In autonomous mobile robot applications, local obstacle avoidance methods are frequently coupled with an initialized global map in order to achieve a complete navigation scheme. Unfortunately, global map information is often unavailable for global map initialization. In these situations, the designer must develop a navigation scheme such that the mobile robot either doesn't need a global map to achieve its goal or it builds the global map autonomously. This work presents a simple algorithm for developing a quasi-free space global map. The algorithm is based on the premise that the robot will be given multiple attempts at a particular goal. During early attempts, the mobile robot explores using solely local obstacle avoidance. While exploring, the robot records where it has been and uses this information on subsequent attempts. Further, this paper also outlines the look-ahead method by which the global map is implemented. Finally, both simulated and experimental results are presented. Testing of this algorithm was performed on an outdoor mobile robot, known as Navigator, which was developed at Virginia Tech.