Efficient Strategies for Robot Navigation in Unknown Environment

We propose two strategies called the adaptive- bias heuristic and the adjusted- bias heuristic for navigating a robot in unknown environment containing rectangular and rectilinear obstacles. For each of these strategies we study the ratio of the dead-free path length made by the strategy to the shortest path length between the start point and the target point when all obstacles satisfy some limitations on their aspect ratios and side lengths. For the adaptive- bias heuristic and the adjusted-bias heuristic we show that the ratios are at most arbitrarily close to 1+3/5k and 1+3/5f, respectively, as n grows, if the start point and the target are at the same horizontal level, where any side length of each obstacle is at most k and the aspect ratio of any obstacle is at most f, respectively. We also study the ratios for unknown environment where the start point and the target may be at different levels. These ratios are better than the ratios obtained by strategies previously known for the classes of scenes considered in this paper.