Where to Drop Sensors from Aerial Robots to Monitor a Surface-Level Phenomenon?

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.