Visibility Graphs, Dismantlability, and the Cops and Robbers Game

We study versions of cop and robber pursuit-evasion games on the visibility graphs of polygons, and inside polygons with straight and curved sides. Each player has full information about the other player's location, players take turns, and the robber is captured when the cop arrives at the same point as the robber. In visibility graphs we show the cop can always win because visibility graphs are dismantlable, which is interesting as one of the few results relating visibility graphs to other known graph classes. We extend this to show that the cop wins games in which players move along straight line segments inside any polygon and, more generally, inside any simply connected planar region with a reasonable boundary. Essentially, our problem is a type of pursuit-evasion using the link metric rather than the Euclidean metric, and our result provides an interesting class of infinite cop-win graphs.Comment: 23 page

An improved lion strategy for the lion and man problem

In this paper, a novel lion strategy for David Gale's lion and man problem is proposed. The devised approach enhances a popular strategy proposed by Sgall, which relies on the computation of a suitable "center". The key idea of the new strategy is to update the center at each move, instead of computing it once and for all at the beginning of the game. Convergence of the proposed lion strategy is proven and an upper bound on the game length is derived, which dominates the existing bounds.Comment: Preprint submitted to IEEE Control Systems Letter

Search and Pursuit-Evasion in Mobile Robotics, A survey

This paper surveys recent results in pursuitevasion and autonomous search relevant to applications in mobile robotics. We provide a taxonomy of search problems that highlights the differences resulting from varying assumptions on the searchers, targets, and the environment. We then list a number of fundamental results in the areas of pursuit-evasion and probabilistic search, and we discuss field implementations on mobile robotic systems. In addition, we highlight current open problems in the area and explore avenues for future work

Visibility maintenance via controlled invariance for leader-follower Dubins-like vehicles

The paper studies the visibility maintenance problem (VMP) for a leader-follower pair of Dubins-like vehicles with input constraints, and proposes an original solution based on the notion of controlled invariance. The nonlinear model describing the relative dynamics of the vehicles is interpreted as linear uncertain system, with the leader robot acting as an external disturbance. The VMP is then reformulated as a linear constrained regulation problem with additive disturbances (DLCRP). Positive D-invariance conditions for linear uncertain systems with parametric disturbance matrix are introduced and used to solve the VMP when box bounds on the state, control input and disturbance are considered. The proposed design procedure is shown to be easily adaptable to more general working scenarios. Extensive simulation results are provided to illustrate the theory and show the effectiveness of our approachComment: 17 pages, 24 figures, extended version of the journal paper of the authors submitted to Automatic

Multi-robot Automated Search for Non-Adversarial Moving Evaders in an Unknown Environment

In this paper, the problem of searching for moving evaders in unknown environment using group of mobile robots is investigated. The aim is to find the moving evaders as fast as possible. Three different search techniques are proposed and evaluated through extensive experimentation. In the first two techniques, robots do not cooperate or coordinate their actions. Alternatively, they implement simple movement strategies to locate the evaders. On the contrary, in the third technique, robots employ explicit coordination among each other and they implement a relatively complex algorithm based on voronio graph to find the evaders. In the later technique, each robot needs to be equipped with communication and localization capabilities. The results showed that graph-based technique led to shortest search time. However, it also showed that a reasonable performance is possible with cheap robots implementing simple and non-coordination techniques. Keywords: Search, Multi-Robot, Voronio Graph, Moving Target, Coordination

Environment Characterization for Non-Recontaminating Frontier-Based Robotic Exploration

This paper addresses the problem of obtaining a concise description of a physical environment for robotic exploration. We aim to determine the number of robots required to clear an environment using non-recontaminating exploration. We introduce the medial axis as a configuration space and derive a mathematical representation of a continuous environment that captures its underlying topology and geometry. We show that this representation provides a concise description of arbitrary environments, and that reasoning about points in this representation is equivalent to reasoning about robots in physical space. We leverage this to derive a lower bound on the number of required pursuers. We provide a transformation from this continuous representation into a symbolic representation. Finally, we present a generalized pursuit-evasion algorithm. Given an environment we can compute how many pursuers we need, and generate an optimal pursuit strategy that will guarantee the evaders are detected with the minimum number of pursuers.Singapore-MIT Alliance for Research and Technology Center (Future Urban Mobility Project)United States. Air Force Office of Scientific Research (Award FA9550-08-1-0159)National Science Foundation (U.S.) (Award CNS-0715397)National Science Foundation (U.S.) (Award CCF-0726514)National Science Foundation (U.S.) (Grant 0735953

Optimal Intermittent Sensing for Pursuit-Evasion Games

We consider a class of pursuit-evasion differential games in which the evader has continuous access to the pursuer's location, but not vice-versa. There is a remote sensor (e.g., a radar station) that can sense the evader's location upon a request from the pursuer and communicate that sensed location to the pursuer. The pursuer has a budget on the total number of sensing requests. The outcome of the game is determined by the sensing and motion strategies of the players. We obtain an equilibrium sensing strategy for the pursuer and an equilibrium motion strategy for the evader. We quantify the degradation in the pursuer's pay-off due to its sensing limitations