An Improved Method for Estimating the Domain of Attraction of Passive Biped Walker
An indicator of a passive biped walker’s global stability is its domain of attraction, which is usually estimated by the simple cell mapping method. It needs to calculate a large number of cells’ Poincare mapping result in the estimating process. However, the Poincare mapping is usually computationa...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2019/2868543 |
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| author | Yu Wang Heng Cao JinLin Jiang |
| author_facet | Yu Wang Heng Cao JinLin Jiang |
| author_sort | Yu Wang |
| collection | DOAJ |
| description | An indicator of a passive biped walker’s global stability is its domain of attraction, which is usually estimated by the simple cell mapping method. It needs to calculate a large number of cells’ Poincare mapping result in the estimating process. However, the Poincare mapping is usually computationally expensive and time-consuming due to the complex dynamical equation of the passive biped walker. How to estimate the domain of attraction efficiently and reliably is a problem to be solved. Based on the simple cell mapping method, an improved method is proposed to solve it. The proposed method uses the multiple iteration algorithm to calculate a stable domain of attraction and effectively decreases the total number of Poincare mappings. Through the simulation of the simplest passive biped walker, the improved method can obtain the same domain of attraction as that calculated using the simple cell mapping method and reduce calculation time significantly. Furthermore, this improved method not only proposes a way of rapid estimating the domain of attraction, but also provides a feasible tool for selecting the domain of interest and its discretization level. |
| format | Article |
| id | doaj-art-5f86f42508344a7fa237da4e9895f580 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-5f86f42508344a7fa237da4e9895f5802025-02-03T01:26:30ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/28685432868543An Improved Method for Estimating the Domain of Attraction of Passive Biped WalkerYu Wang0Heng Cao1JinLin Jiang2School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, ChinaSchool of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, ChinaSchool of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, ChinaAn indicator of a passive biped walker’s global stability is its domain of attraction, which is usually estimated by the simple cell mapping method. It needs to calculate a large number of cells’ Poincare mapping result in the estimating process. However, the Poincare mapping is usually computationally expensive and time-consuming due to the complex dynamical equation of the passive biped walker. How to estimate the domain of attraction efficiently and reliably is a problem to be solved. Based on the simple cell mapping method, an improved method is proposed to solve it. The proposed method uses the multiple iteration algorithm to calculate a stable domain of attraction and effectively decreases the total number of Poincare mappings. Through the simulation of the simplest passive biped walker, the improved method can obtain the same domain of attraction as that calculated using the simple cell mapping method and reduce calculation time significantly. Furthermore, this improved method not only proposes a way of rapid estimating the domain of attraction, but also provides a feasible tool for selecting the domain of interest and its discretization level.http://dx.doi.org/10.1155/2019/2868543 |
| spellingShingle | Yu Wang Heng Cao JinLin Jiang An Improved Method for Estimating the Domain of Attraction of Passive Biped Walker Discrete Dynamics in Nature and Society |
| title | An Improved Method for Estimating the Domain of Attraction of Passive Biped Walker |
| title_full | An Improved Method for Estimating the Domain of Attraction of Passive Biped Walker |
| title_fullStr | An Improved Method for Estimating the Domain of Attraction of Passive Biped Walker |
| title_full_unstemmed | An Improved Method for Estimating the Domain of Attraction of Passive Biped Walker |
| title_short | An Improved Method for Estimating the Domain of Attraction of Passive Biped Walker |
| title_sort | improved method for estimating the domain of attraction of passive biped walker |
| url | http://dx.doi.org/10.1155/2019/2868543 |
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