  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.
