Related papers: A Differentiable Distance Metric for Robotics Thro…
This paper addresses to the problem of finding the (minimum) Euclidean distance between two linear varieties. This problem is, usually, solved minimising a target function. We propose a novel approach: to use the Moore-Penrose generalised…
Although Bayesian methods are robust and principled, their application in practice could be limited since they typically rely on computationally intensive Markov Chain Monte Carlo algorithms for their implementation. One possible solution…
It has been shown beneficial for many types of data which present an underlying hierarchical structure to be embedded in hyperbolic spaces. Consequently, many tools of machine learning were extended to such spaces, but only few…
Collision detection appears as a canonical operation in a large range of robotics applications from robot control to simulation, including motion planning and estimation. While the seminal works on the topic date back to the 80s, it is only…
We geometrically analyze the problem of estimating parameters related to the shape and size of a two-dimensional target object on the plane by using randomly distributed distance sensors whose locations are unknown. Based on the analysis…
We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables to directly compare different atomic environments with an arbitrary number of…
It is well-known that parallel manipulators are prone to singularities. However, there is still a lack of distance evaluation functions, referred to as metrics, for computing the distance between two 3-RPR configurations. The proposed…
We have developed a notion of global bisimulation distance between processes which goes somehow beyond the notions of bisimulation distance already existing in the literature, mainly based on bisimulation games. Our proposal is based on the…
All known algorithms for the Fr\'echet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; second, they use this oracle to find the optimum from a finite set of critical values.…
Path planning for multiple robots is well studied in the AI and robotics communities. For a given discretized environment, robots need to find collision-free paths to a set of specified goal locations. Robots can be fully anonymous,…
Understanding distance metrics in high-dimensional spaces is crucial for various fields such as data analysis, machine learning, and optimization. The Manhattan distance, a fundamental metric in multi-dimensional settings, measures the…
Transparent object perception is a rapidly developing research problem in artificial intelligence. The ability to perceive transparent objects enables robots to achieve higher levels of autonomy, unlocking new applications in various…
The development of autonomous robotic systems that can learn from human demonstrations to imitate a desired behavior - rather than being manually programmed - has huge technological potential. One major challenge in imitation learning is…
Objective: In this work, we propose a framework for differentiable forward and back-projector that enables scalable, accurate, and memory-efficient gradient computation for rigid motion estimation tasks. Methods: Unlike existing approaches…
To safely navigate unknown environments, robots must accurately perceive dynamic obstacles. Instead of directly measuring the scene depth with a LiDAR sensor, we explore the use of a much cheaper and higher resolution sensor: programmable…
A coordinate system is proposed that replaces the usual three-dimensional Cartesian x,y,z position coordinates, for use in robotic localization applications. Range, azimuth, and elevation measurement models become greatly simplified, and,…
Comparing spherical probability distributions is of great interest in various fields, including geology, medical domains, computer vision, and deep representation learning. The utility of optimal transport-based distances, such as the…
For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…
A central aspect of robotic motion planning is collision avoidance, where a multitude of different approaches are currently in use. Optimization-based motion planning is one method, that often heavily relies on distance computations between…
Given two arbitrary closed sets in Euclidean space, a simple transversality condition guarantees that the method of alternating projections converges locally, at linear rate, to a point in the intersection. Exact projection onto nonconvex…