In this paper we propose the use of game theory as a general formalism for representing, comparing, and providing insight into solutions to a wide class of robotics problems. Particularly, we show how game theory can be applied to problems of multiple robot coordination, high-level strategy planning, information gathering through manipulation and/or sensor planning, and pursuit-evasion scenario...

Isaacs' treatise on diierential games was a breakthrough for the analysis of the pursuit-and-evasion (PE) domain within the context of strategies representable by diierential equations. Current experimental work in Artiicial Life steps outside of the formalism of diierential games, but the formalism it steps into is yet to be identiied. We introduce a formulation of PE that allows a formalism t...

We give two characterizations of the graphs on which k cops have a winning strategy in the game of Cops and Robber. One of these is in terms of an order relation, and one is in terms of a vertex ordering. Both generalize characterizations known for the case k = 1. © 2012 Elsevier B.V. All rights reserved.

In this paper we study the concurrent cops and robber (CCCR) game. CCCR follows the same rules as the classical, turn-based game, except for the fact that the players move simultaneously. The cops' goal is to capture the robber and the concurrent cop number of a graph is defined the minimum number of cops which guarantees capture. For the variant in which it it required to capture the robber in...

We consider a Cops-and-Robber game played on the subsets of an n-set. The robber starts at the full set; the cops start at the empty set. In each round, each cop moves up one level by gaining an element, and the robber moves down one level by discarding an element. The question is how many cops are needed to ensure catching the robber when the robber reaches the middle level. Alan Hill posed th...

We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that in an n-dimensional grid, at least n cops are necessary if one wants to catch the robber under all possible initial configurations. We also present a set of cop strategies for which n cops are provably sufficient to catch the robber.

We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that for an ndimensional grid, at least n cops are necessary to ensure capture of the robber. We also present a set of cop strategies for which n cops are provably sufficient to catch the robber. Further, for two-dimensional grid, we provide an efficient cop strategy for which the robber...

Pursuit-evasion games have been used for modeling various forms of conflict arising between two agents modeled as dynamical systems. Although analytical solutions of some simple pursuit-evasion games are known, most interesting instances can only be solved using numerical methods requiring significant offline computation. In this paper, a novel incremental sampling-based algorithm is presented ...

In this work, we investigate a jamming attack on the communication network of a team of UAVs flying in a formation. We propose a communication and motion model for the UAVs. The communication model provides a relation in the spatial domain for effective jamming by an aerial intruder. We formulate the problem as a zero-sum pursuit-evasion game. In our earlier work we used Isaacs’ approach to obt...

This paper addresses the control of a team of autonomous agents pursuing a smart evader in a nonaccurately mapped terrain. By describing this problem as a partial information Markov game, we are able to integrate map-learning and pursuit. We propose receding horizon control policies, in which the pursuers and the evader try to respectively maximize and minimize the probability of capture at the...