  We present a multi-rate control architecture that leverages fundamental
properties of differential flatness to synthesize controllers for
safety-critical nonlinear dynamical systems. We propose a two-layer
architecture, where the high-level generates reference trajectories using a
linear Model Predictive Controller, and the low-level tracks this reference
using a feedback controller. The novelty lies in how we couple these layers, to
achieve formal guarantees on recursive feasibility of the MPC problem, and
safety of the nonlinear system. Furthermore, using differential flatness, we
provide a constructive means to synthesize the multi-rate controller, thereby
removing the need to search for suitable Lyapunov or barrier functions, or to
approximately linearize/discretize nonlinear dynamics. We show the synthesized
controller is a convex optimization problem, making it amenable to real-time
implementations. The method is demonstrated experimentally on a ground rover
and a quadruped robotic system.
