Visually smooth multi-UAV formation transformation

Unmanned airborne vehicles (UAVs) are useful in both military and civilian operations. In this paper, we consider a recreational scenario, i.e., multi-UAV formation transformation show. A visually smooth transformation needs to enforce the following three requirements at the same time: (1) visually pleasing contour morphing - for any intermediate frame, the agents form a meaningful shape and align with the contour, (2) uniform placement - for any intermediate frame, the agents are (isotropically) evenly spaced, and (3) smooth trajectories - the trajectory of each agent is as rigid/smooth as possible and completely collision free. First, we use the technique of 2-Wasserstein distance based interpolation to generate a sequence of intermediate shape contours. Second, we consider the spatio-temporal motion of all the agents altogether, and integrate the uniformity requirement and the spatial coherence into one objective function. Finally, the optimal formation transformation plan can be inferred by collaborative optimization. Extensive experimental results show that our algorithm outperforms the existing algorithms in terms of visual smoothness of transformation, boundary alignment, uniformity of agents, and rigidity of trajectories. Furthermore, our algorithm is able to cope with some challenging scenarios including (1) source/target shapes with multiple connected components, (2) source/target shapes with different typology structures, and (3) existence of obstacles. Therefore, it has a great potential in the real multi-UAV light show. We created an animation to demonstrate how our algorithm works; See the demo at https://1drv.ms/v/s!AheMg5fKdtdugVL0aNFfEt_deTbT?e=le5poN .