Biological organisms have acquired sophisticated body shapes for walking or climbing through million-year evolutionary processes. In contrast, the components of locomoting soft robots, such as legs and arms, are designed in trial-and-error loops guided by a priori knowledge and experience, which leaves considerable room for improvement. Here, we present optimized soft robots that performed a specific locomotion task without any a priori assumptions or knowledge of the layout and shapes of the limbs by fully exploiting the computational capabilities for topology optimization. The only requirements introduced were a design domain and a periodically acting pneumatic actuator. The freeform shape of a soft body was derived from iterative updates in a gradient-based topology optimization that incorporated complex physical phenomena, such as large deformations, contacts, material viscosity, and fluid-structure interactions, in transient problems. The locomotion tasks included a horizontal movement on flat ground (walking) and a vertical movement between two walls (climbing). Without any human intervention, optimized soft robots have limbs and exhibit locomotion similar to those of biological organisms. Linkage-like structures were formed for the climbing task to assign different movements to multiple legs with limited degrees of freedom in the actuator. We fabricated the optimized design using 3D printing and confirmed the performance of these robots. This study presents a new and efficient strategy for designing soft robots and other bioinspired systems, suggesting that a purely mathematical process can produce shapes reminiscent of nature's long-term evolution.

翻译：生物有机体通过数百万年的进化过程获得了用于行走或攀爬的精巧身体形状。相比之下，运动软体机器人的组件（如腿和臂）是在先验知识和经验引导的试错循环中设计的，这留下了相当大的改进空间。在此，我们提出通过充分利用拓扑优化的计算能力，在不对肢体布局和形状做任何先验假设或知识的情况下，优化出执行特定运动任务的软体机器人。引入的唯一要求是设计域和周期性气动致动器。软体自由形状通过基于梯度的拓扑优化迭代更新获得，该优化在瞬态问题中纳入了大变形、接触、材料粘性和流固耦合等复杂物理现象。运动任务包括水平地面移动（行走）和两壁间垂直移动（攀爬）。无需任何人工干预，优化后的软体机器人拥有肢体并展现出与生物有机体类似的运动方式。针对攀爬任务，形成了连杆式结构以在致动器自由度受限的情况下为多条腿分配不同运动。我们采用3D打印制造了优化设计，并验证了这些机器人的性能。本研究为设计软体机器人及其他仿生系统提供了一种新颖高效的策略，表明纯粹的数学过程可产生与自然界长期进化形态相似的形状。