Optimal coverage of a known arbitrary environment

The problem of coverage of known space by a mobile robot has many applications. Of particular interest is providing a solution that guarantees the complete coverage of the free space by traversing an optimal path, in terms of the distance travelled. In this paper we introduce a new algorithm based on the Boustrophedon cellular decomposition. The presented algorithm encodes the areas (cells) to be covered as edges of the Reeb graph. The optimal solution to the Chinese Postman Problem (CPP) is used to calculate an Euler tour, which guarantees complete coverage of the available free space while minimizing the path of the robot. In addition, we extend the classical solution of the CPP to account for the entry point of the robot for cell coverage by changing the weights of the Reeb graph edges. Proof of correctness is provided together with experimental results in different environments.