  Real-time navigation in a priori unknown environment remains a challenging
task, especially when an unexpected (unmodeled) disturbance occurs. In this
paper, we propose the framework Safe Returning Fast and Safe Tracking (SR-F)
that merges concepts from 1) Robust Control Lyapunov-Value Functions (R-CLVF),
and 2) the Fast and Safe Tracking (FaSTrack) framework. The SR-F computes an
R-CLVF offline between a model of the true system and a simplified planning
model. Online, a planning algorithm is used to generate a trajectory in the
simplified planning space, and the R-CLVF is used to provide a tracking
controller that exponentially stabilizes to the planning model. When an
unexpected disturbance occurs, the proposed SR-F algorithm provides a means for
the true system to recover to the planning model. We take advantage of this
mechanism to induce an artificial disturbance by ``jumping'' the planning model
in open environments, forcing faster navigation. Therefore, this algorithm can
both reject unexpected true disturbances and accelerate navigation speed. We
validate our framework using a 10D quadrotor system and show that SR-F is
empirically 20\% faster than the original FaSTrack while maintaining safety.
