An optimal on-line strategy for walking in streets with minimal sensing

This paper considers the problem of walking in the street with a mobile robot. The robot starts from a point s to search the target point t. The robot is equipped with a minimal sensing sensor that can only detect the discontinuities in depth information (or gaps), but has no prior knowledge of the street. The performance of our strategy is measured in terms of the competitive ratio, with respect to the length of the optimal path for walking in the street with complete knowledge. We propose a new 9-competitive strategy, and prove that it is optimal by showing a matching lower bound, whereas the previous best approach proposed by Tabatabaei et al. has a competitive ratio of 11.