This article presents an algorithm for robust nonlinear explicit model predictive control. A low complexity receding horizon control law is obtained by approximating the optimal control law using multiscale basis function approximation. Feasibility and input-to-stability of the system in closed-loop with the approximate control law are verified using reachability analysis where zonotopes, DC programming, and recursive splitting, are used to compute a capture basin. The resulting control law is built on a grid hierarchy that is fast to evaluate in real-time systems.