The dynamic window approach is a well known navigation scheme developed by Fox, Burgard and Thrun and extended by Brock and Khatib. It is safe by construction and has been shown to perform very efficiently in experimental setups. However, one can construct examples where the proposed scheme fails to attain the goal configuration. What has been lacking is a theoretical treatment of the algorithm’s convergence properties. Here we present such a treatment. Furthermore, we highlight the similarity between the Dynamic Window Approach and the Control Lyapunov Function and Receding Horizon Control synthesis put forth by Primbs, Nevestic and Doyle. Inspired by these similarities we propose a version of the Dynamic Window Approach that is provably convergent.