The anticipation of human behavior is a crucial capability for robots to interact with humans safely and efficiently. We employ a smart edge sensor network to provide global observations along with future predictions and goal information to integrate anticipatory behavior for the control of a mobile manipulation robot. We present approaches to anticipate human behavior in the context of safe navigation and a collaborative mobile manipulation task. First, we anticipate human motion by employing projections of human trajectories from smart edge sensor network observations into the planning map of a mobile robot. Second, we anticipate human intentions in a collaborative furniture-carrying task to achieve a given goal. Our experiments indicate that anticipating human behavior allows for safer navigation and more efficient collaboration. Finally, we showcase an integrated system that anticipates human behavior and collaborates with a human to achieve a target room layout, including the placement of tables and chairs.