  This paper considers the problem of fast and safe autonomous navigation in
partially known environments. Our main contribution is a control policy design
based on ellipsoidal trajectory bounds obtained from a quadratic
state-dependent distance metric. The ellipsoidal bounds are used to embed
directional preference in the control design, leading to system behavior that
is adapted to the local environment geometry, carefully considering medial
obstacles while paying less attention to lateral ones. We use a virtual
reference governor system to adaptively follow a desired navigation path,
slowing down when system safety may be violated and speeding up otherwise. The
resulting controller is able to navigate complex environments faster than
common Euclidean-norm and Lyapunov-function-based designs, while retaining
stability and collision avoidance guarantees.
