This paper is concerned with online coverage of unknown planar environments by a mobile robot of size D operating with a limited energy capacity battery. The battery capacity is represented by the path length L that the robot can travel under a full battery charge. Starting at S, the robot has to cover a planar environment containing unknown obstacles, and return to S upon task completion. During task execution, the robot may return to S at any time to recharge its battery. This paper first describes a battery powered offline coverage methodology, then introduces the battery powered coverage (BPC) algorithm that performs online battery powered coverage using position and local obstacle detection sensors. The performance of the BPC algorithm is measured by its competitiveness, determined by measuring the mobile robot's total online path length, l, relative to the optimal offline solution lopt. This paper establishes that the BPC algorithm has a competitive performance of l ≤ ( L/ D) lopt. This paper additionally establishes a universal lower bound of l ≥ log( L/ 4 D) lopt over all online battery powered coverage algorithms. Execution example illustrates the usefulness of the BPC algorithm.

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) loptover 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.