Abstract We consider the problem of coverage planning for a particular type of very simple mobile robot. The robot must be able to translate in a commanded direction (specified in a global reference frame), with bounded error on the motion direction, until reaching the environment boundary. The objective, for a given environment map, is to generate a sequence of motions that is guaranteed to cover as large a portion of that environment as possible, in spite of the severe limits on the robot's sensing and actuation abilities. We show how to model the knowledge available to this kind of robot its own position within the environment, show how to compute the region whose coverage can be guaranteed for a given plan, and characterize regions whose coverage cannot be guaranteed by any plan. We also describe a heuristic algorithm that generates coverage plans for this robot, based on a search across a specially-constructed graph. Simulation results demonstrate the effectiveness of the approach.