ScissorBot: Learning Generalizable Scissor Skill for Paper Cutting via Simulation, Imitation, and Sim2Real
Authors: Jiangran Lyu
Yuxing Chen
Tao Du
Feng Zhu
Huiquan Liu
Yizhou Wang
He Wang
Venue: CoRL 2024 (2024)
Keywords: Deformable Object Manipulation
Imitation Learning
Sim-to-Real
TL;DR: The first learning-based robotic paper-cutting system with scissors

Abstract: This paper tackles the challenging robotic task of generalizable paper cutting using scissors. 
In this task, scissors attached to a robot arm are driven to accurately cut curves drawn on the paper, which is hung with the top edge fixed. 
Due to the frequent paper-scissor contact and consequent fracture, the paper features continual deformation and changing topology, which is diffult for accurate modeling.To deal with such versatile scenarios, we propose ScissorBot, the first learning-based system for robotic paper cutting with scissors via simulation, imitation learning and sim2real. Given the lack of sufficient data for this task, we build PaperCutting-Sim, a paper simulator supporting interactive fracture coupling with scissors, enabling demonstration generation with a heuristic-based oracle policy. 
To ensure effective execution, we customize an action primitive sequence for imitation learning to constrain its action space, thus alleviating potential compounding errors.
Finally, by integrating sim-to-real techniques to bridge the gap between simulation and reality, our policy can be effectively deployed on the real robot.
Experimental results demonstrate that our method surpasses all baselines in both simulation and real-world benchmarks and achives performance comparable to human operation with a single hand under the same conditions.

ScissorBot: Learning Generalizable Scissor Skill for Paper Cutting via Simulation, Imitation, and Sim2Real
Jiangran Lyul?, Yuxing Chen Tao Du Feng Zhu?, Huiquan Liu', Yizhou Wanght He Wang 12. IIII, Tsinghua University
CFCS, School of Computer Science, Peking University Galboo
Challenges
Rotate
Close
Deformation
Push
Occlusion
Result
Robotic paper cutting with scissors. Left: The objective is to drive scissors to accurately cut curves drawn on the paper. which is hung with the top edge fixed. Middle: Our execution follows an action primitive sequence, namely Rotate, Close, Open, Push. The meticulous action, visualized as scissors before (orange) and after (green) each action, ensures accurate cutting the real world. Right:
Figure I:
During execution, large deformation of paper and severe occlusion between scissors and target curves occasionally occurs. Project Page: https://pku epic. gi github. io/ScissooBot/
Abstract:
This paper tackles the challenging robotic task of generalizable paper cutting us- ing scissors. In this task, scissors attached robot arm are driven accurately cut curves drawn the paper, which is hung with the top edge fixed. Due the frequent paper-scissor contact and consequent fracttrr, the paper features contin- ual deformation and changing topology, which is diffult for accurate modeling. To deal with such versatile scenarios, we propose ScissorBot, the first learning based system for robotic paper cutting with scissors via simulation, imitation learning and sim2real. Given the lack sufficient data for this task, we build PaperCutting- Sim, paper simulator supporting interactive fracture coupling with scissors, en- abling demonstration generation with neuristic-based oracle policy. To ensure effective execution, customize action primitive sequence for imitation learn- ing to constrain its action space, thus alleviating potential compounding errors. Fi- nally, by integrating sim-to-reat techniques to bridge the gap between simulation and reality, our policy can be effectively deployed on the real robot. Experimental results demonstrate that our method surpasses all baselines in both simulation and real-world benchmarks and achieves performance comparable to human operation with single hand under the same conditions.
Keywords: Deformable Object Manipulation, Imitation Learning, Sim-to-Real
Introduction
Paper cutting, an ancient craft dating back to least the 6th century [1], has evolved alongside hu- man civilization, serving as medium for emotional and symbolic expression [2]. In modern society,
Corresponding Authors
8th Conference Robot Learning (CoRL. 2024), Munich, Germany.

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it has wide applications ranging from decorative art [3] and education to advanced manufacturing and technology (4. 5]. Humans can use scissors to perform paper cutting, showcasing their dexterity in tool usage. However, robots have yet to master this generalizable cutting skill, which indicates using scissors to cut painted patterns on paper with visual observation. The main obstacle lies in the intricate interaction between paper and scissors, characterized by the continual deformation and changing topology of the paper. Accurately modeling this dynamics based on first principles and achieving precise control using Linear Quadratic Regulator Model Predictive Control is highly challenging. In contrast, barning-based methods, benefiting from data-driven, offer promising alternative without the need for explicit modeling of this complex system and have the potential to achieve generalization across diverse cutting tasks.
8, Despite the strengths of learning-based approaches for many robotic tasks [6. 7, 8, 9, 10, 11], they
fall short on this task partly due the following challenges. First, there is insufficient data for paper- a real-world
cutting tasks so far. Collecting accurate scissor-cutting demonstrations directly robot system is laborious and hazardous, making simulation essential for data generation. However, existing simulators for thin-shell objects [12, 13, 14] do not support detailed interaction with scissors including contact and consequent fracture. Second, learning a generalizable and accurate scissor policy is intrinsically difficult for this paper cutting task. Given its contact-rich and deformable nature, even millimetric movements of the scissors can induce significant bending (as illustrated in Fig. 1) or lead to curves deviating substantially from the intended target. Meanwhile, the scissors occasionally occlude the target curve, leading to an ill-posed decision-making problem. In this scenario, reinforcement learning methods struggle with poor data efficiency. Third, the significant sim-to-real gap. both physical and visual, hinders the deployment of the policy in the real world. The physical gap, arising from the complex factors in the real world, sometimes leads to deviations in the cutting trajectory during execution. Additionally, the visual gap for this task is mainly due to the edge bleeding artifact [15], where real-world sensor depth blurs at object edges. This blurring causes jittery observations of the scissor-paper interaction, leading to incorrect policy decisions.
To address the above challenges, we introduce ScissorBot, the first learning- based robotic system for paper cutting with scissors via a combination of simulation, imitation learning and sim2real tech- a paper-cutting simulator
niques. To mitigate the data scarcity issue, we develop PaperCutting- supporting interactive fracture coupling with scissors, enabling large-scale demonstration genera- tion with a heuristic-based oracle policy. This oracle policy leverages privileged information that is inaccessible in the real world, allowing to distill its knowledge into vision-based imitation learning policy. To handle tasks of significant complexity with improved efficiency, we customize an action primitive sequence which constrains the action space of learning and allivating potential compounding errors. We also use multi-frame point clouds as input to complete the occluded and underlying dynamics information. To bridge the physical and visual gaps between simulation and reality, we propose data augmentation on deviation correction and artifact mimicry, respectively. The former method can adaptively correct compounding errors via adding out-of-distribution data which pairs deviation states with corresponding correction action. The latter aims to mimic edge bleeding artifact in the simulation to achieve visual alignment with reality.
Through extensive simulated and real-world experiments, we evaluate the efficacy and generaliz- ability of our learning policy across three different task difficulty levels: Easy, Middle, and Hard. Our method improves cutting accuracy by at least fivefold compared to the best alternative methods, as measured by Chamfer distance. Furthermore, despite training only on Easy data from simulation, our method achieves Chamfer distance of 2mm and an IoU of 89 for Middle and Hard patterns in the real world, performance that is comparable to humans with single-hand operation. Our research opens up new oppotunities for contact-rich and fine manipulation of deformable objects.
2 Related Work
2.1
Deformable Object Manipulation
The manipulation of deformable objects, such as dough [16, 171, cloth [18, 8, 19] and rope [20, 13] has been extensively studied in the in the scentific and engincering disciplines. Zhao et al. [21]

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Simulation
Imitation Learning
SimZReal
Litars Fain
Push
PointNute
F
MLP
Openn
Heutbllk-ban basdd Denoratation Generviio
Alignment
Domonatration
Recurrent Eoecution
Augroettztion
Antiuc Miniery
Figure 2: An overview the learning system. The system first generates expert demonstrations in our built simulation which supports interactive fracture of the paper. These demonstrations are then used train a basod imitation learning policy that inputs multi-frame point clouds (Blade point cloud is highlighted in green only for visualization) and outputs parameters of action primi- tive. Meanwhile, Deviation Correction and Visual Artifact Mimicry provide data augmentation to imitation learning which ensures a robust transfer from simulation to real world.
train robots in the real world to learn paper-flipping skills, and Namiki al. [22] explore paper folding using motion primitives. Other studies focus on kirigami [23, 24], the traditional art of folding and cutting paper to create intricate designs. For paper cutting, these studies typically use desktop cutting plotters rather than fully automated robotic systems. Additionally, various robotic systems have been developed for cutting deformable objects in different domains, such as vegetables [25, 26), dough [16, 17], and soft objects with rigid cores [27]. However, these systems generally employ tabletop knife cutting, which differs from our approach of using scissors for cutting.
2.2 Simulation Environments for Paper Cutting
One line works build simulators to boost robotic skill learning for thin-shell materials [13, 14, 28, 12, 29], however they couldn't simulate the fracture during the scissors cutting. Some works focus on simulating the cutting process of soft materials [30, 27J. Other works studies paper fracture process either from the theoretical analysis [31. 32], re-meshing algorithm [33, 34] or its application in kirigami [35, 36]. Overall, none of the existing works implements the paper cutting simulation for robot learning, which combines dynamic modeling of paper and interactive fracture interweaving paper remeshing according to scissor motion.
2.3 Imitation Learning
Imitation Learning (II.) [37, 6, 7, 38] supervised learning methodology for training embod- ied agents using expert demonstrations. The commonly used Behavior Cloning (BC) [37] strategy directly trains the policy to imitate expert actions. Despite its simplicity, this approach has demon- strated remarkable effectiveness in robotic manipulation [39, 40]. In this paper, we adopt imitation learning and ultilze action primitive sequence to ensure robustness during execution.
Method
3.1 Task Formulation and Method Overview
The objective of this task is to accurately cut paper along drawn curves using scissors, guided by single-view point cloud input. The scissors are mounted on a single robotic arm, with the top edge of the paper fixed and the bottom edge free, enabling generalization various scenarios.
In order to learn such generalizable scissor skills, we introduce ScissorBot, a robotic system de- signed to learn visuo-motor policies via simulation, imitation learning and sim2real techniques. As the system depicted in Fig. 2, we first present our training data source in Sec. 3.2, where we develop the first paper-cutting simulator, PaperCutting-Se in Sec. 3.3. We then detail the vision-based imitation learning design in Sec. 3.4 and sim2real techniques in Sec. 3.5. Finally, present hardware setup for deploying our policy in real-world scenarios in See. 3.6.
and heuristic-based demonstrations generation

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(1) Detection of intersection points
(2) Remeshing
Figure 3: Interactive Fracture in our PaperCutting-Sin (1): As the scissors close, the fracture occurs along the cutting direction. Intersection points (red star) can be computed from edge-edge detection and vertex-face detection between the cutting direction (orange dashed) and the paper mesh. (2): (a) The original paper mesh (blue triangles).
(b) Intersection point (red star) and cutting direction (orange dashed). (c) According to the intersection points, new vertices are added on the existing edges and the endpoint is inserted inside the triangle. The new edges (green solid) are connected between the new inserted vertex and the opposite vertex in the triangle. (d) The edges between these newly added vertices are split into pieces (black solid).
3.2 PaperCutting-Sin
We build a paper-cutting simulator, PaperCutting-Sin to support the modeling of both paper and scissors, as well as their contacts and the consequent fracture. The simulator is implemented in Python and Taichi [41], which supports parallel computation on GPUs.
Dynamic Model. Following the Kirchhoff- shell theory, we model the elastic energy of the paper as the sum of stretching elastic energy and bending elastic energy. The stretching elastic energy modeled co-rotational linear elasticity, and the bending elastic energy is calculated using squared difference of mean curvature [42]. We perform spatial discretization using the Finite Element Method [33], and update positions and velocities through implicit time integration [43], which optimizes the incremental potential via Newton's 's method. To model the contact between the paper and the scissors, we represent the scissors using a signed distance field, utilize the cubic of the signed distance to calculate collision energy, and apply Coulomb friction.
Interactive Fracture. Different from cutting simulation with predefined fracture surfaces [30], interactively handling fracture coupled with contact a non-trivial problem. To address this, we design a two-phase geometry-baser approach, as illustrated in Fig. 3. First, during the closing process of the scissors, we propose using edge-edge detection and vertex-face detection detect the intersection points between the cutting trajectory and the paper mesh. Then these intersection points are added to the paper mesh and related edges are connected and split according to the vertex position relationship inside triangles. We refer the reader to Appendix B for more details.
3.3 Demonstration Generation
In this section, we devise an action primitive sequence and a heuristic Oracle policy for large- scale demonstration generation. For distillation, we preserve high-quality demonstrations measured by chamfer distance.
Action Primitive Sequence. We designed four action primitives for the seissors in heuristic manner, namely Open, Push, Rotate, and Close. These primitives can be combined into sequence to cut straight line on the paper as follows: (1) Open the scissors to the maximum extent. (2) Push the scissors to the starting point of the line. (3) Rotate the scissors towards the endpoint of the line. (4) Close the seissors breaking the paper. Note that the pushing action is a 1D translation along the cutting direction as we approximate that the starting point in the scissor cut direction.
Oracle Policy. The oracle policy initially discretizes the target smooth curve into several line seg- ments, with this approximation scarcely impacting visual appearance. Subsequently, the entire curve can be cut by multiple action sequences for line segments iteratively. As oracle policy can access the 3D position of target line during each step, the pushing distance (p E IR), rotation matrix (R E (O()), and closed angle (c E R') can be computed by relative position between scissors and target line. Please refer to Appendix C for more details.
3.4 based Imitation Learning
This section presents the design of our learning framework, with multi-framm point clouds input and action parameters as ouput. The complete network architecture is depicted in Fig. 2.

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Temporal Observation Encoding. We first pre-process raw single-view point cloud using bounding-bov cropping and FPS sampling. Then sequential T-frame point clouds (Pr-e-1)=1> along with a binary mask indicating whether a visible point originates from the target curve, are fed into a shared PointNet++ encoder [44] to obtain features {Fr-i+1 These features are concatenated and passed through shallow MLP regress actions parameters.
Primitive Learning. In contrast to selecting the direct 7 DoF scissor pose as our output action space, the output action parameters are associated with the designed action primitives mentioned in Sec. 3.3. These actions are recurrently executed for each stage which keeps the order of Push, Rotate, Close, Open repeatedly. We employ Mean Squared Error (MSE) loss for the Push and Close terms, and 9D L1 Loss [45] for Rotate. The overall loss is formulated as:
L = A Adlc 2)2 + AR. Σ
R.j - Riyl
(1)
i,
where Ap. de, AR are respective weights, and p, è, R are ground truth action values.
3.5 Sim-to-Real Transfer
Deviation Correction. We introduce deviation correc- tion enhance the robustness for drifting scenarios which somestimes occurs in the real world. In this ap- proach, we fine-tune the trained model using correction data, which comprises dusto--distribution states paired with corrective actions. These data are generated by intro- ducing random rotation perturbances to the action during oracle policy execution. As the oracle policy consistently cuts towards the endpoint of each line segment, the next action naturally corrects minor drifting errors.
Figure 4: Visualization of Visual Artifact Mimicing (a) Perfect point cloud in simulation with scissors blade highlighted (green points) (b) Point cloud with our proposed visual artifact mimicry. (c) Point cloud captured in the real world with artifact.
Visual Artifact Mimicry. We propose a simple yet effec- tive method mimic edge bleeding artifact in the sim- ulation. To create continuous value at the edge between foreground and background in simulated depth image, preprocess the depth with average pooling kernel and add random noise perpendicular to the surface of the paper to the point cloud of the blade. In this way, the artifact can be mimicked (Fig. 4(b)) in our training data thus reaching a visual alignment from simulation to reality.
3.6 Hardware System Design
We design a hardware system for the paper-cutting task, Fig. 5 shown. The setup includes Realman robot equipped with scissor extension for manipulation and single Kinect DK camera to capture RGBD observations. To secure the paper, we use plastic clips to fix the top edge, leaving the lower edge free. The target curves are drawn in red on white paper, with corresponding binary masks obtained through simple RGB-based segmentation. We use A4 printer paper (210 mm x 297 mm, 75 g/ //m?) as the material for the following experiments.
4 Experiments
In this section, we first evaluate the cutting performance our proposed method through compari- son with various baselines and variants in simulated environments. We further validate our approach in the Please refer to Appendix A for additional experiment information including gen- eralization to different materials, ablation studies and more qualitative results.
5

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Eaey
RGED
Sciscct
Tuagel
Figure 6: Example curves for Easy, Middle and Hard tracks.
Figure 5: Hardware System
4.1 Benchmark
Task Datasets. We focus on simple smooth curve cutting and split it into three distinct tracks, illustrated in Fig. 6. In each track, curves generated using Bézier curves parameterized by four control points. By manipulating the positional relationship of these control points, we can control the second-order derivative of the curve, which in turn determines the complexity of the scissors' motion. The discussion on non-smooth and non-simple curves can be found in the Sec.
Easy: In this track, the second-order derivatives of curves are consistently positive negative.
Middle: Curves in this track exhibit varying positive and negative second-orde -odder derivatives.
Hard: This track comprises several patterns, each composed of two curves from the Easy track. In real-world settings, this track can be further required to cut the origami sheet to obtain an axisymmetric closed-shape pattern.
To demonstrate the generalization capability of our policy, our training set consists of approximately 5k trajectories solely from the Easy track. There are 100 curves each track for testing.
Evaluation Metries. In our evaluation process, we utilize various metrics to gauge the quality of results across different difficulty levels. For the all three tracks, we employ the chamfer distance as measure of deviation between the cropped curve and the target curve. Additionally, we report the Recall metric under different thresholds of chamfer distance, indicating the proportion of well- cut instances. For trials completing closed shapes in the Hard track, we further assess the quality by calculating the mean Intersection over Union (mIoU) between the cropped pattern and the target pattern, providing a comprehensive measure of similarity and accuracy.
4.2 Policy Evaluation in Simulation
Non-ingg Baselines.
Open-loop Planning detects the target goal curve prior to cutting. Then it discretizes the detected curve into isometric line segments and plans the scissor translation and rotation at each step.
Online Firring employs an step-by-step line fitting utilizing RANSAC. The fitted line target from the captured point cloud determines the movement distance and scissor rotation at each step.
Learning based Baselines.
Direct Pose Regression. This methodology directly regresses the 7 Degrees of Freedom (DoF) scissor pose (6D Pose and ID joint angle).
Action Chunking [7]. In this policy, actions for the next k timesteps are predicted. The current action to execute is determined from weighted averages across the previous overlapping action chunk. We adopt the implementation from [7].
Comparison to Non-learning based Baselines. Our method exhibits significantly superior cutting accuracy when compared non-learning based approaches. depicted in Fig. 7, the cutting trajectories of Open-loop Planning substantially deviates from the target curve. The reason lies in that Open-loop Planning lacks adaptability to environmental changes and accumulates lot of errors during the highly non-linear interaction between scissors and paper. Although Online Fitting

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Bilsoor aegarate from the peper
(a) Open-loop Planning
(b) Online Fisting
(c) Direct Regression
(d) ScissoeBot
Figure 7: Visualization of Cutting Results on UV plane of the paper. Target curves are in red
while cropped lines by scissors are in green.
Easy
Middle
Hard
Methods
Chamfer (mm)
Chamfer (mm)
Recall@
&.c
Recall 1.5
Recall@
Chamfer (mm)
mloU
Open-loop Planing
10.8
9.3
25.0
6.8
10.5
36.3
18.1
31.2
Online Fitting
5.5
31.4
73.6
21.0
Ours
1.1
85.1
98.6
1.5
79.6
96.6
1.9
91.3
Oracle
1.4
98.2
1.4
98.2
1.9
92.2
Table 1: Comparison with non-learning based baselines in simulation.
demonstrates some adaptability by adjusting its cutting action based on current observations, it falls short of making optimal decisions, particularly in instances of occasional occlusion. In contrast, our learning policy showcases remarkable adaptability to dynamic conditions, resulting notably precise operations, with chamfer distance of 1.1 mm compared 10.8 mm and 5.5 mm for Open- loop Planning and Online Fitting respectively.
Effeet of the Primitive Learning. The comparison with learning-based baselines cxhibits the effectiveness our primitive learning. As shown in Fig. 7(c), the al- ternative frequently causes separation be- tween scissors and paper and thus fails perform the paper-cutting tasks to the end. We only report its chamber distance with the first one-third of the target curve in Tab.2. Even incorporating Action Chunking, designed to mitigate compounding errors, there is no substantial improvement in completing the target curves. This is due to the drastic state transitions each step, which complicate the accurate prediction future actions. These results highlight the highly nonlinear nature of the task. In contrast, designed primitive constraints the action space of scissors, which minimizes possible errors during execution.
Chamfer (mm)
Method
Recall@
Recal1@5.0
Direct Pose Regression
11.2"
9.0"
21.1"
Action Chunking (7)
11.4
8.9"
25.1"
Ours
1.1
85.1
98.6
Chunking [7]
Table 2: Comparison with learning-basel baselines in simulation. For Direct pose regression and variance, only calculate its chamber distance with the first one-third of the target curve (*).
Generalization to Novel Curves and Patterns. Middle and Hard targets pose additional challenges due to more varied patterns, leading to more complex deformation and fratcure during cutting. De- spite being trained on the Easy track of curves, our policy demonstrates robustness and achieves performance comparable the oracle policy when handling Middle and Hard targets. This success due to its generalizability from careful system design.
4.3 Policy Evaluation in the Real World
We evaluate the performance of our sim2real model on real-world platform. Quantitative and qualitative results are presented in Table 3 and Fig. 8, Fig. 11, respectively.
Experiment Details. To understand the capability our system, we conduct comprehensive user study gather statistics human performance. Specifically, we invite 10 subjects aged between 10 and 60 years, including both males and females. They are asked to cut paper using daily scissor with one hand while the paper was hanging under the same conditions as our robot system. Each subject complete ten trials for each track.
We define "finished" as the line having chamfer distance of less than 3 em from the target curve, with no tearing folding of the paper. After each trial for both policy and human, capture the cropped paper using an RGBD camera and compute metrics such as chamfer distance and IoU. We report the median and extremum of these metrics in the form of x +

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Easy
Middle
Hard
Methods
Chamfer (mm)
Chamfer (mm)
Finished Rate
Finished Rate
Finished Rate
IoU
Human
10/10
2
10/10
2
10/10
92 +
Ours w/o Visual Artifact Mimicry
0/10
0/10
0/10
Ours w/o Deviation Correction Ours
7/10
2
7/10
3
7/10
9/10
2
2
5
Table 3: Quantitative results in the real world.
Time
Final State
Easy
Middle
Hard
Figure 8: Realworld cutting process on Easy, Middle and Hard tracks.
(a) Difting Failure
(b) Persistent Error
(c) Deviation Correction
Figure 9: Qualitative result of our Deviation Correction. Without using Deviation Correction, policy trained from simulation frequently falls into drifting failures (a) keeps perisitent errors (b). Our Deviation Correction (c) leads to a accurate and robust deployment.
Result Analysis. As evidenced Table 3, our policy consistently fails without any sim2real, as result of confused perception with the interactions between blades and paper. Our mimiery strategy mitigates the visual gap and minimize erratic action prediction, thereby achieve successful deploy- ment. However, the performance is still still unsatisfactory. As illustrated in Fig. 9, policies some- times experience drifting failures (Fig. 9a) or persistently exhibit errors (Fig. 9b). To this end, the correction mechanism addaptively corrects the deviation and enhances the stability and accuracy of the deployed policy. For example, it enhances the finished rate from 7/10 to 9/10 the "Fasy" track and reducing deviation by mm in the Middle track. Combining the above sim2real techniques, our system achieves comparable performance human single-hame hand manipulation under same condition, which has only mm error from the target curve. Furthermore, it achieves IoU of 89 on the Hard track, which is particularly challenging due more drastic bending.
5 Conclusion, Limitations and Future Directions
We introduce ScissorBot, the first learning-based robotic system for generalizable paper cutting using scissors. The system utilizes demonstrations collected in our newly developed paper-cutting simulator to train primitive-baut based imitation learning policy and combines sim2real techniques to achieve robust deployment in the real world. Extensive experiments exhibit the generalizability and accuracy of our system on simple smooth curves which cover most of cutting scenarios. However, scissor cutting for non-simple or non-smooth curves is still an open problem. Non-smooth curves like zig-zag patterns must result in the sudden relative pose change frequently for scissors while non-simple curves will result in circle in the scissor trajectory. Both two kinds of scissors' motion can't be achieved considering single-arm workspace. To solve these challenging situations, it may be dexterous dual-arm cooperation system containing one arm holding and rotating the paper and the other manipulating scissors. We leave this bimanual hardware system with policy design as future works.

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Acknowledgments
We would like to express our deepest gratitude to Ruihai Wu for his invaluable guidance during the early stages of this work, which was crucial its success. We also thank Jiayi Chen for providing many valuable discussions, offering insightful feedback, and pointing out several key issues and potential improvements. We are grateful to Mi Yan, Jiazhao Zhang, Songlin Wei, Wenbo Cui, and Weikang Wan for their constructive feedback on the writing, figures, and tables in this paper. We also appreciate the help of Xiaomeng Fang and Hao Shen with the camera calibration, as well as the support and guidance of Jilong Wang on the robot workspace and motion planning. Additionally, we acknowledge Jiqiao Li, Mingdong Lu, Xinzhe Jin, Yuanchen Cao, Zhiqiang Xu, and Chenxu Zhao for their care and encouragement throughout this work.
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A More Experiments and Results
A.1 Generalization to Different Materials
We highlight experiments that demonstrate the generalization to different materials. Specifically, we select six different materials for evaluation: cardboard, A3 printer paper, rice paper, plastic sheet, photo fabric, and aluminum foil. These materials exhibit varying physical properties, such as thickness, density, stiffness, and their bending and stretching characteristics. For example, cardboard verythick and hardly bends during cutting, while rice paper is very thin and deforms significantly. A3 printer paper is larger in size than the A4 paper used in our previous experiments, and foil has an uneven surface. We conducted 10 trials for each material using the Easy track of curves.
By applying domain randomization to physical parameters of the paper including size, mass and Young's modulus, our policy successfully generalizes to these different materials without requiring customized training. We exhibit that learning papers with scissors is generalizable to different materials than specialized cutting machines. Videos can be found website.
A3 printer paper
Cardhoard
Rice paper
Photo fabric
Plastic sheet
Aluminum foil
Figure 10: Test on unseen materials.
Metric
Cardboard
A3 printer paper
Rice paper
Photo fabric
Plastic sheet
Aluminum foil
Finish rate
7/10
9/10
9/10
8/10
8/10
8/10
Chamfer
3+1
2+1
2+1
2+1
2+1
3+1
Table 4: Experiments on different materials.
A.2 More Qualatative Results
Figure 11: Realworld results patterns from Hard tracks. The cropped pattern from system has a accurate overlap with the target pattern.
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Time
Hard
Figure 12: Cutting process of our method in the simulation on Middle and Hard tracks.
Basic length (mm)
Steps
Chamfer (mm)
20
29
1.9
15
~ 37
1.4
10
53
1.3
Table 5: Effects of Discretization Granularity for curves, i.e, the basic length of line segments.
A.3 Ablation Studies
In this section, conduct experiments to analyze the effects of critical parameters and design choices.
Discretization Granularity. During the generation of expert data, smooth curves are discretized into line segments as an approximation. We aim to study the impact discretization granularity on efficiency and quality, as reported in Table 5. It's evident that as the length of each line segment decreases, the number of execution steps increases while the quality improves. When the basic length decreases from 15 0.1 mm. Thus, we opt for trade-off choice of 15 mm, with balance between efficiency and quality.
10 mm, the reduction in chamfer distance marginal, merely
Observation Horizon (L). We analyze the effect of different observation horizons, as detailed in Ta- ble 6. Policies with frame horizons outperform that without temporal inputs by approximately 10 points on Recall @ 1.5. The superiority of our spatial-temporal encoding lies in its robustness to occlusion and deformable dynamics. Although increasing the horizon from improvements in cutting quality, e.g., 0.3 for Recall @ 1.5, we opt for horizon of 4 in our system to maintain favorable balance between performance and efficiency.
yields marginal
Filtering Threshold (r). We train our imitation policy using various demonstration filtering thresh- olds ranging from to 1.6, as well as no filtering, as summarized Table 7. stricter threshold yields better performance and lower data usage rate, necessitating the generation of more demon- strations for distillation. In system, select 1.0 to strike balance between data quality and efficiency.
B Details of PaperCutting-Sim
We consider the occurrence of paper fractures due to the intersection of the scissor blades. As the scissors close, the intersection point of the two blades, denoted as P, moves along the paper surface. The trajectory of this movement forms the fracture line on the paper. At each time step, we detect this moving trajectory on the paper mesh and perform remeshing, which includes vertex insertion, edge connection, and edge splitting.
New Vertex Insertion: For each time step t, the movement of P can be represented as segment E (P Pt Vv), where is the velocity and V is the cutting direction of the scissors. Per-
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Horizon
Chamfer(mm)
Recall 1.5
Recall 5.0
w/o multi-frame
1.5
74.4
94.2
I 2
1.6
70.4
93.1
=
1.1
85.1
98.6
=
1.1
85.4
98.9
Table Ablation study of Temporal encoding and Observation Horizon.
Filter
Data usage
Chamfer(mm)
Recall 1.5
Recall @5.00
w/o filtering
100%
1.7
74.5
92.5
r 1.6
90%
1.4
81.8
97.8
7 == 1.0
70%
1.1
85.1
98.6
5 0.7
30%
1.1
85.0
98.6
Table 7: Ablation study on the Filtering threshold T.
forming edge-edge detection between E and the paper mesh M will yield most intersection points. For the endpoints of E, they may not be located at existing edge, so also perform vertex-face detection to get the intersection points. We insert all the intersection points
vertices in order.
New Edge Connection. With the insertion of vertices, we perform edge connection. For a newly inserted vertex on an existing edge, we connect it to the opposite vertices in all triangles containing that edge. For a newly inserted vertex inside a triangle but not on the edge, we connect with three vertices of the triangle.
Edge Splitting: For each newly connected edge, if its two endpoints are newly inserted vertices, then this edge need to be splitter.
C Details of Demonstration Generation
The action parameters are computed through relative pose between scissors (blade intersection Pa and cutting direction V,) and target line segment (Tar (s s, .4+1)) for each step
When is the step for Push, the pushing distance is computed as:
Pr (s Pt) V V2
(2)
||
When is the step for Rotate, the Rotation R. computed using Rodrigues' rotation formula:
w V. x Tar,
(3)
0 cos
(V, Tar
(4)
0
W2
Wly
K
W2
W
(5)
Wy
Wp
0
R I + sin OK
cos
K)²
where I the identity matrix. When f the step for Close, the closed angle c is computed as
C Distance2Angle (sitt2 -P)) V V(v,)
|V.12
where Distance2Ange is a function to map the cutting distance to closed angle. The function depended on the mechanical structure of scissors and obtain it via calibration.
D Details of the Benchmark
We consider the generation of curves in the space of the paper. In each track, curves generated using Bézier curves parameterized by four control points, which are equidistant along the u-axis.
14

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By connecting these four points with three line segments, can compute the gradients of these lines. We approximate the second-order derivatives of the curve by calculating the differences in gradients between these lines. For the Easy track, the gradient differences are always either positive or negative, ensuring a consistent curve direction. For the Middle track, the gradient differences include both positive and negative values, creating more complex curves. Considering the robotic arm workspace, scissors cannot undergo significant rotations, i.e., exceeding 90" relative to the initial orientation along the moving trajectory. Empirically, we constrain the gradient of the first line to be within |- tan(40%), tan(40)) and the gradient of the last line within [ tan(60"), tan(60%))
E
Implementation of Policy Learning
E.1 Point Cloud Pre-processing
We preprocess the visual input by cropping the global point cloud into a 3 x 3 cm3 local patch centered around the scissors. This means that the policy only "sees" the local pattern rather than the entire curve. Since the local structures are generally consistent across curves, this approach helps the model generalize across different tracks.
E.2 Vision Encoder
The sequential point cloud features from the PointNet++ encoder are concatenated and fed into three action heads. Each action head is shallow MLP with the shape of [L x 512 256 - -64 - a]. where the length of the observation horizon and the dimension of the action parameter. We train the model from scratch for 120,000 iterations. The learning rate initialized at 1 10-4 and decays by factor of 0.1 60,000 and 110,000 iterations, respectively.
E.3 Primitive Parameterization and Learning
The push primitive is parameterized by ID distance, indicating the amount of pushing along the current direction. The rotate primitive parameterized using a rotation matrix, indicating the delta rotation the scissors current frame. The close primitive is parameterized by a ID distance, which represents the length aims to cut. The open primitive is not parameterized separately because shares IDoF with the close action. Essentially, we fix the open action predefined position (e.g., maximum opening) and do not need separate parameterization.
The model outputs parameters for all three primitives (rotate, close, push) in a single forward pass, but only selects one action to execute based on the predefined order and discards the other two outputs. The sequence four action primitives is repeated until the curve is completed, which is referred to as Recurrent Execution Fig. 2. For hyperparameter the loss function, we simply choose A Re An 1, and we find it is effective enough.
E.4 Action Chunking
For Action Chunking, we follow the implementation of [7], which predicts k future actions using an exponential weighting scheme where e mxx with wo representing the weight for the most recent action. In our experiments, we set and m 0.01.
F More Discussion on Limitations
As we claim in the main paper, scissor cutting for non-simple or non-smooth curves is still an open problem. We adopt the definitions from MathWorld / httpss//mmatwrlddd wolfram com/). curve simple if does not eross itself. A smooth curve continuous map from a one- dimensional space an n-dimensional space that has continuous derivatives up desired order on its domain. Curves that do not meet these definitions considered non-simple or non-smooth, respectively.
15

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The limitation arises from the relatively long length of the scissors compared to regular end effectors. Due to the limited workspace, our small 6-DoF arm typically cannot rotate the scissors by more than 90 degrees while maintaining their position unchanged. As a result, non-smooth curves with significant turning angles are not achievable. Additionally, non-simple curves involve loops in the scissors' trajectory, which are also unattainable due the constraints of the hardware setup, the learning method itself. Addressing these limitations might require designing dexterous dual-arm cooperation system, which could be a direction for future research.
16


Reviews:
[{"review_id": "KroeJqUlnZ", "reviewer": "Reviewer_n7FW", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": 3, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "This paper proposes a complete solution for robotic paper cutting. The authors design a simulator, demonstration generation, and a sim-to-real learning pipeline to transfer the paper cutting skill to the real world. They first create a simulator for this task and generate demonstrations using heuristics given ground-truth information. They bridge the sim-to-real gap by introducing Deviation Correction and accurately modeling depth sensing noise. They also abstract the action space into a few primitive skills to simplify learning. The authors demonstrate improved performance over several competitive baselines.", "summary_of_recommendation": "This paper presents a well-engineered effort for a complicated problem. I’m concerned with the generalizability of the proposed system.", "technical_quality": 3, "clarity_of_presentation": 3, "potential_impact": 2, "robotics_focus": 4, "quality_of_limitations": 3, "questions_for_rebuttal": "From Figure 9(c), the target seems to be cutting along the red line instead of in the red line. Can you clarify how the goal is defined by the reward?\n\nCan the authors comment on why previous deformable object simulators [10, 11, 12, 26] cannot simulate paper cutting? Is it due to efficiency issues or do they have fundamental limitations in terms of implementation?\n\nCan the proposed system also generalize to different materials (such as rectangle cloth or fabric) or different types of scissors (with varying sharpness)?\n\nHow many trials when doing the evaluation?", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Ahw7LwzI1w", "reviewer": "Reviewer_2CTS", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": 4, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "The paper proposed a novel learning-based robotics system to use scissor to cut paper following predefined paths. The system is composed of a paper simulation engine, a learning method using 3D perception and primitive action, and a sim2real adjustment mechanism.", "summary_of_recommendation": "This paper presents a novel approach for a robot learning to cut paper with scissors, leveraging a robust thin-shell object simulation that transfers effectively to real-world applications. While the method and results are impressive, the scope of the paper is relatively limited. If the authors can better motivate the point why scissor is needed over specialized cutting machines, that'll make the paper's argument much stronger.", "technical_quality": 4, "clarity_of_presentation": 4, "potential_impact": 3, "robotics_focus": 4, "quality_of_limitations": 1, "questions_for_rebuttal": "- Can the lessons learned from this task be generalized towards other robotic tasks?\n- Can the authors include some failure cases in the summary video as well as the main paper? What are some major failure modes?\n- Is there cases where the scissor breaks the paper during pushing?\n- What happens if the scissor cuts deep into the paper causing the base of the scissor or part of the robot arm collides with the paper causing it to deform in undesirable ways? Does this happen during experiments and will this influence the results?\n- The authors mentioned that \"Non-smooth curves like zig-zag patterns must result in the sudden relative pose change frequently for scissors while non-simple curves will result in a circle in the scissor trajectory. Both two kinds of scissors’ motion can’t be achieved considering our single-arm workspace.\" Could you clearly define what non-smooth and non-simple mean? Why are non-smooth patterns not achievable with a single-arm workspace? Isn't it the limitation of the method which doesn't allow sudden relative pose change instead of the single-arm workspace itself?", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "sZXVKx43lQ", "reviewer": "Reviewer_Wc2M", "summary": "", "questions": "", "limitations": "", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": 4, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "The presented work tackles the novel task of learning robotic scissor skills through a sim2real pipeline. The authors introduce a simulation for paper cutting that accurately models the behavior of the real world and use it to generate demonstrations. With a combination of vision-based imitation learning and randomization, the learned policies transfer to the real world and show generalization to unseen cutting shapes as well as robustness to perturbations of the paper.", "summary_of_recommendation": "The work aims to solve the novel task of robotic scissor skills, develops a corresponding simulation, and showcases the efficacy of imitation learning and sim2real to solve the task in a challenging real-world setting.", "technical_quality": 4, "clarity_of_presentation": 4, "potential_impact": 3, "robotics_focus": 4, "quality_of_limitations": 3, "questions_for_rebuttal": "1. The paper provides insufficient information about the learned primitives. How are these parameterized? Why is Close parameterized but Open not? What does “Recurrent Execution” mean? Does the model predict parameters for all primitives in one forward pass or is there a conditioning of some form?\n\n2. How much does the choice of λ_p, λ_c, λ_R (Equation 1) matter and how much tuning did you have to do?\n\n3. How robust is the method to the type of paper and scissors used in the real experiments? What if the paperweight is increased, making it harder to cut? What if the scissors become dull over time? Or in other words: how much simulation tuning is involved to bridge the sim2real gap?\n\n4. While the results show generalization capabilities of the trained policy from Easy to Middle and Hard tracks, it is unclear what design choice causes this. From an architecture and learning perspective, I’d assume the model would overfit to the Easy red lines seen in sim and perform poorly on unseen Medium and Hard tracks. The information provided is very vague and doesn’t provide sufficient explanations.\n- Line 100-101 “The scissors are mounted on a single robotic arm, with the top edge of the paper fixed and the bottom edge free, enabling generalization to various scenarios.”\n- Line 247-248 “This success is due to its generalizability from careful system design.”\nA discussion of why the model generalizes would make the paper stronger.\n\n5. Why is the oracle in Table 1 worse than the learned policy?\n\n6. Line 253-254 “Finished rate, subjectively defining ”Finished” for trials which execute smoothly without falling into tearing, folding, or significant deviation from the target.”\nAs noted this metric is very subjective. While tearing and folding are intuitive, “significant deviation from the target” should be better defined. Instead, using a success metric based on thresholding the chamfer distance might provide more clarity.\n\n7. Line 266-267 “[The] system achieves comparable performance to human single-hand manipulation under the same condition, which has only 2 mm error from the target curve.”\nThe paper provides no information on which setting the data was collected, how many subjects completed the study, and how proficient the subjects were at the task. Without a proper controlled use study, these numbers don’t mean anything.", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper proposes a pipeline for scissor cutting. The method is somewhat domain-specific, but results are good enough for this to be a valuable contribution to the robot learning community. The rebuttal led to two reviewers increasing their scores, so now there is a strong accept and two weak accepts. The authors are encouraged to add more details about the user study to the final paper.

Strengths:

* A novel pipeline for sim2real cutting, with real world experiments shown.
* The cutting application is distinct from prior work that has done cutting.

Weaknesses:

* Multiple reviewers commented that the application might be too narrow (cutting). It would be good to motivate the need for this over specialized cutting machines.
* The success metric might be too subjective, and the paper should clarify the comparison with human performance.
Decision: Accept