Continuous Graph Partitioning for Camera Network Surveillance

In this work we design surveillance trajectories for a network of autonomous cameras to detect intruders in an environment. Intruders, which appear at arbitrary times and locations, are classified as static or dynamic. While static intruders remain stationary, dynamic intruders are aware of the cameras configuration and move to avoid detection, if possible. As performance criteria we consider the worst-case detection time of static and dynamic intruders. We model the environment and the camera network by means of a robotic roadmap. We show that optimal cameras trajectories against static intruders are obtained by solving a continuous graph partitioning problem. We design centralized and distributed algorithms to solve this continuous graph partitioning problem. Our centralized solution relies on tools from convex optimization. For the distributed case we consider three distinct cameras communication models and propose a corresponding algorithm for each of the models. Regarding dynamic intruders, we identify necessary and sufficient conditions on the cameras locations to detect dynamic intruders infinite time. Additionally, we construct constant-factor optimal trajectories for the case of ring and tree roadmaps.