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.

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