎曼流形上学习任意函数。我们成功地将该模型应用于在多个黎曼流形上学习到达时间场，并将该方法的准确性和模型规模与针对每个流形单独调整的多层感知器进行了比较。
英文摘要
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.
Comments5 pages, 2 figures, Spotlight Paper at IEEE/RSJ IROS Workshop on Geometric Representations in Robotics
