An On-Line Algorithm for Improving Performance in Navigation

We consider the following scenario. A point robot is placed at some start location ¡ in a 2dimensional scene containing oriented rectangular obstacles. The robot must repeatedly travel back and forth between ¡ and a second location ¢ in the scene. The robot knows the coordinates of ¡ and ¢ but initially knows nothing about the positions or sizes of the obstacles. It can only determine the obstacles’ locations by bumping into them. We would like an intelligent strategy for the robot so that its trips between ¡ and ¢ both are relatively fast initially, and improve as more trips are taken and more information is gathered. In this paper we describe an algorithm for this problem with the following guarantee: in the first £¥¤§¦ trips, the average distance per trip is at most ¨©  ¦ £  times the length of the shortest ¡ ¢ path in the scene, where ¦ is the Euclidean distance between ¡ and ¢ . We also show a matching lower bound for deterministic strategies. These r...

• Type: Conference
• Year: 1993
• Where: FOCS
• Authors: Avrim Blum, Prasad Chalasani
• Keywords: FOCS 1993, Oriented Rectangular Obstacles, Point Robot, Robot, Theoretical Computer Science