Smooth Trajectory Generation for Predefined Path With Pseudo Spectral Method
In view of smooth trajectory generation for a 3-axis machine tool, many methods have been presented. Among them, the optimal control based method is increasingly concerned, because it is considered to be able to make full use of kinematic abilities of machine tools. Under the unified framework of op...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9180338/ |
| _version_ | 1818618476838780928 |
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| author | Kai Zhao Zhongjian Kang Xiaobo Guo |
| author_facet | Kai Zhao Zhongjian Kang Xiaobo Guo |
| author_sort | Kai Zhao |
| collection | DOAJ |
| description | In view of smooth trajectory generation for a 3-axis machine tool, many methods have been presented. Among them, the optimal control based method is increasingly concerned, because it is considered to be able to make full use of kinematic abilities of machine tools. Under the unified framework of optimal control, the feedrate can be adjusted flexibly by adding or removing axial constraints and tangential constraints. But the problem of smooth trajectory generation (PSTG) based on optimal control for a machine tool is not easily to be solved. In this article, to efficiently solve the PSTG, it is divided into two sub-problems: the problem of minimum time trajectory planning (PMTTP) and the pseudo problem of smooth trajectory generation (PPSTG). Since both sub-problems are convex, the existence of unique solutions can be guaranteed. Then, the PMTTP and the PPSTG are transformed into nonlinear programming (NLP) problems with radau-pseudo-spectral (RPM) method successively. Due to convexity, the two NLP problems can be efficiently solved with mature optimization methods. In addition, the RPM method allows two sub-problems to have different Legendre-Gauss-Radau (LGR) points, thereby further saving computational costs. Finally, three different predefined paths are employed to test the proposed method, and simulation results show the effectiveness of proposed method. |
| first_indexed | 2024-12-16T17:22:12Z |
| format | Article |
| id | doaj.art-06aad237675b4512978787a8bc7525a4 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-16T17:22:12Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-06aad237675b4512978787a8bc7525a42022-12-21T22:23:09ZengIEEEIEEE Access2169-35362020-01-01815873515874410.1109/ACCESS.2020.30202979180338Smooth Trajectory Generation for Predefined Path With Pseudo Spectral MethodKai Zhao0https://orcid.org/0000-0002-6343-2770Zhongjian Kang1https://orcid.org/0000-0003-2538-2116Xiaobo Guo2College of Control Science and Engineering, China University of Petroleum (East China), Qingdao, ChinaCollege of New Energy, China University of Petroleum (East China), Qingdao, ChinaCollege of Computer Science and Information Engineering, Anyang Institute of Technology, Anyang, ChinaIn view of smooth trajectory generation for a 3-axis machine tool, many methods have been presented. Among them, the optimal control based method is increasingly concerned, because it is considered to be able to make full use of kinematic abilities of machine tools. Under the unified framework of optimal control, the feedrate can be adjusted flexibly by adding or removing axial constraints and tangential constraints. But the problem of smooth trajectory generation (PSTG) based on optimal control for a machine tool is not easily to be solved. In this article, to efficiently solve the PSTG, it is divided into two sub-problems: the problem of minimum time trajectory planning (PMTTP) and the pseudo problem of smooth trajectory generation (PPSTG). Since both sub-problems are convex, the existence of unique solutions can be guaranteed. Then, the PMTTP and the PPSTG are transformed into nonlinear programming (NLP) problems with radau-pseudo-spectral (RPM) method successively. Due to convexity, the two NLP problems can be efficiently solved with mature optimization methods. In addition, the RPM method allows two sub-problems to have different Legendre-Gauss-Radau (LGR) points, thereby further saving computational costs. Finally, three different predefined paths are employed to test the proposed method, and simulation results show the effectiveness of proposed method.https://ieeexplore.ieee.org/document/9180338/Trajectory planningnumerical solutionpseudo spectral methodoptimal control |
| spellingShingle | Kai Zhao Zhongjian Kang Xiaobo Guo Smooth Trajectory Generation for Predefined Path With Pseudo Spectral Method IEEE Access Trajectory planning numerical solution pseudo spectral method optimal control |
| title | Smooth Trajectory Generation for Predefined Path With Pseudo Spectral Method |
| title_full | Smooth Trajectory Generation for Predefined Path With Pseudo Spectral Method |
| title_fullStr | Smooth Trajectory Generation for Predefined Path With Pseudo Spectral Method |
| title_full_unstemmed | Smooth Trajectory Generation for Predefined Path With Pseudo Spectral Method |
| title_short | Smooth Trajectory Generation for Predefined Path With Pseudo Spectral Method |
| title_sort | smooth trajectory generation for predefined path with pseudo spectral method |
| topic | Trajectory planning numerical solution pseudo spectral method optimal control |
| url | https://ieeexplore.ieee.org/document/9180338/ |
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