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We consider the problem of searching for an intruder in a geometric domain by utilizing multiple search robots. The domain is a simply connected orthogonal polygon with edges parallel to the cartesian coordinate axes. Each robot has a…

Robotics · Computer Science 2025-11-06 Swadhin Agrawal , Sujoy Bhore , Joseph S. B. Mitchell , P. B. Sujit , Aayush Gohil

Most of the existing research on pursuit-evasion game (PEG) is conducted in a two-dimensional (2D) environment. In this paper, we investigate the PEG in a 3D space. We extend the Apollonius circle (AC) to the 3D space and introduce its…

Systems and Control · Electrical Eng. & Systems 2025-03-12 Penglin Hu

We consider a variation of the Cops and Robber game where the cops can only see the robber when the distance between them is at most a fixed parameter $\ell$. We consider the basic consequences of this definition for some simple graph…

Discrete Mathematics · Computer Science 2017-08-25 N. E. Clarke , D. Cox , C. Duffy , D. Dyer , S. Fitzpatrick , M. E. Messinger

The localization game is a pursuit-evasion game analogous to Cops and Robbers, where the robber is invisible and the cops send distance probes in an attempt to identify the location of the robber. We present a novel graph parameter called…

Combinatorics · Mathematics 2021-05-21 Natalie C. Behague , Anthony Bonato , Melissa A. Huggan , Trent G. Marbach , Brittany Pittman

We consider a variation of a cops and robbers game in which the cop---here referred to as "hunter"---is not constrained by the graph but must play in the dark against a "mole." We characterize the graphs---which we will call…

Combinatorics · Mathematics 2014-05-15 Natasha Komarov , Peter Winkler

This paper presents a multiplayer Homicidal Chauffeur reach-avoid differential game, which involves Dubins-car pursuers and simple-motion evaders. The goal of the pursuers is to cooperatively protect a planar convex region from the evaders,…

Systems and Control · Electrical Eng. & Systems 2023-12-25 Rui Yan , Xiaoming Duan , Rui Zou , Xin He , Zongying Shi , Francesco Bullo

A fundamental task in mobile robotics is keeping an intelligent agent under surveillance with an autonomous robot as it travels in the environment. This work studies a theoretical version of that problem involving one of the most popular…

Robotics · Computer Science 2025-01-09 Ubaldo Ruiz

In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not {\em who} wins but rather {\em how fast} can one win. These type of problems were studied earlier for…

Combinatorics · Mathematics 2008-06-03 Dan Hefetz , Michael Krivelevich , Miloš Stojaković , Tibor Szabó

In this work, we extend the convex bodies chasing problem (CBC) to an adversarial setting, where an agent (the Player) is tasked with chasing a sequence of convex bodies generated adversarially by another agent (the Opponent). The Player…

Systems and Control · Electrical Eng. & Systems 2023-03-20 Yue Guan , Longxu Pan , Daigo Shishika , Panagiotis Tsiotras

Computing worst-case robust strategies in pursuit-evasion games (PEGs) is time-consuming, especially when real-world factors like partial observability are considered. While important for general security purposes, real-time applicable…

Machine Learning · Computer Science 2026-05-15 Runyu Lu , Ruochuan Shi , Yuanheng Zhu , Dongbin Zhao

This paper aims to put forward the concept that learning to take safe actions in unknown environments, even with probability one guarantees, can be achieved without the need for an unbounded number of exploratory trials, provided that one…

Machine Learning · Computer Science 2021-04-01 Agustin Castellano , Juan Bazerque , Enrique Mallada

There is an old conjecture by Shermer \cite{sher} that in a polygon with $n$ vertices and $h$ holes, $\lfloor \dfrac{n+h}{3} \rfloor$ vertex guards are sufficient to guard the entire polygon. The conjecture is proved for $h=1$ by Shermer…

Computational Geometry · Computer Science 2021-02-23 Sharareh Alipour

An important feature of a dynamic game is its monitoring structure namely, what the players effectively see from the played actions. We consider games with arbitrary monitoring structures. One of the purposes of this paper is to know to…

Information Theory · Computer Science 2012-10-24 Maël Le Treust , Samson Lasaulce

This work derives two basic engagement zone models, describing regions of potential risk or capture for a mobile vehicle by a pursuer. The pursuer is modeled as having turn-constraints rather than simple motion. Turn-only (C-Paths) and…

Optimization and Control · Mathematics 2025-02-04 Thomas Chapman , Isaac E. Weintraub , Alexander Von Moll , Eloy Garcia

We consider a variant of the target defense problem in a planar conical environment where a single defender is tasked to capture a sequence of incoming attackers. The attackers' objective is to breach the target boundary without being…

Systems and Control · Electrical Eng. & Systems 2025-09-18 Arman Pourghorban , Dipankar Maity

This article presents a distributed algorithm for a group of robotic agents with omnidirectional vision to deploy into nonconvex polygonal environments with holes. Agents begin deployment from a common point, possess no prior knowledge of…

Robotics · Computer Science 2010-12-03 Karl J. Obermeyer , Anurag Ganguli , Francesco Bullo

This paper investigates the difference between the circular and elliptical cases in one-on-one pursuit and evasion problems. Using the simultaneous differential equation derived by Barton and Eliezer, we derive a dynamical system based on…

Optimization and Control · Mathematics 2026-05-25 Sota Yoshihara

We consider a variation of cop vs.\ robber on graph in which the robber is not restricted by the graph edges; instead, he picks a time-independent probability distribution on $V(G)$ and moves according to this fixed distribution. The cop…

Combinatorics · Mathematics 2013-08-23 Natasha Komarov , Peter Winkler

In this paper we study a linear pursuit differential game described by an infinite system of first-order differential equations in Hilbert space. The control functions of players are subject to geometric constraints. The pursuer attempts to…

Optimization and Control · Mathematics 2020-02-19 Gafurjan Ibragimov , Massimiliano Ferrara , Idham Arif Alias , Mehdi Salimi

A fundamental component of modern trackers is an online learned tracking model, which is typically modeled either globally or locally. The two kinds of models perform differently in terms of effectiveness and robustness under different…

Computer Vision and Pattern Recognition · Computer Science 2016-09-12 Yao Sui , Guanghui Wang , Yafei Tang , Li Zhang