Proposal of tool path generation for recycle pad in Chemical Mechanical Polishing based on piecewise linear interpolation method

Abstract In recent years, the UAV (Unmanned Aerial Vehicle) inspection for the electrical line has received increasing attentions due to the advantages of low costs, easiness to control and flexibility. The UAV can inspect the electrical tower independently and automatically by planning the flight path. But during the inspection along the path, the UAV is easily impacted by gust wind due to its light weight and small size, which always leads to the crash into the electrical tower. Thus, in this paper, a safe flight approach (SFA) is proposed to make the flight be safer during the inspection. The main contributions include: firstly, the piecewise linear interpolation method is proposed to fit the distribution curve of the electrical towers based on the GPS coordinates of the electrical towers; secondly, the no-fly zone on the both sides of the distribution curve are created, and a security distance formula (SDF) is raised to decide the width of the no-fly zone; thirdly, a gust wind formula (GWF) is proposed to improve the artificial potential field approach, which can contribute to the path planning of the UAV; finally, a flight path of the UAV can be planned using the SFA to make the UAV avoid colliding with the electric tower. The proposed approach is tested on the experiment to demonstrate its effectiveness.

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Open Architecture Controllers for Machine Tools, Part 2: A Real Time Quintic Spline Interpolator

Journal of Manufacturing Science and Engineering ◽

10.1115/1.2830143 ◽

1998 ◽

Vol 120 (2) ◽

pp. 425-432 ◽

Cited By ~ 36

Author(s):

Fu-Chung Wang ◽

P. K. Wright

Keyword(s):

Real Time ◽

Tool Path ◽

Interpolation Method ◽

Tool Path Generation ◽

Open Architecture ◽

Free Form ◽

Path Generation ◽

Arc Length ◽

Quintic Spline ◽

Data Points

In Part 2 of this two-part paper, we describe a new quintic spline interpolator for real time trajectory generation during free form curve machining on the Open Architecture machine tool platform described in Part I. The research provides new capabilities for advanced CAD/CAM systems. Complicated curves and shapes designed in a CAD system are usually represented by a set of discrete data points. Subsequently, for manufacturing by a CAM system, these data points need to be converted into tool paths for machining. Therefore, the paper presents a new interpolation method that interpolates the designated data points with a quintic spline curve for real-time tool path generation. The resultant curve, generated by the proposed interpolation method, is nearly arc-length parametrized and has C3 continuity. The near arc-length parametrization property makes the real time generation of the reference commands of the cutting tool path easier. The C3 continuity guarantees the smooth motion of continuous speed, acceleration and even jerk during the machining. The combined properties of this new interpolation method enable a new quintic spline interpolator to be developed for real time tool path generation.

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Interp-SUM: Unsupervised Video Summarization with Piecewise Linear Interpolation

Sensors ◽

10.3390/s21134562 ◽

2021 ◽

Vol 21 (13) ◽

pp. 4562

Author(s):

Ui-Nyoung Yoon ◽

Myung-Duk Hong ◽

Geun-Sik Jo

Keyword(s):

Large Scale ◽

Interpolation Method ◽

Piecewise Linear ◽

Video Summarization ◽

Linear Interpolation ◽

The State ◽

Experimental Result ◽

Natural Sequence ◽

Reward Function ◽

Piecewise Linear Interpolation

This paper addresses the problem of unsupervised video summarization. Video summarization helps people browse large-scale videos easily with a summary from the selected frames of the video. In this paper, we propose an unsupervised video summarization method with piecewise linear interpolation (Interp-SUM). Our method aims to improve summarization performance and generate a natural sequence of keyframes with predicting importance scores of each frame utilizing the interpolation method. To train the video summarization network, we exploit a reinforcement learning-based framework with an explicit reward function. We employ the objective function of the exploring under-appreciated reward method for training efficiently. In addition, we present a modified reconstruction loss to promote the representativeness of the summary. We evaluate the proposed method on two datasets, SumMe and TVSum. The experimental result showed that Interp-SUM generates the most natural sequence of summary frames than any other the state-of-the-art methods. In addition, Interp-SUM still showed comparable performance with the state-of-art research on unsupervised video summarization methods, which is shown and analyzed in the experiments of this paper.

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Spiral Tool Path Generation Method on Mesh Surfaces Guided by Radial Curves

Journal of Manufacturing Science and Engineering ◽

10.1115/1.4039918 ◽

2018 ◽

Vol 140 (7) ◽

Cited By ~ 10

Author(s):

Jinting Xu ◽

Yukun Ji ◽

Yuwen Sun ◽

Yuan-Shin Lee

Keyword(s):

High Speed ◽

Tool Path ◽

Interpolation Method ◽

Tool Path Generation ◽

Numerical Control ◽

Path Generation ◽

Cnc Milling ◽

Tool Paths ◽

Spiral Tool Path ◽

Mesh Surface

This paper presents a new spiral smoothing method to generate smooth curved tool paths directly on mesh surfaces. Spiral tool paths are preferable for computer numerical control (CNC) milling, especially for high-speed machining. At present, most spiral tool path generation methods aim mainly for pocketing, and a few methods for machining complex surface also suffer from some inherent problems, such as selection of projecting direction, preprocessing of complex offset contours, easily affected by the mesh or mesh deformation. To address the limitations, a new spiral tool path method is proposed, in which the radial curves play a key role as the guiding curves for spiral tool path generation. The radial curve is defined as one on the mesh surface that connects smoothly one point on the mesh surface and its boundary. To reduce the complexity of constructing the radial curves directly on the mesh surface, the mesh surface is first mapped onto a circular region. In this region, the radial lines, starting from the center, are planned and then mapped inversely onto the mesh surface, thereby forming the desired radial curves. By traversing these radial curves using the proposed linear interpolation method, a polyline spiral is generated, and then, the unfavorable overcuts and undercuts are identified and eliminated by supplementing additional spiral points. Spline-based technique of rounding the corners is also discussed to smooth the polyline spiral, thereby obtaining a smooth continuous spiral tool path. This method is able to not only greatly simplify the construction of radial curves and spiral tool path but also to have the ability of processing and smoothing complex surfaces. Experimental results are presented to validate the proposed method.

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The linear interpolation method: a sampling theorem approach

Sba Controle & Automação Sociedade Brasileira de Automatica ◽

10.1590/s0103-17592003000400012 ◽

2003 ◽

Vol 14 (4) ◽

pp. 439-444 ◽

Cited By ~ 2

Author(s):

Pedro L. D. Peres ◽

Ivanil S. Bonatti ◽

Walter C. Borelli

Keyword(s):

Linear Approximation ◽

Interpolation Method ◽

Piecewise Linear ◽

Linear Interpolation ◽

Sampling Theorem ◽

Piecewise Linear Approximation ◽

Original Function ◽

Quadratic Error ◽

Linear Interpolation Method ◽

The Relationship

A lecture note introducing the sampling theorem as an interpolation method is presented. The relationship between piecewise linear approximation and the sampling theorem is highlighted by the use of triangular pulses instead of sampling functions. Furthermore, a comparison of the linear interpolation with a series on a nonorthogonal basis composed of equally spaced triangular pulses is provided. The interpolation uses the sample values of the function whereas the series coefficients are obtained by minimizing the quadratic error between the original function and the series.

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An adaptive interpolation method for tool path generation based on iso-phote for large scale wedge /aspheric lens element grinding

10.1117/12.966849 ◽

2012 ◽

Author(s):

Ningning Zhang ◽

Feng Yang ◽

Dongxu Zhang ◽

Meiyun Chen ◽

Zhenzhong Wang ◽

...

Keyword(s):

Large Scale ◽

Tool Path ◽

Interpolation Method ◽

Tool Path Generation ◽

Path Generation ◽

Aspheric Lens ◽

Lens Element ◽

Adaptive Interpolation

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Exploring the effects of missing data on the estimation of fractal and multifractal parameters based on bootstrap method

10.5194/npg-2018-38 ◽

2018 ◽

Author(s):

Xin Gao ◽

Xuan Wang

Keyword(s):

Time Series ◽

Statistical Inference ◽

Missing Values ◽

Interpolation Method ◽

Piecewise Linear ◽

Bootstrap Method ◽

Linear Interpolation ◽

Estimation Accuracy ◽

Bootstrap Resampling ◽

Piecewise Linear Interpolation

Abstract. A time series collected in the nature is often incomplete or contains some missing values, and statistical inference on the population or process with missing values, especially the population or process having multifractal properties is easy to ignore. In this study, the simulation and actual data were used to obtain the probability distributions of fractal parameters through a new bootstrap resampling mechanism with the aim to statistically infer the estimation accuracy of the time series containing missing values and four kinds of interpolated series. Firstly, the RMS errors results showed that compared with the four interpolation methods for one parameter H required for fBm the direct use of the series with missing values has the highest estimation accuracy, while it shows certain instability in the estimations of the multifractal parameters C1 and α, especially at higher missing levels, however, the accuracy of the parameters estimated by preprocessing of piecewise linear interpolation method can be improved; in addition, it is also concluded that α is more sensitive to the changes caused by these processing than another parameter C1. Secondly, the effects on the ability of statistical inference for a population caused from the data losses are explored through the estimation of confidence intervals and hypothesis testing by proposing a new bootstrap resampling mechanism, and the conclusions showed that whether it is a mono-fractal parameter or multifractal parameters, the large deviations from the estimates of original series occur on the series with missing values when the losses are serious, while the defects can be compensated by the preprocessing using PLI and PBI methods; similarly, although the results of the incomplete series at the low missing levels are close to the original and PLI series, while at the high missing levels, the probabilities of Type II Errors of the neighboring values are unable to ignore, but the PLI or PBI method can avoid the erroneous judgments.

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