Predicting the mean first passage time (MFPT) to reach any state for a passive dynamic walker with steady state variability

Isuri Wijesundera, Malka N Halgamuge, Ampalavanapillai Nirmalathas and Thrishantha Nanayakkara

PLOS ONE, 2018, vol. 13, issue 11, 1-19

Abstract: 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0207665

DOI: 10.1371/journal.pone.0207665

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