Time Efficient Inspection of Ground Vehicles by a UAV Team Using a Markov Inequality Based Rule

We present a control design for N unmanned aerial vehicles (UAVs) tasked with a time efficient inspection of M ground moving vehicles. The navigation and intent of each ground vehicle are unknown, therefore, the uncertainty of its navigation has to be anticipated in the navigation of each UAV. We use the minimum time stochastic optimal control to navigate each UAV towards the inspection of ground vehicles. Based on this control, we formulate assignments of ground vehicles to be inspected by UAVs as an optimization problem to inspect all ground vehicles in the minimum expected time. Accounting for ground vehicle uncertain trajectories, we update the optimal assignment by a Markov inequality rule. The rule prevents the possibility of indefinite updating of assignments without finishing the inspection of all vehicles. On the other hand, it updates an assignment if it leads to a statistically significant improvement of the expected time of inspection. The presented approach is illustrated by a numerical example.