Closed-loop shape control of deformable linear objects based on Cosserat model

TL;DR

This work presents a closed-loop shape controller for deformable linear objects by embedding a Cosserat rod model into a vision-assisted feedback loop. A locally computed deformation Jacobian links variations in the initial Cosserat state to control-point deformations, enabling real-time correction and convergence to a desired shape. The approach achieves sub-millimeter accuracy across diverse, anisotropic DLOs and demonstrates robustness to uncertain elastic parameters, though it remains limited to one-dimensional objects and predefined contacts. Experimental validation with dual-arm manipulation shows strong repeatability and competitive performance relative to state-of-the-art methods, with clear pathways for handling more complex interactions and broader generalization.

Abstract

The robotic shape control of deformable linear objects has garnered increasing interest within the robotics community. Despite recent progress, the majority of shape control approaches can be classified into two main groups: open-loop control, which relies on physically realistic models to represent the object, and closed-loop control, which employs less precise models alongside visual data to compute commands. In this work, we present a novel 3D shape control approach that includes the physically realistic Cosserat model into a closed-loop control framework, using vision feedback to rectify errors in real-time. This approach capitalizes on the advantages of both groups: the realism and precision provided by physics-based models, and the rapid computation, therefore enabling real-time correction of model errors, and robustness to elastic parameter estimation inherent in vision-based approaches. This is achieved by computing a deformation Jacobian derived from both the Cosserat model and visual data. To demonstrate the effectiveness of the method, we conduct a series of shape control experiments where robots are tasked with deforming linear objects towards a desired shape.

Figures (9)

• Figure 1: Problem formulation: minimize $\epsilon_{p}$
• Figure 2: Bloc diagram representing the control loop
• Figure 3: Different objects used through the experiments
• Figure 4: Fixation of the cable before (left) and after the manipulation (right)
• Figure 5: Experimental protocol