Abstract
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.
Abstract (translated)
学习软体连续体机器人的逆动力学仍是一项挑战，因其具有高维非线性与复杂驱动耦合特性。传统基于反馈的控制器常因校正振荡导致控制颤振，而基于确定性回归的学习器则难以捕捉精确动态跟踪所需的复杂非线性映射。受限于上述不足，本文提出一种用于开环前馈控制的逆动力学框架，该框架将系统微分动力学学习为生成式传输映射。具体而言，逆动力学被重构为条件流匹配问题，并采用整流流作为轻量级实例，以生成物理一致的控制输入而非条件均值。为进一步提升物理一致性，引入两种变体：利用物理先验进行残差建模的RF-Physical，以及在流匹配中集成前向动力学一致性损失的RF-FWD。广泛评估表明，与标准回归基线（MLP、LSTM、Transformer）相比，本框架将轨迹跟踪均方根误差降低了50%以上。系统在峰值末端执行器速度达1.14米/秒时仍能保持稳定开环运行，且推理延迟低于毫秒级（0.995毫秒）。本研究验证了流匹配作为学习软体机器人系统微分逆动力学的稳健高性能范式。
URL
https://arxiv.org/abs/2604.03006
