  We consider the problem of routing a team of energy-constrained Unmanned
Aerial Vehicles (UAVs) to drop unmovable sensors for monitoring a task area in
the presence of stochastic wind disturbances. In prior work on mobile sensor
routing problems, sensors and their carrier are one integrated platform, and
sensors are assumed to be able to take measurements at exactly desired
locations. By contrast, airdropping the sensors onto the ground can introduce
stochasticity in the landing locations of the sensors. We focus on addressing
this stochasticity in sensor locations from the path-planning perspective.
Specifically, we formulate the problem (Multi-UAV Sensor Drop) as a variant of
the Submodular Team Orienteering Problem with one additional constraint on the
number of sensors on each UAV. The objective is to maximize the Mutual
Information between the phenomenon at Points of Interest (PoIs) and the
measurements that sensors will take at stochastic locations. We show that such
an objective is computationally expensive to evaluate. To tackle this
challenge, we propose a surrogate objective with a closed-form expression based
on the expected mean and expected covariance of the Gaussian Process. We
propose a heuristic algorithm to solve the optimization problem with the
surrogate objective. The formulation and the algorithms are validated through
extensive simulations.
