Learning Deformable Object Manipulation Using Task-Level Iterative Learning Control

TL;DR

A Task-Level Iterative Learning Control method for dynamic manipulation of deformable objects that achieves a 100\% success rate within 10 trials on all ropes and can successfully transfer between most rope types in approximately 2--5 trials.

Abstract

Dynamic manipulation of deformable objects is challenging for humans and robots because they have infinite degrees of freedom and exhibit underactuated dynamics. We introduce a Task-Level Iterative Learning Control method for dynamic manipulation of deformable objects. We demonstrate this method on a non-planar rope manipulation task called the flying knot. Using a single human demonstration and a simplified rope model, the method learns directly on hardware without reliance on large amounts of demonstration data or massive amounts of simulation. At each iteration, the algorithm constructs a local inverse model of the robot and rope by solving a quadratic program to propagate task-space errors into action updates. We evaluate performance across 7 different kinds of ropes, including chain, latex surgical tubing, and braided and twisted ropes, ranging in thicknesses of 7--25mm and densities of 0.013--0.5 kg/m. Learning achieves a 100\% success rate within 10 trials on all ropes. Furthermore, the method can successfully transfer between most rope types in approximately 2--5 trials. https://flying-knots.github.io

Figures (11)

• Figure 1: Stages of a flying knot by both a human and a robot over 0.56s
• Figure 2: Critical point for the flying knot across 4 demonstration variations. The shape of the rope at collision is used for the learning objective.
• Figure 3: Task-Level Iterative Learning Control System: A demonstration is converted to an initial command. The command trajectory $\mathbf{u}(t)$ is executed on the real system, and the resulting trajectory $\mathbf{x}(t)$ is measured. The task error $\mathbf{\tilde{x}}(t)$ at the critical point is mapped through the inverse model $\mathcal{M}^{-1}$ to command trajectory corrections $\mathbf{\Delta u}(t)$, which are applied to the current feedforward command, closing the learning loop.
• Figure 4: Critical point vs equal-weighted objective learned commands. Each row is a real trial after 8 iterations with the corresponding objective. The green rope is the measured state from the real trial, and the red rope is the goal rope from the demonstration. The rope state at 0.46s is the critical point. The critical point objective trial results in a successful flying knot, while the equal-weighted objective trial results in a failure.
• Figure 5: Left: Kinematic robot model at various stages of a command. The opaque robot is at the point of contact. Right: Graphical representation of the point mass rope model. The robot's fingertip trajectory kinematically drives the first red dot. The remaining links are bound by distance constraints, and each joint has stiffness and damping. Together, the robot and rope models define our system dynamics model. All 3D visualization are created using Viser yi2025viser.