LIFE2013 2013年9月2日

GS3-4-34日 山梨 (山梨大学)⏬ീࢹ࣮ࢱࡢࡳࢆ⏝࠸ࡓᗙ఩ࣂࣛࣥࢫಖᣢᶵᵓࡢࣔࢹࣝ໬ModelingHumanBodies
BodiesWithwithImageImageData
ModelingofofSeatedSeated HumanDate‫ۑ‬๓⏣Ὀᘯ㸦᪂₲኱㝔㸧 ᖹඖ࿴ᙪ㸦᪂₲኱㸧 ᕘぢṊ⿱㸦⛅⏣኱㸧 ᓥ⏣ὒ୍㸦⛅⏣኱㸧Yasuhiro MAEDA, Graduate School of Niigata University
Kazuhiko HIRAMOTO, Niigata University
Takehiro IWAMI, Akita University
Yoichi SHIMADA, Akita University
Abstract: Modeling of the balancing mechanism of seated human bodies is carried out with experimental image data. In the present study, anew system identification method for the postural control of sitting human is proposed. We assume a two- link- rigid body mechanism as thedynamic model of sitting bodies. In the proposed method, the feedback/feedforward control law for the postural control and unknown bodysegment parameters (BSPs) of the sitting human body are identified simultaneously. Unknown parameters in the postural control and BSPs
are obtained so that the error between the angular velocity of a joint is minimized. It means that the accuracy of the system identification canbe evaluated directly with available (not computed) data. Moreover, the proposed system identification method does not need any reaction
force plate data. With the result for some subjects, the effectiveness of the proposed system identification method is examined.
Key Words: Modeling Human Bodies, System Identification, Human Balancing Mechanismࡣࡌࡵ࡟࡚࠸ࡿ࡜௬ᐃࡍࡿ㸬ࣜࣥࢡ㛫ࡢ㛵⠇ゅᗘࡣ㸪㌟య࡟㈞ࡾ

 ⌧ᅾ㸪᪥ᮏࡢ㌿ಽ஦ᨾࡢෆ㸪㧗㱋⪅ࡢ๭ྜࡀ 10㹼40%௜ࡅࡽࢀࡓ࣐࣮࢝ࢆࣅࢹ࣓࡛࢜࢝ࣛ᧜ᙳࡍࡿࡇ࡜࡟ࡼࡗ࡟࡞ࡗ࡚࠾ࡾ㸪ࡑࡢ࠺ࡕࡢ 5㹼10㸣ࡣ㦵ᢡࡋ࡚࠸ࡿ㸬ࡑࡢ࡚ᚓࡽࢀࡿ㸬๓㏙ࡢ๛యࣔࢹࣝ࡟ไᚚ⣔ࡀ௜ຍࡉࢀࡓࣂ⤖ᯝ㸪㦵ᢡ἞⒪ࡢࡓࡵࡢᏳ㟼⮩ᗋ࡟ࡼࡾయຊࡀపୗࡋ㸪ࣛࣥࢫಖᣢᶵᵓࢆ௬ᐃࡋ㸪ᐇ㦂࡟ࡼࡗ࡚ồࡵࡽࢀࡓ㐠ື᭱ᝏࡢሙྜ㸪ᐷࡓࡁࡾ࡟࡞ࡗ࡚ࡋࡲ࠺ྍ⬟ᛶࡀ࠶ࡿ㸬㌿ࢹ࣮ࢱࢆ⏝࠸࡚㐠ື᪉⛬ᘧࢆồࡵࡿ㸬ᮏࣜࣥࢡࣔࢹࣝࡢಽࡢཎᅉࡣ୺࡟㸪ຍ㱋࡟క࠺ࣂࣛࣥࢫ⬟ຊࡸṌ⾜⬟ຊࡢ㐠ື᪉⛬ᘧࡣ㸪ḟᘧ࡜࡞ࡿ㸬પሺࣂሻࣂሷ ൅ ‫ܐ‬൫ࣂǡ ࣂሶ൯ ൅ ܏ሺࣂሻ ൌ ࣎           పୗ࡟ࡼࡗ࡚㌿ಽࣜࢫࢡࡀቑ࠼ࡿࡇ࡜࡛࠶ࡾ㸪どぬ࣭๓ᗞჾ࣭యᛶឤぬࡢࣇ࢕࣮ࢻࣂࢵࢡ࡟ࡼࡿ⥲ྜⓗ࡞ࣂࣛࣥࢫ⬟ຊࡢᐃ㔞ⓗホ౯ࡸࣂࣛࣥࢫಖᣢ࣓࢝ࢽࢬ࣒ࡢゎ᫂࡜ຍ㱋࡟ࡼࡿ⬟ຊຎ໬ࡢᐃ㔞ⓗホ౯ࡀ㔜せ࡛࠶ࡿ㸬ࡋ࠿ࡋ㸪ேయࡢࣔࢹࣜࣥࢢࡣ㠀ᖖ࡟ᅔ㞴࡛࠶ࡿ࡜࡜ࡶ࡟㸪ே㛫ࡀ࡝ࡢࡼ࠺࡟ጼໃࢆไᚚࡋ࡚࠸ࡿࡢ࠿ࡣࡼࡃゎ᫂ࡉࢀ࡚࠾ࡽࡎ㸪ࡇࢀࡽࡢၥ㢟࡟ᑐࡍࡿゎỴ᪉ἲࡀồࡵࡽࢀ࡚࠸ࡿ㸬 ᮏሗ࿌࡛ࡣ㸪⏬ീࢹ࣮ࢱࡢࡳࢆ⏝࠸ࡓᗙ఩ࣂࣛࣥࢫಖᣢᶵᵓࡢࣔࢹࣜࣥࢢࢆ᳨ウࡍࡿ㸬ᗙ఩ጼໃ᫬ࡢ㌟యࢆ 2ࣜࣥࢡ๛యࣔࢹࣝ࡜௬ᐃࡋ㸪᧜ᙳࡉࢀࡓ⏬ീࡢࡳࢆ⏝࠸࡚㌟యࣃ࣓࣮ࣛࢱ࡜ጼໃไᚚࢆ⾜࠺ไᚚ๎ࢆྠ᫬࡟ồࡵࡿᡭἲࢆᥦ᱌ࡍࡿ㸬ࡇࡢᡭἲ࡛ࡣ㸪㛵⠇࣮࣓ࣔࣥࢺ࡞࡝ࡢෆຊࢆᇶ‽࡜ࡋࡓྠᐃᡭἲ࡜ࡣ␗࡞ࡾ㸪ྠᐃࡉࢀࡓࣔࢹࣝࡢⰋྰࢆ㐠ືࢹ࣮ࢱ࠿ࡽ┤᥋ホ౯ྍ⬟࡛࠶ࡿ࡜ྠ᫬࡟㸪ᗙ㠃ࡢ཯ຊࡢィࡶ୙せ࡛࠶ࡿ࡜࠸࠺࣓ࣜࢵࢺࡀ࠶‫ܯ‬ଵଶ൨‫ܯ‬ଶଶ‫ܯ‬ଵଵ ൌ ݉ଵ ݈ଵଶ ൅ ‫ܫ‬ଵ ൅ ݉ଶ ሺ݈ଵ ൅ ݈ଶଷ ሻଶ ൅ ݉ଶ ݈ଶଶ൅ʹ݉ଶ ݈ଶ ሺ݈ଵ ൅ ݈ଶଷ ሻଶሺ݈‫ܯ‬ଵଶ ൌ ݉ଶ ݈ଶ ൅ ݉ଶ ݈ଶ ଵ ൅ ݈ଶଷ ሻ ܿ‫ߠ ݏ݋‬ଶ ൅ ‫ܫ‬ଶ‫ܯ‬ଶଵ ൌ ‫ܯ‬ଵଶ ߠଶ ൅ ‫ܫ‬ଶ‫ܯ‬ଶଶ ൌ ݉ଶ ݈ଶଶ ൅ ‫ܫ‬ଶ‫ܐ‬൫ࣂǡ ࣂሶ൯ ൌ ቈെ݉ଶ ݈ଶ ሺ݈ଵ ൅ ݈ଶଷ ሻ  ߠଶ ሺʹߠଵሶ ߠଶሶ ൅ ߠሶଶଶ ሻ ൅ ʹܿ଴ ሺߠଵሶ െ ߠ௦ሶ ሻ቉െ݉ଶ ݈ଶ ሺ݈ଵ ൅ ݈ଶଷ ሻ  ߠଶ ߠଵሶ ߠଶሶଵ܏ሺࣂሻ ൌ ቂ ቃଶଵ ൌ െ݉ଵ ݈݃ଵ  ߠଵ ൅ ʹ݇ଵ ሺߠଵ െ ߠ௦ ሻെ݉ଶ ݃ሺ݈ଵ ൅ ݈ଶଷ ሻ  ߠଵ െ ݈ଶ ሺߠଵ ൅ ߠଶ ሻ ଶ ൌ െ݉ଶ ݈݃ଶ ሺߠଵ ൅ ߠଶ ሻࡇࡇ࡛ θ ࡣࣜࣥࢡゅᗘ㸪I ࡣ㔜ᚰ࿘ࡾࡢ័ᛶ࣮࣓ࣔࣥࢺ㸪ࡿ㸬‫ܯ‬પሺࣂሻ ൌ ൤ ଵଵ‫ܯ‬ଶଵ(1)    m ࡣࣜࣥࢡ㉁㔞㸪l ࡣࣜࣥࢡ㛗㸪τ ࡣ㛵⠇ࢺࣝࢡ㸪k ࡣࡤࡡᗙ఩ጼໃಖᣢᶵᵓࡢࣔࢹࣝ໬ ᮏ◊✲࡛ࡣᗙ఩ጼໃ᫬ࡢࣂࣛࣥࢫಖᣢ࡟᭱ࡶᐤ୚ࡍࡿ

ᐃᩘ㸪c ࡣῶ⾶ಀᩘ࡛࠶ࡿ㸬ࡲࡓῧᏐࡣ㸪s ࡀᗙ㠃㸪1 ࡀ࡜⪃࠼ࡽࢀ࡚࠸ࡿ➨஧㸪➨୕⭜᳝㛫ࡢࢺࣝࢡ࡟ὀ┠ࡋ㸪ୗయ㸪2 ࡀୖయ㸪23 ࡀ⭜㒊ࢆ⾲ࡍ㸬ᗙ఩ጼໃࡢே㛫ࢆᅗ 1 ࡢࡼ࠺࡞➨஧➨୕⭜᳝㛫࡛ศ๭ࡉ ྛ⠇ࡢ㔜ᚰࡣ㛵⠇㛫㍈ୖ࡟఩⨨ࡍࡿ࡜௬ᐃࡋ㸪ྛ㛵⠇

ࢀࡓ 2 ࣜࣥࢡࡢ๛యࣔࢹ࡛ࣝ⾲ࡍ㸬ࡉࡽ࡟㸪௬᝿ⓗ࡞ࡶࡢ⢓ᙎᛶࡣ↓どࡍࡿ㸬ࡲࡓ㸪័ᛶ୺㍈࡜ྛ⠇ࡢᗙᶆ⣔ࡣࡢ࡜ࡋ࡚ᗙ㠃࠿ࡽ➨஧➨୕⭜᳝㛫࿘㎶ࡢ➽㦵᱁⣔ࡀᗙ㠃୍⮴ࡍࡿ㸬ࡲࡓ㸪ୗ⫥ࡢᙳ㡪ࢆ⪃៖ࡍࡿࡓࡵ㸪⭜㒊ࣜࣥ࡟ࡤࡡࡸࢲࣥࣃ࡛᥋⥆ࡉࢀࡓ➽㦵᱁⣔࡛࠶ࡿ࡜௬ᐃࡍࡿ㸬ࢡ࡟ࡣୗ⫥ࡢ㉁㔞㸪័ᛶຊࢆྵࡵࡓ㸬⠇㉁㔞ࡣయ㉁㔞࡜ᗙ఩ࣂࣛࣥࢫಖᣢࡢࡓࡵ࡟㛵⠇࡛Ⓨ⏕ࡍࡿࢺࣝࢡࡣ㛵⠇⠇㛗ࢆ⏝࠸ࡓᅇᖐᘧ࡟ࡼࡾ᥎ᐃࡋࡓ㸬ࡲࡓ㸪⠇័ᛶ࣮ࣔゅᗘ㸪ᗙ㠃ゅᗘ࡞࡝ࡢ᝟ሗࢆ⏝࠸ࡿࡇ࡜࡟ࡼࡗ࡚Ⓨ⏕ࡋ࣓ࣥࢺࡶྠᵝ࡟ࡋ࡚ồࡵࡓ㸬

GS3-4-3-1

LIFE2013 2013年9月2日
݈ଶߠଶ

4日 山梨 (山梨大学)

 ᗙ㠃ࡢືࡁࡀ࿘ᮇⓗ࡛࠶ࡿࡇ࡜ࢆ⪃៖ࡋ㸪ே㛫ࡀᗙ㠃ࡢゅᗘࡸゅ㏿ᗘࢆࡶ࡜࡟ࣇ࢕࣮ࢻࣇ࢛࣮࣡ࢻไᚚࢆ⾜ࡗ࡚࠸ࡿ࡜௬ᐃࡍࡿ㸬ไᚚ๎ࡣ௨ୗ࡛⾲ࡉࢀࡿ㸬݉ଶ ǡ ‫ܫ‬ଶ݉ଵ ǡ ‫ܫ‬ଵ݈ଶଷɒ

ߠଵߠ௦‫ݑ‬௙௙ ൌ ‫ܨ‬௙ ൤ ሶ ൨ߠ௦ࡇࡇ࡛‫ܨ‬௙ ࡣࣇ࢕࣮ࢻࣇ࢛࣮࣡ࢻࢤ࢖ࣥ⾜ิ࡛࠶ࡿ㸬‫ܨ‬௙ ࢆkc௨ୗࡢࡼ࠺࡟⾲ࡍ㸬ᗙ㠃‫ܨ‬௙ ൌ ൣ݂௙ଵ

ߠ௦

݈ଵ

(4)

݂௙ଶ ൧(5)ᇶ‽㠃㛵⠇࣮࣓ࣔࣥࢺ

Figure1: Rigid link model of human body

3-1㸪3-2 ⠇ࡼࡾ㸪ᗙ఩ࣂࣛࣥࢫಖᣢࡢࡓࡵࡢ㛵⠇࣮࣓ࣔᩥ ⊩ [1]࡛ ࡣ ༙⌫ ≧ ࡢᗙ 㠃ࢆ ⏝ ࠸࡚ ᗙ఩ ጼ ໃࡢࣔ ࢹ ࣝ ໬ࢆ⾜ࡗ࡚࠸ࡿࡀ㸪ࡑࡢࣔࢹ࡛ࣝࡣึᮇ᮲௳࡟ᑐࡍࡿࣂࣛࣥࢫಖᣢືసࡔࡅࡀᑐ㇟࡜࡞ࡾ㸪ᣢ⥆ⓗ࡞እ஘࡟ᑐࡍࡿࣥࢺࡣ௨ୗࡢࡼ࠺࡟⾲ࡉࢀࡿ㸬ɒ ൌ ‫ݑ‬௙௕ ൅ ‫ݑ‬௙௙(6) 㠀⥺ᙧᛶไᚚࣂࣛࣥࢫಖᣢࣔࢹࣝࢆྠᐃࡍࡿࡇ࡜ࡀ࡛ࡁ࡞࠸㸬୍᪉㸪 ࢩࢫࢸ࣒ࡢ㠀⥺ᙧᛶࢆ⪃៖ࡋ࡚㸪㠀⥺ᙧᛶไᚚ๎ࢆຍᮏሗ࿌ࡢᡭἲ࡛ࡣ㸪ᗙ㠃࡜㌟యࢆ௬᝿ⓗ࡞ࡤࡡ㸪ࢲࣥࣃ࠼㸪㛵⠇ゅᗘࡢᚤศ್ࡢ⣼஌࡟ẚ౛ࡋࡓ㠀⥺ᙧࣇ࢕࣮ࢻ࡛᥋⥆ࡉࢀࡓࣔࢹࣝࢆ⪃࠼ࡿࡇ࡜࡟ࡼࡗ࡚㸪ᣢ⥆ⓗ࡞እࣂࢵࢡࢺࣝࢡ㸪㠀⥺ᙧ᚟ඖࢺࣝࢡ࡜㠀⥺ᙧῶ⾶ࢺࣝࢡࡀ஘࡛࠶ࡿᗙ㠃ࡢゅᗘኚືࢆධຊ࡜ࡋࡓᗙ఩ࣂࣛࣥࢫಖᣢⓎ⏕ࡋ࡚࠸ࡿ࡜௬ᐃࡋࡓ㸬ࡑࢀࡒࢀࡢࢺࣝࢡࢆḟᘧࡢࡼᶵᵓࡢྠᐃࡀྍ⬟࡟࡞ࡿ㸬࠺࡟⾲ࡍ㸬ଶଷȣ߆௡ܷ௙௕ ൌ ൬‫ܨ‬௕ଵ ቂ ሶ ቃ ൅ ‫ܨ‬௕ଶ ൤߆ ଶ ൨ ൅ ‫ܨ‬௕ଶ ൤߆ ଷ ൨ ൅ ‫ ڮ‬൅ ‫ܨ‬௕௡ ቂ ሶ ௡ ቃ൰ሶሶȣ߆߆߆ࣂࣛࣥࢫಖᣢᶵᵓࡢྠᐃ ᮏ◊✲࡛ࡣ㸪ᗙ఩ࣂࣛࣥࢫಖᣢᶵᵓࡀ㸪ᗙ㠃࠿ࡽࡢእ஘ࡸ㸪ࡑࢀ࡟ࡼࡗ࡚⏕ࡎࡿ㛵⠇ゅᗘࡸゅ㏿ᗘࡢ᝟ሗࢆ⏝࠸࡚㸪๓㏙ࡢࣜࣥࢡᶵᵓࡢ➨ 2㸪3 ⭜᳝㛫ࡢ㛵⠇࣮࣓ࣔࣥߠ௦ߠ௦௡ߠଶߠଷܷ௙௙ ൌ ቆ‫ܨ‬௙ଵ ൤ ሶ ൨ ൅ ‫ܨ‬௙ଶ ቈ ௦ଶ ቉ ൅ ‫ܨ‬௙ଷ ቈ ௦ଷ ቉ ൅ ‫ ڮ‬൅ ‫ܨ‬௙௡ ൤ ሶ ௡ ൨ቇߠ௦ߠ௦ߠሶ௦ߠሶ௦(7)(8)‫ ܭ‬ൌ ʹ ൈ ሼ݇ଵ ሺߠଵ െ ߠ௦ ሻ ൅ ݇ଶ ሺߠଵ െ ߠ௦ ሻଶ ൅ ‫ ڮ‬൅ ݇௡ ሺߠଵ െ ߠ௦ ሻ௡ ሽ(9)ଶ௡๎ࡣ㸪ᗙ㠃እ஘ゅᗘࡸゅ㏿ᗘࢆ┤᥋⏝࠸ࡿࣇ࢕࣮ࢻࣇ࢛‫ ܥ‬ൌ ʹ ൈ ቄܿ଴ ൫ߠሶଵ െ ߠሶ௦ ൯ ൅ ܿଵ ൫ߠሶଵ െ ߠሶ௦ ൯ ൅ ‫ ڮ‬൅ ܿ௡ ൫ߠሶଵ െ ߠሶ௦ ൯ ቅ (10)࣮࣡ࢻไᚚ࡜㛵⠇ゅᗘࡸゅ㏿ᗘࡢࣇ࢕࣮ࢻࣂࢵࢡไᚚࢆ

ࡿࡇ࡜࡟ࡼࡗ࡚㸪ࣂࣛࣥࢫಖᣢไᚚ๎ࡢ㠀⥺ᙧᛶࢆࡼࡾ⪃࠼ࡿ㸬ࡲࡓ㸪ไᚚ࡛ࡣ⏝࠸ࡽࢀࡿほ኱ࡁࡃホ౯ࡋ࡚࠸ࡿ࡜ゝ࠼ࡿ㸬ࢺࢆⓎ⏕ࡍࡿࡇ࡜࡟ࡼࡗ࡚㸪㛵⠇ゅᗘࢆᑠࡉࡃࡍࡿࡼ࠺࡞ไᚚࢆ⾜࠺ࡶࡢ࡜⪃࠼ࡿ㸬ࣂࣛࣥࢫಖᣢࡢࡓࡵࡢไᚚࢹ࣮ࢱ ౛ᗙ㠃ࡇࡇ࡛㸪n ࡣ⿕㦂⪅ࡈ࡜࡟ኚ࠼ࡿࡇ࡜࡜ࡋ㸪n ࢆ኱ࡁࡃࡍゅᗘ ࡢ⣼஌ࡢ㡯ࢆᑟධࡋࡓ㠀⥺ᙧไᚚࡶ⪃៖ ࡋ࡚࠸ࡿ㸬 ྠᐃᡭἲ ᮏ◊✲࡛ࡣ㸪ୖグࡢไᚚᶵᵓ୰ࡢࢤ࢖ࣥࡢ್࡜㸪ࡉࡽ ᮏ◊✲࡛ࡣ㸪3-1㹼3-4 ⠇࡛⪃࠼ࡓไᚚᶵᵓ୰ࡢࣃ࣓ࣛ࡟㸪⏕యࡢ㌟యࣃ࣓࣮ࣛࢱ࡛࠶ࡿ๓⠇࡛♧ࡋࡓࣜࣥࢡ⣔࣮ࢱ࡜㸪ᘧ(1)୰ࡢ㌟యࣃ࣓࣮ࣛࢱࢆ㸪᧜ᙳࡉࢀࡓື⏬࠿ࡢࣃ࣓࣮ࣛࢱ ࣜࣥࢡ㉁㔞࡞࡝ ࡢኚᩘࢆ㸪ᐇ㦂࡛ᚓࡽࢀࡽᚓࡽࢀࡿࣜࣥࢡゅᗘ㸪ゅ㏿ᗘࢹ࣮ࢱࡢࡳࢆ⏝࠸࡚ྠᐃࡓࢹ࣮ࢱࢆඖ࡟ྠᐃࡍࡿ㸬ࡇࡢྠᐃၥ㢟࡛ࡣ㸪ྠᐃㄗᕪࡍࡿ㸬௨ୗ࡛ᡭἲࢆ♧ࡍ㸬ᘧ(1)㸫(10)ࢆ⏝࠸ࡿ࡜㸪ไᚚᶵᵓࢆྵࢇࡔ๛యࣜࣥࢡ⣔ࡀྠᐃࡉࢀࡿࣃ࣓࣮ࣛࢱ࡟㛵ࡍࡿ⥺ᙧ㛵ᩘ࡛⾲ࡉࢀ࡞࠸ࡓࡵ㸪㏻ᖖࡢ᭱ᑠ஧஌ἲ࡟ࡼࡿࣃ࣓࣮ࣛࢱྠᐃἲࢆ㐺⏝ࡣ㸪௨ୗࡢࡼ࠺࡞㠀⥺ᙧ≧ែ᪉⛬ᘧ࡛⾲ࡉࢀࡿ㸬ࡍࡿࡇ࡜ࡀ࡛ࡁ࡞࠸㸬ᮏ◊✲࡛ࡣ㸪ᒁᡤࣛࣥࢲ࣒᥈⣴࡟ ࣜࣥࢡᶵᵓࡢ㛵⠇࡟ࡣ࢔ࢡࢳ࢚࣮ࣗࢱࡀタ⨨ࡉࢀ㸪ࣂௗఏሺ௧ሻߠሶ ሺ‫ݐ‬ሻௗ௧൩ቈ቉ൌ൥ߠሷ ሺ‫ݐ‬ሻ݂൛ߠሺ‫ݐ‬ሻǡ ߠሶ ሺ‫ݐ‬ሻൟࣛࣥࢫಖᣢࡢࡓࡵࡢࢺࣝࢡ 㛵⠇࣮࣓ࣔࣥࢺ ࢆⓎ⏕ࡋ࡚ᶵᵓࡢࣃ࣓࣮ࣛࢱࢆ࠶ࡿ್࡟ࡋࡓ࡜ࡁ㸪ࣜࣥࢡゅ㏿ᗘ࣋࠸ࡿ࡜ࡍࡿ㸬㛵⠇࣮࣓ࣔࣥࢺࡣ㛵⠇ゅᗘࡸゅ㏿ᗘࡢ᝟ሗࢡࢺࣝࡢȟ⛊ᚋࡢண ್(ࡢ㏆ఝ)ࢆ௨ୗ࡛⾲ࡍ㸬ߠ௙ሶ ሺ‫ ݐ‬൅ ߂‫ݐ‬ሻ ؆ ߠሶ௘ ሺ‫ݐ‬ሻ ൅ ߂ߠሷ௥ ሺ‫ݐ‬ሻ㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 (12)㻌

ࡼࡗ࡚ࣃ࣓࣮ࣛࢱࢆྠᐃࡍࡿ㸬 ࣇ࢕࣮ࢻࣂࢵࢡไᚚࢆ⏝࠸࡚Ỵᐃࡉࢀ࡚࠸ࡿ࡜௬ᐃࡋ㸪ࡇࡇ࡛ࡣఱࡽ࠿ࡢࣇ࢕࣮ࢻࣂࢵࢡไᚚࢆ⾜ࡗ࡚࠸ࡿ࡜⪃࠼ࡿ㸬߆‫ݑ‬௙௕ ൌ െ‫ܨ‬௕ ቂ ሶ ቃ
߆

(2)

(11)

⌧ᅾ᫬้ࢆ t ࡜ࡍࡿ㸬ࣜࣥࢡ⣔ࡢ㌟యࣃ࣓࣮ࣛࢱࡸไᚚ

ࡇࡇ࡛㸪ߠሶ௘ ሺ‫ݐ‬ሻࡣ㸪᧜ᙳࡉࢀࡓື⏬࠿ࡽᚓࡽࢀࡓゅ㏿ᗘ࣋ࢡࢺࣝࡢᐇ㦂್࡛࠶ࡾ㸪ߠሷ௥ ሺ‫ݐ‬ሻࡣ㸪ᘧ(11)ߠሺ‫ݐ‬ሻ࠾ࡼࡧߠሶሺ‫ݐ‬ሻ࡟㸪ࡇࡇ࡛‫ܨ‬௕ ࡣࣇ࢕࣮ࢻࣂࢵࢡࢤ࢖ࣥ⾜ิ࡛࠶ࡿ㸬‫ܨ‬௕ ࢆḟࡢࡼࡑࢀࡒࢀߠ௘ ሺ‫ݐ‬ሻ࠾ࡼࡧߠሶ௘ ሺ‫ݐ‬ሻࢆ௦ධࡍࡿࡇ࡜࡟ࡼࡗ࡚ᚓࡽࢀ
ࡿゅຍ㏿ᗘ࣋ࢡࢺࣝࡢ᥎ᐃ್࡛࠶ࡿ㸬ߠሷ௥ ሺ‫ݐ‬ሻࡣ㸪ᘧ(11)ࡢ㛵(3)ࣜࣥࢡᶵᵓ୰ࡢ㌟యࣃ࣓࣮ࣛࢱࡸ㸪ไᚚᶵᵓ୰ࡢࣃ࣓ࣛ

࠺࡟⪃࠼ࡿ㸬‫ܨ‬௕ ൌ ሾ݂௕ଵ݂௕ଶ

݂௕ଷ݂௕ସ ሿࣇ࢕࣮ࢻࣇ࢛࣮࣡ࢻไᚚ

ᩘ݂൛ߠሺ‫ݐ‬ሻǡ ߠሶ ሺ‫ݐ‬ሻൟࡀ☜ᐃࡋࡓ࡜ࡁ㸪ࡍ࡞ࢃࡕ㸪ᘧ(1)㹼(10)ࡢ

࣮ࢱࡀ࠶ࡿ್࡟ᅛᐃࡉࢀ࡚࠸ࢀࡤồࡵࡿࡇ࡜ࡀ࡛ࡁࡿ㸬

GS3-4-3-2

LIFE2013 2013年9月2日
θ್䢳ᐇ㦂࡟ࡼࡗ࡚ᚓࡽࢀࡓゅ㏿ᗘ࣋ࢡࢺࣝࡢᐇ㦂್ߠሶ௘ ሺ‫ݐ‬ሻ࡜㸪࠶ࡿࣂࣛࣥࢫಖᣢࣔࢹࣝࢆ௬ᐃࡋ࡚ᚓࡽࢀࡓゅ㏿ᗘ࣋ࢡࢺࣝߠ௙ሶ ሺ‫ݐ‬ሻ࡜ࡢㄗᕪ࣋ࢡࢺࣝࡣ㸪ḟᘧ࡛ᐃ⩏ࡉࢀࡿ㸬ߠ௙ ሺ‫ݐ‬ሻ െ ߠ௘ ሺ‫ݐ‬ሻ݁ሺ‫ݐ‬ሻ ൌ ቈ ሶ቉㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 (13)㻌
ߠ௙ ሺ‫ݐ‬ሻ െ ߠሶ௘ ሺ‫ݐ‬ሻAngularvelocity [rad/s]䣘䣧䣮䣱䣥䣫䣶䣻䢢䣝䣴䣣䣦䢱䣵䣟ྠᵝࡢᡭἲ࡛㸪ᘧ(11)ࢆ⏝࠸࡚ኚ఩࣋ࢡࢺࣝࡢணߠ௙ሶ ሺ‫ ݐ‬൅ ߂‫ݐ‬ሻࡶồࡵࡿࡇ࡜ࡀ࡛ࡁࡿ㸬

4日 山梨 (山梨大学)

䢲䢰䢲䢶
䢲䢰䢲䢴
䢲䢯䢲䢰䢲䢴䢯䢲䢰䢲䢶䢯䢲䢰䢲䢸䢲ᘧ(13)ࢆ⏝࠸࡚㸪ྠᐃㄗᕪࢆホ౯ࡍࡿホ౯㛵ᩘࢆ௨ୗࡢ䢷䢳䢲䢳䢷䢴䢲䢴䢷

䣶䢢䣝䣵䣧䣥䣟
θࡼ࠺࡟ᐃ⩏ࡍࡿ㸬

ࡇࡇ࡛㸪Q ࡣ㔜ࡳ⾜ิ࡛࠶ࡿ㸬

ᘧ(14)ࡢホ౯㛵ᩘ‫ࢆܬ‬᭱ᑠ࡜ࡍࡿࡼ࠺࡞ࣜࣥࢡᶵᵓ࠾ࡼࡧไᚚᶵᵓࡢࣃ࣓࣮ࣛࢱࢆ㸪ᒁᡤࣛࣥࢲ࣒᥈⣴ࢆ⏝࠸࡚ồࡵࡿ㸬ᒁᡤࣛࣥࢲ࣒᥈⣴ࢆ⾜࠺㝿㸪㌟యࣃ࣓࣮ࣛࢱ࡟
ࡣ㸪ᩥ⊩[2]ࢆཧ⪃࡟ࡋ࡚ୖ㝈࡜ୗ㝈ࢆタࡅ㸪ྠᐃࡉࢀࡿ䢴

Angularvelocity [rad/s]䣘䣧䣮䣱䣥䣫䣶䣻䢢䣝䣴䣣䣦䢱䣵䣟௧‫ ܬ‬ൌ ‫׬‬଴ ݁ሺ‫ݐ‬ሻܳ݁ሺ‫ݐ‬ሻ் ݀‫ݐ‬㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 (14)㻌

䢢䢲䢰䢳䢲䢰䢲䢷䢲䢯䢲䢰䢲䢷䣕䣫䣯䣷䣮䣣䣶䣫䣱䣰䢪䣰䣱䣰䣮䣫䣰䣧䣣䣴䢫䢯䢲䢰䢳 䢢䢲䢷䢳䢲䢳䢷䢴䢲䣇䣺䣲䣧䣴䣫䣯䣧䣰䣶ࣃ࣓࣮ࣛࢱࡀ⌧ᐇⓗ࡞್ࢆᣢࡘࡼ࠺࡟ࡋࡓ㸬䣶䢢䣝䣵䣧䣥䣟䢴䢷䣕䣫䣯䣷䣮䣣䣶䣫䣱䣰

Figure2: Joint angle velocity of the Subject1⤖ᯝ ᥦ᱌ࡍࡿྠᐃᡭἲࢆ 2 ྡࡢ⿕㦂⪅࡟ᑐࡋ࡚㐺⏝ࡋࡓ㸬ࡲࡓ㸪⌮ㄽ್࡜ᐇ㦂್ࡢᕪ࠿ࡽィ⟬ࡉࢀࡓホ౯㛵ᩘ J ࡢ್ࡶేࡏ࡚♧ࡍ㸬Table1: Subject anthropometric data
SubjectSex

Age

Height [m]Weight [kg]

1

Male

22

1.68

52.0

2

Male

24

1.70

76.0䢳

䢲䢰䢳䣘䣧䣮䣱䣥䣫䣶䣻䢢䣝䣴䣣䣦䢱䣵䣟࡟㸪ྛ⿕㦂⪅࡟ᑐࡋ࡚ྠᐃࡉࢀࡓ㌟యࣃ࣓࣮ࣛࢱࢆ♧ࡍ㸬θAngular velocity [rad/s]

⾲ 1 ࡟㸪⿕㦂⪅ 2 ྡࡢࡑࢀࡒࢀࡢ㌟యࢹ࣮ࢱࢆ♧ࡍ㸬⾲ 2䢲䢰䢲䢷䢲䢯䢲䢰䢲䢷䢯䢲䢰䢳
䢲

䢷

䢳䢲䢳䢷

䢴䢲䢴䢷䣶䢢䣝䣵䣧䣥䣟θ

Angularvelocity [rad/s]䣘䣧䣮䣱䣥䣫䣶䣻䢢䣝䣴䣣䣦䢱䣵䣟䢴

Table2: Result of the system identification(Body segmentparameters and the evaluation function)
Subject
݉ଵ
ଵ

݉ଶ
ଶ

݈ଵ

[kg]
[݉ ଶ][kg]

220.03941.0032.984

2.8431䢲䢰䢲䢶䢲䢰䢲䢴
䢲
䢯䢲䢰䢲䢴
䢯䢲䢰䢲䢶
䢯䢲䢰䢲䢸

䣕䣫䣯䣷䣮䣣䣶䣫䣱䣰䢪䣰䣱䣰䣮䣫䣰䣧䣣䣴䢫䢯䢲䢰䢲䢺 䢢䢲䢷䢳䢲䢳䢷䣶䢢䣝䣵䣧䣥䣟

20.238䢴䢲䣇䣺䣲䣧䣴䣫䣯䣧䣰䣶䢴䢷䣕䣫䣯䣷䣮䣣䣶䣫䣱䣰25.072Figure3: Joint angle velocity of the Subject2[݉ ଶ]2.99512.8873[m]

0.24358

0.38953[m]0.20060.20598⢭ᗘ࡛ྠᐃࡍࡿࡇ࡜࡛ࡁࡓࡀ㸪ࡉࡽ࡟㠀⥺ᙧไᚚࢆᑟධ

[m]

0.299360.3971ࡍࡿࡇ࡜࡟ࡼࡗ࡚ྠᐃ⢭ᗘࡣྥୖࡋ࡚࠸ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬

0.1163

0.09305݈ଶଷ݈ଶ1䢢䢲䢰䢲䢸

J୍᪉㸪⿕㦂⪅ 2 ࡟㛵ࡋ࡚ࡣ㸪⥺ᙧไᚚࡔࡅࡢሙྜ㸪≉࡟ߠଶ ࡟࠾࠸࡚ㄗᕪࡀ኱ࡁࡃ࡞ࡗ࡚࠸ࡿࡢ࡟ᑐࡋ㸪㠀⥺ᙧᛶไᚚࢆ⪃៖ࡋྠᐃࡍࡿࡇ࡜࡟ࡼࡗ࡚㸪ྠᐃ⢭ᗘࡀ኱ᖜ࡟

ᅗ 2-3 ࡣ㸪๓㏙ࡢ 2 ࡘࡢ㛵⠇ゅ㏿ᗘࡢ᫬้Ṕ࡛࠶ࡾ㸪㉥Ⰽྥୖࡋࡓ㸬ࡇࡢ⤖ᯝࡼࡾ㸪ᮏ◊✲࡛⏝࠸ࡓྠᐃἲࡢ᭷ຠ
ࡢᐇ⥺ࡀ㸪㛵⠇ゅᗘࢆ᫬㛫ᚤศࡋࡓ㛵⠇ゅ㏿ᗘ ᐇ㦂್ᛶࡀ♧ࡉࢀ࡚࠸ࡿ㸬࡛࠶ࡾ㸪◚⥺ࡀ㐠ືࢹ࣮ࢱࢆ⏝࠸࡚ 1 ࢫࢸࢵࣉඛࡢᛂ⟅ࢆணࡲ࡜ࡵࡋồࡵࡽࢀࡓ㛵⠇ゅ㏿ᗘ ⌮ㄽ್ ࢆ⾲ࡋ࡚࠸ࡿ㸬 ᮏ✏࡛ࡣᗙ఩ጼໃ᫬ࡢேయࣔࢹࣝࢆᥦ᱌ࡋ㸪㛵⠇ゅ㏿⥳Ⰽࡢ◚⥺ࡣ㸪㠀⥺ᙧᛶไᚚࢆ⪃៖ࡋ࡞࠸ࣇ࢕࣮ࢻࣂࢵ
ᗘࡢྠᐃࢆ⾜ࡗࡓ㸬ࣂࣛࣥࢫಖᣢไᚚࡀ㸪ࣇ࢕࣮ࢻࣂࢵࢡไᚚ࡜ࣇ࢕࣮ࢻࣇ࢛࣮࣡ࢻไᚚࡔࡅ࡛ồࡵࡽࢀࡓ⌮ㄽࢡ࠾ࡼࡧࣇ࢕࣮ࢻࣇ࢛࣮࣡ࢻไᚚせ⣲㸪ࡤࡡ࡟ࡼࡿ᚟ඖ
್࡛࠶ࡾ㸪㟷Ⰽࡢ◚⥺ࡀ㠀⥺ᙧᛶไᚚࢆ⪃៖ࡋ࡚ྠᐃࢆ
ࢺࣝࢡ࡜ࢲࣥࣃ࡟ࡼࡿῶ⾶ࢺࣝࢡ࡟ࡼࡗ࡚⾜ࢃࢀ࡚࠸ࡿ⾜ࡗࡓ⤖ᯝࢆ⾲ࡋ࡚࠸ࡿ㸬ྠᐃࡉࢀࡓ⤖ᯝࡣ㸪⿕㦂⪅ 1࡜௬ᐃࡋ㸪㛵⠇ゅ㏿ᗘࡢྠᐃࢆ⾜࠸㸪ᐇ㦂್࡟㏆ఝࡍࡿ࡟㛵ࡋ࡚ࡣ㠀⥺ᙧไᚚ⪃៖ࡋ࡞࠸ሙྜ࡛ࡶ࠶ࡿ⛬ᗘ㧗࠸㛵⠇ゅ㏿ᗘࡢᛂ⟅ࢆồࡵࡿࡇ࡜ࡀ࡛ࡁࡓ㸬ࡲࡓ㸪᭱㐺໬

GS3-4-3-3

LIFE2013 2013年9月2日
ᡭἲ࡟ᇶ࡙ࡃྠᐃᡭἲ⏝࠸࡚㌟యࣃ࣓࣮ࣛࢱࢆ᥎ᐃࡶྠ
᫬࡟⾜ࡗࡓ⤖ᯝ㸪ᐇ㦂ࢹ࣮ࢱ࡟ᩚྜࡍࡿࡼ࠺࡞ࣃ࣓࣮ࣛࢱࢆྠᐃࡍࡿࡇ࡜ࡀ࡛ࡁࡓ㸬 ௒ᚋࡣ㸪ࣂࣛࣥࢫಖᣢ⬟ຊࡢ⿕㦂⪅ࡈ࡜ࡢඃຎࡢᕪ࡜㸪ྠᐃࡉࢀࡿไᚚ༶࡜ࡢ㛵ಀࢆ㸪Ⓨ⏕ࡍࡿ㛵⠇࣮࣓ࣔࣥࢺ࡞࡝ࢆ⏝࠸࡚ㄪ࡭㸪ࣂࣛࣥࢫಖᣢ⬟ຊࡢඃຎࢆỴᐃࡍࡿᅉᏊࢆỴᐃࡍࡿࡇ࡜ࡀ࡛ࡁࡿ࠿࡝࠺࠿᳨ウࢆ⾜࠺㸬ࡉࡽ࡟㸪㧗㱋⪅ࡶྵࡴከࡃࡢ⿕㦂⪅࡟ᑐࡋ࡚ࡶྠᐃࢆ⾜࠸㸪ࢺ࣮ࣞࢽࣥࢢࡸຍ㱋࡟ࡼࡿࣂࣛࣥࢫಖᣢ⬟ຊࡢᨵၿ࣭ຎ
໬ࡢุᐃྍ⬟ᛶ࡟ࡘ࠸࡚ࡶ᳨ウࡍࡿ㸬ཧ⪃ᩥ⊩[1]N㸬Peter Reeves㸪Jacek Cholewicki㸪Kumpati S㸬Narenbra㸪
Effects of reflex delays on postural control during unstableseated balance㸪Journal of Biomechanics㸪42㸪164-170(2009)[2]㜿Ụ㏻Ⰻ௚㸪᪥ᮏே࢔ࢫ࣮ࣜࢺࡢ㌟య㒊ศឤᛶ≉ᛶࡢ᥎ᐃ㸪ࣂ࢖࣓࢜࢝ࢽࢬ࣒㸪11㸪23-33(1992)㸬

GS3-4-3-4

4日 山梨 (山梨大学)