The giving tree: Constructing trees for efficient offline and online multi-robot coverage

This paper discusses the problem of building efficient coverage paths for a team of robots. An efficient multi-robot coverage algorithm should result in a coverage path for every robot, such that the union of all paths generates a full coverage of the terrain and the total coverage time is minimized. A method underlying several coverage algorithms, suggests the use of spanning trees as base for creating coverage paths. However, overall performance of the coverage is heavily dependent on the given spanning tree. This paper focuses on the challenge of constructing a coverage spanning tree for both online and offline coverage that minimizes the time to complete coverage. Our general approach involves building a spanning tree by growing sub-trees from the initial location of the robots. This paper first describes a polynomial time tree-construction algorithm for offline coverage. The use of this algorithm is shown by extensive simulations to significantly improve the coverage time of the terrain even when used as a basis for a simple, inefficient, coverage algorithm. Second, this paper provides an algorithm for online coverage of a finite terrain based on spanning-trees, that is complete and guarantees linear time coverage with no redundancy in the coverage. In addition, the solutions proposed by this paper guarantee robustness to failing robots: the offline trees are used as base for robust multi-robot coverage algorithms, and the online algorithm is proven to be robust.