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.

翻译：学习软体连续机器人的逆动力学由于高维非线性和复杂的驱动耦合仍然具有挑战性。传统的基于反馈的控制器常因修正振荡而导致控制抖动，而基于确定性回归的学习器难以捕捉实现精确动态跟踪所需的复杂非线性映射。受这些局限性的启发，我们提出了一种面向开环前馈控制的逆动力学框架，将系统的微分动力学学习为生成性传输映射。具体而言，逆动力学被重新表述为条件流匹配问题，并采用校正流（RF）作为轻量级实例以生成物理一致的控制输入而非条件均值。为进一步增强物理一致性，引入了两种变体：RF-Physical，利用基于物理的先验进行残差建模；以及RF-FWD，在流匹配过程中整合前向动力学一致性损失。广泛评估表明，与标准回归基线（MLP、LSTM、Transformer）相比，我们的框架将轨迹跟踪均方根误差降低了超过50%。该系统在末端执行器峰值速度达到1.14米/秒时，仍能维持稳定的开环执行，且推理延迟低于毫秒级（0.995毫秒）。本工作证明了流匹配作为软体机器人系统中学习微分逆动力学的鲁棒高性能范式。