An algorithmic solution method is presented for the problem of autonomous robot motion in completely unknown environments. Our approach is based on the alternate execution of two fundamental processes: map building and navigation. In the former, range measures are collected through the robot exteroceptive sensors and processed in order to build a local representation of the surrounding area. This representation is then integrated in the global map so far reconstructed by filtering out insufficient or conflicting information. In the navigation phase, an A*-based planner generates a local path from the current robot position to the goal. Such a path is safe inside the explored area and provides a direction for further exploration. The robot follows the path up to the boundary of the explored area, terminating its motion if unexpected obstacles are encountered. The most peculiar aspects of our method are the use of fuzzy logic for the efficient building and modification of the environment map, and the iterative application of A*, a complete planning algorithm which takes full advantage of local information. Experimental results for a NOMAD 200 mobile robot show the real-time performance of the proposed method, both in static and moderately dynamic environments.