  Fast and safe navigation of dynamical systems through a priori unknown
cluttered environments is vital to many applications of autonomous systems.
However, trajectory planning for autonomous systems is computationally
intensive, often requiring simplified dynamics that sacrifice safety and
dynamic feasibility in order to plan efficiently. Conversely, safe trajectories
can be computed using more sophisticated dynamic models, but this is typically
too slow to be used for real-time planning. We propose a new algorithm
FaSTrack: Fast and Safe Tracking for High Dimensional systems. A path or
trajectory planner using simplified dynamics to plan quickly can be
incorporated into the FaSTrack framework, which provides a safety controller
for the vehicle along with a guaranteed tracking error bound. This bound
captures all possible deviations due to high dimensional dynamics and external
disturbances. Note that FaSTrack is modular and can be used with most current
path or trajectory planners. We demonstrate this framework using a 10D
nonlinear quadrotor model tracking a 3D path obtained from an RRT planner.
