On-line path planning in an unknown polygonal environment

We consider the navigation problem of a robot from a starting point S to a target point T inside an unknown rectilinear polygon. The robot knows the directions of the points S and T and it can detect the edges of the polygon through its tactile sensors. We present a competitive strategy for the robot to reach the target T. The competitive ratio of our strategy is ⩽4.5 d( κ−1)( κ+2)+O(1), where, κ=3 ( d/2)−1 and d is the L 1 distance between S and T. We do not assume any structural restriction on the polygon, however the point S must be on one of the extreme edges of the polygon. This is the first strategy to search for a target inside an arbitrary unknown polygon with competitive ratio independent of the number of edges of the polygon.