  This paper presents a novel information-based mission planner for a drone
tasked to monitor a spatially distributed dynamical phenomenon. For the sake of
simplicity, the area to be monitored is discretized. The insight behind the
proposed approach is that, thanks to the spatio-temporal dependencies of the
observed phenomenon, one does not need to collect data on the entire area. In
fact, unmeasured states can be estimated using an estimator, such as a Kalman
filter. In this context the planning problem becomes the one of generating a
flight path that maximizes the quality of the state estimation while satisfying
the flight constraints (e.g. flight time). The first result of this paper is to
formulate this problem as a special Orienteering Problem where the cost
function is a measure of the quality of the estimation. This approach provides
a Mixed-Integer Semi-Definite formulation to the problem which can be optimally
solved for small instances. For larger instances, two heuristics are proposed
which provide good sub-optimal results. To conclude, numerical simulations are
shown to prove the capabilities and efficiency of the proposed path planning
strategy. We believe this approach has the potential to increase dramatically
the area that a drone can monitor, thus increasing the number of applications
where monitoring with drones can become economically convenient.
