The contribution of this dissertation is the presentation of a new algorithm for the construction of feedback controllers with global convergence, safety, and smoothness guarantees. This algorithm integrates motion planning’s emphasis on collision avoidance and algorithmic completeness with control theory’s insistence on the use of feedback to achieve robust, efficient, real time control. This combination of features renders this algorithm uniquely applicable to real world robot navigation problems. Historically, the motion planning problem is to compute a continuous, collisionfree path between given initial and goal configurations, or to return that no such path exists. These algorithms typically assume both perfect sensing and perfect control; i.e., the environment and the robot’s configuration are perfectly known at all times, and the robot’s motion is perfectly predictable. From a practical point of view, however, neither of these assumptions is actually valid. Even if a collisionfree path can be computed, the robot cannot follow it exactly; once it has deviated from the precomputed trajectory, what should the robot do? Questions like these