Computing Time-Optimal Clearing Strategies for Pursuit-Evasion Problems with Linear Programming

This paper addresses and solves the problem of finding optimal clearing strategies for a team of robots in an environment given as a graph. The graph-clear model is used in which sweeping of locations, and their recontamination by intruders, is modelled over a surveillance graph. Optimization of strategies is carried out for shortest total travel distance and time taken by the robot team and under constraints of clearing costs of locations. The physical constraints of access and timely movements by the robots are also accounted for, as well as the ability of the robots to prevent recontamination of already cleared areas. The main result of the paper is that this complex problem can be reduced to a computable LP problem. To further reduce complexity, an algorithm is presented for the case when graph clear strategies are a priori available by using other methods, for instance by model checking.