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Orthogonal Trajectories

Orthogonal Trajectories

Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...

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Operation of the Collaborative Composite Manufacturing CCM System

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A Method of Machining Trajectory Planning Based on Multi-View Stereo Vision and Color Regional Growth.

Yizhen Yin¹, Yilong Shi¹, Weifeng He^1,2

¹Institute of Aeronautics Engine, School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, China.

Annals of the New York Academy of Sciences

|April 7, 2026

Summary

This study presents a novel method for robotic manufacturing of curved surfaces using 3D point cloud reconstruction and segmentation. The approach enhances trajectory planning accuracy for complex aerospace components.

Keywords:

3D reconstruction color regional growth curve fitting point cloud segmentation trajectory planning

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Area of Science:

Robotics and Manufacturing
Computer Vision
Geometric Modeling

Background:

Local trajectory planning for curved surfaces in robotic manufacturing presents significant challenges.
Accurate 3D reconstruction and segmentation are crucial for precise robotic operations.

Purpose of the Study:

To develop an effective method for local trajectory planning in robotic manufacturing of curved surface components.
To improve the accuracy and efficiency of robotic grinding processes on complex geometries.

Main Methods:

Multi-view stereo reconstruction using an improved PatchmatchNet model for high-quality 3D point cloud generation.
Color regional growth segmentation based on HSI color space and local color distribution similarity.
Non-uniform rational B-splines (NURBS) curve fitting for deriving local processing trajectory feature lines.

Main Results:

Achieved 10.42% improvement in accuracy and 10.59% in completeness for 3D point cloud reconstruction.
Segmentation performance reached 82.2% Cat.mIoU and 77.1% Ins.mIoU on aerospace components.
NURBS curve fitting resulted in R² > 0.94 and 30% lower RMSE compared to other methods.
Experimental validation confirmed precise localization and effective material removal.

Conclusions:

The proposed method effectively addresses challenges in local trajectory planning for curved surfaces.
It offers significant practical value for aerospace manufacturing, particularly in grinding complex components.
The integration of advanced reconstruction, segmentation, and fitting techniques enhances robotic precision.