  We present a safe-by-design approach to path planning and control for
nonlinear systems. The planner uses a low fidelity model of the plant to
compute reference trajectories by solving an MPC problem, while the plant being
controlled utilizes a feedback control law that tracks those trajectories with
an upper-bound on the tracking error. Our main goal is to allow for maximum
permissiveness (that is, room for constraint feasibility) of the planner, while
maintaining safety after accounting for the tracking error bound. We achieve
this by parametrizing the state and input constraints imposed on the planner
and deriving corresponding parametrized tracking control laws and tracking
error bounds, which are computed offline through Sum-of-Squares programming.
The parameters are then optimally chosen to maximize planner permissiveness,
while guaranteeing safety.
