相关论文: A Riemannian Take on Distance Fields and Geodesic …

Solving the inverse kinematics problem is a fundamental challenge in motion planning, control, and calibration for articulated robots. Kinematic models for these robots are typically parametrized by joint angles, generating a complicated…

Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…

The success of intelligent robotic missions relies on integrating various research tasks, each demanding distinct representations. Designing task-specific representations for each task is costly and impractical. Unified representations…

Geodesic distances play a fundamental role in robotics, as they efficiently encode global geometric information of the domain. Recent methods use neural networks to approximate geodesic distances by solving the Eikonal equation through…

For robots to work alongside humans and perform in unstructured environments, they must learn new motion skills and adapt them to unseen situations on the fly. This demands learning models that capture relevant motion patterns, while…

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…

The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…

Faithfully modeling the space of articulations is a crucial task that allows recovery and generation of realistic poses, and remains a notorious challenge. To this end, we introduce Neural Riemannian Distance Fields (NRDFs), data-driven…

The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…

Computing distances on Riemannian manifolds is a challenging problem with numerous applications, from physics, through statistics, to machine learning. In this paper, we introduce the metric-constrained Eikonal solver to obtain continuous,…

In many robot motion planning problems, task objectives and physical constraints induce non-Euclidean geometry on the configuration space, yet many planners operate using Euclidean distances that ignore this structure. We address the…

We give bounds on geodesic distances on the Stiefel manifold, derived from new geometric insights. The considered geodesic distances are induced by the one-parameter family of Riemannian metrics introduced by H\"uper et al. (2021), which…

Riemannian metric learning is an emerging field in machine learning, unlocking new ways to encode complex data structures beyond traditional distance metric learning. While classical approaches rely on global distances in Euclidean space,…

Autonomous robots should operate in real-world dynamic environments and collaborate with humans in tight spaces. A key component for allowing robots to leave structured lab and manufacturing settings is their ability to evaluate online and…

Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…

Geodesic nets on Riemannian manifolds form a natural class of stationary objects generalizing geodesics. Yet almost nothing is known about their classification or general properties even when the ambient Riemannian manifold is the Euclidean…

Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…

This paper introduces a novel approach to improve robotic grasping in dynamic environments by integrating Gaussian Process Distance Fields (GPDF), SE(3) equivariant networks, and Riemannian Mixture Models. The aim is to enable robots to…

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…

In recent decades, advancements in motion learning have enabled robots to acquire new skills and adapt to unseen conditions in both structured and unstructured environments. In practice, motion learning methods capture relevant patterns and…