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

TL;DR

Addressing memory overhead in image-based mean-shift swarm shape assembly, the paper introduces a memory-efficient tree-map encoding that supports both 2D and 3D shapes. A distributed, assignment-free controller uses a tree-search with a coarse neighboring map to guide robots, reducing reliance on high-resolution image maps. The approach achieves memory reductions of one to two orders of magnitude and accelerates shape entry by two to three times while preserving uniformity comparable to state-of-the-art baselines, validated in 2D/3D simulations and physical UAV experiments. This work enables scalable, real-world swarm formation on resource-constrained platforms and suggests avenues to remove global frame dependence and improve communication robustness.

Abstract

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.

Figures (5)

• Figure 1: Physical experiment with 7 UAVs forming a 3D arrow. Final UAV positions are marked with white circles. Trajectories are shown as smooth blue curves passing through five sampled positions for each UAV, with color gradually deepening with time. Note that the curves depict smoothed connections rather than exact flight paths.
• Figure 2: Overview of the Proposed Framework. (a) Shape encoding: The target shape image is shown on the left, while the middle and right panels depict the encoded tree map as a tree structure and a grid view, respectively. A complete encoding path from node $a$ at $d=1$ to node $e$ at $d_\text{max} = 5$ is highlighted in red in both the tree structure and the grid view. (b) Shape decoding: Physical lengths are assigned to the root node $r$, and thus to the entire tree map. A neighboring map is established at $d=3$ and used for each robot $i$ to perceive its neighborhood. The sensing range of robot $i$ is shown as a green circle and the sensed neighborhood is outlined in red. (c) Shape assembly controller: Examples of the two velocity commands under different cases are illustrated. The collision-avoidance range of each robot is shown as a red circle.
• Figure 3: 2D Simulation Results. (a) Robot trajectories for four target shapes with $n_\text{robot}=200$. The first row shows baseline results using full-grid maps (gray-scale omitted for clarity), and the second row shows results of the proposed method with tree maps. (b) Evaluation metrics: memory usage for $d_\text{max}$ from 4 to 8, and entering rate and uniformity over time with $n_\text{robot}=200$. (c) Summary of memory reduction ratio, entering time, and final uniformity. The reduction ratio is computed for $d_\text{max}=4$ to $8$, while the other two metrics are evaluated with $n_\text{robot}$ from 50 to 400.
• Figure 4: 3D Simulation Results. (a) Robot trajectories from the proposed method for four target shapes with $n_\text{robot}=200$. (b) Evaluation metrics: memory usage for $d_\text{max}$ from 4 to 8, and entering rate and uniformity over time with $n_\text{robot}$ from 50 to 400. (c) Memory reduction ratio, entering time, and final uniformity. The reduction ratio is computed for $d_\text{max}=4$ to 8, while the other two metrics are evaluated with $n_\text{robot}$ from 50 to 400.
• Figure 5: Physical Experiment Results. (a) Experimental system setup. (b) Robot trajectories and entering rate. Snapshots of the swarm during the experiments of (c) triangle assembly and (d) arrow assembly are shown from two viewing angles.