The robotic manipulation of Deformable Linear Objects (DLOs) is a fundamental challenge due to the high-dimensional, non-linear dynamics of flexible structures and the complexity of maintaining topological integrity during contact-rich tasks. While recent data-driven methods have utilized Recurrent and Graph Neural Networks for dynamics modeling, they often struggle with self-intersections and non-physical deformations, such as tangling and link stretching. In this paper, we propose a latent dynamics framework that combines a Recurrent State Space Model with a Quaternionic Kinematic Chain representation to enable robust, long-term forecasting of DLO states. By encoding the DLO as a sequence of relative rotations (quaternions) rather than independent Cartesian positions, we inherently constrain the model to a physically valid manifold that preserves link-length constancy. Furthermore, we introduce a dual-decoder architecture that decouples state reconstruction from future-state prediction, forcing the latent space to capture the underlying physics of deformation. We evaluate our approach on a large-scale simulated dataset of complex pick-and-place trajectories involving self-intersections. Our results demonstrate that the proposed model achieves a 40.52% reduction in open-loop prediction error over 50-step horizons compared to the state-of-the-art baseline, while reducing inference time by 31.17%. Our model further maintains superior topological consistency in scenarios with multiple crossings, proving its efficacy as a compositional primitive for long-horizon manipulation planning.

翻译：可变形线性物体（DLO）的机器人操控是一项基础性挑战，原因在于柔性结构的高维非线性动力学特性，以及接触密集任务中保持拓扑完整性的复杂性。尽管近期数据驱动方法已利用递归神经网络和图神经网络进行动力学建模，但这些方法在处理自交缠及非物理变形（如打结与连杆拉伸）时仍存在困难。本文提出一种潜在动力学框架，将递归状态空间模型与四元数运动学链表示相结合，以实现DLO状态的鲁棒长期预测。通过将DLO编码为相对旋转序列（四元数）而非独立笛卡尔坐标，我们固有地约束模型处于保持连杆长度恒定的物理有效流形上。此外，我们引入双解码器架构，将状态重构与未来状态预测解耦，迫使潜在空间捕获变形的底层物理机制。我们在大规模模拟数据集（包含复杂抓取-放置轨迹及自交缠场景）上评估了该方法。结果表明，与当前最优基线相比，所提模型在50步预测范围内的开环预测误差降低40.52%，推理时间减少31.17%。在多次交叉场景中，我们的模型进一步保持优越的拓扑一致性，验证了其作为长时域操控规划的组合基元的有效性。