Locomotive soft robots (SoRos) have gained prominence due to their adaptability. Traditional locomotive SoRo design is based on limb structures inspired by biological organisms and requires human intervention. Evolutionary robotics, designed using evolutionary algorithms (EAs), have shown potential for automatic design. However, EA-based methods face the challenge of high computational cost when considering multiphysics in locomotion, including materials, actuations, and interactions with environments. Here, we present a design approach for pneumatic SoRos that integrates gradient-based topology optimization with multiphysics material point method (MPM) simulations. This approach starts with a simple initial shape (a cube with a central cavity). The topology optimization with MPM then automatically and iteratively designs the SoRo shape. We design two SoRos, one for walking and one for climbing. These SoRos are 3D printed and exhibit the same locomotion features as in the simulations. This study presents an efficient strategy for designing SoRos, demonstrating that a purely mathematical process can produce limb-like structures seen in biological organisms.

翻译：运动软体机器人因其卓越的适应性而备受关注。传统的运动软体机器人设计基于受生物启发的肢体结构，且需要人工干预。利用进化算法设计的进化机器人已展现出自动化设计的潜力。然而，当考虑运动过程中涉及材料、驱动及环境交互等多物理场因素时，基于进化算法的方法面临计算成本高昂的挑战。本文提出一种气动运动软体机器人的设计方法，该方法将基于梯度的拓扑优化与多物理场物质点法模拟相结合。此方法从一个简单的初始形状（具有中心空腔的立方体）出发，随后通过结合物质点法的拓扑优化过程自动迭代地设计软体机器人的形态。我们设计了两款软体机器人，分别用于行走与攀爬。这些机器人经3D打印制成，并展现出与模拟中一致的运动特性。本研究提出了一种高效的软体机器人设计策略，证明了纯数学过程能够生成生物体中常见的类肢体结构。