Hybrid Perception and Equivariant Diffusion for Robust Multi-Node Rebar Tying

TL;DR

This paper presents a hybrid perception and diffusion-based motion planning system that enables robust, efficient, and data-efficient multi-node rebar tying in complex construction environments, advancing automation in construction tasks.

Contribution

It introduces a novel integration of geometry-based perception with Equivariant Denoising Diffusion on SE(3) for robotic rebar tying, requiring minimal training data.

Findings

High success rates in complex rebar configurations

Effective node detection and orientation estimation

Robust tying with minimal demonstration data

Abstract

Rebar tying is a repetitive but critical task in reinforced concrete construction, typically performed manually at considerable ergonomic risk. Recent advances in robotic manipulation hold the potential to automate the tying process, yet face challenges in accurately estimating tying poses in congested rebar nodes. In this paper, we introduce a hybrid perception and motion planning approach that integrates geometry-based perception with Equivariant Denoising Diffusion on SE(3) (Diffusion-EDFs) to enable robust multi-node rebar tying with minimal training data. Our perception module utilizes density-based clustering (DBSCAN), geometry-based node feature extraction, and principal component analysis (PCA) to segment rebar bars, identify rebar nodes, and estimate orientation vectors for sequential ranking, even in complex, unstructured environments. The motion planner, based on Diffusion-EDFs, is trained on as few as 5-10 demonstrations to generate sequential end-effector poses that optimize collision avoidance and tying efficiency. The proposed system is validated on various rebar meshes, including single-layer, multi-layer, and cluttered configurations, demonstrating high success rates in node detection and accurate sequential tying. Compared with conventional approaches that rely on large datasets or extensive manual parameter tuning, our method achieves robust, efficient, and adaptable multi-node tying while significantly reducing data requirements. This result underscores the potential of hybrid perception and diffusion-driven planning to enhance automation in on-site construction tasks, improving both safety and labor efficiency.

Tables

Table 1. TABLE I: Statistics of the datasets

Symbol	Demos	Conditions
Train \Romannum1	10	1-node, BG (2 Ob), noise (-)
Train \Romannum2	10	1-node, BG (-), noise (-)
Test \Romannum1	50	4-node, BG (-), noise (-)
Test \Romannum2	50	4-node, BG (4 Ob), noise (-)
Test \Romannum3	50	4-node, BG (-), noise ([0,0.5])
Test \Romannum4	50	8-node, BG (-), noise (-)
Test \Romannum5	50	8-node, BG (4 Ob), noise (-)
Test \Romannum6	50	8-node, BG (-), noise ([0,0.5])
Test \Romannum7	50	16-node, BG (-), noise (-)
Test \Romannum8	50	16-node, BG (4 Ob), noise (-)
Test \Romannum9	50	16-node, BG (-), noise ([0,0.5])
Test \Romannum10	50	32-node, BG (-), noise (-)
Test \Romannum11	50	36-node, BG (-), noise (-)
Demos: Demonstrations
BG: background, noise: Gaussian noise, obstacles: Ob
-: not considered (clear)

Table 2. TABLE II: Nodes Detection Results

Evaluation purpose	Symbol	Condition	$R_s$
Robustness to noise	Test \Romannum1	4-node,BG(-), noise(-)	$96\%$
	Test \Romannum3	4-node, BG (-), noise ([0,0.5])	$98\%$
	Test \Romannum4	8-node, BG (-), noise (-)	$94\%$
	Test \Romannum6	8-node, BG (-), noise ([0,0.5])	$90\%$
	Test \Romannum7	16-node, BG (-), noise (-)	$98\%$
	Test \Romannum9	16-node, BG (-), noise ([0,0.5])	$94\%$
Robustness to background obstacles	Test \Romannum1	4-node, BG (-), noise (-)	$96\%$
	Test \Romannum2	4-node, BG (4 Ob), noise (-)	$90\%$
	Test \Romannum4	8-node, BG (-), noise (-)	$94\%$
	Test \Romannum5	8-node, BG (4 Ob), noise (-)	$82\%$
	Test \Romannum7	16-node, BG (-), noise (-)	$98\%$
	Test \Romannum8	16-node, BG (4 Ob), noise (-)	$84\%$
Effectiveness for complex node distribution	Test \Romannum1	4-node, BG (-), noise (-)	$96\%$
	Test \Romannum4	8-node, BG (-), noise (-)	$94\%$
	Test \Romannum7	16-node, BG (-), noise (-)	$98\%$
	Test \Romannum10	32-node, BG (-), noise (-)	$96\%$
	Test \Romannum11	36-node, BG (-), noise (-)	$98\%$
BG: background, noise: Gaussian noise, obstacles: Ob
-: not considered (clear)

Equations

$$g^{t+dt}=g^t\exp [dW],$$

$$P^t(g)={\int }_{SE(3)}{P}^{t\mid 0}(g\mid g^0)P^0(g^0)d{g}^0,$$

$$g^{t+dt}=g^t\exp \left[\frac{1}{2}{s}^t(g^t\mid o_s,o_r)dt+dW\right].$$

$$M1=len(len(D[D<R_{res}])\ge len(D)\times 1/2$$

$$M2=len(len(D[D>P_{res}])\ge len(D)\times 1/3$$

$$M=M1\&M2$$

$$R_s=\frac{1}{N}\sum _{i=1}^N\frac{N_{si}}{L},$$

$$D_g(g,\hat{g})<T_g,$$

$$E_r=\frac{1}{N}\sum _{i=1}^N\left[\frac{1}{L}\sum _{l=1}^L{D}_g(g_{il},{\hat{g}}_{il})\right],$$

$$D_g(g_1,g_2)=d_p(p_1,p_2)+\gamma {\theta }_q(q_1,q_2),$$

$$d_t(p_1,p_2)=\Vert p_1-p_2{\Vert }^2,$$

$${\theta }_q(q_1,q_2)=2{\cos }^{-1}(\mathrm{real}(q_1\cdot \overline{q_2})),$$

Full text

I INTRODUCTION

Rebar tying entails fastening intersecting steel bars with wire in reinforced concrete construction. This task is both labor intensive and ergonomically challenging, raising concerns about worker injuries and reduced productivity [1]. Various robotic solutions have been proposed to automate rebar tying; however, these systems often require extensive on-site infrastructure (gantry mounts) or lack adaptive perception for cluttered environments [2]. Although commercial tying robots, such as TyBOT, can achieve over 1,000 ties per hour [3], they generally operate only on flat decks with minimal obstructions, limiting their adoption.

A key hurdle in automating rebar tying lies in reliable detection of rebar nodes (the intersection points) and the robot’s ability to perform multi-node tying in sequence without perturbing the loosely laid rebars [16]. Many solutions rely on large-scale learning approaches, demanding comprehensive datasets to handle the variability in rebar arrangements [4, 5]. Additionally, rebar misalignment or multi-layer configurations introduce further complexity, often leading to incorrect tying or collisions [6]. To this end, this requires both robust perception and adaptive motion planning that can generalize across different scenes.

We propose an integrated framework that marries a point cloud clustering-based geometry analysis and a Diffusion model with an Equivariant Descriptor Fields (Diffusion-EDFs) for multi-node tying (with an example in Fig. 1). On the perception side, density-based clustering (DBSCAN) is exploited to segment rebars from background data, and geometry-based node feature extraction combined with principal component analysis (PCA) is applied to accurately identify intersections for each node and rank them in sequence. These steps effectively localize tie positions even in the presence of overlapping bars or background clutter [17]. On the planning side, the Diffusion-EDFs architecture, known to require as few as 5-10 demonstrations for training [7], generates collision-free sequential poses in SE(3). By leveraging symmetry constraints in orientation and translation, the diffusion model efficiently learns how to place the tying tool around multiple intersections in a single pass.

We summarize our contributions as

• •

the design of a multi-node detection algorithm to isolate, cluster, and order rebar intersections for tying,

• •

the integration of Diffusion-EDFs for pose generation with minimal demonstrations, enabling sampling-efficient sequential planning, and

• •

extensive tests and verifications on planar and multi-layer rebar meshes, demonstrating high tying accuracy under real-world conditions.

This hybrid approach, combining domain heuristics with an equivariant generative model, significantly reduces the need for large and curated datasets while maintaining robustness in cluttered or unstructured construction settings. The proposed system points to a future where agile and data-efficient robots handle demanding tasks on site, alleviating labor shortages and worker fatigue in reinforced concrete construction [18].

II RELATED WORK

II-A Automated Rebar Tying Systems

Robotic rebar tying has evolved from stationary lab-based platforms to partially on-site automation. Momeni et al. [8] automated the production of steel cages in a controlled facility by using a robotic arm, yielding a high throughput but limited generalization outside the lab. Jin et al. [9] investigated a crawler tying robot that traversed the rebar mesh; despite its mobility, the robot was prone to displacing unfastened rebars during locomotion. Commercially, TyBOT [3] and other gantry-mounted tying robots excel at tying thousands of intersections on large, open decks but face constraints in irregular or congested environments. Overall, robust solutions for multi-layer or cluttered sites remain an active area of research [2, 19].

II-B Rebar Node Detection

A reliable perception pipeline is essential for identifying rebar ties in various rebar configurations. Classical geometric methods segment rebars as linear structures in point clouds and derive crossing points from estimated principal axes [6]. Such methods can be highly interpretive and rely on prior manual information. For instance, rebars are usually straight and orthogonal. Vision-based approaches often employ deep neural networks, trained on synthetic or lab-captured images, to identify intersections [4, 5]. Although powerful, these detectors can fail under complex real-world conditions (lighting shifts, heavy occlusions) unless the training data are extensive and well-curated [10]. For robust on-site performance, recent work combines depth sensing with traditional geometric filters to ensure reliable intersection detection, even with limited training data [11, 20]. This aligns with our approach, where a lightweight and geometry-based pipeline is used to isolate rebar nodes across multiple layers or non-uniform meshes.

However, the pipeline combining two-dimensional detection with point cloud post-processing suffers from the difficult alignment and calibration between image and depth information. Additionally, the mentioned methods, especially  [11], only consider the horizontally positioned rebars and the transformation in real world can reduce detection performance. Thus, transformation-invariant methods are in obvious demand.

II-C * Diffusion-EDFs for Robotic Planning*

Pose estimation and motion planning in construction robotics often involve enumerating potential collision-free paths, which becomes unwieldy as the scene complexity grows [12]. Diffusion models address the challenge by learning a continuous distribution over feasible trajectories. Early work by Ho et al. [13] established diffusion models in image generation, inspiring research on applying the same principles to robot control [14]. Janner et al. [15] demonstrated that a diffusion-based model can outperform conventional trajectory optimization on multi-step tasks. Critically, Ryu et al. [7] introduced Diffusion-EDFs, a bi-equivariant model defined on SE(3) that has been successfully applied to tasks such as pick-and-place operations.

Our method integrates geometry-based perception with an equivariant denoising diffusion trajectory planner on SE(3), aiming to tackle the real-world challenges of rebar tying limited data, cluttered meshes, and tight space with minimal data scale. This synergy between geometry-based perception and advanced generative models underscores the potential of data-efficient robotics in construction automation.

As the method on SE(3) ensures the transformation invariance, it naturally fits in the geometry and characters of rebars. Thus, we modify Diffusion-EDF to perform a continuous tying pipeline, which holds its advantages by avoiding complex alignment between image and depth information as well as end-to-end generating the tying pose, with promising application for tying rebars positioned both horizontally and vertically.

III Method

In this section, we present the details of our methodology. The system design and overall architecture are illustrated in Fig. 2 and 3. A tying gun is mounted on the end joint of a robotic arm with a 3D camera (RVC-P32200) capturing the colored point cloud of the rebars positioned vertically. Fig. 1 demonstrates a robotic arm sequentially tying a 4-node rebar structure using our pipeline. Our pipeline operates through the following steps. First, the scene point cloud and the robotic arm point cloud, captured by the 3D camera, are fed into the single-node detector model to compute an initial transformation of the robotic arm, denoted as T-prev. This transformation is then utilized to assist in clustering and isolating the rebar point cloud from the scene point cloud. Next, the extracted rebar point cloud is processed by the rebar node extraction module to identify and extract the nodes, which are subsequently separated and sorted in a specific order. Finally, the single-node rebar point cloud is sliced, and the single-node detection model is applied to compute the transformations for each node individually. Notably, the pipeline is aimed at tying all rebar nodes in the view, and users can customize the tying order. In this work, the nodes are sorted in ascending order along the $x$-, $y$-, and $z$-axes, respectively.

III-A Single-node Detection Model

Our single-node detection model is designed to identify the pose of individual rebar nodes, built upon the Diffusion-EDFs framework. It is specifically trained to handle tasks involving the tying of a single rebar node. Diffusion-EDFs is a generative model in SE(3) conditioned on observed point clouds, designed for a robotic picking and placing task. The method models the target end-effector pose to normal distribution in SE(3) via a Lie group Stochastic Differential Equation (SDE) as

[TABLE]

where $dt$ is the diffusion step and $dW$ is the standard Wiener process defined on SE(3) Lie algebra for $g^{t}$. The model considers scene-pcd and gripper point cloud (rebar-tying-pcd in our case), so $g^{t}$ is sampled from $P^{t}(g_{n}\mid o_{s},o_{r})$. The model is trained on a score function $s^{t}(g^{t}\mid o_{s},o_{r})=\nabla\log P^{t}(g\mid o_{s},o_{r})$, where $P^{t}$ is defined via a diffusion process on SE(3) as

[TABLE]

which diffuses the target pose distribution $P_{n}^{0}$ to a standard initial distribution $P_{n}^{t}$. The sampling (denoising) process is leveraged via the annealed Langevin MCMC in SE(3) based on the score function, namely

[TABLE]

III-B Rebar Point Cloud Detection

Although the single-node Diffusion-EDFs model is relatively effective for grasping individual rebar nodes, the similarity among intersections in multi-node point clouds makes the selected node each time essentially random. In practical applications, we need to bind nodes in a specified order; however, Diffusion-EDFs alone cannot guarantee the correct node choice among multiple similar intersections. Therefore, we propose a method to first identify and sort the rebar nodes. Each time the single-node model is applied, only the point cloud segment corresponding to a specific node is fed as an input. This ensures that the robotic arm can sequentially bind the nodes in a predetermined order, as detailed in Section III-B, Section III-C and Section III-D.

The main aim of this part is to separate the rebar point cloud from the background point cloud. To achieve point clustering, we employ the DBSCAN algorithm proposed by Ester et al. [21], a density-based spatial clustering method capable of identifying clusters of any shape based on density conditions. It relies on three key concepts:

• •

Eps: The radius defining the neighborhood for identifying core and noise points.

• •

MinPts: The minimum number of points required to define a core point.

• •

Core points: Points with more than MinPts in their neighborhood.

DBSCAN operates by:

identifying core points and forming clusters from their Eps neighborhoods, and 2. 2.

expanding clusters by connecting density-reachable points.

The algorithm selects a point $p$ and checks if it satisfies the Eps and MinPts conditions. If $p$ is a core point, its neighborhood forms a cluster; if it is a boundary point, it is marked as noise. By iteratively querying neighborhoods, DBSCAN efficiently mitigates noise and clusters point clouds, effectively distinguishing rebar points from background elements.

Subsequently, we employ comparison methods to identify the rebar point cloud among these clusters. Initially, we execute the single-node detection model to obtain T-prev, a transformation matrix designed to guide the robotic arm to grasp a random node within the rebar point cloud. Concurrently, we can calculate the robotic arm’s position after applying this transformation, denoted as pose-prev. Next, we extract a small segment of the point cloud near pose-prev to form a reference cluster, which is highly likely to be part of the rebar point cloud rather than other background objects. For each classified target cluster, we calculate the total number of points in the reference cluster that contain points from the target cluster within a search radius. The higher this count, the greater the similarity between the clusters. Ultimately, the target cluster with the highest count is identified as the rebar point cloud. An example of the clustering process and the selection of the rebar point cloud is illustrated in Fig. 4.

III-C Rebar Nodes Extraction

To precisely locate the nodes within the rebar point clouds, we capitalize on the unique geometric features of the rebar nodes. This approach enables us to efficiently extract points in the vicinity of the nodes while significantly mitigating the interference from background noise. Feature matching is based on orthogonality. Near the locations of the rebar nodes, the point clouds tend to form orthogonal lines. In contrast, near noise-background objects and other similar areas, the point clouds tend to be distributed irregularly. Utilizing this feature, we design an orthogonal feature filter to sort the points near the rebar nodes. The adjustable parameters include:

• •

$r_{eps}$: The radius defining the neighborhood used to determine core and noise points.

• •

$R_{res}$: The threshold for determining whether two vectors are approximately perpendicular, which is expected to be set to a value close to 0.

• •

$P_{res}$: The threshold for judging whether two vectors are approximately parallel, which is expected to be set to a value close to 1.0.

The algorithm follows five steps:

Constructing a k-d tree and searching for neighbors within the radius $r_{eps}$ for each point; 2. 2.

For each point $p$ and its neighbors $N_{1}$, $N_{2}$, …, $N_{k}$, the set of vectors from $p$ to its neighbors can be represented as $\{v_{1},v_{2},...v_{k}\}$, where each vector $v_{i}$ is defined as $v_{i}=N_{i}-p$; 3. 3.

The vectors $\{v_{1},v_{2},...v_{k}\}$ are randomly divided into two groups, representing as $\boldsymbol{a}=[a_{1},a_{2},...,a_{k/2}]^{\top}$ and $\boldsymbol{b}=[b_{1},b_{2},...,b_{k/2}]^{\top}$. Then we calculate their dot product of each element as: $\boldsymbol{D}=[a_{1}\cdot b_{1},a_{2}\cdot b_{2},...,a_{k/2}\cdot b_{k/2}]^{\top}$. In the two-dimensional case, if the neighboring points are uniformly distributed in an ideal cross shape centered at $p$, due to symmetry, there is a $1/2$ probability that a point lies on the vertical axis and a $1/2$ probability that it lies on the horizontal axis. Consequently, the absolute value of the dot product between any two such vectors can only be 1 or 0, each with a probability of $1/2$. In the three-dimensional case, the probability that a vector is parallel to each of the three mutually orthogonal axes is 1/3. The absolute value of the dot product between two such random vectors has a probability of $P_{1}=\sum_{i=1}^{3}1/3\times 1/3=1/3$ of being 1 and a probability of $P_{0}=1-P_{1}=2/3$ of being 0. With consideration of both two-dimensional and three-dimensional cases, the ideal threshold is set to the minimum value. 4. 4.

Given that rebars have a certain width and that actual point cloud contains some noise, the distribution of the actual point cloud cannot lie on an ideal straight line. The absolute dot production probability of being 1 and 0 are both slightly shifted, so we set as adjustable parameters $R_{res}$ and $P_{res}$. The mask is represented as

[TABLE]

[TABLE]

[TABLE] 5. 5.

The resulting mask is applied to filter each point, retaining only those that satisfy the condition. For instance, the blue points in Fig. 5b and Fig. 5d respectively illustrate the filtered results of Fig. 5a and Fig. 5c.

For the filtered points, DBSCAN clustering is employed again to separate the point sets at different nodes.

III-D Ordering the Nodes

In Section III-C, we have obtained separate point clusters near different nodes, and we can calculate the mean value of each cluster to determine the approximate position of each node. To sort them in a certain order, we establish a coordinate system and perform a projection. The direction vectors of the rebar point clouds are estimated by using a Principal Component Analysis (PCA) [22], which is a statistical method to reduce the dimensionality of data while retaining the most significant features. Given that the rebar point cloud data exhibit three primary orthogonal directional distributions, these directions can be effectively estimated through the PCA with the following steps,

Given a point cloud $P=\{p_{1},p_{2},...,p_{N}\}$, where each point $p_{i}=[x_{i},y_{i},z_{i}]^{\top}$, calculate the mean of the points as $\overline{p}=\frac{1}{N}\sum_{i=1}^{N}p_{i}$. 2. 2.

Compute the covariance matrix $C$ by $C=\frac{1}{N}\sum_{i=1}^{N}(p_{i}-\bar{p})(p_{i}-\bar{p})^{\top}$. 3. 3.

Perform eigenvalue decomposition on the covariance matrix $C$, yielding the eigenvectors and eigenvalues. The eigenvectors correspond to the principal axes of the point cloud, likely aligned with the direction vectors. 4. 4.

A coordinate system is established by defining the average of the rebar points as the origin. Three direction vectors are used to determine the axes of the coordinate system. The vector closest to the vertical axis of the rebar is selected as the $z$-axis. The y-axis is determined by identifying the direction vector most aligned with the direction from pose-prev (calculated in Section III-B) to the mean point of the rebar point cloud. Finally, the $x$-axis is derived by computing the cross product of the $z$-axis and $y$-axis vectors.

First, we construct a coordinate system based on the entire rebar point cloud. To enhance accuracy and reduce the influence of noise or interference from connected background objects, we further refine this process by applying the same steps to the point cloud of each individual rebar node crop. The mean of the coordinate systems derived from these individual crops is then computed to establish a more precise and robust coordinate system. Subsequently, each rebar node is projected along the three coordinate axes within this refined system, and the points are sequentially sorted along the negative $y$-axis, positive $z$-axis, and positive $x$-axis directions. For example, the red arrowed lines in Fig. 5b and Fig. 5d respectively illustrate the axis vector estimation of Fig. 5a and Fig. 5c.

IV Experiment

IV-A Experiment Setup

In this section, we gather datasets through simulations that encompass a variety of rebar tying scenarios. The experimental process is divided into two main phases. First, we evaluate the robustness of our algorithm. Next, we define two key performance metrics, e.g., success rate and prediction error, and apply them to three representative datasets for assessing the efficacy of the proposed algorithm. All experiments are conducted on a single NVIDIA GeForce RTX 3090 GPU. To conduct a thorough evaluation, we have tested the pipeline on multiple datasets across various scenarios, with specific settings detailed in Table I and some example visualizations provided in Fig. 10.

The training sets (Train \Romannum1 and Train \Romannum2) have 10 demostrations used to train the single-node detection model. Train \Romannum1 is for the pre-detection part, and Train \Romannum2 is for the later single node detection part. To assess the robustness of our algorithm, we focus on three key capabilities of the pipeline, e.g., resistance to noise, resilience against background obstacles, and performance with complex node distributions. For clarity, we measure the success rate based on the total number of detected nodes and compare these outcomes across datasets that vary in Gaussian noise levels, quantity of background obstacles, and intricate test scenarios. The success rate and prediction error to evaluate the algorithm in grasping tasks are calculated as follows:

• •

The success rate ($R_{s}$) is calculated using the formula:

[TABLE]

where $N_{si}$ represents the number of successful predictions at pose $i$. A prediction is considered successful if

[TABLE]

with $D_{g}(g,\hat{g})$ denoting the distance between the ground-truth $g$ and predicted poses $\hat{g}$, respectively, and $T_{g}$ being the distance threshold for determining tying success.

• •

The prediction error $E_{r}$ is defined as the average pose distance between the predicted poses and the target ground-truth poses over all poses and demonstrations. It is calculated by using

[TABLE]

where $g_{il}$ and $\hat{g}_{il}$ are the ground-truth and predicted poses for the $i$-th demonstration and the $l$-th pose, respectively. Herein we use the pose distance $D_{g}$ to measure the difference between two poses $g_{1}=\{q_{1},p_{1}\}$ and $g_{2}=\{q_{2},p_{2}\}$ defined in quaternion form, which combines the angular distance and the linear distance. The pose distance is calculated as

[TABLE]

where

[TABLE]

and

[TABLE]

with $\gamma$ being the regularization term, $\bar{q_{2}}$ the conjugate of $q_{2}$, and $\gamma$ the regularization term.

We select three representative datasets to evaluate our algorithm, e.g., the first denotes rebar nodes on a line in Test \Romannum2, the second rebar nodes on a plane in Test \Romannum5, and the third denotes rebar nodes in space in Test \Romannum8. As our method works on SE(3) with 3D point cloud input, it is not necessary to compare it with the object detection-based pipeline. Thus, we test the model on diverse simulated data under different conditions and real-world data for verifying the performance of the pipeline.

IV-B Experiment Results

The results in Table II highlight the robustness of our method in handling noise, background obstacles, and complex node distributions. Our approach achieves a 98% success rate in identifying rebar nodes, even in highly complex distributions with 36 nodes. It maintains success rates above 90% in noisy environments and exceeds 80% in scenarios with significant background interference.

Furthermore, Fig. 7 demonstrates the precision of our method in detecting rebar nodes and estimating direction vectors, even in highly complex configurations such as the 32-node and 36-node setups. Our filtering technique effectively minimizes background interference, ensuring accurate node data extraction even when background elements are in close proximity to the rebar point cloud. Additionally, the results highlight the robustness of our method to random Gaussian noise.

Fig. 8 presents a comprehensive comparison of the prediction error ($E_{r}$) and success rate ($R_{s}$) across three datasets: 4-node datasets in Test \Romannum2, 8-node datasets in Test \Romannum5, and 16-node datasets in Test \Romannum8, evaluated under conditions of no noise and 4 background obstacles, with varying threshold values ($T_{g}$). Fig. 8a illustrates the prediction error ($E_{r}$), showing that the error remains relatively stable across different $T_{g}$ values, with only minor fluctuations. Notably, the 4-node dataset in Test \Romannum2 exhibits the lowest prediction error, closely followed by the 8-node dataset in Test \Romannum5 and the 16-node dataset in Test \Romannum8, all maintaining errors around 0.6.

Fig. 8b illustrates the success rate ($R_{s}$) for the same datasets shown in Fig. 8a, evaluated across different $T_{g}$ values. The success rate increases significantly as $T_{g}$ approaches 1. The 16-node dataset in Test \Romannum8 achieves the highest success rate, peaking at 79.63% at $T_{g}$=1, whereas the 4-node dataset in Test \Romannum2 and the 8-node dataset in Test \Romannum5 show slightly lower success rates of 74.50% and 69.52%, respectively. These results underscore the robustness and reliability of our method across different node configurations, highlighting its potential for practical applications in real-world scenarios. The consistent performance across varying $T_{g}$ values demonstrates the method’s effectiveness in accurately predicting rebar nodes and estimating direction vectors, even in complex distributions.

IV-C Real-world Test and Limitations

To verify the potential of our system in a real-world application, we use our hardware system (details in Section III) to collect real-world data with 4 nodes. The model trained on simulated data is applied directly on the collected real data, and the tying process is visualized in Fig. 9. Although the reabrs are positioned in an uneven manner and with noisy background, the pipeline can still achieve the sequential 4-node tying. However, some failures can also be observed, e.g., failure of generating a tying pose (Fig. 10a) and generation of a wrong tying pose (Fig. 10b). These limitations can possibly be resolved by training the model on complex real-world datasets.

V CONCLUSIONS

In this paper, we propose an integrated framework for rebar node detection and sorting tailored to industrial rebar tying tasks. Our system features a single-node detection module based on a diffusion generative model in SE(3) and an adaptive orthogonal feature filtering algorithm that leverages the geometric characteristics of rebar structures. Combined with a coordinate system established via a principal component analysis (PCA), this approach enables efficient extraction and accurate sorting of rebar nodes. Unlike traditional methods, our framework demonstrates exceptional robustness in single-node detection and stable node recognition under complex and noisy conditions through multi-level feature fusion and effective spatial information utilization. Experimental results show that our method effectively handles noise, background obstacles, and complex node configurations, robustly supporting the positioning and grasping tasks of industrial robots in rebar tying. In the future work, we will further optimize model parameters and explore deploying this framework in practical industrial scenarios, continuously improving detection and positioning accuracy to better support automation in related fields.

ACKNOWLEDGMENT

This paper was funded by InnoHK-HKCRC and Shenzhen Startup Funding (No. QD2023014C) supported by Meituan.