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.

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