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Manipulation of Deformable Linear Objects Using Model Predictive Path Integral Control with Bidirectional Long Short-Term Memory Learning

Lukas Zeh, Johannes Meiwaldt, Zexu Zhou, Armin Lechler, Alexander Verl

arXiv:2609.26238v1cs.ROeess.SY

TL;DR

DLO manipulation is difficult because deformation and nonlinear dynamics demand accurate, computationally efficient models, and simulation-trained models must be assessed for real-world generalization. This paper trains a biLSTM on simulated trajectories and uses it with MPPI control; the approach shaped DLOs toward target shapes in simulation and experiments.

  • Problem

    DLO manipulation requires accurate, computationally efficient models of deformation and nonlinear dynamics, while the real-world generalization of simulation-trained models needs assessment.

    Source: §1 · p. 1, §2.2 · p. 2

  • Method

    The paper trains a biLSTM dynamics model on simulated DLO data and uses it in an MPPI controller to generate manipulation trajectories.

    Source: §1 · p. 1

  • Results

    The MPPI controller with a biLSTM dynamics model is reported to shape DLOs into desired target shapes, with evaluation in simulation and experiments.

    Source: §1 · p. 2, §6 · p. 11

  • Takeaways & Limitations

    Training on relative capsule positions is reported to support transfer to new scenarios, while substantial target-shape differences require MPPI retuning.

    Source: §5.2 · p. 9

    The controller struggles with significant deformations, targets opposite the cable's pre-bend, and trials that begin with deformation in the wrong direction.

    Source: §5.3 · p. 11

Abstract

from arXiv · show

The manipulation of Deformable Linear Objects (DLOs) such as cables poses a significant challenge for automation due to their infinite degrees of freedom and non-linear dynamics. In this paper we present a machine learning based optimal control approach for the manipulation of DLOs. This approach is divided into two main components: modeling and control. For modeling the dynamics of the DLO, we propose a learning based approach using a bidirectional Long Short-Term Memory (biLSTM) network. The biLSTM network is trained on synthetic data generated by the MuJoCo physics engine. For manipulating the DLO, a model predictive control strategy that employs Model Predictive Path Integral (MPPI) control is selected. The proposed approach is evaluated through simulation and experiments. The results demonstrate the effectiveness of the proposed method in achieving accurate and efficient manipulation of DLOs.

1 INTRODUCTION

Manipulating DLOs requires models that capture deformation and nonlinear dynamics while remaining accurate and computationally efficient for real-time use. The paper combines a learned biLSTM dynamics model with MPPI control and evaluates the approach in simulation and experiments.

  • DLO deformation and nonlinear dynamics make accurate, computationally efficient real-time modeling challenging.External forces move and reshape DLOs, whose infinite degrees of freedom complicate modeling.Source: §1 · p. 1
  • The approach trains a biLSTM dynamics model on simulation data and uses it within an MPPI controller to determine manipulation trajectories.Source: §1 · p. 1
  • The work contributes cable-modeling datasets, an architecture, and model weights, alongside a framework using MPPI to manipulate deformable objects.Source: §1 · pp. 1–2
  • The proposed method is demonstrated effective for DLO manipulation in simulation and experiments.Source: §1 · p. 2

2 RELATED WORK

Related work spans physics-based and data-driven DLO models and predictive control; the paper applies MPPI with a biLSTM model to manipulate different DLO types.

2 RELATED WORK

  • DLO modeling approaches are broadly divided into physics-based and data-driven methods.Source: §2 · p. 2

2.1 Physics-Based Modeling Approaches

  • Physics-based DLO models trade computational efficiency, physical accuracy, parameter requirements, and suitability for real-time or large-deformation tasks.Particle and mass-spring models require precise parameters; PBD is less physically accurate, while FEM is computationally intensive and needs material parameters.Source: §2.1 · p. 2

2.2 Data-Driven Approaches

  • Data-driven models capture complex DLO dynamics using simulated or real-world data, but robust performance may require large datasets and simulation-to-reality generalization remains an open assessment.Prior work includes biLSTMs, interaction-biLSTMs, GNNs, and radial-basis-function approaches.Source: §2.2 · p. 2

2.3 Model Predictive Control for DLO Manipulation

  • MPC uses predictive models to optimize actions over a horizon, while prior MPPI work spans robotic control and rope-state estimation.The paper extends existing work by applying MPPI to manipulate different DLO types, using a biLSTM chosen for inference speed, acceptable accuracy, and flexible control.Source: §2.3 · p. 3

3 DATASET

The biLSTM training data are generated in MuJoCo by moving a cable's free end through randomized trajectories. The paper represents the DLO using capsule positions relative to the end effector and combines that state with the end-effector state.

3 DATASET

  • The dataset section introduces the data used to train the biLSTM model.Source: §3 · p. 3

3.1 Simulation Environment

  • MuJoCo simulations generate cable trajectories by moving the free end from a straight configuration toward randomly selected positions.The simulated cable is 0.5 m long and uses 50 capsules; gravity, friction, and air drag are excluded. The figure depicts the free end moving to a random position within the green box.Source: §3.1 · pp. 3–4, Figure 1 · p. 4

3.2 Representation of DLO in 2D

  • The 2D DLO representation subsamples the simulated capsules and uses their x-y positions relative to the end effector, yielding translational invariance.Capsule velocities are computed from relative-position differences across time steps.Source: §3.2 · p. 4
  • The system state combines the DLO state with the end-effector state, which includes its Cartesian position and rotation around the z-axis.Source: §3.2 · p. 4

4 PROPOSED FRAMEWORK

The proposed framework combines a learned biLSTM model of cable dynamics with MPPI control for 2D manipulation toward a desired shape.

4.1 System Overview

  • Given the current DLO state and target shape, MPPI samples candidate trajectories that the biLSTM predicts before cost-based selection and robot execution.The resulting state feeds the next control iteration until the desired shape is reached.Source: §4.1 · pp. 4–5

4.2 biLSTM Cable Model

  • The biLSTM processes capsule positions and velocities alongside end-effector state, predicting capsule velocities for the next timestep.The architecture has an input layer, stacked biLSTM layers, and a fully connected output layer.Source: §4.2 · p. 5, Figure 3 · p. 5

4.2.1 Training

  • Training used 10,000 simulated trajectories with an 80/20 split; gains after 50 epochs were not significant, and grid search compared validation losses.The selected model used a learning rate of 1e-4, weight decay of 1e-7, batch size 128, and three biLSTM layers of 512 neurons each.Source: §4.2.1 · pp. 5–6, Figure 4 · p. 6

4.2.2 Model Evaluation

  • Across 100 rollouts of 150 time steps (3 seconds), biLSTM averaged shape error eshape,biLSTM of 3.3 cm and velocity error evel,biLSTM of 61.59%; both errors increased with time steps.Source: §4.2.2 · pp. 6–7

4.3 Model Predictive Path Integral for Manipulation

  • MPPI samples disturbed control sequences, scores shape deviation and control effort, updates nominal inputs toward lower-cost trajectories, and executes the first optimized input.Trajectory weights give lower-cost candidates greater influence on the update.Source: §4.3 · pp. 7–8

5 SIMULATION AND EXPERIMENTS

Across simulation and three cable-shaping experiments, MPPI with a biLSTM dynamics model shaped DLOs toward U-shaped targets, with success varying by setting. The experiments also exposed reduced robustness for untrained or substantially different conditions.

5.1 Simulation and Experimental Setup

  • The simulation used a 50 cm cable with a fixed end, while the robot-and-camera experiment tracked cable shape using markers or FastDLO estimation.The experiment setup used zip ties to fix the other cable end; the third scenario used virtual markers derived from FastDLO estimates.Source: §5.1 · p. 8, §5.3 · p. 10

5.2 Simulation Results

  • 93% of 100 simulated U-shape trials succeeded, averaging 7.26 s per successful trial under a 2 cm maximum-deviation criterion.A successful trial reached the desired U-shape within 30 seconds.Source: Figure 7 · p. 9, §5.2 · p. 9
  • Across 1,000 simulated random-goal trials, success was 20.5%, with an average 13.3 s per successful trial.Source: §5.2 · p. 9

5.3 Experiment Results

  • 85% success (15.7 s average), 50% (28.3 s), and 60% (25.4 s) were achieved in the planar cable, raised-platform, and thin-wire experiments, respectively.Each value is the success rate and average time per successful trial for its corresponding scenario.Source: Figure 8 · p. 10, Figure 9 · p. 10, §5.3 · pp. 10–11
  • The raised-platform scenario was untrained and less robust, while the thin-wire scenario also showed lower robustness than the planar cable case.The paper reports that scenarios differing substantially from the controller's tuning case require retuning; severe deformations require additional parameterization.Source: §5.3 · pp. 10–11
  • Simulation results indicate that different target shapes are harder when they depart from a U-shape, especially when substantial deformation or an initial deformation in the wrong direction is required.Source: §5.3 · p. 11

6 DISCUSSION AND FUTURE WORKS

The paper concludes that a biLSTM dynamics model combined with MPPI can shape DLOs into target shapes and generalize across objects with different physical properties. Future work proposes real-data tuning, alternative neural models, and changes to MPPI sampling and cost functions.

  • The biLSTM–MPPI approach shaped DLOs into desired targets in simulation and experiments and generalized to DLOs with different physical properties.Source: §6 · p. 11
  • Future work proposes tuning pretrained models with real data to reduce the simulation-to-reality gap and testing MLPs and GNNs within the MPC loop.Source: §6 · p. 11
  • The authors also plan to investigate alternative MPPI sampling strategies and cost functions.Source: §6 · p. 11
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