Precise shape control of Deformable Linear Objects (DLOs) is crucial in robotic applications such as industrial and medical fields. However, existing methods face challenges in handling complex large deformation tasks, especially those involving opposite curvatures, and lack efficiency and precision. To address this, we propose a two-stage framework combining Reinforcement Learning (RL) and online visual servoing. In the large-deformation stage, a model-based reinforcement learning approach using an ensemble of dynamics models is introduced to significantly improve sample efficiency. Additionally, we design a self-curriculum goal generation mechanism that dynamically selects intermediate-difficulty goals with high diversity through imagined evaluations, thereby optimizing the policy learning process. In the small-deformation stage, a Jacobian-based visual servo controller is deployed to ensure high-precision convergence. Simulation results show that the proposed method enables efficient policy learning and significantly outperforms mainstream baselines in shape control success rate and precision. Furthermore, the framework effectively transfers the policy trained in simulation to real-world tasks with zero-shot adaptation. It successfully completes all 30 cases with diverse initial and target shapes across DLOs of different sizes and materials. The project website is available at: https://anonymous.4open.science/w/sc-mbrl-dlo-EB48/
Figures & tables
Fig. 1 : Illustration of the task with large deformations exhibiting opposite curvatures. The initial and target shapes have completely opposite concavities. The policy is trained in a simulator and transferred to the real-world scenario.
Fig. 2 : Overview of the proposed DLO shape control framework. In the large-deformation stage, policy is trained with transition augmentation using ensemble model, while a self-curriculum module adaptively selects interaction goals. In the small-deformation stage, an online visual servo controller refines the motion to achieve precise convergence.
Fig. 3 : The architecture of the MBRL framework with ensemble dynamics models.
Fig. 4 : The proposed self-curriculum goal generation method. (a) Candidate goals are randomly sampled from the replay buffer. (b) Imagined evaluations are conducted to categorize intermediate-difficulty goals. (c) Weighted Farthest Point Sampling (FPS) selects the final interaction goal set Ginteract .
Fig. 5 : Policy learning curves under two initial conditions: (a) straight-line initialization and (b) diverse-shape initialization.
Fig. 6 : Self-curriculum goal evolution under two initial conditions; the rightmost plot shows the average goal deformation versus epoch.
Fig. 7 : Representative shape control cases in simulation. (a) Six test cases showing the initial (transparent) and final (opaque) DLO shapes. Red dots denote the target shape. (b) Corresponding shape error curves of different methods. (Refer to our supplementary video for the full control processes.)
Scenario
Method
Avg. min. error (all) (mm) ↓
Success rate ↑
Avg. min. error (succ.) (mm) ↓
Avg. time (succ.) (s) ↓
Straight Initial
Ours
4.678
47/50
1.696
2.147
MPC
43.15
30/50
2.342
6.592
Visual Servo
47.37
13/50
2.862
1.959
RL-Only
29.69
10/50
7.835
1.450
Diverse Initial
Ours
12.49
43/50
2.204
2.464
MPC
36.45
26/50
2.395
4.907
TABLE I : Simulation comparison of shape control strategies under straight and diverse initializations.
Fig. 8 : Real-world experiment setup and DLOs used in the experiment.
Scenario
Method
Avg. min. error (all) (mm) ↓
Success rate ↑
Avg. min. error (succ.) (mm) ↓
Avg. time (succ.) (s) ↓
Straight Initial
Ours
1.985
15/15
1.985
14.285
MPC
12.749
12/15
1.780
24.880
Visual Servo
38.648
4/15
5.759
17.168
RL-Only
15.719
6/15
7.130
14.380
Diverse Initial
Ours
2.064
15/15
2.064
20.434
MPC
23.238
8/15
3.070
40.399
TABLE II : Real-world comparison of shape control strategies under straight and diverse initializations.
Fig. 9 : Real-world shape control process of six cases. (a) Initial shape. (b) Shape at the large deformation stage. (c) Transition point between large and small deformation stages. (d) Final shape achieved. (e) Corresponding shape error curves of different methods. Green circles represent the target shape. (Refer to our supplementary video for the full control processes.)
Ropes, cables, and other deformable linear objects appear in tasks from untangling to cable routing and suturing, yet controlling their shape remains a challenge in robot manipulation. We study model-based shape control in a general setting: the object lies unfixated on a support surface and two arms may grasp and move it anywhere along its length. Because each arm chooses a grasp point, direction, and magnitude, the joint action space is combinatorially large, and the dynamics model's per-prediction cost bounds how much of it a planner can search. We present ForwardDLO, a recurrent latent dynamics model for this unfixated bimanual setting that predicts per-segment displacements grounded in the observed rope state at every step. Our model reaches accuracy comparable to more expensive baselines while containing no explicit segment-to-segment operations, which makes batched evaluation of candidate actions cheap. On open-loop prediction of real rope motion it reaches the lowest error of the learned models we evaluate, 13% below the strongest baseline. Within a fixed time budget it scores 8 to 22 times more candidate actions than models of comparable accuracy while matching them in real-world shape matching; and on a simulated routing task at a 30Hz control rate, this throughput converts into 98% task success versus at most 30% for the baselines at their own budgets. We release the model, code, and a dataset of 2.42 million simulated and 14,107 real rope transitions at https://anonymous.4open.science/r/ForwardDLO/
Tim Missal, Berk Guler, Lucas Domingues +3
Technical University of Darmstadt · Honda Research Institute Europe GmbH · School of Electrical and Computer Engineering, Universidade Estadual de Campinas (UNICAMP), Brazil +4
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.
Most research on the manipulation of deformable objects focuses on lightweight systems with negligible mechanical response, effectively restricting attention to quasi-static regimes. This assumption excludes a broad class of practically relevant objects, such as hoses, pipes, and wiring harnesses, whose dynamics cannot be ignored during manipulation. In this work, we address this limitation by introducing a closed-loop control architecture that explicitly accounts for object dynamics and recasts manipulation as a shape-regulation problem. Control is achieved by modulating forces and torques applied at multiple fixed points along the object. This approach builds on three methodological contributions: a fully dynamic model of linear deformable objects based on discrete strain parameterizations; an extension of the notion of actuation coordinates to SE(3), yielding a structured and inherently underactuated control architecture; and nonlinear feedback strategies providing explicit conditions for steady-state convergence to desired configurations. Extensive simulations on representative manipulation tasks demonstrate the performance gains enabled by the proposed modelbased formulation. We finally validate the approach experimentally through a real-time closed-loop implementation with online shape estimation, confirming its practical feasibility and effectiveness
Daniel Feliu-Talegon, Cosimo Della Santina
Department of Cognitive Robotics, Delft University of Technology, 2628 CN Delft, The Netherlands · Institute of Robotics and Mechatronics, German Aerospace Center (DLR), 82234 Oberpfaffenhofen, Germany