In this paper, we report on experiments with a core system for autonomous navigation in outdoor natural terrain. The system consists of three parts: a perception module which processes range images to identify untraversable regions of the terrain, a local map management module which maintains a representation of the environment in the vicinity of the vehicle, and a planning module which issues commands to the vehicle controller. Our approach uses reactive planning for generating commands to drive the vehicle along with "early traversability evaluation," in which the perception module decides which parts of the terrain are traversable as soon as a new image is taken. We argue that our approach leads to a robust and efficient navigation system. We illustrate our approach by an experiment in which a vehicle travelled autonomously for one kilometer through unmapped cross-country terrain.