Steering Flexible Linear Objects in Planar Environments by Two Robot Hands Using Euler's Elastica Solutions

2025-01-06

AI Summary

This work addresses real-time motion planning for dual-arm cooperative manipulation of flexible linear objects (e.g., cables, soft food items) in planar environments, with the goal of preventing self-intersection, knotting, instability, and obstacle collisions. We propose the first optimal control framework integrating closed-form analytical solutions of Euler’s elastica to model coupled endpoint position and tangential orientation dynamics. Analytical criteria ensuring collision-free, self-intersection-free, and dynamically stable manipulation are rigorously derived. By combining analytic geometric modeling, efficient collision detection, and real-time optimization, our approach enables robust, tangle-free manipulation of flexible objects amid sparse obstacles. Comprehensive simulations and physical experiments demonstrate significant improvements in tracking accuracy, computational efficiency (real-time performance), and generalizability across diverse object properties and environmental configurations.

Technology Category

• Intelligent Robots: Manipulation
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

The manipulation of flexible objects such as cables, wires and fresh food items by robot hands forms a special challenge in robot grasp mechanics. This paper considers the steering of flexible linear objects in planar environments by two robot hands. The flexible linear object, modeled as an elastic non-stretchable rod, is manipulated by varying the gripping endpoint positions while keeping equal endpoint tangents. The flexible linear object shape has a closed form solution in terms of the grasp endpoint positions and tangents, called Euler's elastica. This paper obtains the elastica solutions under the optimal control framework, then uses the elastica solutions to obtain closed-form criteria for non self-intersection, stability and obstacle avoidance of the flexible linear object. The new tools are incorporated into a planning scheme for steering flexible linear objects in planar environments populated by sparsely spaced obstacles. The scheme is fully implemented and demonstrated with detailed examples.

Problem

• Manipulation
• Flexible Objects
• Obstacle Avoidance

Innovation

• Euler's elastica solution
• Soft object manipulation
• Dual robotic hands