Memory-Efficient 2D/3D Shape Assembly of Robot Swarms

Mean-shift-based approaches have recently emerged as the most effective methods for robot swarm shape assembly tasks. These methods rely on image-based representations of target shapes to compute local density gradients and perform mean-shift exploration, which constitute their core mechanism. However, such image representations incur substantial memory overhead, which can become prohibitive for high-resolution or 3D shapes. To overcome this limitation, we propose a memory-efficient tree map representation that hierarchically encodes user-specified shapes and is applicable to both 2D and 3D scenarios. Building on this representation, we design a behavior-based distributed controller that enables assignment-free shape assembly. Comparative 2D and 3D simulations against a state-of-the-art mean-shift algorithm demonstrate one to two orders of magnitude lower memory usage and two to three times faster shape entry while maintaining comparable uniformity. Finally, we validate the framework through physical experiments with 6 to 7 UAVs, confirming its real-world practicality.