  Fast and Safe Tracking (FaSTrack) is a modular framework that provides safety
guarantees while planning and executing trajectories in real time via value
functions of Hamilton-Jacobi (HJ) reachability. These value functions are
computed through dynamic programming, which is notorious for being
computationally inefficient. Moreover, the resulting trajectory does not adapt
online to the environment, such as sudden disturbances or obstacles. DeepReach
is a scalable deep learning method to HJ reachability that allows
parameterization of states, which opens up possibilities for online adaptation
to various controls and disturbances. In this paper, we propose Parametric
FaSTrack, which uses DeepReach to approximate a value function that
parameterizes the control bounds of the planning model. The new framework can
smoothly trade off between the navigation speed and the tracking error
(therefore maneuverability) while guaranteeing obstacle avoidance in a priori
unknown environments. We demonstrate our method through two examples and a
benchmark comparison with existing methods, showing the safety, efficiency, and
faster solution times of the framework.
