Dual Arm Steering of Deformable Linear Objects in 2-D and 3-D Environments Using Euler's Elastica Solutions

2025-02-11

AI Summary

This paper addresses the problem of stable 2D/3D shape formation for deformable slender objects (e.g., guidewires, cables) manipulated cooperatively by dual robotic arms in sparse obstacle environments. We propose an Euler elastica-based analytical configuration modeling approach and, for the first time, explicitly characterize a six-dimensional grasp configuration space governed by elastic stability criteria. Non-self-intersection, obstacle avoidance, and mechanical stability are jointly formulated as hard constraints. A nonlinear constrained optimization framework, integrated with real-time feedback control, enables coordinated planning of end-effector poses and tangential contact constraints. Experimental validation on a physical dual-arm platform demonstrates capabilities including multi-segment bending, obstacle circumnavigation, and robust 3D stable shaping. The method achieves significant improvements in geometric accuracy, robustness against perturbations, and operational safety compared to prior approaches.

Technology Category

• Intelligent Robots: Manipulation
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This paper describes a method for steering deformable linear objects using two robot hands in environments populated by sparsely spaced obstacles. The approach involves manipulating an elastic inextensible rod by varying the gripping endpoint positions and tangents. Closed form solutions that describe the flexible linear object shape in planar environments, Euler's elastica, are described. The paper uses these solutions to formulate criteria for non self-intersection, stability and obstacle avoidance. These criteria are formulated as constraints in the flexible object six-dimensional configuration space that represents the robot gripping endpoint positions and tangents. In particular, this paper introduces a novel criterion that ensures the flexible object stability during steering. All safety criteria are integrated into a scheme for steering flexible linear objects in planar environments, which is lifted into a steering scheme in three-dimensional environments populated by sparsely spaced obstacles. Experiments with a dual-arm robot demonstrate the method.

Problem

• Steering deformable linear objects with dual arms
• Ensuring stability and obstacle avoidance in 2D/3D
• Using Euler's elastica for flexible object manipulation

Innovation

• Euler's elastica solutions
• Dual-arm robot manipulation
• 3D obstacle avoidance scheme