Through the Looking Glass: Off-Line Versus On-Line Coverage of Planar Environments by a Battery Powered Autonomous Mobile Robot

This paper is concerned with off-line and on-line coverage of planar environments by an autonomous mobile robot of size D, under the constraint of a limited energy source such as a battery. Starting at S, the robot has to cover a planar environment containing obstacles, and return to S upon task completion. The robot may return to S at any time to recharge its battery. In the off-line case the robot is given a geometric description of the environment, while in the on-line case the robot has no prior knowledge of the environment, but is able to accumulate local information using on-board sensors and data storage. The paper first describes a battery powered off-line coverage methodology, then introduces the BPC (Battery Powered Coverage) algorithm that performs on-line battery powered coverage using position and local obstacle detection sensors. On-line battery coverage turns out to be perfectly opposite to off-line coverage, hence the looking glass analogy. The performance of the BPC algorithm is measured by its competitiveness, determined by measuring its total on-line path length, l, relative to the optimal off-line solution lopt. The paper establishes that the BPC algorithm has a competitive performance of l≤ L D lopt, where 2L is the maximum path length generated by a single full battery charge, and D is the robot’s size. The paper additionally establishes a universal lower bound of l ≥ log( L 4D )lopt over all online battery powered coverage algorithms. Execution examples and experiments illustrate the usefulness of the BPC algorithm.