Presents a globally convergent range-sensor based navigation algorithm in three-dimensions, called 3D Bug. The 3D Bug algorithm navigates a point robot in a three-dimensional unknown environment using position and range sensors. The algorithm strives to process the sensory data in the most reactive way possible, without sacrificing the global convergence guarantee. Moreover, unlike previous reactive-like algorithms, 3D Bug uses three-dimensional range data and plans three-dimensional motion throughout the navigation process. The algorithm alternates between two modes of motion. During motion towards the target, which is the first motion mode of the algorithm, the robot follows the locally shortest path in a purely reactive fashion. During traversal of an obstacle surface, which is the second mode of motion, the robot incrementally constructs a reduced data structure of an obstacle, while performing local shortcuts based on range data. We resent preliminary simulation results of the algorithm, which show that 3D Bug generates paths that resemble the globally shortest path in simple scenarios. Moreover, the algorithm generates reasonably short paths even in concave, room-like environments.