We address a problem of area protection in graph-based scenarios with multiple agents. The problem consists of two adversarial teams of agents that move in an undirected graph shared by both teams. Agents are placed in vertices of the graph; at most one agent can occupy a vertex; and they can move into adjacent vertices in a conflict free way. Teams have asymmetric goals: the aim of one team - attackers - is to invade into given area while the aim of the opponent team - defenders - is to protect the area from being entered by attackers by occupying selected vertices. We study strategies for allocating vertices to be occupied by the team of defenders to block attacking agents. We show that the decision version of the problem of area protection is PSPACE-hard under the assumption that agents can allocate their target vertices multiple times. Further we develop various on-line vertex-allocation strategies for the defender team in a simplified variant of the problem with single stage vertex allocation and evaluated their performance in multiple benchmarks. The success of a strategy is heavily dependent on the type of the instance, and so one of the contributions of this work is that we identify suitable vertex-allocation strategies for diverse instance types. In particular, we introduce a simulation-based method that identifies and tries to capture bottlenecks in the graph, that are frequently used by the attackers. Our experimental evaluation suggests that this method often allows a successful defense even in instances where the attackers significantly outnumber the defenders.
Aside from CPF algorithms, systems with mobile agents that act in the adversarial manner represent another related area. These studies often focus on patrolling strategies that are robust with respect to various attackers trying to penetrate through the patrol path @cite_9 . Theoretical works related to APP also include studies on pursuit evasion @cite_2 or predator-prey @cite_0 problems. The major difference between these works and the concept of APP is that we consider relatively higher number of agents and our agents are more limited in their abilities.
@cite_0 @cite_9 @cite_2
2122762267 2167163748 2160484294
A set of k mobile agents are placed on the boundary of a simply connected planar object represented by a cycle of unit length. Each agent has its own predefined maximal speed, and is capable of moving around this boundary without exceeding its maximal speed. The agents are required to protect the boundary from an intruder which attempts to penetrate to the interior of the object through a point of the boundary, unknown to the agents. The intruder needs some time interval of length τ to accomplish the intrusion. Will the intruder be able to penetrate into the object, or is there an algorithm allowing the agents to move perpetually along the boundary, so that no point of the boundary remains unprotected for a time period τ? Such a problem may be solved by designing an algorithm which defines the motion of agents so as to minimize the idle time I, i.e., the longest time interval during which any fixed boundary point remains unvisited by some agent, with the obvious goal of achieving I < τ. Depending on the type of the environment, this problem is known as either boundary patrolling or fence patrolling in the robotics literature. The most common heuristics adopted in the past include the cyclic strategy, where agents move in one direction around the cycle covering the environment, and the partition strategy, in which the environment is partitioned into sections patrolled separately by individual agents. This paper is, to our knowledge, the first study of the fundamental problem of boundary patrolling by agents with distinct maximal speeds. In this scenario, we give special attention to the performance of the cyclic strategy and the partition strategy. We propose general bounds and methods for analyzing these strategies, obtaining exact results for cases with 2, 3, and 4 agents. We show that there are cases when the cyclic strategy is optimal, cases when the partition strategy is optimal and, perhaps more surprisingly, novel, alternative methods have to be used to achieve optimality. In this paper we present a novel graph theoretic problem, called GRAPH-CLEAR, useful to model surveillance tasks where multiple robots are used to detect all possible intruders in a given indoor environment. We provide a formal definition of the problem and we investigate its basic theoretical properties, showing that the problem is NP-complete. We then present an algorithm to compute a strategy for the restriction of the problem to trees and present a method how to use this solution in applications. The method is then tested in simple simulations. GRAPH-CLEAR is useful to describe multirobot pursuit evasion games when robots have limited sensing capabilities, i.e. multiple agents are needed to perform basic patrolling operations. In a class of games known as Stackelberg games, one agent (the leader) must commit to a strategy that can be observed by the other agent (the follower or adversary) before the adversary chooses its own strategy. We consider Bayesian Stackelberg games, in which the leader is uncertain about the types of adversary it may face. Such games are important in security domains, where, for example, a security agent (leader) must commit to a strategy of patrolling certain areas, and a robber (follower) has a chance to observe this strategy over time before choosing its own strategy of where to attack. This paper presents an efficient exact algorithm for finding the optimal strategy for the leader to commit to in these games. This algorithm, DOBSS, is based on a novel and compact mixed-integer linear programming formulation. Compared to the most efficient algorithm known previously for this problem, DOBSS is not only faster, but also leads to higher quality solutions, and does not suffer from problems of infeasibility that were faced by this previous algorithm. Note that DOBSS is at the heart of the ARMOR system that is currently being tested for security scheduling at the Los Angeles International Airport. Patrolling involves generating patrol paths for mobile robots such that every point on the paths is repeatedly covered. This paper focuses on patrolling in closed areas, where every point in the area is to be visited repeatedly by one or more robots. Previous work has often examined paths that allow for repeated coverage, but ignored the frequency in which points in the area are visited. In contrast, we first present formal frequency-based optimization criteria used for evaluation of patrol algorithms. Then, we present a patrol algorithm that guarantees maximal uniform frequency, i.e., each point in the target area is covered at the same optimal frequency. This solution is based on finding a circular path that visits all points in the area, while taking into account terrain directionality and velocity constraints. Robots are positioned uniformly along this path in minimal time, using a second algorithm. Moreover, the solution is guaranteed to be robust in the sense that uniform frequency of the patrol is achieved as long as at least one robot works properly. We then present a set of algorithms for handling events along the patrol path. The algorithms differ in the way they handle the event, as a function of the time constraints for handling them. However, all the algorithms handle events while maintaining the patrol path, and minimizing the disturbance to the system.