相关论文: Minkowski Operations of Sets with Application to R…
In many applications of autonomous mobile robots the following problem is encountered. Two maps of the same environment are available, one a prior map and the other a sensor map built by the robot. To benefit from all available information…
A conformally invariant model of two interacting massless particles in Minkowski space was proposed by Casalbuoni and Gomis [1]. We generalize this model to the case of de Sitter space from the perspective of geodesic distance, in such a…
A classical result from topology called Uryshon's lemma asserts the existence of a continuous separator of two disjoint closed sets in a sufficiently regular topological space. In this work we make a search for this separator constructive…
In this paper we propose a modular nonlinear least squares filtering approach for systems composed of independent subsystems. The state and error covariance estimate of each subsystem is updated independently, even when a relative…
Despite the number of works published in recent years, vehicle localization remains an open, challenging problem. While map-based localization and SLAM algorithms are getting better and better, they remain a single point of failure in…
We study concircular tensors in spaces of constant curvature and then apply the results obtained to the problem of the orthogonal separation of the Hamilton-Jacobi equation on these spaces. Any coordinates which separate the geodesic…
The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally…
The notion of separating automata was introduced by Bojanczyk and Czerwinski for understanding the first quasipolynomial time algorithm for parity games. In this paper we show that separating automata is a powerful tool for constructing…
Knowledge about the own pose is key for all mobile robot applications. Thus pose estimation is part of the core functionalities of mobile robots. Over the last two decades, LiDAR scanners have become the standard sensor for robot…
Whisker-like touch sensors offer unique advantages for short-range perception in environments where visual and long-range sensing are unreliable, such as confined, cluttered, or low-visibility settings. This paper presents a framework for…
Given a bichromatic point set $P=\textbf{R} \cup \textbf{B}$ of red and blue points, a separator is an object of a certain type that separates $\textbf{R}$ and $\textbf{B}$. We study the geometric separability problem when the separator is…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
The Separation of Variables theory for the Hamilton-Jacobi equation is 'by definition' related to the use of special kinds of coordinates, for example Jacobi coordinates on the ellipsoid or St\"ackel systems in the Euclidean space. However,…
This paper studies a coordinate alignment problem for cooperative mobile sensor network localization with range-based measurements. The network consists of target nodes, each of which has only access position information in a local fixed…
Minkowski sums cover a wide range of applications in many different fields like algebra, morphing, robotics, mechanical CAD/CAM systems ... This paper deals with sums of polytopes in a n dimensional space provided that both H-representation…
Robotic assembly planning enables architects to explicitly account for the assembly process during the design phase, and enables efficient building methods that profit from the robots' different capabilities. Previous work has addressed…
Assembly of large scale structural systems in space is understood as critical to serving applications that cannot be deployed from a single launch. Recent literature proposes the use of discrete modular structures for in-space assembly and…
Keypoint detection is an essential building block for many robotic applications like motion capture and pose estimation. Historically, keypoints are detected using uniquely engineered markers such as checkerboards or fiducials. More…
The exterior algebra of Minkowski space naturally has the structure of a sixteen-dimensional Clifford algebra representation, and so can be used as the space of spinors. We examine plane, circular, and spherical solutions to the free Dirac…
Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial…