## Abstract

Purpose: This paper presents a method for extracting the geometric primitives of a circle in a three-dimensional space from a discrete point cloud data set obtained by a laser stripe sensor. This paper aims to first establish a reference frame for the robotic drilling process by detecting the position and orientation of a reference hole on structural parts in a pre-drilling step, and second, to perform quality inspection of the hole in a post-drilling step. Design/methodology/approach: The method is divided into the following steps: a plane is initially fitted on the data by evaluating the principle component analysis using singular value decomposition; the data points or measurements are then rotated around an arbitrary axis using the Rodrigues’ rotation formula such that the normal direction of the estimated plane and the z-axis direction is parallel; the Delaunay triangulation is constructed on the point cloud and the confidence interval is estimated for segmenting the data set located at the circular boundary; and finally, a circular profile is fitted on the extracted set and transformed back to the original position. Findings: The geometric estimation of the circle in three-dimensional space constitutes of the position of the center, the diameter and the orientation, which is represented by the normal vector of the plane that the circle lives in. The method is applied on both simulated data set with the addition of several noise levels and experimental data sets. The main purpose of both the tests is to quantify the accuracy of the estimated diameter. The results show good accuracy (mean relative error < 1 per cent) and high robustness to noise. Research limitations/implications: The proposed method is applied here to estimate the geometric primitives of only one circle (the reference hole). If multiple circles are needed, an addition clustering procedure is required to cluster the segmented data into multiple data sets. Each data set represents a circle. Also, the method does not operate efficiently on a sparse data sets. Dense data are required to cover the hole (at least ten scans to cover the hole diameter). Practical implications: Researchers and practitioners can integrate this method with several robotic manufacturing applications where high accuracy is required. The extracted position and orientation of the hole are used to minimize the positioning and alignment errors between the mounted tool tip and the workpiece. Originality/value: The method introduces data analytics for estimating the geometric primitives in the robotic drilling application. The main advantage of the proposed method is to register the top surface of the workpiece with respect to robot base frame with a high accuracy. An accurate workpiece registration is extremely necessary in the lateral direction (identifying where to drill), as well as in the vertical direction (identifying how far to drill).

Original language | British English |
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Pages (from-to) | 371-378 |

Number of pages | 8 |

Journal | Industrial Robot |

Volume | 45 |

Issue number | 3 |

DOIs | |

State | Published - 19 Jul 2018 |

## Keywords

- 3D point cloud
- Data analytics