ForwardDLO: Model-Based Bimanual Shape Matching of Unconstrained Deformable Linear Objects

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.

Deformable Linear Objects (DLOs) such as ropes and cables are widely encountered in both household and industrial applications, yet remain challenging to manipulate due to their infinite-dimensional configuration space and frequent self-occlusion. Imitation learning from teleoperation offers a practical path to bimanual DLO manipulation, but its scalability is limited by human effort, making the choice of observation space critical for generalization from small datasets. In this study, we investigate whether the lack of generalization in egocentric visual policies for the knot-untangling task stems from the observation space itself, rather than from the policy architecture or data scale. We compare two Action Chunking with Transformers policies trained on the same bimanual teleoperation data: a vision-based policy conditioned on two egocentric RGB streams from wrist-mounted cameras, and a state-based policy conditioned on the DLO's 3D particle state, extracted from an initial observation via multi-view fusion and evolved in a particle-based eXtended Position-Based Dynamics simulation. Evaluated open-loop on an unseen rope configuration, the state-based policy outperforms its visual counterpart with a 30.8% reduction in L1 error when predicting the initial grasp-and-pull action, quantifying the observability gap between pixels and physics-consistent state, and pointing toward more data-efficient robot learning for the DLO manipulation task from limited human demonstrations.

We address the challenge of enabling robots to manipulate deformable linear objects (DLOs), such as ropes, cables, and rubber bands. Prior work has primarily focused on narrow, task-specific problems, often relying on real-world demonstrations or handcrafted heuristics. Such approaches, however, struggle to scale to the wide variety of materials and tasks encountered in practice, and collecting sufficiently diverse real-world data is often impractical. Additionally, existing simulation environments offer limited support for the broad spectrum of material behaviors necessary for generalizable DLO manipulation. To overcome these limitations, we introduce a differentiable simulator explicitly designed for versatile DLO manipulation. Our simulator models a wide range of material properties-including (in)extensibility, elasticity, bending plasticity, and complex interactions with other objects-providing a robust foundation for learning and evaluating manipulation skills. Building on this simulator, we propose a benchmark suite of representative tasks that highlight the unique challenges of DLO manipulation. The successful execution of these tasks is often hindered by the topological complexity and grasp sensitivity inherent to DLOs. Therefore, we introduce a specialized DLO agent that explicitly manages these challenges by proposing strategic grasping points and decomposing long-horizon tasks to maximize control authority. Finally, we evaluate various policy-learning algorithms using our framework, alongside sim-to-real transfer experiments, demonstrating our platform's potential to advance DLO manipulation.