A simple visual navigation system with convergence property

Abstract

The aim of this paper is to present a convergence property of a simple vision based navigation system for a mobile robot. A robot equipped with a single camera is guided by a human operator along a path consisting of straight segments. During this guided tour, local image invariants are extracted from acquired frames and odometric data are collected. When navigating learned path, the vision is used to reckon direction to the start point of next straight segment. Odometric measurements are utilized to estimate distance to this point. A simple linear model of this navigation system is lined up and its properties are examined. We proclaim a theorem, which states, that for a limited odometric error and "reasonable" trajectory, the robot uncertainty in position estimation does not diverge. A formal proof of this theorem is given for regular polygonal trajectories. The proclaimed convergence theorem is also experimentally verified. © 2008 Springer-Verlag Berlin Heidelberg.