  Robot design aims at learning to create robots that can be easily controlled
and perform tasks efficiently. Previous works on robot design have proven its
ability to generate robots for various tasks. However, these works searched the
robots directly from the vast design space and ignored common structures,
resulting in abnormal robots and poor performance. To tackle this problem, we
propose a Symmetry-Aware Robot Design (SARD) framework that exploits the
structure of the design space by incorporating symmetry searching into the
robot design process. Specifically, we represent symmetries with the subgroups
of the dihedral group and search for the optimal symmetry in structured
subgroups. Then robots are designed under the searched symmetry. In this way,
SARD can design efficient symmetric robots while covering the original design
space, which is theoretically analyzed. We further empirically evaluate SARD on
various tasks, and the results show its superior efficiency and
generalizability.
