In this paper, we propose a search and surveillance with mobile robots to collect information while minimizing repeated coverage to maximize efficiency. The problem of search and surveillance is defined as one having a mobile robot or covering a working area with sensor footprints. The problem is applicable to tasks such as floor cleaning, map building, surveillance, security patrols, and search and rescue operations. We use a reaction-diffusion equation on a graph (RDEG), we make and remake plans online base on incoming environmental information. The strategy is applicable to patrolling tasks after an environment has been completely explorated. Tasks are allocated to multiple mobile robots, among which a temporary leader, i.e., the robot detecting a drastic change in the environment, plans a strategy for other mobile robots on the team. Sensing and positioning data for each robot is broadcast and shared among robots. Simulation in different scenarios using one to three robots demonstrated the feasibility of increasing the number of robots on a team.
