Optimal robot localization in trees

• Authors: Rudolf Fleischer;Kathleen Romanik;Sven Schuierer;Gerhard Trippen
• Venue: Information and Computation
• Year: 2002

The problem of localization, that is, of a robot finding itsposition on a map, is an important task for autonomous mobilerobots. It has applications in numerous areas of robotics rangingfrom aerial photography to autonomous vehicle exploration. In thispaper we present a new strategy LPS(Localize-by-Placement-Separation) for a robot to find its positionon a map, where the map is represented as a geometric tree ofbounded degree. Our strategy exploits to a high degree theself-similarities that may occur in the environment. We use theframework of competitive analysis to analyze the performance of ourstrategy. In particular, we show that the distance traveled by therobot is at most O (√n) times longer than the shortestpossible route to localize the robot, where n is the numberof vertices of the tree. This is a significant improvement over thebest known previous bound of O(n2/3). Moreover,since there is a lower bound of Ω(√n), our strategy isoptimal up to a constant factor. Using the same approach we canalso show that the problem of searching for a target in a geometrictree, where the robot is given a map of the tree and the locationof the target but does not know its own position, can be solved bya strategy with a competitive ratio of O(√n), which is againoptimal up to a constant factor. 2001 Elsevier Science