Stability Analysis for Variable Impedance Control of Robot

ߪߓ߼ߦ

ੱ㑆ߣࡠࡏ࠶࠻߇ജቇ⊛ߦද⺞ߒߥ߇ࠄㆇ៝૞ᬺ

߿ᢎ␜૞ᬺࠍⴕ߁⎇ⓥߢߪ ^1-7)㧘ࡠࡏ࠶࠻ߩ೙ᓮᴺߣ ߒߡࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮ߇ᐢߊ↪޿ࠄࠇߡ޿ࠆ ^2-7)㧚

ࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮߦ߅ߌࠆࠪࠬ࠹ࡓߩ቟ቯᕈߪ㧘ࡠ ࡏ࠶࠻ߩㆇേ․ᕈߣߒߡ⸳ቯߐࠇࠆࠗࡦࡇ࡯࠳ࡦࠬ․

ᕈߦଐሽߔࠆߎߣ߇⍮ࠄࠇߡ߅ࠅ㧘㜞೰ᕈߩⅣႺߦኻ ߔࠆធ⸅߿᜔᧤߇↢ߓࠆ႐วߦߪࠪࠬ࠹ࡓ߇ਇ቟ቯߦ ߥࠆធ⸅቟ቯᕈߩ໧㗴߇ᜰ៰ߐࠇߡ޿ࠆ ^3,8-12)㧚ੱ㑆 ߣࡠࡏ࠶࠻ߩද⺞૞ᬺߦ㑐ߔࠆ⎇ⓥߢߪ㧘ࡠࡏ࠶࠻߇ ធߔࠆⅣႺ߿ੱ㑆ߩ․ᕈߦᔕߓߡࠗࡦࡇ࡯࠳ࡦࠬ․ᕈ ߩ⺞ᢛࠍⴕ߁೙ᓮᴺ߇⠨᩺ߐࠇߡ߅ࠅ ^2,6)㧘⺞ᢛߦ ࠃߞߡࠪࠬ࠹ࡓߩ቟ቯᕈ߇ะ਄ߔࠆߣߩႎ๔߇ⴕࠊࠇ ߡ޿ࠆ³⁾㧚ߒ߆ߒ㧘ᓥ᧪ߩ⎇ⓥߢߪౕ૕⊛ߥࠪࠬ࠹ࡓ

ߦ㑐ߔࠆ቟ቯᕈ߿ࠗࡦࡇ࡯࠳ࡦࠬ․ᕈߩ⺞ᢛᣇᴺߦ㑐 ߔࠆᅷᒰᕈߦߟ޿ߡߪ᣿ࠄ߆ߦߐࠇߡ޿ߥ߆ߞߚ^2,3,6)㧚

⸃ᨆ⊛߅ࠃ߮ታ㛎⊛ߦࠪࠬ࠹ࡓߩ቟ቯ⸃ᨆࠍⴕ߁ߎߣ ߇ߢ߈ࠇ߫㧘ࠪࠬ࠹ࡓߩ቟ቯᕈࠍ᣿⏕ߦߢ߈ࠆߛߌߢ ߥߊ㧘ቯ㊂⊛ߥ⸃ᨆ⚿ᨐߦၮߠ޿ߚᅷᒰߥࡄ࡜ࡔ࡯࠲

⺞ᢛࠍⴕ߁ߎߣ߇น⢻ߦߥࠆߎߣ߆ࠄ㧘㕖Ᏹߦ᦭↪ߢ

޽ࠆߣ⠨߃ࠄࠇࠆ㧚․ߦੱ㑆ߣࡠࡏ࠶࠻ߩද⺞૞ᬺߢ ߪ㧘૞ᬺ⠪ߣࡠࡏ࠶࠻߇੕޿ߦធߔࠆߎߣߢജቇ⊛ߥ

⋧੕૞↪ࠍታ⃻ߔࠆߚ߼㧘ࠪࠬ࠹ࡓߩ቟ቯᕈߦኻߒߡ චಽߦ㈩ᘦߔࠆᔅⷐ߇޽ࠆ㧚

ߘߎߢ㧘ᧄ⎇ⓥߢߪࡠࡏ࠶࠻ߣធߔࠆᄖㇱⅣႺߩ

೰ᕈଥᢙߦᔕߓߡࠗࡦࡇ࡯࠳ࡦࠬ․ᕈߩ☼ᕈଥᢙࠍ⺞

ᢛߔࠆนᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮ⁶⁾ߦኻߔࠆ቟ቯ⸃ᨆ߅ ࠃ߮ታ㛎ࠍⴕ޿㧘ࠪࠬ࠹ࡓߩ቟ቯᕈࠍ᣿ࠄ߆ߦߔࠆ㧚

቟ቯ⸃ᨆߢߪࠪࠬ࠹ࡓࠍਇ቟ቯߦߔࠆේ࿃ߣߒߡ᜼ߍ

* Department of Biomedical Engineering, Doshisha University, Kyoto Telephone㧦+81-774-65-6497, E-mail : ttsumugi@mail.doshisha.ac.jp

** E-mail : ryokogaw@mail.doshisha.ac.jp

Stability Analysis for Variable Impedance Control of Robot

Toru T

SUMUGIWA^*

and Ryuichi Y

OKOGAWA^**

(Received May 20, 2010)

This paper presents stability analysis for variable impedance control strategy of a robot for a human-robot cooperative task.

The objective of this study is to analytically and experimentally verify advantages of the variable impedance control, which makes a robotic control system stable. In this study, a viscosity coefficient of impedance characteristics of robot motion is adjusted in proportion to an estimated stiffness of a human operator’s arm. The analysis reveals an increase of a stability margin of the control system with the variable impedance characteristics. To confirm the results of the stability analysis, experiments of a human-robot cooperative task were carried out using a Mitsubishi PA-10 robot arm. Experimental results show that the variable impedance control makes the system stable in the human-robot cooperative task.

䎮䏈䏜䎃䎺䏒䏕䏇䏖䎃䎝 robot, stability analysis, variable impedance control, human-robot cooperative task 䭴䯃䮶䯃䮐䎃䰆䎃ࡠࡏ࠶࠻㧘቟ቯ⸃ᨆ㧘นᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮ㧘ੱ㑆㧙ࡠࡏ࠶࠻ද⺞೙ᓮ

ੱ㑆㧙ࡠࡏ࠶࠻ද⺞♽ߦ߅ߌࠆนᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮߩ቟ቯ⸃ᨆ

Ⓧ㓙

ᔀ^*㧘ᮮᎹ

㓉৻^{* *}

ࠄࠇࠆࡠࡏ࠶࠻ߩ೙ᓮㆃࠇ߿ੱ㑆ߩ෻ᔕᤨ㑆ߦࠃࠆㆃ ࠇ㧘ࡠࡏ࠶࠻ߩࠦࡦࡊ࡜ࠗࠕࡦࠬ․ᕈࠍ⠨ᘦߒߚࡕ࠺

࡞ൻࠍⴕ߁ ¹²⁾㧚⸃ᨆኻ⽎ߪ᭽ޘߥ⎇ⓥߢ೑↪ߐࠇߡ

޿ࠆ᳢↪ࡠࡏ࠶࠻

PA-10㧔ਃ⪉㊀Ꮏ⵾㧕ࠍ↪޿ߚࠪࠬ

࠹ࡓߣߒ㧘૞ᬺኻ⽎ߪࡠࡏ࠶࠻ߩᚻవߦขࠅઃߌߚ╩

ࠍੱ㑆߇⋥ធᛠᜬߒߡⴕ߁ᦠሼേ૞㧔ᦠ㆏㧕ߦ⸳ቯߒ ߚ㧔Fig. 1ෳᾖ㧕㧚ᦠሼേ૞ߪੱ㑆߇ቯ߼ߚ⋡ᮡ゠〔

߳ߩㅊᓥേ૞ࠍⴕ߁૞ᬺߢ޽ࠆߚ߼ᢎ␜૞ᬺߦ޽ߚࠅ㧘

╩ࠍㆇ៝‛ߣ⠨߃ࠇ߫ㆇ៝૞ᬺߦ޽ߚࠆ㧚ࠪࠬ࠹ࡓ߇ ਇ቟ቯߦߥࠄߕ㧘ੱ㑆ߩᚲᦸߔࠆㆇേ߇ታ⃻ߢ߈ࠇ߫㧘 ⷙ▸ߤ߅ࠅߩᢥሼࠍឬߊߎߣ߇น⢻ߦߥࠆߣ⠨߃ࠄࠇ㧘 ታ㛎⚿ᨐ߆ࠄ቟ቯᕈߩ್೎ࠍⴕ߁ߎߣ߇ߢ߈ࠆ㧚

ᧄ⺰ᢥߢߪ㧘ᢙ୯ࠪࡒࡘ࡟࡯࡚ࠪࡦߦࠃࠆ቟ቯ⸃

ᨆࠍⴕ޿㧘นᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮߦࠃߞߡࠪࠬ࠹ࡓ ߩ቟ቯᕈ߇ะ਄ߔࠆߎߣࠍ⏕⹺ߔࠆ㧚ᰴߦᦠሼേ૞ࠍ ⴕ߁ታ㛎ߦࠃߞߡ㧘ࠪࠬ࠹ࡓ߇቟ቯߒߚ⁁ᘒߢ౞Ṗߥ ද⺞૞ᬺ߇ታ⃻ߢ߈ࠆߎߣࠍ⏕⹺ߒ㧘⸃ᨆኻ⽎ߣߒߚ นᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮߩᅷᒰᕈࠍ␜ߔ㧚

ᄖㇱⅣႺ೰ᕈߩផቯߦၮߠߊ นᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮ ࡠࡏ࠶࠻ߩࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮ

ࡠࡏ࠶࠻ߩᚻవ૏⟎ߦ߅ߌࠆㆇേ߇ᑼ(1)ߦ␜ߔࠗ

ࡦࡇ࡯࠳ࡦࠬ․ᕈࠍᜬߟࠃ߁ߦ૏⟎೙ᓮࡌ࡯ࠬߩࠗࡦ ࡇ࡯࠳ࡦࠬ೙ᓮࠍⴕ߁㧚

H R R R

Rp D p F

M

(1)

MR 㧘D_Rߪᘠᕈଥᢙ(kg)㧘☼ᕈଥᢙ(Ns m)ࠍ␜

ߔ㧚◲නߩߚ߼㧘ࡠࡏ࠶࠻ߩㆇേࠍਗㅴㆇേߦ㒢ቯߔ

ࠆߎߣ߆ࠄ㧘M_R 㧘D_Rߪߘࠇߙࠇ3u3ߩኻⷺⴕ೉

ߦߥࠆ㧚F_Hߪੱ㑆߇ട߃ࠆജ(N)㧘p_RߪၮḰᐳᮡ

♽ࠍේὐߣߔࠆࡠࡏ࠶࠻ߩᚻవ૏⟎(m)ߢ޽ࠅ㧘 p_R㧘 pRߪടㅦᐲ(m s²)㧘ㅦᐲ(ms)ࠍ⴫ߔ3u1ߩࡌࠢ࠻

࡞ߢ޽ࠆ㧚

ੱ㑆߇ട߃ࠆജF_Hߪࡠࡏ࠶࠻ߩᚻవ૏⟎ߦขࠅઃ

ߌߚജⷡ࠮ࡦࠨߦࠃߞߡᬌ಴ߐࠇ㧘ᑼ

(1)

ߩࠗࡦࡇ࡯

࠳ࡦࠬ․ᕈߦၮߠ޿ߡࡠࡏ࠶࠻ߩᚻవ૏⟎ߦ߅ߌࠆㆇ

േߦᄌ឵ߐࠇࠆ㧚ߎࠇߦࠃࠅੱ㑆ߣࡠࡏ࠶࠻ߩਔ⠪߇ ജቇ⊛ߦද⺞ߒߡേ૞ࠍⴕ߁ߎߣ߇น⢻ߦߥࠆ㧚

ᄖㇱⅣႺߩ೰ᕈଥᢙߩផቯ

ᧄ⎇ⓥߢߪࡠࡏ࠶࠻ߣធߔࠆᄖㇱⅣႺߪੱ㑆ߩᚻ వߦߥࠆ㧔

Fig. 1

ෳᾖ㧕㧚৻⥸ߦੱ㑆ߩᚻవߦ߅ߌࠆ

േ․ᕈߪ㧘ᘠᕈ㧘☼ᕈ㧘೰ᕈ߆ࠄߥࠆᯏ᪾ࠗࡦࡇ࡯࠳

ࡦࠬ․ᕈߦࠃߞߡ⴫⃻ߢ߈ࠆ ^13-16)㧚ߘߩਛߢ߽ੱ㑆 ߩᚻవߦ߅ߌࠆ೰ᕈߪ㧘ᘠᕈ㧘☼ᕈߦᲧߴߡ⺞ᢛ⢻ജ ߇ᄢ߈ߊ ¹³⁾㧘㜞೰ᕈߦߥࠆߣࠪࠬ࠹ࡓࠍਇ቟ቯߦߔ ࠆߎߣ߆ࠄ ^3,11,17)㧘ᧄ⎇ⓥߢߪੱ㑆ߩᚻవߦ߅ߌࠆ೰

ᕈଥᢙK_H (N m)㧔3u3ߩኻⷺⴕ೉㧕ߩផቯ⚿ᨐࠍ ࡠࡏ࠶࠻ߩࠗࡦࡇ࡯࠳ࡦࠬ․ᕈߩ⺞ᢛߦ೑↪ߔࠆ㧚ੱ

㑆ߩᚻవߣࡠࡏ࠶࠻ߩേ․ᕈࡕ࠺࡞ࠍ

Fig. 2

ߦ␜ߔ㧚

೰ᕈଥᢙߩផቯߦ㒢ቯߔࠇ߫㧘ࡈ࠶ࠢߩᴺೣߦࠃߞ ߡജߣ૏⟎ߩ࠺࡯࠲߆ࠄⴕ߁ߎߣ߇น⢻ߢ޽ࠆ㧚ߒ߆ ߒ㧘ද⺞૞ᬺਛߦ೰ᕈଥᢙߩផቯࠍⴕ߁႐ว㧘೰ᕈଥ ᢙߦ㑐ࠊࠆᐔⴧὐ㧔޽ࠆ޿ߪ઒ᗐ゠㆏㧕߇⒖േߔࠆߣ㧘 ᱜ⏕ߥផቯ߇࿎㔍ߦߥࠆߚ߼㧘ᧄ⎇ⓥߢߪᐔⴧὐߩ⒖

േ㊂߇ዊߐ޿ߣ઒ቯߢ߈ࠆૐㅦᐲၞ㧔

0.02m/s

એਅߣ ߔࠆ㧕ߦ㒢ቯߒ㧘⍴޿ᤨ㑆ߩ࠺࡯࠲ࠍ↪޿ߡផቯࠍⴕ ߁⁶⁾㧚ੱ㑆ߩᚻవ೰ᕈଥᢙK_H ߩផቯߪᰴᑼߩᏅಽᑼ ࠍ↪޿ߡⴕ߁㧚

) ( ) ( )

( _{H H S}

est t t tt

'F F F

(2)

)

( ) ( )

( _{R R S}

est t t tt

'p p p

(3)

)

est(t

'F 㧘'p_est(t)ߪ㧘ᤨೞtߦ߅ߌࠆੱ㑆߇ࡠ ࡏ࠶࠻ߦട߃ߚജ㧘߅ࠃ߮ੱ㑆ߩᚻవ૏⟎㧔ߎߎߢߪ ࡠࡏ࠶࠻ߩᚻవ૏⟎ߣห୯ߣߔࠆ㧕ߩᏅಽ࠺࡯࠲ߢ޽

ࠆ㧚Ꮕಽᤨ㑆t_Sߪ 0.15sec޽ࠇ߫ផቯ߇น⢻ߦߥࠆߎ ߣ߇ታ㛎ߦࠃࠅ್᣿ߒߚ⁶⁾㧚ᑼ

(2)

㧘ᑼ

(3)

ࠍ↪޿ߡ㧘

ᰴᑼߩ㑐ଥ߆ࠄᚻవ೰ᕈଥᢙK_Hߩផቯࠍⴕ߁㧚

) ( )

(t _{H est} t

est K p

F '

'

(4)

ផቯᣇᴺߦߪㅙᰴᦨዊੑਸ਼ᴺ㧔ᔓළଥᢙߪ

0.995

㧕

ࠍ↪޿ߚ^18,19)㧚ᧄផቯᴺߦࠃߞߡᓧࠄࠇࠆផቯ୯ߩ⺋

Human operator PA-10 robot arm

y x

z Writing brush

A direction of coordinates

¦

MR FH

Stiffness model of human arm Impedance model

of robot

Writing brush at the tip of robot

Human hand

Robot model Human model

DR K_H

Fig. 1. Human-robot cooperative task.

Fig.2. Dynamics model of human operator and

movement of robot.

Ꮕߪᦨᄢߢ

17.5%

⒟ᐲߦߥࠆߎߣ߇್᣿ߒߡ޿ࠆ⁶⁾㧚

߹ߚ㧘ផቯኻ⽎߇ᄌ૏ߩ↢ߓߥ޿೰૕ߢ޽ࠆ႐ว߿ࡠ ࡏ࠶࠻ߩᚻవ૏⟎߇ቢోߦ㕒ᱛߔࠆ႐วߦߪᧄᚻᴺࠍ ㆡ↪ߔࠆߎߣߪ࿎㔍ߦߥࠆ⁶⁾㧚

ផቯ೰ᕈߦၮߠߊนᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮ ࡠࡏ࠶࠻ߩࠗࡦࡇ࡯࠳ࡦࠬ․ᕈߦ߅ߌࠆ☼ᕈଥᢙ ߪࠪࠬ࠹ࡓࠍ቟ቯൻߐߖ㧘ࠪࠬ࠹ࡓߩ቟ቯᕈߦᄢ߈ߥ ᓇ㗀ࠍਈ߃ࠆߎߣ߇ႎ๔ߐࠇߡ޿ࠆ^3,11,17)㧚ߘߎߢ㧘 ᧄ⎇ⓥߢߪࠗࡦࡇ࡯࠳ࡦࠬ․ᕈߩ⺞ᢛᣇᴺߣߒߡ㧘ᑼ

(1)

ߦ߅ߌࠆ☼ᕈଥᢙD_Rࠍੱ㑆ߩᚻవ೰ᕈଥᢙK_H ߩផቯ୯ߢ޽ࠆKˆ_Hߩᄢ߈ߐߦᲧ଀ߐߖߡ⺞ᢛࠍⴕ ߁ᣇᴺࠍណ↪ߔࠆ㧔

Fig. 3

ෳᾖ㧕㧚

H

R K

D D ˆ

(5)

ߚߛߒ㧘ቯᢙDߦࠃߞߡᰴరߩ⺞ᢛ߇ⴕࠊࠇࠆߣ ߔࠆ㧚

D

ߪ

0.2

ߣߔࠆ߇㧔Dߩᅷᒰᕈߪᰴ┨એ㒠ࠍ

ෳᾖ㧕㧘☼ᕈଥᢙD_R߇ᄢ߈ߊߥࠅㆊ߉ࠆߣࡠࡏ࠶

࠻ߩേ૞ㅦᐲߩૐਅࠍ᜗ߊߚ߼㧘ᦨᄢ୯ࠍ

100Ns/m

ߦ⸳ቯߔࠆ㧚ೋᦼ୯D_Riniߪ

25Ns/m

ߣߒ㧘DKˆ_H߇

ೋᦼ୯D_Riniࠃࠅዊߐߊߥࠆ႐วߦߪ

25Ns/m

ߦ⸳ቯ ߔࠆ㧚ࡠࡏ࠶࠻ߩᚻవㅦᐲ߇

0.02m/s

ࠍ⿧߃ࠆㅦᐲၞ

ߢߪ㧘ੱ㑆ߩᚻవ೰ᕈଥᢙK_H ߩផቯ♖ᐲ߇ૐਅߔ ࠆߚ߼㧘ೋᦼ୯D_Riniߦߥࠆࠃ߁ᓢޘߦᷫዋߐߖߚ㧚 ߚߛߒ㧘ߎߩࠃ߁ߥ႐วߦ߽ࠪࠬ࠹ࡓߩ቟ቯᕈߦߪᓇ 㗀ࠍਈ߃ߥ޿ߎߣ߇್᣿ߒߡ޿ࠆ⁶⁾㧚߹ߚ㧘☼ᕈଥᢙ

DRࠍ⺞ᢛߒߚᓇ㗀ࠍ᣿⏕ߦߔࠆߚ߼㧘ᘠᕈଥᢙ MRߪ

3kg

ߣ৻ቯߦߒߚ㧚૶↪ߒߚࠗࡦࡇ࡯࠳ࡦࠬ

ࡄ࡜ࡔ࡯࠲ࠍ

Table 1

ߦ␜ߔ㧚

นᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮߩ቟ቯ⸃ᨆ ೙ᓮࠪࠬ࠹ࡓߩࡕ࠺࡞ൻ

ᧄ┨ߢߪࡠࡏ࠶࠻ߩ೙ᓮߦ㑐ߔࠆㆃࠇ㧘߅ࠃ߮ࡠ ࡏ࠶࠻ߩࠦࡦࡊ࡜ࠗࠕࡦࠬߩᓇ㗀ࠍ⠨ᘦߒߡ቟ቯ⸃ᨆ ࠍⴕ߁ ¹⁷⁾㧚◲නߩߚ߼㧘ࡠࡏ࠶࠻ߩᚻవ૏⟎ߦ߅ߌ ࠆyゲᣇะߩ

1

⥄↱ᐲߩਗㅴㆇേߦ㒢ቯߒߡ⸃ᨆࠍⴕ ߁㧚ࡠࡏ࠶࠻ߩേ․ᕈߪࠗࡦࡇ࡯࠳ࡦࠬ․ᕈ㧘ੱ㑆ߩ

േ․ᕈߪ೰ᕈߦࠃߞߡ⴫ߔ㧚ࡠࡏ࠶࠻ߩࠦࡦࡊ࡜ࠗࠕ ࡦࠬߦࠃߞߡ↢ߓࠆേ․ᕈߪ㧘ᘠᕈߣ೰ᕈߦࠃߞߡ⴫

ߔ㧔

Fig. 4

㧘

Fig. 5

ෳᾖ㧕㧚ࡠࡏ࠶࠻ߩ೙ᓮߦ㑐ߔࠆ

ㆃࠇߪ㧘ࡠࡏ࠶࠻ߩㆇേߩㆃࠇߣ㧘㔌ᢔൻߦࠃࠆㆃࠇ 㧔෩ኒߦߪ

1

ࠨࡦࡊ࡞ᤨ㑆ಽߩ߻ߛᤨ㑆㧕ߢ޽ࠆ߇㧘

◲නߩߚ߼㧘ߘࠇߙࠇ㧝ᰴㆃࠇ♽ߦࠃߞߡ⴫ߔ^3,17)㧚 ࡠࡏ࠶࠻ߩࠗࡦࡇ࡯࠳ࡦࠬ․ᕈࠍᰴᑼߩ

1

⥄↱ᐲࡕ

࠺࡞ߦࠃߞߡ⴫ߔ㧔ᑼ

(1)

㧘

Fig. 4

ෳᾖ㧕㧚

H R RP D P F

M _{1 1}

(6)

P1㧘P₁ߪࡠࡏ࠶࠻ߩᚻవㅦᐲ(ms)㧘ടㅦᐲ )

s m

( ² ࠍ⴫ߔ㧚Fig. 4 ߦ߅޿ߡ㧘ࡠࡏ࠶࠻ߩࠦࡦࡊ

࡜ࠗࠕࡦࠬߦࠃࠆᓇ㗀ࠍ⠨ᘦߔࠆߣ㧘ታ㓙ߩࡠࡏ࠶࠻

ߩᚻవ૏⟎ߪP₂ߢ⴫ߔߎߣ߇ߢ߈ࠆ㧚ߎߎߢੱ㑆߇ ട߃ࠆജࠍ౉ജߣߒ㧘ࡠࡏ࠶࠻ߩ೙ᓮߦ㑐ߔࠆㆃࠇ 㧔2 ᰴㆃࠇ㧕ࠍ⠨ᘦߒߚવ㆐㑐ᢙGs ߪ㧘ᰴᑼߦ ࠃߞߡ⴫ߐࠇࠆ㧚

Table 1. Impedance parameters of robot.

MR (kg) 3

D_{R ini} (Ns/m) 25

D_R (Ns/m) 25 100dD_Rd

impedance model compliance model of robot

human model position of tip of robot

DR M_R K_Req M_Req K_H FH P2

P1 position of tip of

impedance characteristic

applied force

1 1

s T_R

1 1 s TH

1 1

s T_D

P2

FH

KH

pR H

R R R

Rp D p F

M

KˆH

D

FH

FH

pR

pR

pR

FH

Fig. 3. Variable impedance controller for human-robot cooperative task.

Fig. 4. Stability analysis model of human-robot cooperative task.

Fig. 5. Block diagram of stability analysis model.

^ `

1 1

1

2 2

2

2

˜

˜ ˜

˜

˜

˜

˜

˜

s T s T

K K s M K s D s M

K s D s s M

G

D R

Req Req Req

Req R R

Req R

R

(7)

KReqߪࡠࡏ࠶࠻ߩᚻవ૏⟎ߦ߅ߌࠆ╬ଔ೰ᕈ㧔ࠦ

ࡦࡊ࡜ࠗࠕࡦࠬߩㅒᢙ㧕㧘M_Reqߪ╬ଔᘠᕈࠍ⴫ߔ㧚

TR㧘T_Dߪ㧘ࡠࡏ࠶࠻ߩㆇേߩㆃࠇᤨ㑆㧘߅ࠃ߮೙

ᓮࠍⴕ߁㓙ߩ㔌ᢔൻߦࠃࠆㆃࠇᤨ㑆ࠍ⴫ߔ㧚ੱ㑆ߩᚻ వ೰ᕈଥᢙK_H ߅ࠃ߮ੱ㑆ߩ෻ᔕᤨ㑆ߦࠃࠆㆃࠇ 㧔◲නߩߚ߼

1

ᰴㆃࠇߣ઒ቯ㧕ߦࠃࠆㆃࠇᤨ㑆T_Hࠍ

⠨ᘦߒߚੱ㑆ߩવ㆐㑐ᢙH s ߪ㧘ᰴᑼߦࠃߞߡ⴫ߐ ࠇࠆ㧚

1

˜s T s K H

H

H

(8)

ᑼ(7)߅ࠃ߮ᑼ

(8)ࠃࠅ㧘ࠪࠬ࠹ࡓߩ৻Ꮌવ㆐㑐ᢙߩ

․ᕈᣇ⒟ᑼߪᰴᑼߦࠃߞߡ⴫ߔߎߣ߇ߢ߈ࠆ㧚

0

1Gs H s

(9)

ߚߛߒ㧘ੱ㑆ߩ෻ᔕᤨ㑆ߦࠃࠆㆃࠇߪ૞ᬺਛߦᤨޘ ೞޘߣᄌൻߔࠆߚ߼㧘৻ቯ୯ߣߒߡขࠅᛒ߁ߎߣߪ࿎

㔍ߢ޽ࠆ ²⁰⁾㧚ߘߎߢ◲නߩߚ߼㧘ᧄ⎇ⓥߦ߅ߌࠆ⸃

ᨆߢߪT_H

= 0sec

ߣߒߡขࠅᛒߞߚ㧚ߥ߅㧘ߎߩㆃࠇ

ߪ቟ቯᕈߦᖡᓇ㗀ࠍਈ߃ࠆߣߩ⸃ᨆ⚿ᨐ߇ᓧࠄࠇߡ޿

ࠆ^3,17)㧚߹ߚ㧘ᧄ⸃ᨆᚻᴺߩᅷᒰᕈߪ╩⠪ࠄߦࠃߞߡ

⏕⹺ߐࠇߡ޿ࠆ¹⁷⁾㧚

นᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮߩ቟ቯ⸃ᨆ

቟ቯ⸃ᨆߦߪࠪࠬ࠹ࡓߩ㐽࡞࡯ࡊવ㆐㑐ᢙߦ߅ߌ

ࠆᭂ㧔․ᕈᣇ⒟ᑼߩᩮ㧕ߩ᜼േࠍ

s

ᐔ㕙਄ߦ␜ߒߚ

࿑ࠍ೑↪ߔࠆ ¹²⁾㧚ࠪࠬ࠹ࡓߩࡄ࡜ࡔ࡯࠲ߢ޽ࠆੱ㑆 ߩᚻవ೰ᕈଥᢙK_H ߩ୯ࠍᄌൻߐߖߥ߇ࠄᭂߩ᜼േ

ࠍ⷗ࠆߎߣߢ㧘ࠪࠬ࠹ࡓߩ቟ቯᕈߩ್೎ࠍⴕ߁ߎߣ߇ ߢ߈ࠆ㧚ᭂ߇ᱜߩታㇱࠍᜬߜ㧘

s

ᐔ㕙ߩฝඨᐔ㕙਄

ߦ㈩⟎ߐࠇࠆ႐ว㧘ߘߩࠪࠬ࠹ࡓߪਇ቟ቯߦߥࠆ㧚

ࠪࠬ࠹ࡓߩ቟ቯ⸃ᨆࠍⴕ߁ߚ߼ߦੱ㑆ߩᚻవ೰ᕈଥ ᢙK_H߇0dK_H d2000ߩ▸࿐ߢᄌൻߔࠆᢙ୯ࠪࡒࡘ

࡟࡯࡚ࠪࡦࠍⴕߞߚ㧚◲නߩߚ߼㧘ࡠࡏ࠶࠻ߩࠗࡦ ࡇ࡯࠳ࡦࠬ․ᕈߩ߁ߜ㧘ᘠᕈଥᢙM_Rߪ

3kg

㧘☼ᕈଥ

ᢙD_Rߪ

25Ns/m

ߣߔࠆ㧚

Fig. 1

ߦ߅ߌࠆታ㛎ᆫ൓ߢߩ

ࡠࡏ࠶࠻ߩᚻవ૏⟎ߩ╬ଔ೰ᕈK_Reqߪ

40000N/m

㧔yゲᣇะ㧕ߢ޽ࠆ^17,21)㧚ࡠࡏ࠶࠻߇ࠦࡦࡊ࡜ࠗࠕࡦ

ࠬ․ᕈࠍ᦭ߔࠆ႐ว㧘ࠦࡦࡊ࡜ࠗࠕࡦࠬߩㅒᢙߢ޽ࠆ

╬ଔ೰ᕈ߇㜞޿߶ߤࠪࠬ࠹ࡓߩ቟ቯᕈ߇ᖡൻߔࠆߎߣ ߇್᣿ߒߡ޿ࠆ¹⁷⁾㧚

Fig. 1

ߩታ㛎ᆫ൓ߢߪyゲᣇะߩ

╬ଔ೰ᕈK_Req߇ᦨ߽㜞ߊ㧘ࠪࠬ࠹ࡓߩ቟ቯᕈߦᦨ߽

ᄢ߈ߊᓇ㗀ߔࠆߎߣ߆ࠄ㧘yゲᣇะߩ቟ቯᕈ߇଻⸽ߐ ࠇࠇ߫ઁߩゲᣇะߦ㑐ߒߡ߽቟ቯߢ޽ࠆߣ⠨߃ࠄࠇࠆ㧚

╬ଔᘠᕈM_Reqߪ㧘ࡠࡏ࠶࠻

PA-10

ߩ

E1

ゲ㧔⢀㑐▵ߩ

╙

1

ゲ㧕ࠃࠅవߦ޽ࠆ⾰㊂ߣห୯ߢ޽ࠆߣߒߡ

9.5kg

ߣ ߒߚ¹⁷⁾㧚ࡠࡏ࠶࠻ߩ೙ᓮߦ㑐ߔࠆㆃࠇߣߒߡ㧘ࡠࡏ࠶

࠻ߩേ૞ߩㆃࠇᤨ㑆T_Rࠍ

0.15

⑽㧔ታ㛎ߦࠃࠅหቯ㧕㧘

೙ᓮࠍⴕ߁㓙ߩ㔌ᢔൻߦࠃࠆㆃࠇᤨ㑆T_Dࠍ

0.01

⑽ 㧔ࠨࡦࡊ࡝ࡦࠣ࠲ࠗࡓߣห୯㧕ߣߒߚ㧚

⸃ᨆ⚿ᨐࠍ

Fig. 6

ߦ␜ߔ㧚ߥ߅㧘ߎߩ⚿ᨐߦߪࠪ

ࠬ࠹ࡓߩ቟ቯᕈߦ㑐ࠊࠆᭂߩߺࠍឬ޿ߡ޿ࠆ㧚☼ᕈଥ ᢙD_R߇৻ቯߢ޽ࠆ⹜ⴕߢߪ㧘ੱ㑆ߩᚻవ೰ᕈଥᢙ

KH ߇

200N/m

ࠃࠅᄢ߈ߊߥࠆߣࠪࠬ࠹ࡓߩᭂߩታ

ㇱ߇ᱜߦߥࠅฝඨᐔ㕙ߦ⒖േߔࠆߚ߼㧘ࠪࠬ࠹ࡓߪਇ

቟ቯߦߥࠆ㧔

Fig. 6(a)

ෳᾖ㧕㧚৻ᣇ㧘☼ᕈଥᢙD_Rߩ

⺞ᢛࠍⴕ߁นᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮߦ߅ߌࠆ⹜ⴕߢߪ㧘

ੱ㑆ߩᚻవ೰ᕈଥᢙK_H ߇

1300N/m

㧔ߎߩߣ߈ Ns/m

R 100

D 㧕ߦߥࠆ߹ߢࠪࠬ࠹ࡓߪਇ቟ቯߦߥࠄ ߥ޿ߎߣ߇ࠊ߆ࠆ㧔

Fig. 6(b)

ෳᾖ㧕㧚☼ᕈଥᢙD_Rߩ

⺞ᢛࠍⴕ߁ߎߣߢ㧘ੱ㑆ߩᚻవ೰ᕈଥᢙK_H ߇㜞ߊ ߥߞߡ߽ࠪࠬ࠹ࡓ߇቟ቯߒߚ߹߹ߩ⁁ᘒߢ૞ᬺࠍⴕ߁ ߎߣ߇น⢻ߦߥࠆߣ⠨߃ࠄࠇࠆ^3,11)㧚ߎࠇࠄߩ⚿ᨐࠃ ࠅ㧘ࠗࡦࡇ࡯࠳ࡦࠬ․ᕈߩ☼ᕈଥᢙߩ⺞ᢛࠍⴕ߁นᄌ

ࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮߩ᦭ലᕈࠍ⏕⹺ߔࠆߎߣ߇ߢ߈ߚ㧚

ታ㛎ⵝ⟎

ታ㛎ߦߪ

7

⥄↱ᐲࠍ᦭ߔࠆࡠࡏ࠶࠻

PA-10

㧔ਃ⪉㊀ Ꮏ⵾㧕ࠍ↪޿ߚ㧚ࡠࡏ࠶࠻ߩᚻవ૏⟎ߦߪ

6

ゲജⷡ࠮

ࡦࠨ

IFS-67M25A50-I40

㧔࠾࠶࠲⵾㧘ಽ⸃⢻㧦ਗㅴജ

-10 -5 0 5 10

-4 -3 -2 -1 0 1 2 3 4

Imag. axis

Real axis -10

-5 0 5 10

-4 -3 -2 -1 0 1 2 3 4

Imag. axis

Real axis (a) human arm stiffness is adjusted in the range of

R 25 D

2000 0dK_Hd with invariable impedance control

H 200 K

H 0

K KH 100

H 2000 K H 500

K

H 1500 K H 1000

K

(b) human arm stiffness is adjusted in the range of with variable impedance control

H 1300 K

H R K

D D 25dD_Rd100

2000 0dK_Hd

H 2000 K H 1500 K

H 1000 500 K KH H 0

K

H 100 K

Fig. 6 Results of stability analysis of impedance

control of the robot.

x㧘yᣇะ

0.012N

㧘zᣇะ

0.024N

㧕ࠍขࠅઃߌ㧘ੱ

㑆߇ട߃ࠆജߩᬌ಴ࠍⴕ߁㧚ࡠࡏ࠶࠻㧘߅ࠃ߮ജⷡ࠮

ࡦࠨߩࠨࡦࡊ࡝ࡦࠣ࠲ࠗࡓߪߣ߽ߦ

10msec

ߢ޽ࠆ㧚 ࡠࡏ࠶࠻ߩ೙ᓮߪ

1

บߩ೙ᓮ↪

PC

㧔

CPU: Pentium3-

700MHz

㧘

Memory: 256MB

㧕ߣ㧘

PA-10

ߦઃዻߔࠆ

ㆇേ೙ᓮࡏ࡯࠼ࠍ↪޿ߡⴕߞߚ㧚ജⷡ࠮ࡦࠨ਄ߦߪ ᦠ㆏↪ߩ╩ࠍขࠅઃߌࠆߚ߼ߩࠕ࡞ࡒ⵾ߩࠫࠣ߇ขࠅ

ઃߌࠄࠇߡ޿ࠆ㧚ࡠࡏ࠶࠻ߩᚻవ૏⟎ߦ߅ߌࠆㆇേߪ ਗㅴㆇേߩߺߦ㒢ቯߒߡ޿ࠆ߇㧘zゲ࿁ࠅߩ╩ߩ࿁ォ ߪⓄవ㧔╩ߩᲫߩవ┵ㇱಽ㧕ߩ⺞ᢛࠍⴕ߁ߚ߼ߦ㊀ⷐ ߥᓎഀࠍᨐߚߔߎߣ߆ࠄ㧘ࡌࠕ࡝ࡦࠣࠍ૶↪ߒߡ⥄↱

࿁ォࠍታ⃻ߒߡ޿ࠆ⁶⁾㧚

ታ㛎 ᦠሼേ૞ߦࠃࠆද⺞૞ᬺታ㛎

ታ㛎ߢߪ㧘ࡠࡏ࠶࠻ߦขࠅઃߌࠄࠇߚ╩ࠍੱ㑆߇ ᚻవߢᛠᜬߒ㧘⎮਄ߢⓄవߩ⺞ᢛࠍⴕߞߚ޽ߣߢ㧘

“

ห

”

ߩᢥሼࠍඨ⚕਄ߦឬߊታ㛎ࠍⴕ߁㧚ታ㛎⹜ⴕߪ㧘 㨇 ⹜ ⴕ

1

㨉 ࠗ ࡦ ࡇ ࡯ ࠳ ࡦ ࠬ ․ ᕈ ߇ ৻ ቯ ߩ ⹜ ⴕ

㧔D_R

=25Ns/m

㧕㧘㨇⹜ⴕ

2

㨉ੱ㑆ߩᚻవ೰ᕈଥᢙߦ

ᔕߓߡ☼ᕈଥᢙࠍ⺞ᢛߔࠆนᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮߦ ࠃࠆ⹜ⴕࠍⴕߞߚ㧚⹜ⴕ

2

ߢߪฦゲᣇะߩਗㅴㆇേߦ ኻߒߡ㧘ߘࠇߙࠇ⁛┙ߒߡ☼ᕈଥᢙߩ⺞ᢛࠍⴕߞߚ㧚 ߥ߅㧘ⵍ㛎⠪ߪᦠ㆏ߩ⚻㛎߇޽ࠆ

20

ᱦઍߩ↵ᕈߣߒ ߚ㧚

ታ㛎⚿ᨐߥࠄ߮ߦ⠨ኤ

Fig. 7

߆ࠄ

Fig. 8

ߦⵍ㛎⠪

A

ߦࠃࠆ

“

ห

”

ߩᢥሼߩ

1

↹⋡ߩ❑↹ㇱಽࠍឬ޿ߚߣ߈ߩyゲᣇะߩታ㛎࠺࡯

࠲ࠍ␜ߔ㧚

Fig. 9

ߦฦ⹜ⴕߦ߅ߌࠆ

2

ੱߩⵍ㛎⠪

A

㧘

B

ߦࠃࠆታ㛎⚿ᨐࠍ␜ߔ㧚

⹜ⴕ

1

ߩࠗࡦࡇ࡯࠳ࡦࠬ․ᕈ߇৻ቯߩታ㛎⚿ᨐߢߪ㧘 ඨ⚕਄ߢ╩ߩ૏⟎᳿߼ࠍⴕ߁⁁ᘒߦ޽ࠆᦠ߈ᆎ߼ㇱಽ

㧔

Fig. 7

ߩ

0

⑽߆ࠄ

2

⑽೨ᓟ㧕ߦ߅޿ߡੱ㑆ߩᚻవ೰

ᕈ߇㜞ߊߥࠅ㧘ࡠࡏ࠶࠻ߩᚻవ૏⟎ߩ゠〔߇ᝄേߒᆎ

߼ߡ޿ࠆ㧚૞ᬺਛ߽ੱ㑆߇ട߃ࠆജ㧘߅ࠃ߮ࡠࡏ࠶࠻

ߩᚻవ૏⟎ߩ゠〔߇ᝄേߒߡ޿ࠆߎߣ߇ࠊ߆ࠆ㧚ߎࠇ ߪੱ㑆ߩᚻవ೰ᕈଥᢙK_H߇

200N/m

એ਄ߦ਄᣹ߒ ߚߎߣߦࠃߞߡ㧘ࠪࠬ࠹ࡓ߇ਇ቟ቯߦߥࠆߎߣ߇ේ

࿃ߣ⠨߃ࠄࠇࠆ㧚߹ߚ㧘ੱ㑆߇ട߃ࠆജߩᄢ߈ߐ߇⹜

ⴕ

2

ߩ⚿ᨐࠃࠅ߽ᄢ߈޿ߎߣߦ㑐ߒߡߪ㧘ੱ㑆߇ᝄേ

ࠍᛥ߃ࠃ߁ߣߒߡᚻవ೰ᕈࠍߐࠄߦ㜞ߊߒߡജࠍട߃ ߡ޿ࠆߎߣ߇ේ࿃ߣ⠨߃ࠄࠇࠆ㧚⚿ᨐߣߒߡ㧘ߐࠄߦ ᝄേ߇ᄢ߈ߊߥࠅࠪࠬ࠹ࡓ߇ਇ቟ቯߥ⁁ᘒ߇⛯޿ߡ޿

-35 -25 -15 -5 5 15 25 35

-10 -5 0 5 10

0 2 4 6 8 10

Viscosity of robot

Time (sec)

Force (N)

Viscosity of robot (Ns/m)

Force 0 400 800 1200 1600

-0.5 -0.4 -0.3 -0.2

0 2 4 6 8 10

Time (sec)

Estimated stiffness (N/m) Trajectory of robot (m)

Estimated stiffness

Trajectory of robot

(a) Estimated stiffness and trajectory of robot (y-axis)

(b) Viscosity of robot and force (y-axis)

-120 -80 -40 0 40 80 120

-4 -2 0 2 4

0 2 4 6 8 10

Time (sec)

Force (N)

Viscosity of robot (Ns/m)

Force Viscosity of robot 0

200 400 600 800 1000 1200

-0.5 -0.4 -0.3 -0.2

0 2 4 6 8 10

Time (sec)

Estimated stiffness (N/m) Trajectory of robot (m)

Trajectory of robot Estimated stiffness

(a) Estimated stiffness and trajectory of robot (y-axis)

(b) Viscosity of robot and force (y-axis)

y

z x

(II) Variable (I) Invariable

(a) Subject A

(b) Subject B (II) Variable (I) Invariable

Fig.8. Experimental results of proposed variable impedance control in y-axis.

Fig.9. Experimental results of human-robot cooperative calligraphy.

Fig.7. Experimental results of conventional

constant impedance control in y-axis.

ࠆ㧚ߎࠇࠄߩᓇ㗀ߦࠃߞߡ

Fig. 9(a)-(I)

ߩ⚿ᨐߢߪ㧘 ឬ޿ߚᢥሼߩ✢᏷߇৻ቯߦߥࠄߥ޿ߛߌߢߥߊ㧘⋥✢

ㇱಽࠍ߹ߞߔߋߦឬߌߡ޿ߥ޿㧚߹ߚ㧘

Fig. 9(b)-(I)

߆ࠄ߽ห᭽ߩ⚿ᨐ߇ᓧࠄࠇߡ޿ࠆߎߣ߇ࠊ߆ࠆ㧚

⹜ⴕ

2

ߩนᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮߦࠃࠆታ㛎⚿ᨐߢ ߪ㧘ᦠ߈ᆎ߼ㇱಽ㧔

Fig. 8

ߩ

0

⑽߆ࠄ

2

⑽೨ᓟ㧕㧘߅ ࠃ߮⚳ੌᤨ㧔

6

⑽એ㒠㧕ߩㇱಽߦ߅޿ߡ㧘ੱ㑆ߩᚻవ

೰ᕈߪ㜞ߊߥߞߡ޿ࠆ߇㧘ߘࠇߦ઻ߞߡࡠࡏ࠶࠻ߩ☼

ᕈଥᢙ߇Ⴧടߔࠆࠃ߁⺞ᢛߐࠇࠆߚ߼㧘ࠪࠬ࠹ࡓߪਇ

቟ቯߦߥࠄߕ㧘ࡠࡏ࠶࠻ᚻవ૏⟎ߩ゠〔߽Ṗࠄ߆ߢ޽

ࠆ㧚߹ߚ㧘ᚻవ೰ᕈߩផቯ⚿ᨐ߇ࡠࡏ࠶࠻ߩࠗࡦࡇ࡯

࠳ࡦࠬ․ᕈߦ෻ᤋߐࠇߥ޿

0.02m/s

ࠍ⿧߃ࠆㅦᐲၞ

㧔

3

⑽߆ࠄ

6

⑽೨ᓟ㧕ߦ߅޿ߡ߽ࡠࡏ࠶࠻ᚻవ૏⟎ߩ

゠〔ߪ቟ቯߒߡ޿ࠆߎߣ߇ࠊ߆ࠆ ⁶⁾㧚

Fig. 9(a)-(II)

ߩ

⚿ᨐ߆ࠄߪ㧘ᢥሼߩ✢᏷߽৻ቯߦߥࠅ㧘⋥✢ㇱಽ߽

߹ߞߔߋߦឬߌߡ޿ࠆ㧚

Fig. 9(b)-(II)

ߩ⚿ᨐ߆ࠄ߽ห

᭽ߩߎߣ߇ࠊ߆ࠅ㧘นᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮߦࠃ ࠆ⹜ⴕߢߪ㧘߶߷ⷙ▸ߤ߅ࠅߩᢥሼ߇ឬߌߡ޿ࠆ㧚 ߎࠇࠄࠃࠅ㧘ᧄ⎇ⓥߢኻ⽎ߣߒߚࠪࠬ࠹ࡓߦ߅ߌࠆ ද⺞ᦠሼേ૞ߢߪ㧘Dࠍ

0.2

ߦ⸳ቯߔࠆߎߣߢࠪࠬ࠹

ࡓ߇ਇ቟ቯߦߥࠆߩࠍ࿁ㆱߢ߈ࠆߎߣ߇ࠊ߆ࠅ㧘ߘߩ ᅷᒰᕈࠍ␜ߔߎߣ߇ߢ߈ߚ㧚

એ਄ߩ⚿ᨐࠃࠅ㧘ੱ㑆ߩᚻవ೰ᕈߦᲧ଀ߒߡࠗࡦ ࡇ࡯࠳ࡦࠬ․ᕈߩ☼ᕈଥᢙࠍ⺞ᢛߔࠆนᄌࠗࡦࡇ࡯࠳

ࡦࠬ೙ᓮࠍ↪޿ࠆߎߣߢ㧘ද⺞૞ᬺਛߦᚻవ೰ᕈ߇㜞 ߊߥࠆ႐วߦ߅޿ߡ߽ࠪࠬ࠹ࡓ߇቟ቯߒߚ⁁ᘒߢ૞ᬺ

ࠍⴕ߃ࠆߎߣ߇ࠊ߆ࠆ㧚

߅ࠊࠅߦ

ᧄ⎇ⓥߢߪ㧘ੱ㑆ߩᚻవ೰ᕈଥᢙߩផቯ୯ߦᲧ଀ߒ ߚ☼ᕈଥᢙࠍࠗࡦࡇ࡯࠳ࡦࠬ․ᕈߣߒߡࡠࡏ࠶࠻ߦ⸳

ቯߔࠆนᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮߦ㑐ߔࠆ቟ቯ⸃ᨆࠍ ⴕߞߚ㧚ᢙ୯ࠪࡒࡘ࡟࡯࡚ࠪࡦߦࠃࠆ቟ቯ⸃ᨆࠍⴕ߁ ߎߣߢ㧘นᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮߦࠃߞߡࠪࠬ࠹ࡓߩ

቟ቯᕈ߇ะ਄ߔࠆߎߣࠍ⏕⹺ߒ㧘ߘߩ᦭ലᕈࠍ␜ߒߚ㧚

߹ߚ㧘ੱ㑆ߣࡠࡏ࠶࠻߇ജቇ⊛ߦද⺞ߒߥ߇ࠄᦠሼേ

૞ࠍⴕ߁ታ㛎ߢߪ㧘นᄌࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮࠍ↪޿ࠆ ߎߣߢࠪࠬ࠹ࡓ߇ਇ቟ቯߦߥࠄߕ㧘౞Ṗߥද⺞૞ᬺࠍ ⴕ߃ࠆߎߣࠍ␜ߒ㧘⸃ᨆߩኻ⽎ߣߒߚนᄌࠗࡦࡇ࡯࠳

ࡦࠬ೙ᓮߩᅷᒰᕈࠍ␜ߔߎߣ߇ߢ߈ߚ㧚

ߥ߅㧘ᧄ⎇ⓥߪᢥㇱ⑼ቇ⋭ޟ⍮⊛ࠢ࡜ࠬ࠲࡯ഃᚑ੐

ᬺޠߩᚑᨐߩ৻ㇱߢ޽ࠆ㧚

ෳ⠨ᢥ₂

1) H. Kazerooni, “Human-Robot Interaction via the Transfer of Power and Information Signals”, IEEE Transaction on systems, man and cybernetics, 20(2), 450-463 (1990).

2) R. Ikeura and H. Inooka, “Variable Impedance Control of a Robot for Cooperation with a Human”, IEEE international Conference on Robotics and Automation, 3097-3102 (1995).

3) ᳰᶆ⦟ᷕ㧘̌ੱ㑆ߣࡠࡏ࠶࠻ߦࠃࠆද⺞૞ᬺ㧘ࠪࠬ࠹

ࡓ㧛೙ᓮ㧛ᖱႎ̍㧘44(12)㧘682-687 (2000).

4) 㗇↰ℂᄩ㧘ዊ⩲৻ᒄ㧘ⷺ⼱ ໪㧘̌ࠝࡉࠫࠚࠢ࠻ࠗࡦ

ࡇ࡯࠳ࡦࠬߦၮߠߊੱߣ෺⣨ဳ⒖േࡠࡏ࠶࠻ߦࠃࠆ‛

૕ߩද⺞ࡂࡦ࠼࡝ࡦࠣ̍㧘ᯏળቇળ⺰ᢥ㓸㧯✬㧘 70(693)㧘1388-1394 (2004).

5) T. Takubo㧘H. Arai㧘Y. Hayashibara and K. Tanie,

“Human-Robot Cooperative Manipulation Using a Virtual Nonholonomic Constraint”, The International Journal of Robotics Research, 21(5-6), 541-553 (2002).

6) T. Tsumugiwa, R. Yokogawa and K. Hara, “Variable Impedance Control Based on Estimation of Human Arm Stiffness for Human-Robot Cooperative Calligraphic Task”, IEEE International Conference on Robotics and Automation, 644-650 (2002).

7) Ⓧ㓙 ᔀ㧘㒋ᧄ ᢕ㧘ᮮᎹ㓉৻㧘ේ ᢘ㧘̌ੱ㑆ߣࡠࡏ࠶

࠻ߦࠃࠆද⺞ㆇ៝࡮♖ኒߪ߼޽޿㧔Peg-in-Hole㧕૞ᬺ

ߦ߅ߌࠆ৻೙ᓮᴺ̍㧘ᯏળቇળ⺰ᢥ㓸㧯✬㧘70(689)㧘 69-76 (2004).

8) N. Hogan, “Stable execution of contact task using impedance control”, IEEE international Conference on Robotics and Automation, 1047-1054 (1987).

9) D. Surdilovic, “Contact Stability Issues in Position Based Impedance Control: Theory and Experiments”, Proceeding of the IEEE International Conference on Robotics and Automation, 1675-1680 (1996).

10) D. A. Lawrence, “Impedance Control Stability Properties in Common Implementations”, Proceeding of the IEEE International Conference on Robotics and Automation, 1185-1190 (1988).

11) J. E. Colgate and G. G. Schenkel, “Passivity of a class of sampled-data systems: application to haptic interfaces”, Journal of Robotic Systems, 14(1), 37-47 (1997).

12) ᭏ᵏ テ㧘⥪ ᥷㧘̌ࠗࡦࡇ࡯࠳ࡦࠬ೙ᓮߩធ⸅቟ቯᕈ ߦߟ޿ߡߩ৻⠨ኤ̍㧘ᣣᧄࡠࡏ࠶࠻ቇળ㧘12(3)㧘489- 496 (1994).

13) ㄞᢅᄦ㧘␹ሼ⧐ᒾ㧘ട⮮⨿ᔒ㧘㊄ሶ⌀㧘Ꮉ᧛⽵ᄦ㧘̌ࠗ

ࡦࡇ࡯࠳ࡦࠬ࡮࠻࡟࡯࠾ࡦࠣ㧦ੱ㑆ߪᚻవࠗࡦࡇ࡯࠳ࡦ

ࠬࠍ⸠✵ߦࠃࠅ⺞ᢛߢ߈ࠆߩ߆㧫̍㧘⸘᷹⥄േ೙ᓮቇળ

⺰ᢥ㓸㧘35(10) 㧘1300-1306 (1999).

14) ㄞ ᢅᄦ㧘ᓟ⮮๺ᒄ㧘દ⮮ብม㧘㐳↸ਃ↢㧘̌ᆫ൓⛽ᜬਛ ߩੱ㑆ߩᚻవࠗࡦࡇ࡯࠳ࡦࠬߩផቯ̍㧘⸘᷹⥄േ೙ᓮቇ ળ⺰ᢥ㓸㧘30(3) 㧘319-328 (1994).

15) ੖๧⵨┨㧘Ꮉੱశ↵㧘̌᳓ᐔ㕙ߦ߅ߌࠆᄙ㑐▵ㆇേਛߩ

ੱ⣨ᯏ᪾ࠗࡦࡇ࡯࠳ࡦࠬߩ⸘᷹̍㧘⸘᷹⥄േ೙ᓮቇળ⺰

ᢥ㓸㧘32(3)㧘369-378 (1996).

16) ᤊችᦸ㧘⿒Ỉၷㅧ㧘╭ㆇേ೙ᓮ♽㧘(ᤘᤩၴ㧘᧲੩㧘

1993).

17) T. Tsumugiwa㧘R. Yokogawa and K. Yoshida,

“Stability Analysis for Impedance Control of Robot in Human-Robot Cooperative Task System”, Journal of

Advanced Mechanical Design, Systems, and Manufacturing, 1(1), 113-121 (2007).

18) ⋧⦟▵ᄦ㧘឴ሶᳯ㧘๺↰ᷡ㧘̌ㅪ⛯ᤨ㑆♽ߩหቯ̍㧘

ࠪࠬ࠹ࡓ㧛೙ᓮ㧛ᖱႎ㧘37(5)㧘284-290 (1993).

19)  ጊᔀ㧘ࠪࠬ࠹ࡓหቯ౉㐷㧘(ࠪࠬ࠹ࡓ೙ᓮᖱႎቇળ㧘

੩ㇺ㧘 1994).

20) ᣣਣື਽㧘㕍ጊ⧷ᐽ㧘㐳↰ ᤼㧘ஜᐽ࡮૕ജ࡮⹏ଔ࡮

ၮḰ୯ㄉౖ㧘(ᩣᑼળ␠߉ࠂ߁ߖ޿㧘᧲੩㧘 1991).

21) Ⓧ㓙 ᔀ㧘ᮮᎹ㓉 ৻㧘ේ ᢘ㧘̌ᄙ⥄↱ᐲࠍ᦭ߔࠆု⋥ᄙ 㑐▵ဳࡠࡏ࠶࠻ߩࠦࡦࡊ࡜ࠗࠕࡦࠬߩ⸘᷹㧔7⥄↱ᐲࠍ

᦭ߔࠆࡠࡏ࠶࠻PA-10 ߳ߩㆡ↪㧕̍㧘ᯏળቇળ⺰ᢥ㓸 㧯✬㧘69(688)㧘3293-3300 (2003).