Predicting the Mean First Passage Time (MFPT) to reach any state for a passive dynamic walker with steady state variability

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Title: Predicting the Mean First Passage Time (MFPT) to reach any state for a passive dynamic walker with steady state variability
Authors: Wijesundera, I
Halgamuge, M
Nirmalathas, A
Nanayakkara, DPT
Item Type: Journal Article
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.
Issue Date: 29-Nov-2018
Date of Acceptance: 12-Nov-2018
ISSN: 1932-6203
Publisher: Public Library of Science (PLoS)
Journal / Book Title: PLoS ONE
Volume: 13
Issue: 11
Copyright Statement: © 2018 Wijesundera et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/N03211X/2
Keywords: Robotics
Probability Learning
predictive control
Metastable systems
Passive dynamic walkers
MD Multidisciplinary
General Science & Technology
Publication Status: Published
Article Number: e0207665
Appears in Collections:Faculty of Engineering
Dyson School of Design Engineering

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