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.