CFDシミュレータを用いた最適化手法に関する研究

Title

CFDシミュレータを用いた最適化手法に関する研究( 本文

_{（FULLTEXT) )}

Author(s)

栗山, 嘉文

Report No.(Doctoral

Degree)

博士(工学) 甲第399号

Issue Date

2011-03-25

Type

博士論文

Version

publisher

URL

http://hdl.handle.net/20.500.12099/36582

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A study

_optimization

_methods

using CFD

simulator

Yoshifumi

Kuriyama

Mechan1'Cal _and C1'V1'1Eng1'neen'ng D1'V1'S1'On,G1'(u Un1'VeY:S1'ty

ABSTFuCT

In _{recent years, numerical simulators for fluid analysis based} on _{computationa1} fluid

dynam-ics _(CFD) have been _used to _study the behavior _{of fluid around} an

objectand its thermal

hydraulics. CFD isa _{technique based} on the Navier-Stokes _equations, as _well as on _energy

and mass _conservation laws. Recently, _with the development _{of computing}

power and the

price plummet of personal computers, the optimization algorithm has been applied an CFD

simulator to finding the optimal control settings or _{optimal shape.}

However, in cases

where the problem has many local solutions due to the effect of the loss

of significant digitsor _underflow error, _{the most widely used general optimization}

algorithrn

like Genetic Algorithm _(GA) is_highlylikely to find a local solution. Of course, this problem

can be solved by enlarging _{the number of population}

members, the number of generations

and the mutation evolution; on the other hand, the computational time for one _condition lasts

only a few _{minutes and the optimization requires hundreds of repeated computations. Thus}

the optimization using the CFD simulator needs a lot of time to _{finish the task. In addition,} a

simulation with low computational cost does not always correspond to actual production of

a _{high-qualityproduct} because

of the unstable solution space.

In this paper, as the optimization _{with CFD simulator,} two _{optimization method} are

intro-duced. In the transferred _{control considering spilling avoidance,} in _the near future, there will

be a _{significant problem obtaining}

workers inthe fields of welfare and nursing care _because

of labor shortage. To solve this problem, many welfare robots, such as an _{upper extremity}

motion assistance robot and a _{meal assistance robot, have been studied. Patients}

usually

drink _soup or beverages _{at meals,} but meal _assistance

robots with liquid transfer control

have not _{yet been} developed. Thus, a 3-D transfer control system for meal _{assist robots that}

incorporates _{spilling avoidance} isdesigned.

Another _method is_{caluculation of the optimal plunger velocity} input for die-casting. In

this background, die casting is _adequate for mass _{production and} ithas the advantage _of

being _able to _yield a _complicated

shape accurately. A defect of die casting for high-speed

injectionmolding isthe occurrence _{of shrinkage cavities.} To avoid the shrinkage _cavities,

ve-locity control ofa _plunger is _{very effective. However, the velocity control input} is_manually

constructed by skillful workers because analysis behavior of molten metal isvery difncult

veloc-ity control input of die casting plunger is_calculated in _order to _{enable the reduction of air}

entrainment and prevent the occurrence _{of shrinkage cavities} in die casting product.

Another _{aim of this study} is to design a _{solution search}

algorithm that requires a _smaller

computational time to find a _{solution which} can be applied to _{the production of high-quality}

products. In this study, two optimization algorithms are _{proposed, and the proposed}

meth-ods apply the optimal plunger velocity problem in die-casting product. One method isthe

Extremal Distribution Sorting Algorithm _(EDSA) ,which searches intensively by using

ap-proximated curve _{and evaluated value at}the improved _point in the nearly extremal _solution.

Another _method isMulti-subcenters Solution Search _{Algorithm(MSSA)} , which consists of

a distribution _control to handle _{the distribution of search points} to _{expand the clearance}

be-tween _{search points, and the convergence control} to _{control the density of search points} to

converge the predicted high _{quality solution space.} Furthermore, _{to create the performance}

of searching the point to produce the high-qualityproducts for the MSSA, Space Searching

Algorithm(SSA)is designed. The _{effectiveness of the proposed systems} are _shown through

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1V E.2.3 _{5Zg&8=h-L}8Bi3@IE#EB%...} E.3 3ftb . . . . ll S3 F 9YhR L 75./-)ti,0%i5igji^hB=rj)7%iEhnjg,S* B]E]3R jiE];A 167 168 169 175 181

1

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taiEe) [29]-[31]b'i@b418_ck5 8=T3? r=. CFD a 8iNavier-Stokes _{7}W]:iEtPf8f4183}

d))jJ-f'-I!i(Y3I-I,)L-ill-(h!-(J-.:i(,LT-'lil_{i:[M-iIVJ tt,i7:liuJUu=%rclni[!< 1kf/[-tli7:1b}t)

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ck

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ll i

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tl.

...I

I_{=O.2 [s]} (_{=0.4 [sJ I-O.6 LsJ} I

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Fig. I.1 Comparison _{of the} fluidbehavior be(wc(nl _{CXPCrimental result aTLd simulation result}

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ilI]iTnO)7,tj tv _{-> >} 9t1:ll_{iiO)n:i7.fTT-FLYL, f=. TL'),'I1.m-lit,'fll-?TIS;fi--u!.

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L33]

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I_:_[II-L)LTLi-_)(iq.f[Tf'lA T)

i :.lJ.ll. _I./I.

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∼

tF?n

FigJ 1.2 A conception diagram _{of die casting and} CFD _simulation

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i L,I, t5G56LiBii@IE,)7 I-9I77?Iba iSIGHT[69]t CFD _->S 1 i/-9%ig]#=

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[65].

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.li-uI];iff;-ui3WO}r5-,lJu1!I:_lit,[i'(f_:.i.'[).

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1h r=[7l]._{3gEWZlj-?hr3 <}, #31X6ZETR%%iAb8= a:89(PBO)W$lJ8=ihB!bSb8 = i

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, -I-0)f=bl:ll(1?Ii,91 ty 7'0)

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1.3

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_->=

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JZ"iLj-I3 T3#if18. i

0) _--? D EL ru)JTr(q,'lih',1SJii (i;.(i-T8 _{JJ+:rt'-u(SdlJf.r!I:_(nJF-I_J,ru:fL"'])0)F.'[,I,r&-T.A}8.

---fJW.Jfd-SLJL'f Jr%#ZEFuO)I5r]i L,I Schwefel Bg5&o)#ZEFW% Fig. 1.3 _{8=j%1. EBB, 6, S&o)PgAb'i}

L=lLt]_{4t. S < a)I.=;i)'Trlrr.'Ii]1,1[T-'((::.I.P.rE"8}

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fE3BE18hSZEPBD[5(J i L,T, 911-IA A I-8=h-8j-8 7o9 1/-yhi7ig&0)%Ze&t %0)#hB (Il'fJJqr-;/rJk-F_{,3['j,'l!-EEfLiJi.,}Fig. 1.4 _E=,I(-4-.I I T. Fig. 1.4 _{(.i;7.T''.[IlnLd-a)I&L}, _{i,0)(2 Zf[3aLi}

[''l.Ill-pEt3573 _{I i #LIY-,I(L,rCL'8. Fig. 1.4}

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I _{4 lei->} I 1 L,-.> 5 _{>0).H--n:3BfnlE=isL-T73}, rlJ(.I'&-i3+ib.h'J:fri.I'*-i3

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, CFD ->

l1

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(i- -InT0)[I'J,JllLmE=;lil('JJt- )ilktfL-:LET-rTJO).7I-J[;TLr.I;:rt'ulJS,a,I)iti

rd-/r5. i 0)f= b, 't;i-*o)Lri;a(L=J:--fL Tt._)iEL r=;iT.T,T[rr_,I31xTt(a:-(_{I-l:ilLT!Jl=rL-u}I)i8=(F'J.'LW.#a=!iL{]'-F_,3I i hqt _{-i-jib,T3SJ*;,.I.IiY3.i-i..I,T.[nr}Jill

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7}Jflzi;a)r.",);Hi.L.S,rLTlA 73

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-:_7 LItiill3GB(r'J,'Iiht.i,TH I.

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l500 Fj O O

a

Fig, 1.3 Multimodal _{search space}

Local _solutions

1.4 _{IrTFrluLUn'Jt4J''rjJ).i} 9

1.4

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8 = i q)7Fhi _{88E#iEIBiH*7)I/jh} 1)X7> (ExtremalDistribution Sorting Algorithm :_nl

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Algorithm)

_%k%18

1:,-1;-[[Tli&J(rJ:Ii,,7LDI,rJ'II-a)3.qtL_r'._}i7,fqfJIEC=

-a-7a

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rE7Jt-F.

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, LIL I,-0)Lk

I) _tiEJlif:

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i-,rlJLk;

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6. j}_{j A 9}

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Zh)

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)_l1 71 _{T)../1{1tr:i.Tf3ii:-jL.,JIJ}L _{,T= i i 0)lfl'!iX}itI/[J--5.}

%3S?1L CFD _->= 1 i,-9%]BjE Lf=Bii&lEoE[]Wr]t _{L,I, 911-f*X}

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91lI JJ 7l _{Tt0)JJ{r:(L'f)i;(r)q&1r.I.'),Ill-n-1,p5i}

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10 #1S #B=

:(AiJifU_)Ll;&^;JJ(Il'f_'i2r.i.q[rfr]

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igTIT CFD _->i i I/-9 %]Bjq L,f=Bi3@IE8=Rb 6418B3iBIE7)Vj1) X^L>0)JEE8E8=

?ulTkB{<8.

^iTl'4 _{L1:',-/Et(iJ-);l!3ti;rE.}i,_{Lri!ll'.rJ:,lO:i-T{j:yf':)..}i-34t8 a:5 rd:lJli&(E7)Lj'_{1)7:LhT.ab 8}

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J-I.rq;rtn

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-> I i

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ll

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4l.I;,(I3uUT1:tli;_-a-a)L'=h'[_JEykJT2-L3-73 _{r=d)0) [;I}

-1r[_jtf)-1U

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i A _{B=#i%8=fiiBO)A,A,81fX7?hb8} a i A, 6, =413f?> Handy-1[77]5P My Spoon[78],

wins ford Feeder[79], Neater Eater[80], Bestic[8l]f3 Ei/*JU3i%$3E]Bt) _,if.yI-_{b,,'mR. P#q}

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r[n-0)1LiJ7rLJJl:iifitCifJ'f-)i3:rE.C=[h]]i 4tT L,_T=l-)ii

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J=-I rE.1<Lr')r)ruLTtE.i,

rl;-rJfallghl-I,(i;-;i-E=i.'iiJ1([RJ,'l1-m.-i.i 1 i,- 9 &JT2JIJ-F73I i (IA:t), ,JI

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i iir.[

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LE t)

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ALt'rT)kJrr;J]hSi]'JL'J7-iT-u)Hfqf7Ei rd:t)

, q1:.'i-n!i L,T, ll l](-JkfTltj,lit.yI-0)-*u)[lJ7-).:.i&1Y)I;

l2 a 2 i 6 _{E] EbFg?=tiol L'-9%FBL'f=iiSGL#PSu#JW}

2.2

iS#3&fTE

I.;I ::.:::.. _ii:I i.'J./.I/.... - lI:..:.;I..lI//'-_ :...-::I....I.;'..L:I...-ll..:...(I.I:

B*%1i5 , 6 BEbB2y=tiDl I/-9Lj: Fig. 2.1 L=i;1*Jrl%*Ay=tfl i,-9%@jq

I"::. i _{.:.:;I.i..:lJ..}.I .. ':: r..i.J..J.L

ill.. _{il.:.::..:.:.;I.(:!:} ;li.,../: ::.;ll..;:/,.:!l::I;.:

I.:I...' ':.. Jl:/I. _ :i.I;ll./.:..,:.:i.I..I.:.:/i:

.,

..;./.:I...]/i.L:ill.I-'.:I.-..../.

Fig. 2.1 Picture _of 6DOF _manipulator

Table 2.1 Maximum _{angular velocity of the} motors

Maximum _{angular Velocity}

lSI _motor j1 200 IdegIS]

2nd motor jl 128 [degIS]

31d motor i 190 [degIS]

4th motor i 210 [degIS]

5th motor j1 210 [degIS]

2.3 CFD _{->Sl I/-9g)EcRJtf 13}

Fig. 2.2 Details of the spoon shape

2.3

CFD->=1

_L/-90)f&zE

1<[r-)FJ-fuLTt(i A 7Q- > _{I-_a)it(Ii[^0)>i'SC!-JuIRJ7I1-1rT8=i-,fL[);[RiI!1rT,) 7 I-FLOW-3d93]iiJ)1Ju},73.

jf-F71f7d9(I,-i l11 L,-90)}.v

=>1ffJ..L5u).;I-'lTi:i:rfjT.:). -> -Ii I/-90)} ty :i _{3_lll.I.,;}

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,p5rf.I;:rLuh',1L'i)(i TJ 7 I L,3: 5. q.:;:l=i,iE(A(n-.J[!

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Ei(F')Zf!_1:rrn.1-:r,'ui:wTfltE rj:I:llE)llT7_<, i]'T)i(fill;0}'i(iDiJuhli-[-I)JtC.I:}ill=iTt=cV7J 3:5 8=,>I i L,- _-> 3 _{yO)n.'IW.frilLtR}

i Fig. 2.3 Di: 5 8=iRJtEut. %o)t%o)-JS 1 i,--> 3 _{'/0)#iGigJ5gt}.y ->10BO)}

)i9}-9%Table 2.2 _{8=/ji1. =0)t%ORE}.y,>1&Ln75000?1b 9, RSimSFmi}

Pentium4 3.OGHz iE#0))i') = _∼/?1jjg15

JZDiPfFFLR7?,A?7t.

Table 2.2 Setting _{mesh parameters of the spoon}

X direction Y direction Z direction

Minimum _Width

IO･02[m] IO･021[m] 0[m]

Maximum _{Width 0･02[m] 0･021[m] 0･015[m]}

TOIal Cells 100 70 25

14 # 2 * 6 BEETjg7=tfl L,-9%ji]L,r=i&i#LqPSIJSUW

Fig. 2.3 Mesh _{setting of the spoon}

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/.-!.:

I.:.I I.

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:I I.:._{:.:.:: I.J..:.l!L:.;./.:i.}:..

:

I_.

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:.: i ...:...:1. :/.. . .r I.::.::::.::_.:.l!lr.I/.'.::. ;:I:.I.: l1. I:.;:. .:.i.:?H:.i.. . I :i -: :. ::..:.!1.:. I;-:. /.:I.i:I.. .,.i:::I.I...:: I: ::_.

ft6# Lf=i@1*[g4Z.iR->I i L/-9 0)1=1aJh%*;'t18 FIB, _{Fig. 2.4 0)Jj;&R8=/j<1i:}5

I-I .I:.:;L. -. t∼ ;/.: :. ...:..;.:...:..LL.;.:.I.:.i"::.:i: .ill-: :.: i::H .:... .-. -_

Table 2.3 Fluid _{parameters of} water

Fluid _{Parameters Water}

Density 100C- [kgIm2]

VISCOSlty 100 X lO15 IPa･S]

Temperature _{OI the Fluid} 292･2 [K]

Surface Tension 0･012 [NIm]

Surface _ROughneSS 0･0025 [m]

Gravity 9･81 [mIS2]

2.3 _{CFD->=1L'-90)u&E} 15

1/:Lit_i..I.I:i. ri _{i..l!.''.:.::.}:/: _{l'/Ill.I./.I/lil_/:::i.H'.I:.I.}:.I/ . _I::...I

:.. /.

%0)P$0)9:B&#SR% Fig, 2.5 L=, hSfW#Sj#% Fig. 2.6 i=/j<1.

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I;.

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-_

.

TL,'8 I i b 6&-3LfL1.T.5 ZE). _{i 6 t= D}

Ji1'-.yf.0)Lll^h[EAiJif;-i;-ijy]%f(ST=L r=1_TtBSWL%RE

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･l.

lu

::_!l_{i.:.://_-I, I..I_.i::i::-..;:I,5'i-I..i...L::I:i.t]--7:.I/.:LJ:.!t:Ll.:"ri=ll.:I:i,}

.J.T

:._

1J.:- '::':lL.!T:I/:/I:..I rI. J/:ttl_{I.il:=!::Ll.I..i.(r:.}I.t=:..I/.-1-_{iy.1.:.:'-:::::lt.I:::.I.1-:..}..

i 1 i/-9rrfBJH L/. f&1*)1y 1{'I)y9tlfBr]W->X51Lh%Nlin18.

0.25

i

.a

S

_[s]

16 A 2 _* 6 _{a EEIF57=tiQI L,-9%]=flL,r=f&i#Lm]E&lJSuTW}

0.550[s]

0.660[s]

0.730[s]

Fig. 2.5 Experimental _{result of the spoon transfer}

0.550[s] 0.660[s] 0.730[s]

2.4 tfh1) _>911 17

2.4

tflr)./91

2.4.I

iEibg

)1',:tt;!AO).-,-'lJ,i:Lii:J:/i,rJ:

Jrjii:htii573i)it._-A<'1'=ti'

_1 L,- 9 TtLi D-H uf&LLY^- A i L I)^tlJ!l

fJ%giRq)i5tJtE%1i5t18. Fig. 2.7 _{8=82%0)a%EB1%'j%L,} a _0)35*%y=tiol i,-90)

1r'J)!TJJ:i:i{-J3iti 7r ,3.

Fig. 2.7 Setup _coordinate

1/+lriLho)J^LIi1:ll,lf&;''l)i:#LYIXI,-E=I(i5. )i;(.LiT.=u (i-<= ti L,- 9 0)flJJti i:TFti!o)1!1l.D..:J1[II)i E=.i"*LJJ-i17J..I." _{(a:'7= titL,- 9 1:;..i.(/TH7-I.'TJ,}

)/HLiT--F'J(J--/Jlh)"-(,(i_{,l7::rLUjJh_)}i 7)-/3.=1 i:y

=H 1)'6 _'I17:{VL;<i-fE4tT=^r]J-1i-1, aJli2 I-!lJi1!Tl-CDIr.r[I,:I;Lf,:Lho)i.r.i.=T:(Ii t),=1 ilr?)31rAJLTJl-_f-_E=;i-kLJJt-F?a. ･t.1 Liln-1,U3-2 [u-Jit!TjO)[.rT.lil-;.JrlfTC=ll'T:*pT7aj=5 _{,:;'iJJi:173.}Etl0))i;i..:i.Lilil i [''.]L=ll;(.Lk-.(I(;i_

;.'pt-F/3.=j (a:;ill-2 r7,ui^!TJ'[q-LEI;[r,:[nt]T7JL;[(,i

LikE=i E),.7.tlEi?J1-2 T)> 9 trrili;6]-cFTtb,3. =1

i E2 h'iRt=Lg.a,r30)?,,a1 - d2 - 0 tr38. 1)>9&t=nj58L _z2 b',hE30)LgJf,8i%3,

h'ti4 ]RJLtlTiO)IHrlri1:lrrlhu)i):i,(Ii

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[.TT'rii:1'rr:n(=TLff:I(]--i-73

Lk-∼)C=1 /3.a;,F^,I =l, I.r" E" 0))i,I(,(.,:0).iiLJJi:iiT.1ZG,. i-4t.1T4t, ?]',-5

rT,!:-Jf!TJ-PT'fr:i-;Ll'lho)-ia.:irLTJk-4j?f= i I

,3C.=J!;-T;)[i.iLt,i 8. =l Ci?}1jL4 r'tlUji rTqtin -c9,:7._ICi:j!l4, 5 _{[nJhJ(l-)[,r-lr:i-;.I'-LIT(=l[J[:-i(TIS}a: i l= i 23.i,, (ihJi5 lun'rl-i l]

r]i:F,l-c}..7..-,LiLfti5, 6 luriltjlHItlTLii.rut

8=tE3E18j:5 8=t8. E4, E5 _{8iLgB,b'irqt=r30)?A,} a4 - d5 - 0 tT38. z6 6rq8i8=

:jli6 [i!Jr!TJ-Lr_,f-lilt.TJ:[I[i I.7JL:rr',Jf..I..ii,.I.:,tlr'l1:_t]2o)r[''Jf tJD- <. I I _{3:Tt.i-2TuL,r= T)> 9 )(5}

}-9%5: tbT Table 2.4 _L=j%1. E7 _{0)BEC!A8i7=tiol i,-90)$5tlkfEb,6}11J}

18 a 2 _jf 6 a EbEFLR7= tiol L,-9%FqU,r=#t}fLWSF]Sr]W

Table 2.4 Link _{parameter of 6DOF manipulator}

I Cyl-1 alll ii Oi 1 0 0 dl 01 2 I9〇. 0 0 02 3 0 a2 ₀ 03 4 _-90. a3 d4 04 5 .90. 0 0 05 6 .90. 0 0 06

3$5h32 a _{8ifR6q)%ESqPj5Bib' 6fifE.##%1$8} b _q)?)A 8. fJ Htj_,if.yI.

MOTOMAN-UPJ 0)3S&*%8=#<. 5tE2 t7Sr= 1)_>9)<9}-9%&FB L,,_{Eq.(2.1)0)BEIE*3*fi5r]}

i-1Ti _{%b'L}8 i Ei_1 b'6 Ei b'i1$6418.}

i-1Ti

-cOi

-SOi 0 ai-1

sOiCCyi-1 COiCCti-1 -SCri-1 SCki-1di

sOiSai-1 COiSai-1 CCki-1 _Cai-1di

0 0 0 1

(2.1)

A-XBEfJ%giRh'6, $5tOBE4Sg%1$8 8=8i _{Eq.(2.2)?11$8}E tb'i77h%8. OT7 0) 1_1i 1

5r]b'6 3 1i3 _{5(]2?hti##%aiL,,} 4 1i 1_{5f]h'6 4113 51]3:?h8i[kfE%i1.} oT6 - OT1 1T22T33T44T55T6 rll r12 r13 x r21 r22 r23 y r31 r32 r33 I 0 0 0 1 (2.2) rll = r21 = r31 = r12 = r22 = r32 = r13 = r23 = r33 =

c1(c23(c4c5c6

-s23s5c6)

_s1(s4c5c6

c4s6)

s1(c23(c4c5c6

-s4s6)

-s23s5c6)

_c4s6)

-s4s6)

-c1(c23(c4c5s6

-s23s5s6)

-s1(s4c5c6

-c4s6)

s1(c23(c4c5s6

-s4s6)

c1(s4c5c6

-c4s6)

-c1(c23(c4s5

-s1(c23(c4s5

s23c5)

c1(a2C2

-d4S23)

s1(a2C2

-d4S23)

_d4C23)

2.4 tf^1) l/91h 19

a a?1, _c1 8i

cos(01),

_cos(02

03)

<-XBilgAt-&18j= 5 8=18. Z-Y-X*-1'9-j5?,#R18 a, ct - 180o

,P - 90 o,7-Oo?'b8. oR7 - OR66R7 - oR6 0 0 1 0 _-1 0 1 0 0 r13 _-r12 rll r23 _-r22 r21 r33 _-r32 r31 (2.5)

Eq.(2.5) &1,.iL[LT,i:-a-,3I i rL7t,bJl[JJ:i:i'-J3iti:y^-A)^i,-.:f!T-f7.SJ=_{-f:xE i+8} I _{i ht.7.i ,3.}

2.4.2

ig3g]g

3Q1:Tilt.4:,-I/i::(itj

J1;Ity I.7L7J(T_-..:,-:a):&'L.4;it-1bI;i.;-lr.,:l=-g-73 r= a 0)(i liUL7rtia)-f-SS.-))_:liAa:hJ7J I i h<h

rL'LLSY_{,3.-1<[f-)FJ)ru(E,(.Ji)}I]1

,3J/i:I[Itj Jli1.:)I,0)a: 5 rd 6 FjufJi7= toi I/- 9 0)3iEliuJ:..J/+I:(i

1''J7l!1'J7.(=[R].'I!L< I i h'iT.iu5. -i.:r1;'T-0)(1(i.iL''l&LYaJ'J-5 T)> 9 _{0)LrlJiliLi.lu(l=}i 8. i-I)_{173 I i T.,}

]'a:h ･y,ti)tJ,i(IT-;rt3 r'ItfH_fi,I;tiLliJ_ti)i)-i(=fu)-t3 D ufJii )JtJifr;.lJIJt,tqfJtEi TJ:7D. 3: -9it,=T:l1,'f-n(;I._i.t{.:

(xr,y,, _zr)h'i2f=8=T380)b'%5Rb8. =n82iBitO) 3 LRWo1, 02, 03 _ck9Rb8 = tb'i

?>%8. 7=tiol i,-9%fitb'65if81t, %3, #4, %5 1)_{∼/9LL X-Y5F5iO)Lg}

,a,%3a9 (I,,y,)8=6]b'55W7jit L,T3iA80)771, EO)5W7jit x#to)r31f5h'i ol trj:

8. _{a:?TEq.(2.6) 0)A:58=f38.}

01

-atan2(yr,

xr)

;*E= ():I_&1YjJ:b,3.():3(i:)(i.u=a:E)Lj-iL64t,3.

03 -atan2(a3,

d4)

a3+dZ-

fC2)

xr2+y,2+x?-a3-aS-d?4

-atan2(c23,

_-s23)

TElai1= tb'l'?h%8. _s23 a _c23 Li)RO)iE?,ai1= tb'qSEr30)?1, 02 _b'i/ie3:8= t8= r38. L

-I,2+(clxr+sly,)2

-((-a3

_-a2C3)zr

-(clxr+slyr)(d4

_-a2S3))/L

-((a2S3-d4)I,

-(a3+a2C3)(clx,+slyr))/L

20 a 2 _j$ 6 BEB&7=tiol i,-9%FBu,Jt#f)iiWSr]SrJW

I I _{73'L3CL :tJ1'.,Bit(I}a:_,3-T=)t3 _{Fj [-LIJ=io)1nJJ'(:i:y}ltb73.J=-4tJ?tat,}

04 -atan2(r11s1+r21c1,

_{-(r11c1+r21s1)c23+r31s23)}

-atan2(s5,c5)

--(rll(clc23c4+

-cls4)

-rll(-cls23)+r21(-sls23-c23r31)

-atan2(s6,c6)

--r13(clc23c4

-sls4)

-r23(slc23c4+cls4)

-rll((cls23c4+sls4)c5-cls23s5)

+r21((slc23c4

-sls23s5)

-r33(s23c4c5

c23s5)

ck? T, [jfll;-:-;tJr+51l[;i_-;'l'LLl=-kJ-L I, ^drRJLiTll4f#k(),.i311'(U..8I i hilrEt% 8.

iHSh3W'hiE LU'b'%6@h'b8 Jt4),_{iWm#* (x,y,z,roll,yaw,pitch)-(0.36,}0, 0.56, 0, 0,₀₎

b' 6, BG!##% (x,y,z,roll,yaw,pitch)-(OA5,0.20, 0.30, 0, 0,₀₎i _L,TiQB&3f%i5 L,I

9;B5i=7=tiol L,-9 _Tej&EE L,Tb8.

Fig. 2.8, Fig. 2.9 _{8i6&5Rb1'hiB3S&3Z8=i5L,r=tB%0) 1) 7} 7 _{i,1/XO)j5jit%n%7=}

tiol I/-9 8=i5 L,r=F$0)f5&FE;S?hb8. a 4*t# 6 *hS1) 7 7 L,'/A tfR&j5Eih'i

---5;ALTU Ira-U'ht,1,Tjli4 LEiLni n-6 ifr:lfl(ii i,(=}.]-gird:1)7 7' _{L,∼/Xi:y-5.ATis} E), i);I:,,,.{iO)

#*LbRiF%1R? r=3f 3:?hb8 a th'ibb'8. %0)Itho)*Li 1)7 7 _{i,∼/X8=}4LTjiW}

8=iBi&L,TU'8 = tb'ibb'8. Fig. 2.10, Fig. 2.ll _{8i9;.S*j:91$641r=f5&%]lB3S#3Z}

8=iBLr= i _{%8=1$6418I3ifEx,y,z t#*ro11,yaw,pitch?,b8. Blgj5fFR8=r5b'? Tis}

7JtiCiL,TL _,73hl1,ia3L_{ITTt-1<>t},thti1-T)141TU,8}i I _,3ht,tb8i)i,I _4tCi-ytE2ZftO)^i]J-1,-4 ,li[ht^iJl-6 _{LfiLIJO)[AJln1,}2 _{[IT-[h])I,T-.-Jlf3j}L,I.I.!;[(:d3)uL, I L 'rd: L_{',lO:i--q-i.:i-,u!jj!-hilt}5_{[deg] 1FiF1)yE_Jt}L,I L, 3f?

r=tjqA 6418. L,b' L,,13ifE8=BgL,Tti1) 7 7 _{I/yX8=iqL,TiBIHL,Th-9} ,faWf3,SE

B!bq7$6nr=. Fig. 2.12 Li3 _{)Rjh,y,z q)1kfE%7oT].y} I. L,r=bO)?>b8. inbO)RV8=

J=!lJL,I Ci,_+I-J1-ltd>&LY L _r='(&l=7t_{I/-*i:yF''i-I/)-k1}8 0)f=thS,i-DnTi.[JjiE8=j=t)_{[i[l:[r.lr7-Xt}

i,%ke= LT L,3: _{5. =OS%B%L}tj:A, E416b'6iB3gh5Zh'iiEL} < R3:?Jt= tbSb JJ1'-5.

2.4 tj=l1)>911 21 40 bJ) O 120 e 2 4 6 8 10 Time[s] 0 2 4 6 8 10 Time[s]

Fig. 2,8 Experimental _{result of angle}

bJ) a 20 cb< 5) -20 C cbLr' _-40 )Tj. .J TTj cb-2 0 4 6 Time[s] 8 10 2 4 6 Time [s] 8 10 2 4 6 Time[s] 8 10

22 # 2 * 6 a djf:%Y=tfl i,-9%fqL,'f=uREm]SrlSurW ,i 0. E S o X .45 _ 0.2 i i 0.1 > a. o.5 X T 0.4 ∼ o.3 bJ) O 'd I o 0 a 5 y 0 1

i-5

Fig. 2L 10 Experimental _{result of position}

2 4 6 8 10 Time[s] 4 6 8 10 Time[s] 0 2 4 6 8 10 Time[s]

2.4 tj=1) >9t1 :3