  We propose an online iterative algorithm to find a suitable convex cover to
under-approximate the free space for autonomous navigation to delineate Safe
Flight Corridors (SFC). The convex cover consists of a set of polytopes such
that the union of the polytopes represents obstacle-free space, allowing us to
find trajectories for robots that lie within the convex cover. In order to find
the SFC that facilitates optimal trajectory generation, we iteratively find
overlapping polytopes of maximum volumes that include specified waypoints
initialized by a geometric or kinematic planner. Constraints at waypoints
appear in two alternating stages of a joint optimization problem, which is
solved by a method inspired by the Alternating Direction Method of Multipliers
(ADMM) with partially distributed variables. We validate the effectiveness of
our proposed algorithm using a range of parameterized environments and show its
applications for two-stage motion planning.
