Spanning-tree based coverage of continuous areas by a mobile robot

This paper considers the problem of covering a continuous planar area by a square-shaped tool attached to a mobile robot. Using a tool-based approximation of the work-area, we present an algorithm that covers every point of the approximate area for tasks such as floor cleaning, lawn mowing, and field determining. The algorithm, called Spanning Tree Covering (STC), subdivides the work-area into disjoint cells corresponding to the square-shaped tool, then follows a spanning tree of the graph induced by the cells, while covering every point precisely once. We present and analyze three versions of the STC algorithm. The first version is off-line, where the robot has perfect apriori knowledge of its environment. The off-line STC algorithm computes an optimal covering path in linear time O(N), where N is the number of cells comprising the approximate area. The second version of STC is on-line, where the rebut uses its sensors to detect obstacles anti construct a spanning tree of the environment while covering the work-area. The on-line STC algorithm completes an optimal covering path in time O(N), bur requires O(N) memory for its implementation, The third version of STC is "ant"-like. In this version, too, the rebut has no apriori knowledge of the environment, but it may leave pheromone-like markers during the coverage process. The ant-like STC algorithm runs in time O(N), and requires only O(l) memory. Finally we present simulation results of the three STC algorithms, demonstrating their effectiveness in cases when the tool size is significantly smaller than the work-area characteristic dimension.