The dynamic window approach is a well known navigation scheme developed by Fox et. al. (1997) and extended by Brock and Khatib (1999). 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. A first step towards such a treatment was previously presented by the authors (2002). Here we continue that work with a computationally tractable algorithm resulting from a careful discretization of the optimal control problem of the previous paper and a way to construct a continuous navigation function. Inspired by the similarities between the dynamic window approach and the control Lyapunov function and receding horizon control synthesis put forth by Primbs et. al. (1999) we propose a version of the dynamic window approach that is tractable and provably convergent.