A parametric interpolation method based on prediction and iterative compensation
Parametric interpolation for spline plays an increasingly important role in modern manufacturing. It is critical to develop a fast parametric interpolator with high accuracy. To improve the computational efficiency while guaranteeing low and controllable feedrate fluctuation, a novel parametric inte...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2019-02-01
|
| Series: | International Journal of Advanced Robotic Systems |
| Online Access: | https://doi.org/10.1177/1729881419828188 |
| _version_ | 1818160123920515072 |
|---|---|
| author | Hepeng Ni Chengrui Zhang Chao Chen Tianliang Hu Yanan Liu |
| author_facet | Hepeng Ni Chengrui Zhang Chao Chen Tianliang Hu Yanan Liu |
| author_sort | Hepeng Ni |
| collection | DOAJ |
| description | Parametric interpolation for spline plays an increasingly important role in modern manufacturing. It is critical to develop a fast parametric interpolator with high accuracy. To improve the computational efficiency while guaranteeing low and controllable feedrate fluctuation, a novel parametric interpolation method based on prediction and iterative compensation is proposed in this article. First, the feedrate fluctuation and Taylor’s expansion are analyzed that there are two main reasons to reduce the calculation accuracy including the truncation errors caused by neglecting the high-order terms and discrepancy errors between the original curve and the actual tool path. Then, to reduce these errors, a novel parametric interpolation method is proposed with two main stages, namely, prediction and iterative compensation. In the first stage, a quintic polynomial prediction algorithm is designed based on the historical interpolation knowledge to estimate the target length used in the second-order Taylor’s expansion, which can improve the calculation accuracy and the convergence rate of iterative process. In the second stage, an iterative compensation algorithm based on the second-order Taylor’s expansion and feedrate fluctuation is designed to approach the target point. Therefore, the calculation accuracy is controllable and can satisfy the specified value through several iterations. When finishing the interpolation of current period, the historical knowledge is updated to prepare for the following interpolation. Finally, a series of simulations are conducted to evaluate the good performance in accuracy and efficiency of the proposed method. |
| first_indexed | 2024-12-11T15:56:53Z |
| format | Article |
| id | doaj.art-c3afdda205f042d4a47fca542465917c |
| institution | Directory Open Access Journal |
| issn | 1729-8814 |
| language | English |
| last_indexed | 2024-12-11T15:56:53Z |
| publishDate | 2019-02-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | International Journal of Advanced Robotic Systems |
| spelling | doaj.art-c3afdda205f042d4a47fca542465917c2022-12-22T00:59:24ZengSAGE PublishingInternational Journal of Advanced Robotic Systems1729-88142019-02-011610.1177/1729881419828188A parametric interpolation method based on prediction and iterative compensationHepeng Ni0Chengrui Zhang1Chao Chen2Tianliang Hu3Yanan Liu4 National Demonstration Center for Experimental Mechanical Engineering Education (Shandong University), Jinan, P.R. China National Demonstration Center for Experimental Mechanical Engineering Education (Shandong University), Jinan, P.R. China National Demonstration Center for Experimental Mechanical Engineering Education (Shandong University), Jinan, P.R. China National Demonstration Center for Experimental Mechanical Engineering Education (Shandong University), Jinan, P.R. China Bristol Robotics Laboratory, University of Bristol, Bristol, UKParametric interpolation for spline plays an increasingly important role in modern manufacturing. It is critical to develop a fast parametric interpolator with high accuracy. To improve the computational efficiency while guaranteeing low and controllable feedrate fluctuation, a novel parametric interpolation method based on prediction and iterative compensation is proposed in this article. First, the feedrate fluctuation and Taylor’s expansion are analyzed that there are two main reasons to reduce the calculation accuracy including the truncation errors caused by neglecting the high-order terms and discrepancy errors between the original curve and the actual tool path. Then, to reduce these errors, a novel parametric interpolation method is proposed with two main stages, namely, prediction and iterative compensation. In the first stage, a quintic polynomial prediction algorithm is designed based on the historical interpolation knowledge to estimate the target length used in the second-order Taylor’s expansion, which can improve the calculation accuracy and the convergence rate of iterative process. In the second stage, an iterative compensation algorithm based on the second-order Taylor’s expansion and feedrate fluctuation is designed to approach the target point. Therefore, the calculation accuracy is controllable and can satisfy the specified value through several iterations. When finishing the interpolation of current period, the historical knowledge is updated to prepare for the following interpolation. Finally, a series of simulations are conducted to evaluate the good performance in accuracy and efficiency of the proposed method.https://doi.org/10.1177/1729881419828188 |
| spellingShingle | Hepeng Ni Chengrui Zhang Chao Chen Tianliang Hu Yanan Liu A parametric interpolation method based on prediction and iterative compensation International Journal of Advanced Robotic Systems |
| title | A parametric interpolation method based on prediction and iterative compensation |
| title_full | A parametric interpolation method based on prediction and iterative compensation |
| title_fullStr | A parametric interpolation method based on prediction and iterative compensation |
| title_full_unstemmed | A parametric interpolation method based on prediction and iterative compensation |
| title_short | A parametric interpolation method based on prediction and iterative compensation |
| title_sort | parametric interpolation method based on prediction and iterative compensation |
| url | https://doi.org/10.1177/1729881419828188 |
| work_keys_str_mv | AT hepengni aparametricinterpolationmethodbasedonpredictionanditerativecompensation AT chengruizhang aparametricinterpolationmethodbasedonpredictionanditerativecompensation AT chaochen aparametricinterpolationmethodbasedonpredictionanditerativecompensation AT tianlianghu aparametricinterpolationmethodbasedonpredictionanditerativecompensation AT yananliu aparametricinterpolationmethodbasedonpredictionanditerativecompensation AT hepengni parametricinterpolationmethodbasedonpredictionanditerativecompensation AT chengruizhang parametricinterpolationmethodbasedonpredictionanditerativecompensation AT chaochen parametricinterpolationmethodbasedonpredictionanditerativecompensation AT tianlianghu parametricinterpolationmethodbasedonpredictionanditerativecompensation AT yananliu parametricinterpolationmethodbasedonpredictionanditerativecompensation |