Predicting the mean first passage time (MFPT) to reach any state for a passive dynamic walker with steady state variability.
Idealized passive dynamic walkers (PDW) exhibit limit cycle stability at steady state. Yet in reality, uncertainty in ground interaction forces result in variability in limit cycles even for a simple walker known as the Rimless Wheel (RW) on seemingly even slopes. This class of walkers is called met...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2018-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0207665 |
| _version_ | 1819016594752274432 |
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| author | Isuri Wijesundera Malka N Halgamuge Ampalavanapillai Nirmalathas Thrishantha Nanayakkara |
| author_facet | Isuri Wijesundera Malka N Halgamuge Ampalavanapillai Nirmalathas Thrishantha Nanayakkara |
| author_sort | Isuri Wijesundera |
| collection | DOAJ |
| description | Idealized passive dynamic walkers (PDW) exhibit limit cycle stability at steady state. Yet in reality, uncertainty in ground interaction forces result in variability in limit cycles even for a simple walker known as the Rimless Wheel (RW) on seemingly even slopes. This class of walkers is called metastable walkers in that they usually walk in a stable limit cycle, though guaranteed to eventually fail. Thus, control action is only needed if a failure state (i.e. RW stopping down the ramp) is imminent. Therefore, efficiency of estimating the time to reach a failure state is key to develop a minimal intervention controller to inject just enough energy to overcome a failure state when required. Current methods use what is known as a Mean First Passage Time (MFPT) from current state (rotary speed of RW at the most recent leg collision) to an arbitrary state deemed to be a failure in the future. The frequently used Markov chain based MFPT prediction requires an absorbing state, which in this case is a collision where the RW comes to a stop without an escape. Here, we propose a novel method to estimate an MFPT from current state to an arbitrary state which is not necessarily an absorbing state. This provides freedom to a controller to adaptively take action when deemed necessary. We demonstrate the proposed MFPT predictions in a minimal intervention controller for a RW. Our results show that the proposed method is useful in controllers for walkers showing up to 44.1% increase of time-to-fail compared to a PID based closed-loop controller. |
| first_indexed | 2024-12-21T02:50:07Z |
| format | Article |
| id | doaj.art-4fe6ee0d81bf4fbaacf8d54b10f5ce5b |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-21T02:50:07Z |
| publishDate | 2018-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-4fe6ee0d81bf4fbaacf8d54b10f5ce5b2022-12-21T19:18:27ZengPublic Library of Science (PLoS)PLoS ONE1932-62032018-01-011311e020766510.1371/journal.pone.0207665Predicting the mean first passage time (MFPT) to reach any state for a passive dynamic walker with steady state variability.Isuri WijesunderaMalka N HalgamugeAmpalavanapillai NirmalathasThrishantha NanayakkaraIdealized passive dynamic walkers (PDW) exhibit limit cycle stability at steady state. Yet in reality, uncertainty in ground interaction forces result in variability in limit cycles even for a simple walker known as the Rimless Wheel (RW) on seemingly even slopes. This class of walkers is called metastable walkers in that they usually walk in a stable limit cycle, though guaranteed to eventually fail. Thus, control action is only needed if a failure state (i.e. RW stopping down the ramp) is imminent. Therefore, efficiency of estimating the time to reach a failure state is key to develop a minimal intervention controller to inject just enough energy to overcome a failure state when required. Current methods use what is known as a Mean First Passage Time (MFPT) from current state (rotary speed of RW at the most recent leg collision) to an arbitrary state deemed to be a failure in the future. The frequently used Markov chain based MFPT prediction requires an absorbing state, which in this case is a collision where the RW comes to a stop without an escape. Here, we propose a novel method to estimate an MFPT from current state to an arbitrary state which is not necessarily an absorbing state. This provides freedom to a controller to adaptively take action when deemed necessary. We demonstrate the proposed MFPT predictions in a minimal intervention controller for a RW. Our results show that the proposed method is useful in controllers for walkers showing up to 44.1% increase of time-to-fail compared to a PID based closed-loop controller.https://doi.org/10.1371/journal.pone.0207665 |
| spellingShingle | Isuri Wijesundera Malka N Halgamuge Ampalavanapillai Nirmalathas Thrishantha Nanayakkara Predicting the mean first passage time (MFPT) to reach any state for a passive dynamic walker with steady state variability. PLoS ONE |
| title | Predicting the mean first passage time (MFPT) to reach any state for a passive dynamic walker with steady state variability. |
| title_full | Predicting the mean first passage time (MFPT) to reach any state for a passive dynamic walker with steady state variability. |
| title_fullStr | Predicting the mean first passage time (MFPT) to reach any state for a passive dynamic walker with steady state variability. |
| title_full_unstemmed | Predicting the mean first passage time (MFPT) to reach any state for a passive dynamic walker with steady state variability. |
| title_short | Predicting the mean first passage time (MFPT) to reach any state for a passive dynamic walker with steady state variability. |
| title_sort | predicting the mean first passage time mfpt to reach any state for a passive dynamic walker with steady state variability |
| url | https://doi.org/10.1371/journal.pone.0207665 |
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