  This paper proposes a physics-inspired solution for low altitude Unmanned
Aircraft System (UAS) Traffic Management (UTM) in urban areas. We decompose UTM
into spatial and temporal planning problems. For the spatial planning problem,
we use the principles of Eulerian continuum mechanics to safely and optimally
allocate finite airspace to a UAS. To this end, the finite airspace is
partitioned into planned and unplanned subspaces with unplanned subspace(s) or
zone(s) enclosing buildings and restricted no-fly regions. The planned subspace
is divided into navigable channels that safely wrap unplanned zone(s). We model
the airspace planning problem as a Markov Decision Process (MDP) with states
defined based on spatial and temporal airspace features and actions authorizing
transitions between safe navigable channels. We apply the proposed traffic
management solution to plan safe coordination of small UAS in the airspace
above downtown Tucson, Arizona.
