Off-line exploration of rectangular cellular environments with a rectangular obstacle

In this paper, we consider exploring a known rectangular cellular environment that has a rectangular obstacle using a mobile robot. The robot has to visit each cell and return to its starting cell. The goal is to find the shortest tour that visits all the cells. We give a linear-time algorithm that finds the exploration tour of optimal length. While the previous algorithms for environments with obstacles are approximation, the algorithm is presented in this paper is optimal. This algorithm also works for L-shaped and C-shaped environments. The main idea of the algorithm is, first, to find the longest simple exploring cycle, then extend it to include the unvisited cells.