Optimal Circular Flight of Multiple UAVs for Target Tracking in Urban Areas

Abstract

This work is an extension of our previous result in which a novel single-target tracking algorithm for fixed-wing UAVs (Unmanned Air Vehicles) was proposed. Our previous algorithm firstly finds the centre of a circular flight path, rc, over the interested ground target which maximises the total chance of keeping the target inside the camera field of view of UAVs, , while the UAVs fly along the circular path. All the UAVs keep their maximum allowed altitude and fly along the same circle centred at rc with the possible minimum turn radius of UAVs. As discussed in [1,4], these circular flights are highly recommended for various target tracking applications especially in urban areas, as for each UAV the maximum altitude flight ensures the maximum visibility and the minimum radius turn keeps the minimum distance to the target at the maximum altitude. Assuming a known probability distribution for the target location, one can quantify , which is incurred by the travel of a single UAV along an arbitrary circle, using line-of-sight vectors. From this observation, (the centre of) an optimal circle among numerous feasible ones can be obtained by a gradient-based search combined with random sampling, as suggested in [1]. This optimal circle is then used by the other UAVs jointly tracking the same target. As the introduction of multiple UAVs may minimise further, the optimal spacing between the UAVs can be naturally considered. In [1], a typical line search method is suggested for this optimal spacing problem. However, as one can easily expect, the computational complexity of this search method may undesirably increase as the number of UAVs increases. The present work suggests a remedy for this seemingly complex optimal spacing problem. Instead of depending on time-consuming search techniques, we develop the following algorithm, which is computationally much more efficient. Firstly, We calculate the distribution (x), where x is an element of , which is the chance of capturing the target by one camera along . Secondly, based on the distribution function, (x), find separation angles between UAVs such that the target can be always tracked by at least one UAV with a guaranteed probabilistic measure. Here, the guaranteed probabilistic measure is chosen by taking into account practical constraints, e.g. required tracking accuracy and UAVs' minimum and maximum speeds. Our proposed spacing scheme and its guaranteed performance are demonstrated via numerical simulations.