This work addresses the problem of distributedly controlling the position of a group of Unmanned Aerial Vehicles (UAVs), that are considered as holonomic three-dimensional agents, to achieve a desired formation while collisions are avoided. We propose a generic control scheme computed by the adaptive convex combination of two control laws dealing with two, possibly conflicting, tasks, which are formation control and obstacle avoidance. The main contributions of the paper are threefold: First, the whole proposed scheme is distributed by nature, since the formation control is formulated as a consensus problem of virtual agents and the collision avoidance strategy is reactive, valid for unknown environments. Second, two control protocols are proposed to guarantee convergence to the desired formation in finite or predefined time; in the last case, the formation is achieved in a constant time independently of the initial UAVs positions. And finally, the control scheme generates continuous control signals in spite of activation and deactivation of the obstacle avoidance task, and stability is proved even in the transition of tasks. The effectiveness of the proposed approach is shown through realistic simulations and real experiments for a group of quadrotors.

这项工作解决了分布式控制一组无人机（UAV）的位置问题，这些无人机被认为是完整的三维代理，以在避免碰撞的同时实现所需的编队。我们提出了一种通用控制方案，通过两个控制律的自适应凸组合计算，处理两个可能冲突的任务，即编队控制和避障。该论文的主要贡献有三点：首先，整个提议的方案本质上是分布式的，因为编队控制被表述为虚拟代理的共识问题，并且碰撞避免策略是被动的，对未知环境有效。其次，提出了两种控制协议，以保证在有限或预定义的时间内收敛到所需的编队；在最后一种情况下，编队是在恒定时间内完成的，与无人机的初始位置无关。最后，尽管避障任务的激活和停用，控制方案仍会产生连续的控制信号，并且即使在任务转换中也证明了稳定性。通过对一组四旋翼飞行器的真实模拟和真实实验证明了所提出方法的有效性。