Dual Arm Steering of Flexible Linear Objects in 2-D and 3-D Environments Using Eulers Elastica Solutions
Aharon Levin, Itay Grinberg, Elon Rimon, Amir Shapiro
AI summary
Problem
Steering flexible linear objects with robots is hindered by their high dimensionality, risk of self-intersection, and snap-buckling instability, while existing sampling-based planners lack analytical safety guarantees and suffer from computational overhead.
Approach
The authors model flexible cables using Euler’s elastica equations to derive analytic stability and non-self-intersection criteria, embedding them as constraints in a low-dimensional configuration space that maps directly to dual-arm gripping states for efficient obstacle-aware path planning.
Key results
- Analytic closed-form criteria for local cable stability and non-self-intersection
- A 6D elastica parameter space mapping to dual-arm endpoint positions and tangents
- Efficient piecewise convex collision detection for sparse obstacle avoidance
- Experimental validation of 2-D and semi-spatial 3-D dual-arm steering
Why it matters
Provides a computationally efficient and theoretically sound framework for reliable robotic manipulation of deformable linear objects in complex environments.
Abstract
This paper describes a method for steering flexible linear objects using two robot hands in environments populated by sparsely spaced obstacles. The approach involves manipulat- ing 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 the elastica solutions to formulate criteria for non self-intersection, stability and obsta- cle avoidance in analytic closed form manner. 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.