Extracting surveillance graphs from robot maps

Abstract — GRAPH-CLEAR is a recently introduced theo-retical framework to model surveillance tasks accomplished by multiple robots patrolling complex indoor environments. In this paper we provide a first step to close the loop between its graph-based theoretical formulation and practical scenarios. We show how it is possible to algorithmically extract suitable so-called surveillance graphs from occupancy grid maps. We also identify local graph modification operators, called contractions, that alter the graph being extracted so that the original surveillance problem can be solved using less robots. The algorithm we present is based on the Generalized Voronoi Diagram, a structure that can be simply computed using watershed like algorithms. Our algorithm is evaluated by processing maps produced by mobile robots exploring indoor environments. It turns out that the proposed algorithm is fast, robust to noise, and opportunistically modifies the graph so that less expensive strategies can be computed. I

Risk Aversion in Finite Markov Decision Processes Using Total Cost Criteria and Average Value at Risk

In this paper we present an algorithm to compute risk averse policies in Markov Decision Processes (MDP) when the total cost criterion is used together with the average value at risk (AVaR) metric. Risk averse policies are needed when large deviations from the expected behavior may have detrimental effects, and conventional MDP algorithms usually ignore this aspect. We provide conditions for the structure of the underlying MDP ensuring that approximations for the exact problem can be derived and solved efficiently. Our findings are novel inasmuch as average value at risk has not previously been considered in association with the total cost criterion. Our method is demonstrated in a rapid deployment scenario, whereby a robot is tasked with the objective of reaching a target location within a temporal deadline where increased speed is associated with increased probability of failure. We demonstrate that the proposed algorithm not only produces a risk averse policy reducing the probability of exceeding the expected temporal deadline, but also provides the statistical distribution of costs, thus offering a valuable analysis tool

Computing Time-Optimal Clearing Strategies for Pursuit-Evasion Problems with Linear Programming

This paper addresses and solves the problem of finding optimal clearing strategies for a team of robots in an environment given as a graph. The graph-clear model is used in which sweeping of locations, and their recontamination by intruders, is modelled over a surveillance graph. Optimization of strategies is carried out for shortest total travel distance and time taken by the robot team and under constraints of clearing costs of locations. The physical constraints of access and timely movements by the robots are also accounted for, as well as the ability of the robots to prevent recontamination of already cleared areas. The main result of the paper is that this complex problem can be reduced to a computable LP problem. To further reduce complexity, an algorithm is presented for the case when graph clear strategies are a priori available by using other methods, for instance by model checking

Rapid Multirobot Deployment with Time Constraints

Abstract-In this paper we consider the problem of multirobot deployment under temporal deadlines. The objective is to compute strategies trading off safety for speed in order to maximize the probability of reaching a given set of target locations within a given temporal deadline. We formulate this problem using the theory of Constrained Markov Decision Processes and we show that thanks to this framework it is possible to determine deploying strategies maximizing the probability of success while satisfying a temporal deadline. Moreover, the formulation allows to exactly compute the failure probability of complex deployment tasks. Simulation results illustrate how the proposed method works in different scenarios and show how informed decisions can be made regarding the size of the robot team

Probabilistic Graph-Clear

Abstract — This paper introduces a probabilistic model for multirobot surveillance applications with limited range and possibly faulty sensors. Sensors are described with a footprint and a false negative probability, i.e. the probability of failing to report a target within their sensing range. The model implements a probabilistic extension to our formerly developed deterministic approach for modeling surveillance tasks in large environments with large robot teams known as Graph-Clear. This extension leads to a new algorithm that allows to answer new design and performance questions, namely 1) how many robots are needed to obtain a certain confidence that the environment is free from intruders, and 2) given a certain number of robots, how should they coordinate their actions to minimize their failure rate. I

Patrolling security games: Definition and algorithms for solving largeinstances with single patroller and single intruder

Security games are gaining significant interest in artificial intelligence. They are characterized by two players (a defender and an attacker) and by a set of targets the defender tries to protect from the attacker\u2bcs intrusions by committing to a strategy. To reach their goals, players use resources such as patrollers and intruders. Security games are Stackelberg games where the appropriate solution concept is the leader\u2013follower equilibrium. Current algorithms for solving these games are applicable when the underlying game is in normal form (i.e., each player has a single decision node). In this paper, we define and study security games with an extensive-form infinite-horizon underlying game, where decision nodes are potentially infinite. We introduce a novel scenario where the attacker can undertake actions during the execution of the defender\u2bcs strategy. We call this new game class patrolling security games (PSGs), since its most prominent application is patrolling environments against intruders. We show that PSGs cannot be reduced to security games studied so far and we highlight their generality in tackling adversarial patrolling on arbitrary graphs. We then design algorithms to solve large instances with single patroller and single intruder