Learning Dynamic Rope Manipulation Using Task-Level Iterative Learning Control

Krishna Suresh; Chris Atkeson

cs.ROFeb 24, 2026

Learning Dynamic Rope Manipulation Using Task-Level Iterative Learning Control

Authors: Krishna Suresh, Chris Atkeson

Organizations: Carnegie Mellon University

Abstract

We introduce a Task-Level Iterative Learning Control method for dynamic manipulation of ropes. 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 inverts a 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--25,mm 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 2--5 trials. https://flying-knots.github.io

Figures & tables

Fig. 1: Stages of a flying knot by both a human and an xArm 7 robot arm over 0.56s

Fig. 2: Critical point for the flying knot shown in instructional videos [ 24 , 8 ] . The bottom row is the critical point state across 4 demonstration variations. The shape of the rope at collision is used as the learning objective.

Fig. 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 $\Delta\mathbf{u}(t)$ , which are applied to the current feedforward command, closing the learning loop.

Fig. 4: Critical point vs equally-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 corresponding rope state from the demonstration. The rope state at 0.46s is the critical point . The critical point objective results in a successful flying knot, while the equally-weighted objective results in failure. During learning, the robot learns to deviate from the demonstration motion to reduce tracking error along the rope, which is why the demonstration rope handle position does not match the measured rope handle position.

Fig. 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 visualizations are created using Viser [ 43 ] .

Parameter	Value
Stiffness	$1\times 10^{5}$
Damping	$50$
Link Mass	$1$
End Mass	$5$
Simulation Timestep	$0.005$
# Links	$11$

TABLE I: Rope Model Parameters

Fig. 6: 7 different rope types used for evaluation, including 4 braided ropes of various thickness and mechanical properties, a large twisted rope, a chain, and latex surgical tubing (very elastic); ranging in thicknesses of 7–25 mm and densities of 0.013–0.5 kg/m. Each rope has a mass affixed to aid in the formation of the knot.

Fig. 7: Initial command fingertip trajectory : positions of the demonstration fingertip trajectory are dashed, and the robot’s commanded initial attempt to track the demonstration is solid. The robot fails to track the demonstration motion due to kinematic and dynamic constraints.

Fig. 8: Rope configuration at the critical point over learning iterations: Real rope (green) and demonstration rope (red) states for 5 iterations of Task-Level ILC where trial 5 resulted in a flying knot.

Fig. 9: Left: Critical point objective for 7 rope types over 10 iterations (rope 3 and 7 end early due to marker tracking failures). Squares represent the first successful flying knot, and every large solid dot represents a subsequent successful knot. Right: Execution on the real robot of successful flying knot execution on 7 rope types overlaid. The red highlighted frame is the critical point .

Fig. 10: Learning cost over trials for 4 demonstration types. Large solid dots represent times when the flying knot succeeded, and squares are the first successful command. Learning on Demo Types 1 and 3 is truncated due to rope tracking failures.

Fig. 11: Number of trials to transfer a successful command from rope A to rope B. Red cells are for transfer that did not succeed within 10 trials.

Stiffness	End Mass	Trials Until Success
$\mathbf{1\times 10^{5}}$	5	4
$1\times 10^{4}$	5	4
$1\times 10^{3}$	5	4
$1\times 10^{2}$	5	$>10$
$1\times 10^{5}$	0.05	8
$1\times 10^{5}$	0.005	6

TABLE II: Effect of model parameters on learning performance.

Parameter	Value
$w_{\text{control}}$	$\;0.5\;$
$w_{\text{critical pos}}$	$\;25\;$
$w_{\text{critical vel}}$	$\;0.00375\;$
$w_{pc}$	$\;100\;$
$w_{vc}$	$\;0.1\;$
$w_{Rc}$	$\;5\;$

TABLE III: Inverse Model Parameters

ID	Name	Material	Diameter [mm]	Density [kg/m]	End Weight [g]
1	#10 Sash Spot Cord	Cotton	9	0.040	18
2	#14 Spot Cord	Cotton	12	0.081	80
3	Soft Braided	Cotton	15	0.076	80
4	Shoe Lace	Cotton	7	0.014	5
5	Thick Twisted	Cotton	25	0.139	50
6	3/8” Chain	Steel	20	0.514	50

TABLE IV: List of Rope parameters

Parameter	Value
$\mathbf{q_{\min}}$	$[\;-6.28,-1.8,-6.28,-0.19,-6.28,-1.69,-6.28\;]$
$\mathbf{q_{\max}}$	$[\;6.28,1.9,6.28,3.92,6.28,3.14,6.28\;]$
$\mathbf{\dot{q}_{\min}}$	$-[3.14,3.14,3.14,3.14,3.14,3.14,3.14]$
$\mathbf{\dot{q}_{\max}}$	$[3.14,3.14,3.14,3.14,3.14,3.14,3.14]$
$\mathbf{\ddot{q}_{\min}}$	$-[100,100,100,100,100,100,100]$
$\mathbf{\ddot{q}_{\max}}$	$[100,100,100,100,100,100,100]$

TABLE V: Demonstration Tracking Parameters

Iterative Learning Control

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RopeFormer: Cross-Trial Adaptation from Interaction History for Dynamic Rope Manipulation

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ICL for Robotics Deformable Object Manipulation Dynamic Robotic Manipulation Robot Learning

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Dynamic rope manipulation is highly sensitive to unknown object dynamics: the same robot motion can produce substantially different responses across ropes, while explicitly identifying the relevant physical properties is difficult. We present RopeFormer, a history-conditioned framework that uses prior task interaction as context for subsequent control. The policy retains cross-trial action-response history while keeping its weights fixed and requires no explicit online rope-parameter estimation. In matched simulation evaluations across sustained single-arm rotation, bimanual rotation, and transient whipping, retaining context improves subsequent control relative to resetting the same checkpoint, with the benefit varying across rope dynamics and observation settings. We further deploy the frozen policies on a Unitree H1-2 with previously unseen physical ropes. From T1 to T3, target-acquisition time decreases by 30.9% for Rope Swing and 33.9% for Rope Twirl, while mean Rope Whip target hits increase from 0.2 to 2.3 out of three. These results show that prior interaction can provide effective control context for dynamic deformable-object manipulation. Robot videos, code, and data are available at https://ropeformer.github.io/.

Abstract

Iterative Learning Control

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