This paper presents an algorithm for finding collision free trajectories in a three dimensional environment. Given the starting and destination points, the algorithm constructs a trajectory from the segments of the medial axis of the free space. The moving object is represented by its minimum enclosing sphere. The medial axis is obtained by shrinking the voxel representation, and the trajectory is derived by treating the medial axis as a graph and conducting a heuristic search; both phases are implemented in an inefficient manner in the current algorithm. Improvements in these and other parts are outlined and currently under way.