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 6 4:5dðj 1Þðjþ 2Þ þOð1Þ, where, j 1⁄4 3ðd=2Þ 1 and d is the L1 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. 2003 Elsevier Inc. All rights reserved.