Methods and apparatus for implementing a safety system for a mobile robot are described. The method comprises receiving first sensor data from one or more sensors, the first sensor data being captured at a first time, identifying, based on the first sensor data, a first unobserved portion of a safety field in an environment of a mobile robot, assigning, to each of a plurality of contiguous regions within the first unobserved portion of the safety field, an occupancy state, updating, at a second time after the first time, the occupancy state of one or more of the plurality of contiguous regions, and determining one or more operating parameters for the mobile robot, the one or more operating parameters based, at least in part, on the occupancy state of at least some regions of the plurality of contiguous regions at the second time.