Controlling Deformable Objects with Non-Negligible Dynamics: A Shape-Regulation Approach to End-Point Positioning
Sebastien Tiburzio, Tomás Coleman, Daniel Feliu, Cosimo Della Santina
AI summary
Problem
Traditional manipulation methods neglect object dynamics, limiting control to lightweight or quasi-static scenarios. This paper addresses the gap in reliably controlling heavier, dynamically active deformable objects where inertia and gravity significantly impact behavior.
Approach
The authors develop a strain-based dynamic model for slender objects grasped at one end and cast endpoint positioning as a shape-regulation control problem. This enables a hierarchical controller that combines high-level task mapping with low-level PD control, complete with analytical stability proofs.
Key results
- Finite-dimensional dynamic model using polynomial curvature strain parameterization
- Analytical proof of closed-loop stability with explicit convergence conditions
- Hierarchical control architecture mapping task goals to object base poses
- Experimental validation on a 7-DoF robot manipulating six distinct electric cables
Why it matters
Provides a theoretically grounded, experimentally validated method for dynamic deformable object manipulation, advancing practical applications in cable harnessing, minimally invasive surgery, and soft robotics.
Abstract
Model-based manipulation of deformable objects has traditionally dealt with objects while neglecting their dy- namics, thus mostly focusing on very lightweight objects at steady state. At the same time, soft robotic research has made considerable strides toward general modeling and control, despite soft robots and deformable objects being very similar from a mechanical standpoint. In this work, we leverage these recent results to develop a control-oriented, fully dynamic framework of slender deformable objects grasped at one end by a robotic manipulator. We introduce a dynamic model of this system using functional strain parameterizations and describe the manipula- tion challenge as a regulation control problem. This enables us to define a fully model-based control architecture, for which we can prove analytically closed-loop stability and provide sufficient conditions for steady state convergence to the desired state. The nature of this work is intended to be markedly experimental. We provide an extensive experimental validation of the proposed ideas, tasking a robot arm with controlling the distal end of six different cables, in a given planar position and orientation in space.