From Biological Curves to Soft Modular Robots: Learning-Based Inverse Design with Uncertainty-Guided Refinement

Animals exhibit diverse shape-changing behaviors, from the undulatory swimming of eels to the arching movements of inchworms. Reproducing these biological shapes with modular soft robots offers a promising approach to developing versatile bioinspired robotic systems. However, translating a desired shape into a feasible robotic configuration remains challenging. Existing cable-driven modular soft robots rely on computationally expensive physics-based modeling and combinatorial search for inverse design, making it difficult to efficiently reproduce diverse target shapes. To address this challenge, we present a learning-based real-to-sim-to-real framework that translates biological curves into robotic configurations through surrogate-assisted inverse design and uncertainty-guided refinement. The proposed method combines learned inverse prediction with targeted candidate exploration, using a fast forward surrogate to evaluate and select suitable designs. The learned forward surrogate reduces deformation prediction time from $1.53 \times 10^5$ ms to 0.0008 ms, achieving approximately a $1.9 \times 10^8$-fold speedup. At the same time, the proposed inverse design method reduces design time from $1.99 \times 10^6$ ms to 4.18 ms. On 5,000 test samples generated from previously unseen threading patterns, the method achieves a 93% shape reconstruction success rate under surrogate-based evaluation. Physical demonstrations with four bioinspired robots further illustrate the translation of biological curves into realizable robotic shapes.