Multi-cellular robot design aims to create robots comprised of numerous cells that can be efficiently controlled to perform diverse tasks. Previous research has demonstrated the ability to generate robots for various tasks, but these approaches often optimize robots directly in the vast design space, resulting in robots with complicated morphologies that are hard to control. In response, this paper presents a novel coarse-to-fine method for designing multi-cellular robots. Initially, this strategy seeks optimal coarse-grained robots and progressively refines them. To mitigate the challenge of determining the precise refinement juncture during the coarse-to-fine transition, we introduce the Hyperbolic Embeddings for Robot Design (HERD) framework. HERD unifies robots of various granularity within a shared hyperbolic space and leverages a refined Cross-Entropy Method for optimization. This framework enables our method to autonomously identify areas of exploration in hyperbolic space and concentrate on regions demonstrating promise. Finally, the extensive empirical studies on various challenging tasks sourced from EvoGym show our approach's superior efficiency and generalization capability.

翻译：多细胞机器人设计旨在构建由众多细胞组成的机器人，使其能够被高效控制以执行多样化任务。现有研究已证明可针对不同任务生成机器人，但这些方法通常直接在庞大的设计空间中优化机器人，导致生成的机器人形态复杂且难以控制。为此，本文提出一种新颖的由粗到细的多细胞机器人设计方法。该方法首先寻求最优的粗粒度机器人，并逐步对其进行细化。为缓解由粗到细过渡过程中精确定位细化节点的挑战，我们引入了机器人设计双曲嵌入框架（HERD）。该框架在共享的双曲空间内统一表示不同粒度的机器人，并利用改进的交叉熵方法进行优化。该框架使我们的方法能够自主识别双曲空间中的探索区域，并聚焦于具有潜力的区域。最后，基于EvoGym中多样化挑战性任务的广泛实证研究表明，该方法在效率和泛化能力上均展现出卓越性能。