Estimation and Closed-Loop Control of <i>COG</i>/<i>ZMP</i> in Biped Devices Blending <i>CoP</i> Measures and Kinematic Information

Estimation and Closed-Loop Control of <i>COG</i>/<i>ZMP</i> in Biped Devices Blending <i>CoP</i> Measures and Kinematic Information

The zero moment point (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mi>M</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>) and the linearized inverted pendulum model...

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Main Authors: Giuseppe Menga, Marco Ghirardi
Format: Article
Language:English
Published: MDPI AG 2019-10-01
Series:Robotics
Subjects:
biped robotics
exoskeletons
postural equilibrium
zero moment point
inverted pendulum
robust control
Online Access:https://www.mdpi.com/2218-6581/8/4/89
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author Giuseppe Menga
Marco Ghirardi
author_facet Giuseppe Menga
Marco Ghirardi
author_sort Giuseppe Menga
collection DOAJ
description The zero moment point (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mi>M</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>) and the linearized inverted pendulum model linking the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mi>M</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> to the center of gravity (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>O</mi> <mi>G</mi> </mrow> </semantics> </math> </inline-formula>) have an important role in the control of the postural equilibrium (balance) of biped robots and lower-limb exoskeletons. A solution for balance real time control, closing the loop from the joint actual values of the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>O</mi> <mi>G</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mi>M</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>, has been proposed by Choi. However, this approach cannot be practically implemented: While the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mi>M</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> actual value is available from the center of pressure (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>o</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>) measured under the feet soles, the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>O</mi> <mi>G</mi> </mrow> </semantics> </math> </inline-formula> is not measurable, but it can only be indirectly assessed from the joint-angle measures, the knowledge of the kinematics, and the usually poorly known weight distribution of the links of the chain. Finally, the possible presence of unknown external disturbance forces and the nonlinear, complex nature of the kinematics perturb the simple relationship between the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mi>M</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>O</mi> <mi>G</mi> </mrow> </semantics> </math> </inline-formula> in the linearized model. The aim of this paper is to offer, starting from Choi&#8217;s model, a practical implementation of closed-loop balance control fusing <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>o</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> and joint-angle measures, eliminating possible inconsistencies. In order to achieve this result, we introduce a model of the linearized inverted pendulum for an extended estimation, not only of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>O</mi> <mi>G</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mi>M</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>, but also of external disturbances. This model is then used, instead of Choi&#8217;s equations, for estimation and balance control, using <inline-formula> <math display="inline"> <semantics> <msub> <mi mathvariant="script">H</mi> <mo>&#8734;</mo> </msub> </semantics> </math> </inline-formula> theory. As the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>O</mi> <mi>G</mi> </mrow> </semantics> </math> </inline-formula> information is recovered from the joint-angle measures, the identification of a statistically equivalent serial chain (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mi>E</mi> <mi>S</mi> <mi>C</mi> </mrow> </semantics> </math> </inline-formula>) linking the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>O</mi> <mi>G</mi> </mrow> </semantics> </math> </inline-formula> to the joint angles is also discussed.
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spelling doaj.art-6ef0bb3965bd4d469e2dc808f94f95dd2022-12-22T02:17:56ZengMDPI AGRobotics2218-65812019-10-01848910.3390/robotics8040089robotics8040089Estimation and Closed-Loop Control of <i>COG</i>/<i>ZMP</i> in Biped Devices Blending <i>CoP</i> Measures and Kinematic InformationGiuseppe Menga0Marco Ghirardi1Department of Control and Computer Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, ItalyDepartment of Management and Production Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, ItalyThe zero moment point (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mi>M</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>) and the linearized inverted pendulum model linking the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mi>M</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> to the center of gravity (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>O</mi> <mi>G</mi> </mrow> </semantics> </math> </inline-formula>) have an important role in the control of the postural equilibrium (balance) of biped robots and lower-limb exoskeletons. A solution for balance real time control, closing the loop from the joint actual values of the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>O</mi> <mi>G</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mi>M</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>, has been proposed by Choi. However, this approach cannot be practically implemented: While the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mi>M</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> actual value is available from the center of pressure (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>o</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>) measured under the feet soles, the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>O</mi> <mi>G</mi> </mrow> </semantics> </math> </inline-formula> is not measurable, but it can only be indirectly assessed from the joint-angle measures, the knowledge of the kinematics, and the usually poorly known weight distribution of the links of the chain. Finally, the possible presence of unknown external disturbance forces and the nonlinear, complex nature of the kinematics perturb the simple relationship between the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mi>M</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>O</mi> <mi>G</mi> </mrow> </semantics> </math> </inline-formula> in the linearized model. The aim of this paper is to offer, starting from Choi&#8217;s model, a practical implementation of closed-loop balance control fusing <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>o</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula> and joint-angle measures, eliminating possible inconsistencies. In order to achieve this result, we introduce a model of the linearized inverted pendulum for an extended estimation, not only of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>O</mi> <mi>G</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>Z</mi> <mi>M</mi> <mi>P</mi> </mrow> </semantics> </math> </inline-formula>, but also of external disturbances. This model is then used, instead of Choi&#8217;s equations, for estimation and balance control, using <inline-formula> <math display="inline"> <semantics> <msub> <mi mathvariant="script">H</mi> <mo>&#8734;</mo> </msub> </semantics> </math> </inline-formula> theory. As the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>O</mi> <mi>G</mi> </mrow> </semantics> </math> </inline-formula> information is recovered from the joint-angle measures, the identification of a statistically equivalent serial chain (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mi>E</mi> <mi>S</mi> <mi>C</mi> </mrow> </semantics> </math> </inline-formula>) linking the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>O</mi> <mi>G</mi> </mrow> </semantics> </math> </inline-formula> to the joint angles is also discussed.https://www.mdpi.com/2218-6581/8/4/89biped roboticsexoskeletonspostural equilibriumzero moment pointinverted pendulumrobust control
spellingShingle Giuseppe Menga
Marco Ghirardi
Estimation and Closed-Loop Control of <i>COG</i>/<i>ZMP</i> in Biped Devices Blending <i>CoP</i> Measures and Kinematic Information
Robotics
biped robotics
exoskeletons
postural equilibrium
zero moment point
inverted pendulum
robust control
title Estimation and Closed-Loop Control of <i>COG</i>/<i>ZMP</i> in Biped Devices Blending <i>CoP</i> Measures and Kinematic Information
title_full Estimation and Closed-Loop Control of <i>COG</i>/<i>ZMP</i> in Biped Devices Blending <i>CoP</i> Measures and Kinematic Information
title_fullStr Estimation and Closed-Loop Control of <i>COG</i>/<i>ZMP</i> in Biped Devices Blending <i>CoP</i> Measures and Kinematic Information
title_full_unstemmed Estimation and Closed-Loop Control of <i>COG</i>/<i>ZMP</i> in Biped Devices Blending <i>CoP</i> Measures and Kinematic Information
title_short Estimation and Closed-Loop Control of <i>COG</i>/<i>ZMP</i> in Biped Devices Blending <i>CoP</i> Measures and Kinematic Information
title_sort estimation and closed loop control of i cog i i zmp i in biped devices blending i cop i measures and kinematic information
topic biped robotics
exoskeletons
postural equilibrium
zero moment point
inverted pendulum
robust control
url https://www.mdpi.com/2218-6581/8/4/89
work_keys_str_mv AT giuseppemenga estimationandclosedloopcontroloficogiizmpiinbipeddevicesblendingicopimeasuresandkinematicinformation
AT marcoghirardi estimationandclosedloopcontroloficogiizmpiinbipeddevicesblendingicopimeasuresandkinematicinformation

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