Spiral-STC: an on-line coverage algorithm of grid environments by a mobile robot

We describe an on-line sensor based algorithm for covering planar areas by a square-shaped tool attached to a mobile robot. Let D be the tool size. The algorithm, called Spiral-STC, incrementally subdivides the planar work-area into disjoint D-size cells, while following a spanning tree of the resulting grid. The algorithm covers general grid environments using a path whose 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. We also report that any on-line coverage algorithm generates a covering path whose length is at least (2 - ε)l_opt in the worst case, where l_opt is the length of the optimal covering path. Since (n + m)D ≤ 2l_opt, Spiral-STC is worst-case optimal. Moreover, m << n in practical environments, and the algorithm generates close-to-optimal covering paths in such environments. Simulation results demonstrate the spiral-like covering patterns typical to the algorithm.