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...ith, for example toxic waste observance. The problem of multi-robot patrol is derived from the fundamental problem of multi-robot coverage [4], and has received growing interest of its own (e.g. [1], =-=[6]-=-). Current patrol solutions offer deterministic algorithms for generating a patrol path for a team of robots and maintaining the patrol. Analysis of these algorithms concentrated on assuring some freq...

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...olling around a perimeter in different adversarial environments. The multi-robot patrol task requires a team of robots to jointly repeatedly visit some target area in order to monitor change in state =-=[6, 2]-=-. When working in adversarial environments, the robots’ task is to detect changes in state that are controlled by an adversary. In our case, we assume the adversary is trying to penetrate through the ...

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... has recently gained attention, e.g., see [5]. The situation in which the motion of the robots needs to guarantee a uniform frequency coverage of the environment has been considered, among others, in =-=[6]-=-. However, because we are interested in the worst case scenario, the trajectories proposed in these works are not optimal in our sense. In [7], an empirical evaluation of existing patrolling heuristic...

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...ts efficiency and it is discussed its scalability as well as its possibility to use different team sizes. Finally, the article ends with conclusions and future work. 2. STATE OF THE ART Kaminka et al.=-=[2]-=- described an algorithm that places robots uniformly along a predefined path obtained by computing a minimal Hamiltonian cycle, ensuring the same optimal frequency for every point of the graph. Kollin...

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...und a perimeter (closed polygon) or an open fence (open polyline). 1. Introduction The problem of multi-robot patrol has gained interest in recent years (e.g., Ahmadi & Stone, 2006; Chevaleyre, 2004; =-=Elmaliach, Agmon, & Kaminka, 2007-=-; Paruchuri, Tambe, Ordonez, & Kraus, 2007; Amigoni, Gatti, & Ippedico, 2008), mainly due to its immediate relevance to various security applications. In the multi-robot patrol problem, robots are req...

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...is given. Problems with more than two cells are addressed by a heuristic policy. In [6], the authors proposed a stabilizing speed controller for a single agent so that the accumulated uncertainty over a given path in the environment is bounded, along with an optimal controller that minimizes the maximum steady-state uncertainty, assuming that the agent travels along a closed path and does not change direction. The persistent monitoring problem is 2 also related to robot patrol problems, where a team of robots are required to visit points in the workspace with frequency constraints [12], [13], [14]. Although one-dimensional persistent monitoring problems are of interest in their own right (e.g., see [15]), our ultimate goal is to optimally control a team of cooperating agents in a two or three-dimensional environment. The contribution of this paper is to take a first step toward this goal by formulating and solving an optimal control problem for a team of agents moving in a one-dimensional mission space described by an interval [0, L] ⊂ R in which we minimize the accumulated uncertainty over a given time horizon and over an arbitrary number of sampling points. Even in this simple case, ...

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...uristic decision-making with pathfinder agents and using communication via a central coordinator, one gets the best performing approach in all criteria: Heuristic Pathfinder Cognitive Coordinator. In =-=[5]-=- the area patrol algorithm developed guarantees that each point in the target area is covered at the same optimal frequency. This is done by computing minimalcosts cyclic patrol paths that visit all p...

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... taken and a Markov chain is used to achieve a desired visit-frequency distribution over a set of features. In [2], the authors look at robots modelled by controlled Markov chains, and seek to persistently monitor regions while avoiding forbidden regions. The other main approach to persistent monitoring is to cast the problem as one in combinatorial optimization. This research typically falls under the name of patrolling or persistent surveillance. In the most basic problem, a robot seeks to minimize the time between visits to each point in space. For this problem, both centralized approaches [9, 13, 21], and distributed algorithms for multiple robots [24] have been proposed. Recently, there has been work on minimizing the weighted time between visits to each region of interest, where the weight of a region captures its priority relative to other regions [27, 23]. These works focus on controlling robots along predefined paths. In [27], the authors consider velocity controllers for persistent monitoring along fixed tours, while in [23] the authors focus on coordination issues for multiple robots on fixed tours. An optimal control formulation for persistent monitoring in one-dimensional spaces ...

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...through physical experiments and simulations. I. INTRODUCTION The purpose of a patrol is to continuously travel in an area to protect or supervise it. Common goals are uniform frequency coverage [1], =-=[2]-=-, [3] and detection of adversaries [4], [5]. Frequency-based patrol systems are usually designed for surveillance, but are also useful in tasks such as cleaning, garbage collection, and monitoring. Mu...