A Game-Theoretical Model Applied to an Active Patrolling Camera

Abstract

In patrolling, an agent perceives portions of an environment to detect the presence of an intruder. Usually, the agent cannot perceive the whole environment at once, but can change over time the observed portion. Finding an optimal patrolling strategy that minimizes the possibility of intrusions constitutes one of the main scientific problems in this field. Game theoretical models have been recently employed to compute effective patrolling strategies that explicitly consider the presence of a rational intruder. In this paper, we present a general game theoretical framework for computing patrolling strategies for different kinds of patrollers. In particular, we study the case of an active patrolling camera.

Computing Stackelberg Equilibria in Discounted Stochastic Games

“…Some of the earliest work (Agmon, Kraus, and Kaminka 2008;Agmon, Urieli, and Stone 2011) on adversarial patrolling was done in the context of robotic patrols, but involved a highly simplified defense decision space (for example, with a set of robots moving around a perimeter, and a single parameter governing the probability that they move forward or back). Basilico et al (Basilico, Gatti, and Amigoni 2009;Basilico et al 2010;Basilico, Gatti, and Villa 2011;Bosansky et al 2011) studied general-sum patrolling games in which they assumed that the attacker is infinitely patient, and the execution of an attack can take an arbitrary number of time steps. Considering SSGs in full generality, as we do here, yields the previous settings as special cases (modulo the discount factor).…”

Strategic analysis of complex security scenarios.

“…In a somewhat different vein, [11] study win-lose patrolling games in which the patroller chooses a sequence of targets to visit, while the attacker can only choose a target, and a time of attack, with the goal of mathematically characterizing the value of the game for different classes of graphs. Another line of work on adversarial patrolling studies general-sum patrolling games in which the patroller (defender, leader) first commits to a stochastic policy, which is observed by the attacker who chooses which target to attack and in which context [19,22,21,18,23,20]. An important differentiating assumption of the latter work is that, like in our setting, the attacker is assumed to observe both the defender's policy, as well as its past realizations, and can condition his decision on both.…”

Multi-agent perimeter patrolling subject to mobility constraints

“…Example VI. 2 We consider a set of 50 cameras with the goal of patrolling the interval L = [0, 200]. We assume that the velocities are all equal to the same value v, i.e.,v i = v, for all i ∈ {1, .…”

“…Differently from [2], the particular focus here is on the coordination and communication among cameras, which is studied in the context of distributed algorithms. In this scenario, the case of perimeter patrolling is considered and each camera is located in a fixed position with limited visibility of the scene and limited motion capability: Since the patrolling task corresponds to the action of visually monitoring the environment, each camera needs to coordinate its motion with the its neighbors in order to ensure an optimal coverage policy of the whole monitored area.…”

“…In [2], the case of smart camera patrolling is studied as a particular case of the multiagent network. In this work, the problem of patrolling is cast into a pursuit-evasion paradigm: Two players are considered, a rational patroller and a rational intruder and game-theory techniques are applied in order to design an optimal patrolling strategy for the patroller, in terms of Pan-Tilt-Zoom (PTZ) commands.…”