ChainSplat: A Physics-Inspired Screw-Theoretic Model for Learning Deformable Linear Object Dynamics from Multi-View RGB Videos

Seungyeon Kim; Noémie Jaquier

cs.ROAug 28, 2026

ChainSplat: A Physics-Inspired Screw-Theoretic Model for Learning Deformable Linear Object Dynamics from Multi-View RGB Videos

Authors: Seungyeon Kim, Noémie Jaquier

Organizations: Department of Robotics, Perception and Learning, KTH Royal Institute of Technology

Abstract

Identifying the underlying dynamics and 3D geometry of deformable linear objects (DLOs), such as cables, ropes, and hoses, is essential for accurate robotic manipulation, but remains challenging due to their high-dimensional configuration spaces and diverse behaviors arising from varying material properties. Existing methods often rely on multi-stage pipelines and auxiliary depth inputs, which are prone to errors under dynamic interactions, while their high-dimensional state representations make model-based control computationally expensive. In this paper, we introduce ChainSplat, a physics-inspired framework that jointly learns the 3D geometry, appearance, kinematics, and dynamics of DLOs solely from multi-view RGB videos. ChainSplat represents a DLO as an open-chain structure of rigid links connected by revolute joints, yielding an analytic, screw-theoretic model with a compact state representation parameterized by joint configurations. By integrating this formulation with Gaussian splatting, ChainSplat jointly recovers DLO dynamics, kinematics-aware 3D geometry, and appearance, while enabling high-fidelity RGB rendering from arbitrary states. Through real-world experiments, we demonstrate that ChainSplat achieves state-of-the-art performance in dynamics predictions, 3D geometry reconstruction, and RGB rendering across dynamic interactions. ChainSplat further enables real-time state and force estimation, as well as accurate model-based trajectory optimization, highlighting its practical utility for real-world robotic manipulation of DLOs. Accompanying source code and video are available at: https://chainsplat.github.io.

Figures & tables

Fig. 2: Illustration of screw motion and forward kinematics of an open-chain system. ( Screw motion ) Given a screw axis $\bm{S}$ and a joint displacement $\theta$ , the blue ellipsoid with pose $\bm{T}$ is transformed by the matrix exponential. ( Forward kinematics of open-chain ) The pose $\bm{T}$ of the blue ellipsoid transformed by the last screw motion is given by $e^{[\bm{S}_{3}]\theta_{3}}\bm{T}$ . Considering the preceding screw motion similarly introduces another matrix exponential on the left. Repeating this process along the open chain yields the PoE formula ( 5 ).

Fig. 3: Illustration of link coordinate frames and recursive Newton–Euler algorithm. ( Link coordinate frames ) Each link frame $\{i\}$ is attached to the joint $i$ , while the base frame $\{0\}$ and the end-effector frame $\{n+1\}$ (here, $n=3$ ) are attached to the fixed base and the end-effector, respectively. ( Newton–Euler algorithm ) The forward iteration ( 15 )–( 16 ) and backward iteration ( 17 )–( 18 ) are expressed in frames $\{i+1\}$ and $\{i\}$ (here, $i=2$ ), respectively.

Fig. 4: Core components of ChainSplat . ( Link-aware Gaussians ) Each Gaussian $\mathcal{H}_{i}$ consists of the Gaussian parameters used in Gaussian splatting [ 33 ] , along with a link probability $\bm{\rho}_{i}$ that represents the likelihood of belonging to each link. ( Screw joints ) Each screw joint $\mathcal{S}_{j}$ consists of a screw axis $\bm{S}_{j}$ representing a revolute joint together with the joint spring stiffness $\kappa_{j}$ and damping coefficient $d_{j}$ . The screw joints are serially connected to form an open chain. ( Link inertial parameters ) The parameters $\mathcal{M}_{j}$ consist of the link mass $m_{j}$ and rotational inertia matrix $\bm{I}_{j}$ , and the friction coefficient $\mu_{j}$ between the link and the supporting surface. ( Joint configuration ) The state of the open-chain system at timestep $k$ is given by its joint configuration $\bm{\theta}_{k}$ .

Fig. 5: Replicated Gaussian primitives derived from $\mathcal{H}_{i}$ . For the base link, the blue Gaussian ellipsoid is transformed as $\bm{T}_{b}(k)\bm{T}_{i}$ . For the first link, the Gaussian is additionally transformed by the first screw motion. For each subsequent link, the Gaussian is transformed according to the product-of-exponentials (PoE) formula.

Fig. 6: Illustration of the objective function for the hitting-target manipulation task. ( Left ) A differentiable point-cloud function with part assignments represents the 3D shape of the DLO obtained from ChainSplat . ( Right ) The objective is to hit the target point with any point of the DLO point cloud for tabletop scenarios and with the tip point cloud (i.e., points belonging to the last link) for free-space scenarios.

Fig. 7: Real-world experimental setup for the tabletop and free-space scenarios.

Fig. 8: ChainSplat dynamics rollouts for three DLOs in tabletop scenarios, compared with PGND and PhysTwin w/o 3D. We visualize the ground-truth interaction video and RGB renderings of the dynamics rollout from each approach. Snapshots are shown at $t\in\{0.1,0.7,2.1,3.5\},\text{s}$ for the $20$ cm DLO, $t\in\{0.1,0.4,1.3,1.7\},\text{s}$ for the $30$ cm DLO, and $t\in\{0.1,0.7,1.9,3.0\},\text{s}$ for the $40$ cm DLO. For intuitive comparison, we overlay a gripper mesh on each rendered image based on the end-effector pose at the corresponding timestep. For ChainSplat , we additionally visualize the screw axes and 3D Gaussians transformed according to the predicted joint configuration.

	$20$ cm					$30$ cm					$40$ cm
METHOD	CD $\downarrow$	IoU $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	CD $\downarrow$	IoU $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	CD $\downarrow$	IoU $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
PGND [ 31 ]	$0.0348$	$0.402$	$25.11$	$0.986$	$0.0171$	$0.0261$	$0.511$	$24.85$	$0.982$	$0.0212$	$0.0302$	$0.466$	$22.90$	$0.973$	$0.0315$
Phystwin w/o 3D [ 4 ]	$\bm{0.0201}$	$0.578$	$27.58$	$0.990$	$0.0093$	$\bm{0.0171}$	$0.636$	$26.84$	$0.985$	$0.0133$	$\bm{0.0212}$	$\bm{0.569}$	$24.37$	$0.978$	$\bm{0.0193}$
Phystwin w/ 3D [ 4 ]	$0.0301$	$0.434$	$25.78$	$0.988$	$0.0123$	$0.0240$	$0.520$	$25.23$	$0.983$	$0.0159$	$0.0241$	$0.528$	$24.04$	$0.977$	$0.0204$
ChainSplat (ours)	$0.0263$	$\bm{0.616}$	$\bm{29.54}$	$\bm{0.992}$	$\bm{0.0083}$	$0.0220$	$\bm{0.661}$	$\bm{28.69}$	$\bm{0.988}$	$\bm{0.0114}$	$0.0333$	$0.503$	$\bm{24.61}$	$\bm{0.980}$	$0.0215$

TABLE I: Accuracy of DLO dynamics learning, 3D geometry reconstruction, and RGB appearance for three DLOs in tabletop scenarios.

Fig. 9: ChainSplat dynamics rollout results for three DLOs in free-space scenarios, compared with PGND and PhysTwin w/o 3D. We visualize the ground-truth interaction video and RGB renderings of the dynamics rollout from each approach. Snapshots are shown at $t\in\{0.1,0.8,2.0,2.8\}\,\text{s}$ for the $20$ cm DLO, $t\in\{0.1,1.0,1.4,1.7\}\,\text{s}$ for the $30$ cm DLO, and $t\in\{0.1,0.4,1.6,2.2\}\,\text{s}$ for the $40$ cm DLO. For intuitive comparison, we overlay a gripper mesh on each rendered image based on the end-effector pose at the corresponding timestep. For ChainSplat , we additionally visualize the screw axes and 3D Gaussians transformed according to the predicted joint configuration.

	$20$ cm					$30$ cm					$40$ cm
METHOD	CD $\downarrow$	IoU $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	CD $\downarrow$	IoU $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	CD $\downarrow$	IoU $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
PGND [ 31 ]	$0.0680$	$0.273$	$28.06$	$0.985$	$0.0193$	$0.0722$	$0.228$	$26.21$	$0.979$	$0.0255$	$0.0852$	$0.216$	$25.52$	$0.974$	$0.0324$
Phystwin w/o 3D [ 4 ]	$0.0347$	$0.573$	$31.12$	$0.989$	$0.0103$	$0.0329$	$0.549$	$29.28$	$0.984$	$0.0143$	$0.0446$	$0.475$	$27.85$	$0.979$	$0.0205$
Phystwin w/ 3D [ 4 ]	$0.0380$	$0.549$	$30.96$	$0.988$	$0.0113$	$0.0440$	$0.472$	$28.48$	$0.982$	$0.0179$	$0.0435$	$0.481$	$28.06$	$0.979$	$0.0198$
ChainSplat (ours)	$\bm{0.0293}$	$\bm{0.704}$	$\bm{33.65}$	$\bm{0.992}$	$\bm{0.0084}$	$\bm{0.0265}$	$\bm{0.678}$	$\bm{31.84}$	$\bm{0.988}$	$\bm{0.0115}$	$\bm{0.0329}$	$\bm{0.670}$	$\bm{31.08}$	$\bm{0.985}$	$\bm{0.0144}$

TABLE II: Accuracy of DLO dynamics learning, 3D geometry reconstruction, and RGB appearance for three DLOs in free-space scenarios.

METHOD	Training $\downarrow$	Inference
METHOD	Training $\downarrow$	Rollout $\downarrow$	Render $\downarrow$	Total $\downarrow$
PGND [ 31 ]	$332.0$	$2.02$	$3.88$	$5.89$
Phystwin w/o 3D [ 4 ]	$27.0$	$1.60$	$2.70$	$4.31$
Phystwin w/ 3D [ 4 ]	$29.4$	$1.88$	$6.56$	$8.44$
ChainSplat (ours)	$\bm{17.6}$	$\bm{1.28}$	$\bm{1.14}$	$\bm{2.41}$

TABLE III: Average training time (minutes) and inference time (seconds)

Fig. 10: State estimation of a $30$ cm-long rope in tabletop (snapshots at $t\in\{0.0,4.1,7.0,13.7\}\,\text{s}$ ) and free-space scenarios (snapshots at $t\in\{0.0,2.4,5.4,12.6\}\,\text{s}$ ). Top row: observed RGB images from a single camera and overlay the RGB renderings from ChainSplat . Bottom rows: screw axes and 3D Gaussians transformed according to the estimated joint configurations.

Fig. 11: Force estimation during the interaction of a human with a $30$ cm-long rope in tabletop (snapshots at $t\in\{0.0,3.5,8.8,10.7\}\,\text{s}$ ) and free-space scenarios (snapshots at $t\in\{0.0,3.5,7.0,10.8\}\,\text{s}$ ). We visualize the observed RGB images and overlay the contact point (red circle) and the force applied to the DLO by a human hand (green arrow).

Fig. 12: Model-based manipulation results for three DLOs in tabletop and free-space scenarios. For each trial, we visualize the initial state of the DLO captured by a single RealSense camera together with the target goal points (green circles), as well snapshots of the robot executing the optimized trajectory and the resulting DLO motion toward the goal points.

	METHOD	$20$ cm	$30$ cm	$40$ cm
Table	ChainSplat w/o dyn	$4.43\,{\scriptstyle\pm\,3.78}$	$2.21\,{\scriptstyle\pm\,2.86}$	$2.50\,{\scriptstyle\pm\,2.55}$
Table	ChainSplat	$\bm{0.08\,{\scriptstyle\pm\,0.02}}$	$\bm{0.07\,{\scriptstyle\pm\,0.00}}$	$\bm{0.46\,{\scriptstyle\pm\,0.66}}$
Free	ChainSplat w/o dyn	$3.06\,{\scriptstyle\pm\,1.06}$	$5.05\,{\scriptstyle\pm\,3.60}$	$11.97\,{\scriptstyle\pm\,2.07}$
Free	ChainSplat	$\bm{1.50\,{\scriptstyle\pm\,0.29}}$	$\bm{0.95\,{\scriptstyle\pm\,1.08}}$	$\bm{0.22\,{\scriptstyle\pm\,0.10}}$

TABLE IV: Accuracy of hitting target points (in cm) with DLOs using ChainSplat with initial and optimized dynamics parameters.

Deformable Object Manipulation

Deformable Object Manipulation studies how robots perceive, model, and control flexible objects such as cloth, ropes, cables, and soft tissue.

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RopeDreamer: A Kinematic Recurrent State Space Model for Dynamics of Flexible Deformable Linear Objects

Tim Missal, Lucas Domingues, Berk Guler, Simon Manschitz+2

Technical University of Darmstadt · School of Electrical and Computer Engineering, Universidade Estadual de Campinas (UNICAMP), Brazil · Instituto de Pesquisas Eldorado, Brazil+5

Latent Dynamics Modeling Robotic Manipulation State Space Models

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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.

Abstract

Deformable Object Manipulation

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