Iterated Function System-based Shape Formation for Large-scale Robotic Swarm with Collision Avoidance

In this paper, we present a decentralized control framework for large-scale robotic swarms to achieve complex shape formation and collision avoidance. By leveraging Iterated Function System (IFS) theory, the proposed method enables the generation of fractal-like patterns through affine transformations applied iteratively to the position of agents. The framework operates in a two-layer structure: an upper layer for shape formation via IFS and a lower layer for distributed collision-free motion planning. The IFS-based shape formation algorithm inherently ensures scalability to swarm size variations. To address collision avoidance during swarm evolution, the Optimal Reciprocal Collision Avoidance (ORCA) algorithm is integrated, allowing agents to compute velocity adjustments locally based on neighbor interactions. Numerical simulations in Unity 3D validate the algorithm's scalability and effectiveness.