Mean-shift-based approaches have recently emerged as a representative class of methods for robot swarm shape assembly. They rely on image-based target-shape representations to compute local density gradients and perform mean-shift exploration, which constitute their core mechanism. However, such representations incur substantial memory overhead, especially for high-resolution or 3D shapes. To address this limitation, we propose a memory-efficient tree representation that hierarchically encodes user-specified shapes in both 2D and 3D. Based on this representation, we design a behavior-based distributed controller for assignment-free shape assembly. Comparative 2D and 3D simulations against a state-of-the-art mean-shift algorithm show one to two orders of magnitude lower memory usage and two to four times faster shape entry. Physical experiments with 6 to 7 UAVs further validate real-world practicality.

翻译：基于均值漂移的方法近年来已成为机器人集群形态组装领域的代表性技术。该类方法依赖基于图像的目标形态表示来计算局部密度梯度并执行均值漂移探索，这构成了其核心机制。然而，此类表示方式会带来显著的内存开销，尤其对于高分辨率或三维形态。为克服这一局限，我们提出一种高效内存的树状表示法，可在二维和三维空间中分层编码用户指定的形态。基于此表示方法，我们设计了一种基于行为的分布式控制器，用于实现无需任务分配的形态组装。通过与最先进的均值漂移算法进行二维和三维仿真对比，本方法展现出降低一至两个数量级的内存使用量，以及提升二至四倍的形态进入速度。使用6至7架无人机开展的物理实验进一步验证了该方法的实际应用可行性。