A method for evaluating, at video rate, the quality of actions for a single camera while mapping unknown indoor environments is presented. The strategy maximizes mutual information between measurements and states to help the camera avoid making ill-conditioned measurements that are appropriate to lack of depth in monocular vision systems. Our system prompts a user with the appropriate motion commands during 6-DOF visual simultaneous localization and mapping with a handheld camera. Additionally, the system has been ported to a mobile robotic platform, thus closing the control-estimation loop. To show the viability of the approach, simulations and experiments are presented for the unconstrained motion of a handheld camera and for the motion of a mobile robot with nonholonomic constraints. When combined with a path planner, the technique safely drives to a marked goal while, at the same time, producing an optimal estimated map.