Optimal Strategy for Walking in Streets with Minimum Number of Turns for a Simple Robot

Abstract

We consider the problem of walking a simple robot in an unknown street. The robot that cannot infer any geometric properties of the street traverses the environment to reach a target $$t$$ , starting from a point $$s$$ . The robot has a minimal sensing capability that can only report the discontinuities in the depth information (gaps), and location of the target point once it enters in its visibility region. Also, the robot can only move towards the gaps while moving along straight lines is cheap, but rotation is expensive for the robot. We maintain the location of some gaps in a tree data structure of constant size. The tree is dynamically updated during the movement. Using the data structure, we present an online strategy that generates a search path for the robot with optimal number of turns.