Nature has inspired humans in different ways. The formation behavior of animals can perform tasks that exceed individual capability. For example, army ants could transverse gaps by forming bridges, and fishes could group up to protect themselves from predators. The pattern formation task is essential in a multiagent robotic system because it usually serves as the initial configuration of downstream tasks, such as collective manipulation and adaptation to various environments. The formation of complex shapes, especially hollow shapes, remains an open question. Traditional approaches either require global coordinates for each robot or are prone to failure when attempting to close the hole due to accumulated localization errors. Inspired by the ribbon idea introduced in the additive self-assembly algorithm by the Kilobot team, we develop a two-stage algorithm that does not require global coordinates information and effectively forms shapes with holes. In this paper, we investigate the partitioning of the shape using ribbons in a hexagonal lattice setting and propose the add-subtract algorithm based on the movement sequence induced by the ribbon structure. This advancement opens the door to tasks requiring complex pattern formations, such as the assembly of nanobots for medical applications involving intricate structures and the deployment of robots along the boundaries of areas of interest. We also provide simulation results on complex shapes, an analysis of the robustness as well as a proof of correctness of the proposed algorithm.

翻译：自然界以不同方式启发着人类。动物的集群行为能够执行超越个体能力的任务。例如，军蚁可通过构建桥梁穿越沟壑，鱼群可通过聚集抵御捕食者。在多智能体机器人系统中，模式形成任务至关重要，因为它通常作为下游任务（如集体操控和适应各种环境）的初始配置。复杂形状（尤其是中空形状）的集群形成仍是一个开放性问题。传统方法要么需要每个机器人的全局坐标，要么在尝试闭合孔洞时因累积定位误差而容易失败。受Kilobot团队在加法自组装算法中提出的带状结构启发，我们开发了一种无需全局坐标信息且能有效形成带孔形状的两阶段算法。本文研究了在六边形晶格设置下使用带状结构对形状进行分区的方法，并根据带状结构诱导的运动序列提出了加减算法。这一进展为需要复杂模式形成的任务（如涉及精细结构的医疗纳米机器人组装，以及沿感兴趣区域边界的机器人部署）打开了大门。我们还提供了复杂形状的仿真结果、鲁棒性分析以及所提算法的正确性证明。