Optimal minimax pursuit evasion on a Manhattan grid

The optimal control of a pursuer searching for a slower moving evader on a Manhattan grid road network is considered. The pursuer does not have on-board capability to detect the evader and relies instead on Unattended Ground Sensors (UGSs) to locate the evader. We assume that all the intersections in the road network have been instrumented with UGSs. When an evader passes by an UGS location, it triggers the UGS and this time-stamped information is stored by the UGS. When the pursuer arrives at an UGS location, the UGS informs the pursuer if and when the evader passed by. When the evader and the pursuer arrive at an UGS location simultaneously, the UGS is triggered and this information is instantly relayed to the pursuer, thereby enabling “capture”.We derive exact values for the optimal worst case time to capture the evader on the Manhattan grid and the corresponding pursuit policy.