Current NASA plans envision human beings returning to the Moon in 2018 and, once there, establishing a permanent outpost from which we may initiate a long-term effort to visit other planetary bodies in the Solar System. This will be a bold, risky, and costly journey, comparable to the Great Navigations of the fifteenth and sixteenth centuries. Therefore, it is important that all possible actions be taken to maximize the astronauts' safety and productivity. This can be achieved by deploying fleets of autonomous robots for mineral prospecting and mining, habitat construction, fuel production, inspection and maintenance, etc.; and by providing the humans with the capability to telesupervise the robots' operation and to teleoperate them whenever necessary or appropriate, all from a safe, "shirtsleeve" environment. This paper describes the authors' work in progress on the development of a Robot Supervision Architecture (RSA) for safe and efficient space exploration and operation. By combining the humans' advanced reasoning capabilities with the robots' suitability for harsh space environments, we will demonstrate significant productivity gains while reducing the amount of weight that must be lifted from Earth -and, therefore, cost.Our first instantiation of the RSA is a wide-area mineral prospecting task, where a fleet of robots survey a pre-determined area autonomously, sampling for minerals of interest. When the robots require assistance -e.g., when they encounter navigation problems, reach a prospecting site, or find a potentially interesting rock formationthey signal a human telesupervisor at base, who intervenes via a high-fidelity geometrically-correct stereoscopic telepresence system (Figure 1a). In addition to prospecting, the RSA applies to a variety of other tasks, both on the surface: mining, transporting, and construction -and on-orbit: construction, inspection, and repair of large space structures and satellites (Figure 1b).