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We consider two or more simple symmetric walks on some graphs, e.g. the real line, the plane or the two dimensional comb lattice, and investigate the properties of the distance among the walkers.
This paper gives an introduction to the problem of mapping simple polygons with autonomous agents. We focus on minimalistic agents that move from vertex to vertex along straight lines inside a polygon, using their sensors to gather local…
This paper focuses on the problem of localising a transmitting mobile station (MS) using multiple cooperative base stations (BSs). There are two technical difficulties: one is the data association between intermediate parameters and…
Global mobile robot localization is the problem of determining a robot's pose in an environment, using sensor data, when the starting position is unknown. A family of probabilistic algorithms known as Monte Carlo Localization (MCL) is…
We study the network localization problem, i.e., the problem of determining node positions of a wireless sensor network modeled as a unit disk graph. In an arbitrarily deployed network, positions of all nodes of the network may not be…
This paper gives a complete description of the solutions of the global positioning problem, emphasizing the under-determined case. We show that the solutions form a quadric, which may degenerate in various ways. Perhaps more surprisingly,…
Crossing minimization is one of the central problems in graph drawing. Recently, there has been an increased interest in the problem of minimizing crossings between paths in drawings of graphs. This is the metro-line crossing minimization…
The design of distributed gathering and convergence algorithms for tiny robots has recently received much attention. In particular, it has been shown that convergence problems can even be solved for very weak, \emph{oblivious} robots:…
We consider the problem of estimating the locations of a set of points in a k-dimensional euclidean space given a subset of the pairwise distance measurements between the points. We focus on the case when some fraction of these measurements…
In the distributed localization problem (DLP), $n$ anonymous robots (agents) $a_0, a_1, ..., a_{n-1}$ begin at arbitrary positions $p_0, ..., p_{n-1}$ in $S$, where $S$ is an Euclidean space. The primary goal in DLP is for agents to reach a…
In this paper, we present a framework for self-localization of parking robots in a parking lot innovatively using square-like landmarks, aiming to provide a positioning solution with low cost but high accuracy. It utilizes square structures…
This paper introduces an efficient procedure to localize user-defined points on the surface of deformable objects and track their positions in 3D space over time. To cope with a deformable object's infinite number of DOF, we propose a…
A Semidefinite Programming (SDP) relaxation is an effective computational method to solve a Sensor Network Localization problem, which attempts to determine the locations of a group of sensors given the distances between some of them [11].…
In this paper we study a generalized version of the Weber problem of finding a point that minimizes the sum of its distances to a finite number of given points. In our setting these distances may be $cut$ $off$ at a given value $C > 0$, and…
This paper addresses the distributed localization problem for a network of sensors placed in a three-dimensional space, in which sensors are able to perform range measurements, i.e., measure the relative distance between them, and exchange…
An appearance-based robot self-localization problem is considered in the machine learning framework. The appearance space is composed of all possible images, which can be captured by a robot's visual system under all robot localizations.…
We consider a problem of localizing a path-signal that evolves over time on a graph. A path-signal can be viewed as the trajectory of a moving agent on a graph in several consecutive time points. Combining dynamic programming and graph…
Visual place recognition is a fundamental capability for the localization of mobile robots. It places image retrieval in the practical context of physical agents operating in a physical world. It is an active field of research and many…
We study several natural instances of the geometric hitting set problem for input consisting of sets of line segments (and rays, lines) having a small number of distinct slopes. These problems model path monitoring (e.g., on road networks)…
The locality of a graph problem is the smallest distance $T$ such that each node can choose its own part of the solution based on its radius-$T$ neighborhood. In many settings, a graph problem can be solved efficiently with a distributed or…