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 .

无人驾驶飞行器 (UAV) 在军事和民用行动中都很有用。在本文中，我们考虑了一个娱乐场景，即多无人机编队变换表演。视觉平滑变换需要同时执行以下三个要求：(1) 视觉上令人愉悦的轮廓变形——对于任何中间帧，代理形成有意义的形状并与轮廓对齐，(2) 均匀放置——对于任何中间帧在框架中，代理（各向同性）均匀分布，以及 (3) 平滑轨迹 - 每个代理的轨迹尽可能刚性/平滑且完全无碰撞。首先，我们使用基于 2-Wasserstein 距离的插值技术来生成一系列中间形状轮廓。其次，我们一起考虑所有代理的时空运动，并将均匀性要求和空间相干性整合为一个目标函数。最后，通过协同优化可以推断出最优的编队改造方案。

大量的实验结果表明，我们的算法在变换的视觉平滑度、边界对齐、代理的均匀性和轨迹的刚性方面优于现有算法。此外，我们的算法能够应对一些具有挑战性的场景，包括（1）具有多个连接组件的源/目标形状，（2）具有不同类型结构的源/目标形状，以及（3）存在障碍物。因此，它在真正的多无人机灯光秀中具有很大的潜力。我们创建了一个动画来演示我们的算法是如何工作的；请参阅 https://1drv.ms/v/s!AheMg5fKdtdugVL0aNFfEt_deTbT?e=le5poN 上的演示。