We consider the following differential game of pursuit and evasion involving two unmanned aerial vehicle agents (UAVs): an evading UAV (“evader”), which has limited maneuverability, and a pursuing UAV (“pursuer”), which is assumed to be completely agile. The two UAVs move on the Euclidean plane with different but constant speeds. Whereas the pursuer can change the orientation of its velocity ve...

Two players, Red and Blue, each independently choose a vertex of a connected graph G. Red must then pay Blue an amount equal to the distance between the vertices chosen. In this note, w e investigate the value v(G) of this pursuit-evasion game for various classes of graphs G, as well as those optimal mixed strategies for achieving v(G). It is shown that some rather counterintuitive behavior can...

In typical 2D Voronoi diagrams, the distance from a site to a point in the plane is unaffected by the existance of other sites. In 2D pursuit/evasion Voronoi diagrams, the distance from an evader to a point is the length of the shortest path to that point that avoids all pursuers. Since pursuers can move, the paths that evaders follow to reach certain points in the plane can be quite complicate...

Pursuit-evasion games, such as the game of Revolutionaries and Spies, are a simplified model for network security. In the game we consider in this paper, a team of r revolutionaries tries to hold an unguarded meeting consisting of m revolutionaries. A team of s spies wants to prevent this forever. For given r and m, the minimum number of spies required to win on a graph G is the spy number σ(G,...

The interception of a maneuvering antisurface missile, as in ballistic missile defense and ship defense scenarios, is formulated as an imperfect information, zero-sum, pursuit-evasion game with a state constraint imposed on the evader. Assuming that the perfect informationversion of the gamedoes not yield a successful result for the defense, the solution of this game is in mixed strategies. The...

The two games considered are mixtures of Searching and Cops and Robber. The cops have partial information, provided first via selected vertices of a graph, and then via selected edges. This partial information includes the robber's position, but not the direction in which he is moving. The robber has perfect information. In both cases, we give bounds on the amount of such information required b...

The cops-and-robber (CR) game has been used in mobile robotics as a discretized model of pursuit/evasion problems. The “classical” CR version is a perfect information game: the cop’s (pursuer’s) location is always known to the robber (evader) and vice versa. More relevant to robotics are versions where one (or both) player is invisible. In this paper we study the extent to which the CR game bec...

The games considered aremixtures of Searching andCops andRobber. The cops havepartial information provided viawitnesseswho report ‘‘sightings’’ of the robber. Thewitnesses are able to provide information about the robber’s position but not the direction in which he is moving. The robber has perfect information. In the case when sightings occur at regular intervals, we present a recognition theo...

In this paper, we study the vertex pursuit game of Cops and Robbers where cops try to capture a robber loose on the vertices of a graph. The minimum number of cops required to win on a given graph G is the cop number of G. We present asymptotic results for the game of Cops and Robbers played on a random graph G(n, p) focusing on the case when the cop number does not grow with the size of a grap...

This paper reports on research into the origins of communication and coordination. Several problems with deening communication and coordination are noted. A research methodology is described that circumvents these problems. The methodology is used in an experiment concerning the development of coordination. The aim of the experiment is to see whether a learning agent can use coordination signal...