  In this paper, we consider the problem of caging and eventual capture of an
underwater entity using multiple Autonomous Underwater Vehicles (AUVs) in a 3D
water volume We solve this problem both with and without taking bathymetry into
account. Our proposed algorithm for range-limited sensing in 3D environments
captures a finite-speed entity based on sparse and irregular observations.
After an isolated initial sighting of the entity, the uncertainty of its
whereabouts grows while deployment of the AUV system is underway. To contain
the entity, an initial cage, or barrier of sensing footprints, is created
around the initial sighting, using islands and other terrain as part of the
cage if available. After the initial cage is established, the system waits for
a second sighting, and the possible opportunity to create a smaller, shrinkable
cage. This process continues until at some point it is possible to create this
smaller cage, resulting in capture, meaning the entity is sensed directly and
continuously. We present a set of algorithms for addressing the scenario above,
and illustrate their performance on a set of examples. The proposed algorithm
is a combination of solutions to the min-cut problem, the set cover problem,
the linear bottleneck assignment problem and the Thomson problem.
