  Path planning for autonomous vehicles in arbitrary environments requires a
guarantee of safety, but this can be impractical to ensure in real-time when
the vehicle is described with a high-fidelity model. To address this problem,
this paper develops a method to perform trajectory design by considering a
low-fidelity model that accounts for model mismatch. The presented method
begins by computing a conservative Forward Reachable Set (FRS) of a
high-fidelity model's trajectories produced when tracking trajectories of a
low-fidelity model over a finite time horizon. At runtime, the vehicle
intersects this FRS with obstacles in the environment to eliminate trajectories
that can lead to a collision, then selects an optimal plan from the remaining
safe set. By bounding the time for this set intersection and subsequent path
selection, this paper proves a lower bound for the FRS time horizon and sensing
horizon to guarantee safety. This method is demonstrated in simulation using a
kinematic Dubin's car as the low-fidelity model and a dynamic unicycle as the
high-fidelity model.
