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Optimal Cosserat-based deformation control for robotic manipulation of linear objects

Azad Artinian, Faiz Ben Amar, Veronique Perdereau

TL;DR

This article modify the framework initially developed for linear soft robot control in order to adapt it to deformable object robotic manipulation, and reformulate the problem as an optimization problem where the whole shape of the object is taken into account instead of solely focusing on the tip of theobject’s position and orientation.

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.

Optimal Cosserat-based deformation control for robotic manipulation of linear objects

TL;DR

This article modify the framework initially developed for linear soft robot control in order to adapt it to deformable object robotic manipulation, and reformulate the problem as an optimization problem where the whole shape of the object is taken into account instead of solely focusing on the tip of theobject’s position and orientation.

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.
Paper Structure (14 sections, 12 equations, 10 figures, 1 table)

This paper contains 14 sections, 12 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Classical static Cosserat rod model
  3. Kinematics
  4. Static equilibrium
  5. Constitutive Equations
  6. Model-based optimization under constraints
  7. Shape Control Approach
  8. Deformation Energy
  9. Numerical resolution
  10. Optimal trajectory generation
  11. Experimental Validation
  12. Experimental Setup
  13. Results
  14. Discussion and future work

Figures (10)

  • Figure 1: Section from 0 to L of a Cosserat rod, deformed under the action of external forces f and moments l. Internal forces n and moments m are also represented at s = 0 and s = L.
  • Figure 2: Representation of the issue with the classic control points (blue) - objective points (red). We propose instead to minimize the distances $d_{1}$, $d_{2}$, $d_{3}$
  • Figure 3: schematic representation of a robotic end-effector's operational workspace Ws
  • Figure 4: Optimization process
  • Figure 5: Set of $n_{inter}$ successive optimal configurations from which the end-effector trajectory is derived
  • ...and 5 more figures