In this paper, an algorithm for the complete multi-robot coverage of a connected space with unknown obstacles is presented. The proposed algorithm mainly operates by maintaining, as far as possible, small uncovered regions between covered areas and obstacles. In addition, the bounds on the amount of repeated coverage and time required for complete coverage are also investigated. Furthermore, it is shown that repeated coverage can occur only around regions where the paths between obstacles are less than twice the width of the robots’ coverage range. This property holds even when the robots have no a priori knowledge of the environment, and therefore helps to prevent unnecessary wastage of time and resources.