Related papers: A Combinatorial Bound for Beacon-based Routing in …
This paper investigates a modification of cyclic constant bearing (CB) pursuit in a multi-agent system in which each agent pays attention to a neighbor and a beacon. The problem admits shape equilibria with collective circling about the…
In tasks such as surveying or monitoring remote regions, an autonomous robot must move while transmitting data over a wireless network with unknown, position-dependent transmission rates. For such a robot, this paper considers the problem…
Given an orthogonal polygon $ P $ with $ n $ vertices, the goal of the watchman route problem is finding a path $ S $ of the minimum length in $ P $ such that every point of the polygon $ P $ is visible from at least one of the point of $ S…
Let $P$ be an $x$-monotone orthogonal polygon with $n$ vertices. We call $P$ a simple histogram if its upper boundary is a single edge; and a double histogram if it has a horizontal chord from the left boundary to the right boundary. Two…
For many applications, drones are required to operate entirely or partially autonomously. To fly completely or partially on their own, drones need access to location services to get navigation commands. While using the Global Positioning…
There exist many variants of guarding an orthogonal polygon in an orthogonal fashion: sometimes a guard can see an entire rectangle, or along a staircase, or along an orthogonal path with at most $k$ bends. In this paper, we study all these…
In the arbitrary pattern formation problem, $n$ autonomous, mobile robots must form an arbitrary pattern $P \subseteq \mathbb{R}^2$. The (deterministic) robots are typically assumed to be indistinguishable, disoriented, and unable to…
Range-based localization is ubiquitous: global navigation satellite systems (GNSS) power mobile phone-based navigation, and autonomous mobile robots can use range measurements from a variety of modalities including sonar, radar, and even…
Cyclic pursuit frameworks, which are built upon pursuit interactions between neighboring agents in a cycle graph, provide an efficient way to create useful global behaviors in a collective of autonomous robots. Previous work had considered…
Let $\mathcal{W} \subset \mathbb{R}^2$ be a planar polygonal environment (i.e., a polygon potentially with holes) with a total of $n$ vertices, and let $A,B$ be two robots, each modeled as an axis-aligned unit square, that can translate…
$ \newcommand{\Re}{\mathbb{R}} \newcommand{\reals}{\mathbb{R}} \newcommand{\SetX}{\mathsf{X}} \newcommand{\rad}{r} \newcommand{\Mh}[1]{#1} \newcommand{\query}{q} \newcommand{\eps}{\varepsilon} \newcommand{\VorX}[1]{\mathcal{V} \pth{#1}}…
Let $P$ be a collection of $n$ points moving along pseudo-algebraic trajectories in the plane. One of the hardest open problems in combinatorial and computational geometry is to obtain a nearly quadratic upper bound, or at least a subcubic…
We show that a stochastic flow which is generated by a stochastic differential equation on $\R^d$ with bounded volatility has a random attractor provided that the drift component in the direction towards the origin is larger than a certain…
This paper studies the possibility of upper bounding the position error of an estimate for range based positioning algorithms in wireless sensor networks. In this study, we argue that in certain situations when the measured distances…
Motivated by the applications of routing in PCB buses, the Rectangle Escape Problem was recently introduced and studied. In this problem, we are given a set of rectangles $\mathcal{S}$ in a rectangular region $R$, and we would like to…
It is emphasized that the bunching parameter $\beta=P_B/P_D$ , i.e. the ratio between the probability to measure two bosons and two distinguishable particles at the same state, is a constant of motion and depends only on the overlap between…
In rotor-router aggregation on the square lattice Z^2, particles starting at the origin perform deterministic analogues of random walks until reaching an unoccupied site. The limiting shape of the cluster of occupied sites is a disk. We…
How do we move a robot efficiently from one position to another? To answer this question, we need to understand its configuration space, a 'map' where we can find every possible position of the robot. Unfortunately, these maps are very…
Random Boolean networks, originally invented as models of genetic regulatory networks, are simple models for a broad class of complex systems that show rich dynamical structures. From a biological perspective, the most interesting networks…
We update the method of describing and assessing the process of the study of an abstract environment by a system, proposed earlier. We do not model any biological cognition mechanisms and consider the system as an agent equipped with an…