A log-approximation for coverage path planning with the energy constraint

We consider the problem of covering an environment with a robot when the robot has limited energy budget. The environment is represented as a polygon with a grid, whose resolution is proportional to the robot size, imposed on it. There is a single charging station in the environment. At each time step, the robot can move from one grid cell to an adjacent one. The energy consumption when moving in the environment is assumed to be uniform and proportional to the distance traveled. Our goal is to minimize both the total distance and the number of visits to the charging station. We present a coverage path planning algorithm which has O(lnD) approximation factor for both objectives, where D is the distance of the furthest cell in the environment measured on the grid.