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

Soft-bodied organisms such as octopuses and elephant trunks exhibit remarkable morphological adaptability, dynamically reconfiguring body shape and stiffness, and flexibly adjusting their control strategies to enable versatile behaviors. Inspired by these biological systems, various soft robots have emerged in recent decades, featuring diverse materials, stiffnesses, and morphologies tailored to specific tasks. Despite substantial advances in the materials and structural designs of soft robots, developing a generalizable control framework capable of rapid adaptation across diverse configurations remains a long-standing challenge. Existing controllers are limited to fixed configurations, demanding laborious configuration-specific remodelling and policy redesign for new configurations. Here, we introduce a generalizable control system that enables rapid adaptation across diverse soft robot configurations via reinforcement learning in a shared linear Koopman embedding space. By encoding robot dynamics into this embedding space, our method decouples control policies from specific morphologies, allowing real-time, model-free policy adaptation across diverse configurations without retraining from scratch. We validate our system across 33 distinct robot configurations. Our system achieves a 75 times reduction in transfer samples across configurations, while sustaining robust performance under high-speed motion, heavy payloads, and multiactuator faults, and achieving real-world skills previously unattainable in soft robotics. This work establishes a unified and adaptable control paradigm for diverse soft robot configurations, bridging mechanical reconfigurability with control flexibility, and may offer broader insights for generalizable control in complex physical systems.

Image based shape control provides a simple means of controlling the whole body configuration of soft robots. However, existing data driven approaches are typically developed for fixed robot structures and require new control data when the number of modules changes. This paper presents a module number adaptive visual shape control method for serial modular soft pneumatic robots. A controller trained only on single module actuation shape data is reused for robots with one to five modules by decomposing whole body camera images into local module patches. A single common module segmenter localizes individual modules across all tested configurations, while the same local controller is applied to every extracted patch. Geometric data augmentation improves transferability to downstream modules, and a lightweight mask reconstruction network reconstructs a synthetically removed actuator mask channel. Experiments on physical robots demonstrate shape control across varying numbers of modules and under environmental changes and payload loading. The results show that single module control learning enables scalable whole body control without configuration specific control data collection.

Learning the inverse dynamics of soft continuum robots remains challenging due to high-dimensional nonlinearities and complex actuation coupling. Conventional feedback-based controllers often suffer from control chattering due to corrective oscillations, while deterministic regression-based learners struggle to capture the complex nonlinear mappings required for accurate dynamic tracking. Motivated by these limitations, we propose an inverse-dynamics framework for open-loop feedforward control that learns the system's differential dynamics as a generative transport map. Specifically, inverse dynamics is reformulated as a conditional flow-matching problem, and Rectified Flow (RF) is adopted as a lightweight instance to generate physically consistent control inputs rather than conditional averages. Two variants are introduced to further enhance physical consistency: RF-Physical, utilizing a physics-based prior for residual modeling; and RF-FWD, integrating a forward-dynamics consistency loss during flow matching. Extensive evaluations demonstrate that our framework reduces trajectory tracking RMSE by over 50% compared to standard regression baselines (MLP, LSTM, Transformer). The system sustains stable open-loop execution at a peak end-effector velocity of 1.14 m/s with sub-millisecond inference latency (0.995 ms). This work demonstrates flow matching as a robust, high-performance paradigm for learning differential inverse dynamics in soft robotic systems.