Online Scan Coverage of Grid Environments by a Mobile Robot

Abstract

We describe an on-line sensor based algorithm for covering planar areas with a uniform scan pattern, where the covering is executed by a D×D square-shaped tool attached to a mobile robot. The algorithm, called Scan-STC, incrementally subdivides the planar area into a grid of D-size cells, while following a spanning tree of a graph whose nodes are 2D-size cells. The algorithm covers any planar grid with a scan path whose total length is at most (n + m)D, where n is the number of D-size cells and m ≤ n is the number of boundary cells, defined as cells that share at least one point with the grid boundary. Scan-STC additionally strives to minimize the total length of path segments orthogonal to the scan direction, and we report a preliminary bound on the length of these segments. We also demonstrate that any on-line coverage algorithm generates a covering path whose length is at least (2 − ε)l _opt in worst case, where l _opt is the length of the optimal off-line covering path. Since (n+m)D ≤ 2l _opt , the bound is tight and Scan-STC is worst-case optimal. Moreover, in practical environments m << n, and Scan-STC generates close-to-optimal covering paths in such environments.