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