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Estimating Force Interactions of Deformable Linear Objects from their Shapes

Qi Jing Chen, Shilin Shan, Timothy Bretl, Quang-Cuong Pham

TL;DR

This work tackles estimating external forces acting on deformable linear objects (DLOs) from their shapes alone, without relying on end-effector force sensors. It models the wire as a discretized elastic rod (DER) and derives consistency conditions from force-torque balance to localize disturbances along the wire in quasi-static configurations, enabling the identification of undisturbed versus disturbed sections. Two solvable modes are proposed to recover force directions and magnitudes: (i) zero torque with force-position estimation and (ii) torque with force-position estimation at section midpoints; these are demonstrated in both simulations and real robot experiments manipulating wires. The results support safer trajectory planning around wires and passive obstacles by inferring interaction forces from shape, though the study notes limitations from purely elastic modeling and sensing noise, suggesting avenues for incorporating plasticity models and improved sensing in future work.

Abstract

This work introduces an analytical approach for detecting and estimating external forces acting on deformable linear objects (DLOs) using only their observed shapes. In many robot-wire interaction tasks, contact occurs not at the end-effector but at other points along the robot's body. Such scenarios arise when robots manipulate wires indirectly (e.g., by nudging) or when wires act as passive obstacles in the environment. Accurately identifying these interactions is crucial for safe and efficient trajectory planning, helping to prevent wire damage, avoid restricted robot motions, and mitigate potential hazards. Existing approaches often rely on expensive external force-torque sensor or that contacts occur at the end-effector for accurate force estimation. Using wire shape information acquired from a depth camera and under the assumption that the wire is in or near its static equilibrium, our method estimates both the location and magnitude of external forces without additional prior knowledge. This is achieved by exploiting derived consistency conditions and solving a system of linear equations based on force-torque balance along the wire. The approach was validated through simulation, where it achieved high accuracy, and through real-world experiments, where accurate estimation was demonstrated in selected interaction scenarios.

Estimating Force Interactions of Deformable Linear Objects from their Shapes

TL;DR

This work tackles estimating external forces acting on deformable linear objects (DLOs) from their shapes alone, without relying on end-effector force sensors. It models the wire as a discretized elastic rod (DER) and derives consistency conditions from force-torque balance to localize disturbances along the wire in quasi-static configurations, enabling the identification of undisturbed versus disturbed sections. Two solvable modes are proposed to recover force directions and magnitudes: (i) zero torque with force-position estimation and (ii) torque with force-position estimation at section midpoints; these are demonstrated in both simulations and real robot experiments manipulating wires. The results support safer trajectory planning around wires and passive obstacles by inferring interaction forces from shape, though the study notes limitations from purely elastic modeling and sensing noise, suggesting avenues for incorporating plasticity models and improved sensing in future work.

Abstract

This work introduces an analytical approach for detecting and estimating external forces acting on deformable linear objects (DLOs) using only their observed shapes. In many robot-wire interaction tasks, contact occurs not at the end-effector but at other points along the robot's body. Such scenarios arise when robots manipulate wires indirectly (e.g., by nudging) or when wires act as passive obstacles in the environment. Accurately identifying these interactions is crucial for safe and efficient trajectory planning, helping to prevent wire damage, avoid restricted robot motions, and mitigate potential hazards. Existing approaches often rely on expensive external force-torque sensor or that contacts occur at the end-effector for accurate force estimation. Using wire shape information acquired from a depth camera and under the assumption that the wire is in or near its static equilibrium, our method estimates both the location and magnitude of external forces without additional prior knowledge. This is achieved by exploiting derived consistency conditions and solving a system of linear equations based on force-torque balance along the wire. The approach was validated through simulation, where it achieved high accuracy, and through real-world experiments, where accurate estimation was demonstrated in selected interaction scenarios.
Paper Structure (18 sections, 9 equations, 4 figures, 1 table)

This paper contains 18 sections, 9 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Works
  3. Force Control for DLO Manipulation
  4. Contact Detection and Force Estimation
  5. Problem Definition
  6. Elastic Rod Theory
  7. Formulation
  8. Identifying Positions of Disturbances
  9. Estimating External Disturbances
  10. Estimating External Forces
  11. Estimating External Torques or Force Positions
  12. Simulation Experiments
  13. Physical Experiments
  14. Experimental Set-up
  15. Results
  16. ...and 3 more sections

Figures (4)

  • Figure 1: Overall Force Estimation Process. Rowwise from top left to bottom right: Real image of experiment, depth information, segmentation mask of wire, and final smoothed wire shape with actual and estimated forces (arrows: red - estimated end-clamp force, black - actual force, green - estimated external force).
  • Figure 2: Simulation experiments for force estimation. The top image shows a screen capture of the wire with a force applied through the interactive user visualization window. The actual (black) and estimated (green) forces are shown (overlapping). Two simulation experiments were carried out: P1 shows the force estimation for varying force magnitude and direction on disturbances at the center of the wire length. P2 shows the estimation of force position when the point of force application was varied. The solid and dotted lines are the actual and estimated data, respectively. Video of the experiments found here: https://youtu.be/_jDbKWxA19w.
  • Figure 3: Visual results of force estimation for experiment A where the wire was clamped at both ends and attached to the robot end-effector at its center. The robot end-effector was fitted with a force-torque sensor and moved into 6 different positions. The left column shows the real experiment images (coordinates axes shown in first image) with Cartesian displacement of the grasped point (below), and the right column shows the smoothed wire shape along with the actual and estimated force vector (arrows: red - estimated end-clamp force, black - actual force, green - estimated external force). Note that the accuracy of end-clamp forces are not analyzed.
  • Figure 4: Visual results of force estimation for experiment B where the wire was clamped at both ends and attached to the robot end-effector at a $7cm$ offset along the wire length from its center.