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This paper is concerned with an online tethered coverage (TC), in which a mobile robot of size D is attached to a fixed point S by a cable of finite length L. Starting at S, the robot has to cover an unknown planar environment that contains obstacles and return to S with the cable fully retracted. The paper first establishes an optimal offline TC methodology, then introduces the TC algorithm that performs an online TC using position and local obstacle detection sensors. The performance of the TC algorithm is measured by its competitiveness, determined by measuring its total online path length l relative to the optimal offline solution lopt . The paper establishes that the TC algorithm has a competitive performance of l ≤ 2 L/D lopt. The paper additionally establishes a lower bound of l ≥ log(L/D) lopt over a generic family of TC algorithms of which the TC algorithm is a special case. Execution example and experiments with a tethered recoiling mechanism illustrate the usefulness of the TC algorithm.