Generative design of robots requires navigating a vast search-space, encompassing physical configurations and behavioural parameters. Evolutionary Algorithms (EAs) have shown promising results, but often converge prematurely to a small set of sub-optimal designs. Most EAs fail to maintain sufficient diversity in the population that would allow the discovery of distinct functional robots. To counter premature convergence, we introduce a superquadrics-based representation (SQs) for robot bodies. SQs are interpretable, compact and computationally efficient mathematical representations of 3D geometrical shapes that can be tuned to specific design-spaces. To encourage morphological diversity, we combine this representation with a quality-diversity (QD) algorithm (MAP-Elites). We compare SQs and Compositional Pattern Producing Networks representations as generators of morphologies, combining them with standard EAs and MAP-Elites. In two test environments, we find that using SQs to generate morphology in conjunction with the MAP-Elites algorithm reaches the highest QD-score across both environments, maximising diversity of design and functionality of generated robots. The findings highlight the benefits of using a compact and interpretable geometric representation for exploring a complex design-space and suggest that combining SQs with an explicit diversity mechanism increases the quality and number of designs generated.

翻译：机器人的生成式设计需要探索一个巨大的搜索空间，涵盖物理构型与行为参数。进化算法已展现出有前景的成果，但往往过早收敛至少量次优设计。多数进化算法无法维持种群中足以发现不同功能机器人的充分多样性。为解决过早收敛问题，我们引入基于超椭球的机器人身体表征方法。超椭球是一种可解释、紧凑且计算高效的3D几何形状数学表征，能够针对特定设计空间进行调整。为促进形态多样性，我们将该表征与质量-多样性算法（MAP-Elites）相结合。我们将超椭球与组合模式生成网络表征作为形态生成器，与标准进化算法及MAP-Elites进行对比。在两个测试环境中，我们发现使用超椭球生成形态并结合MAP-Elites算法，在两个环境中均达到最高质量-多样性得分，最大化了所生成机器人的设计与功能多样性。研究结果凸显了使用紧凑且可解释的几何表征探索复杂设计空间的优势，并表明将超椭球与显式多样性机制相结合可提升生成设计的质量与数量。