Robotic knot-tying represents a fundamental challenge in robotics due to the complex interactions between deformable objects and strict topological constraints. We present TWISTED-RL, a framework that improves upon the previous state-of-the-art in demonstration-free knot-tying (TWISTED), which smartly decomposed a single knot-tying problem into manageable subproblems, each addressed by a specialized agent. Our approach replaces TWISTED's single-step inverse model that was learned via supervised learning with a multi-step Reinforcement Learning policy conditioned on abstract topological actions rather than goal states. This change allows more delicate topological state transitions while avoiding costly and ineffective data collection protocols, thus enabling better generalization across diverse knot configurations. Experimental results demonstrate that TWISTED-RL manages to solve previously unattainable knots of higher complexity, including commonly used knots such as the Figure-8 and the Overhand. Furthermore, the increase in success rates and drop in planning time establishes TWISTED-RL as the new state-of-the-art in robotic knot-tying without human demonstrations.
Figures & tables
Fig. 1: The bottom row shows the Figure-8 knot (left) and the Overhand knot (right) performed by TWISTED-RL. The top row shows the complexity of the rope measured in crossing number, and the transitions are labeled with the corresponding Reidemeister moves.
Fig. 2: Illustration of TWISTED-RL System Architecture. Top row: the unmodified TWISTED components showing the reachable configurations and high-level planning. Bottom row: TWISTED-RL low-level execution with three episodes showing progression between crossing numbers. First episode: 0→1 with R1 action, second episode: 1→2 with Cross action, third episode: 2→3 with R1 action, each using its specialized agent. Red arrows indicate MuJoCo simulation steps.
Fig. 3: Left: Anytime performance analysis of TWISTED and TWISTED-RL variants on the 3-Easy test set. Right: Anytime performance analysis of TWISTED-RL-C across all test sets. The X-axis is the runtime in seconds, and the Y-axis is the cumulative success rate (%).
TWISTED-RL
TWISTED
Test Set
G
A
C
AC
Baseline
3-Easy
100
100
100
100
100
3-Medium
28
28
44
26
0
3-Medium-1h
46
54
62
34
0
3-Hard
38
20
46
18
0
3-Eval
43
37
61
35
0
TABLE I: Average Success rate (%) of TWISTED vs TWISTED-RL variants across 5 different seeds.
Robotic manipulation of deformable linear objects (DLOs) presents significant challenges due to complex dynamics and frequent self-occlusions. Existing robotic knot tying methods typically rely on precise topological state tracking with ordered keypoints and explicit edge connectivity. This reliance makes them prone to failures due to tracking drift and topology mismatch caused by repeated bending and crossings during knot formation.To address these limitations, we introduce RoboHitch, a novel framework that learns to perform hitch knot tying from human demonstrations using only disordered 3D keypoints and RGB images. This eliminates the need for explicit topological order, allowing for more flexible manipulation. Our method employs a dynamic Graph Autoencoder to extract geometric features from untracked keypoints, complemented by a Convolutional Autoencoder that captures essential visual context. A bidirectional cross-attention mechanism then fuses these modalities to jointly predict pick and place affordances, facilitating implicit reasoning about the rope's state and enabling knot tying under occlusion.Real-world experiments demonstrate the effectiveness and generalizability of our approach, successfully completing hitch knots in scenarios with self-occlusions.
Jiahui Zuo, Boyang Zhang, Fumin Zhang
Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Hong Kong
Knotting plastic bags is a common task in daily life, yet it is challenging for robots due to the bags' infinite degrees of freedom and complex physical dynamics. Existing methods often struggle in generalization to unseen bag instances or deformations. To address this, we present DexKnot, a framework that combines keypoint affordance with diffusion policy to learn a generalizable bag-knotting policy. Our approach learns a shape-agnostic representation of bags from keypoint correspondence data collected through real-world manual deformation. For an unseen bag configuration, the keypoints can be identified by matching the representation to a reference. These keypoints are then provided to a diffusion transformer, which generates robot action based on a small number of human demonstrations. DexKnot enables effective policy generalization by reducing the dimensionality of observation space into a sparse set of keypoints. Experiments show that DexKnot achieves reliable and consistent knotting performance across a variety of previously unseen instances and deformations.
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