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SCOPE: Smooth Convex Optimization for Planned Evolution of Deformable Linear Objects

Ali Jnadi, Hadi Salloum, Yaroslav Kholodov, Alexander Gasnikov, Karam Almaghout

TL;DR

SCOPE addresses the real-time planning challenge for deformable linear objects by replacing nonlinear energy minimization with a convex trajectory optimization over time-discretized configurations. The method enforces inextensibility and promotes smooth shape evolution via a quadratic smoothness term and a midpoint guide, yielding a convex objective that is efficiently solvable with solvers like CVX. Compared to traditional energy-based DLO models, SCOPE delivers substantial speedups with acceptable accuracy for many robotics applications, making it suitable for real-time control and as a warm-start for more precise solvers. The work highlights a practical trade-off: faster, smooth trajectories at the cost of some local precision, with potential for hybrid pipelines and extensions to more complex geometries and real-world experiments.

Abstract

We present SCOPE, a fast and efficient framework for modeling and manipulating deformable linear objects (DLOs). Unlike conventional energy-based approaches, SCOPE leverages convex approximations to significantly reduce computational cost while maintaining smooth and physically plausible deformations. This trade-off between speed and accuracy makes the method particularly suitable for applications requiring real-time or near-real-time response. The effectiveness of the proposed framework is demonstrated through comprehensive simulation experiments, highlighting its ability to generate smooth shape trajectories under geometric and length constraints.

SCOPE: Smooth Convex Optimization for Planned Evolution of Deformable Linear Objects

TL;DR

SCOPE addresses the real-time planning challenge for deformable linear objects by replacing nonlinear energy minimization with a convex trajectory optimization over time-discretized configurations. The method enforces inextensibility and promotes smooth shape evolution via a quadratic smoothness term and a midpoint guide, yielding a convex objective that is efficiently solvable with solvers like CVX. Compared to traditional energy-based DLO models, SCOPE delivers substantial speedups with acceptable accuracy for many robotics applications, making it suitable for real-time control and as a warm-start for more precise solvers. The work highlights a practical trade-off: faster, smooth trajectories at the cost of some local precision, with potential for hybrid pipelines and extensions to more complex geometries and real-world experiments.

Abstract

We present SCOPE, a fast and efficient framework for modeling and manipulating deformable linear objects (DLOs). Unlike conventional energy-based approaches, SCOPE leverages convex approximations to significantly reduce computational cost while maintaining smooth and physically plausible deformations. This trade-off between speed and accuracy makes the method particularly suitable for applications requiring real-time or near-real-time response. The effectiveness of the proposed framework is demonstrated through comprehensive simulation experiments, highlighting its ability to generate smooth shape trajectories under geometric and length constraints.
Paper Structure (5 sections, 10 equations, 2 figures, 1 table, 1 algorithm)

This paper contains 5 sections, 10 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Methodology
  4. Simulation Results
  5. Conclusion

Figures (2)

  • Figure 1: Model and Application.
  • Figure 2: Results of the optimization experiments. Each row corresponds to a different desired shape conversion, as indicated in the subplot titles. The red solid curve represents the initial cable configuration, while the blue solid curve indicates the final target shape. The solid green trajectories correspond to the intermediate deformations obtained with shape optimization, while the dashed green trajectories correspond to the intermediate deformations obtained with energy-based optimization. This visualization highlights the differences in convergence behavior between the two approaches.