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

Capturing an Evader Using Multiple Pursuers with Sensing Limitations in Convex Environment

A modified continuous-time pursuit-evasion game with multiple pursuers and a single evader is studied. The game has been played in an obstacle-free convex environment which consists an exit gate through which the evader may escape. The geometry of the convex is unknown to all players except pursuers know the location of the exit gate and they can communicate with each other. All players have equal maximum velocities and identical sensing range. An evader is navigating inside the environment and seeking the exit gate to win the game. A novel sweep-pursuit-capture strategy for the pursuers to search and capture the evader under some necessary and sufficient conditions is presented. We also show that three pursuers are sufficient to finish the operation successfully. Non-holonomic wheeled mobile robots of the same configurations have been used as the pursuers and the evader. Simulation studies demonstrate the performance of the proposed strategy in terms of interception time and the distance traveled by the players.

Two-Dimensional Pursuit-Evasion in a Compact Domain with Piecewise Analytic Boundary

In a pursuit-evasion game, a team of pursuers attempt to capture an evader. The players alternate turns, move with equal speed, and have full information about the state of the game. We consider the most restictive capture condition: a pursuer must become colocated with the evader to win the game. We prove two general results about pursuit-evasion games in topological spaces. First, we show that one pursuer has a winning strategy in any CAT(0) space under this restrictive capture criterion. This complements a result of Alexander, Bishop and Ghrist, who provide a winning strategy for a game with positive capture radius. Second, we consider the game played in a compact domain in Euclidean two-space with piecewise analytic boundary and arbitrary Euler characteristic. We show that three pursuers always have a winning strategy by extending recent work of Bhadauria, Klein, Isler and Suri from polygonal environments to our more general setting.Comment: 21 pages, 6 figure

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

Probabilistic Graph-Clear

Abstract — This paper introduces a probabilistic model for multirobot surveillance applications with limited range and possibly faulty sensors. Sensors are described with a footprint and a false negative probability, i.e. the probability of failing to report a target within their sensing range. The model implements a probabilistic extension to our formerly developed deterministic approach for modeling surveillance tasks in large environments with large robot teams known as Graph-Clear. This extension leads to a new algorithm that allows to answer new design and performance questions, namely 1) how many robots are needed to obtain a certain confidence that the environment is free from intruders, and 2) given a certain number of robots, how should they coordinate their actions to minimize their failure rate. I

Robot-Assisted Surveillance in Large Environments

This paper introduces ANSER, a mobile robot designed to perform surveillance in wide indoor and outdoor areas, such as civilian airports, warehouses or other facilities. The paper describes in details the robot subsystems, focusing on its capabilities in autonomous surveillance, localization and navigation