( ) 5. VSS (VIM ) 10. ( ) 11. (ANN ) ( )
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1 1.... ( ) 5. VSS (VIM ) 1. ( ) 11. (ANN ) ( )
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3 1 Lagrange 1..1 Lagrange q, Lagrange D(q)q + C(q; _q)_q + G(q) = (1.1) D(q)q C(q; _q)_q G(q) ( ) D(q) D(q) m ; M < M m (D(q)) (1.) (D(q)) M M < 1 (1.) (M) M (M) C(q; _q) _q jjc(q; _q)jj C M jj _qjj (1.) C(q; 1) C(q; x)y = C(q; y)x (1.5) C(q; x + y) = C(q; x) + C(q; y) (1.) K := _ D(q) C(q; _q) K + K T = x T Kx = for 8 x (1.) G(q) q a (1.1) Y a Y (q; _q; q)a = (1.8)
4 1 LAGRANGE 1.. q q x () x = f(q) (1.9) f () _x _q = J(q) (1.1) x = J(q)x + _ J _q (1.11) q = f 1 (x) (1.1) _q = J 1 _q (1.1) q = J 1 x _ JJ 1 _x (1.1) (1.1) D(f 1 (x))j 1 x + C(f 1 (x);j 1 _x) D(f 1 (x) J) _ J 1 _x + G(f 1 (x)) = (1.15) q x q q W W = T q (1.1) x f x = Jq! q = J 1 x (1.1) W = T q = T J 1 x = J T 1 T x (1.18) f = J T (1.19) (1.15) J T J T D(f 1 (x))j 1 x + J T C(f 1 (x);j 1 _x) D(f 1 (x)) _ J M x (x) := J T D(f 1 (x))j 1 C x (x; _x) := J T C(f 1 (x);j 1 _x) D(f 1 (x)) _ J G x (x) := J T G(f 1 (x)) (1.1) J 1 _x + J T G(f 1 (x)) = J T (1.) J 1 M x (x)x + C x (x; _x)_x + G x (x) = f (1.1) [ ] [ ] ( [ ] )
5 5 1.. ( ) q 1 ;q (q 1 R m1 ;q R m ) f(q 1 ;q )=; f : R m1 R m1! R n (1.) q = f (q 1 ) (1.) f (q 1 )+q = (1.) _q 1 _q = J c _q = (1.5) J c := @q _q 1 _q ( (q 1 ;q ) ) q (1.1) (.) (.) F c D(q)q + C(q; _q)_q + G(q) = F c (1.) F c F c W = F T c q (1.) (.) J c J c = c T 1 1 c T r 5 (1.8)
6 1 LAGRANGE F c = rx i=1 c i i = J T c ; = 1 1 r 5 (1.9) i J c _q = F c D(q)q + C(q; _q)_q + G(q) = J c (1.) (q; _q) q q M(q) (q; ) J c q = J _ c _q (1.1) q (q; ) D(q) Jc T J c rank q = D(q) Jc T J c C(q; _q)_q G(q)+ J _ c _q (1.) = m 1 + m + r (1.) r = m J c =[J 1 J ] (1.) rankj = r (q 1 ;q ) J J c J 1 J 1 J c = J 1 I r =: J 1 I r J c (1.5) D(q)q + C(q; _q)_q + G(q) = J T c (1.) J c (.) := J T _q = J 1 _q 1 (1.) _q _q = I m1 J _q 1 =: J _q 1 ; J := 1 I m1 J 1 (1.8) (1.) q 1 q (t) =q () Z t J 1 _q 1 ()d (1.9)
7 (1:) q = J q 1 + _ J _q 1 (1.) (1.) J T J T J T c =[I m 1 J T 1 ] J T 1 I r = J T 1 J T 1 = (1.1) J T DJ q 1 + J T (CJ + D _ J)_q 1 + J T G = J T (1.) D 1 := J T DJ C 1 := J T (CJ + D _ J) G 1 := J T G 1 := J T m 1 D 1 q 1 + C 1 _q 1 + G 1 = 1 (1.) q = f (q 1 ) (1.) D 1 (q) q 1 ( q = f (q 1 ) ) _q _q + J c (q)_q + = (1.5) ( ; + ) F c = J T c ^(t); ^ R r (1.) ^ D(q)q + C(q; _q)_q + G(q) = J T c ^(t) () + Z + (D(q)q + C(q; _q)_q + G(q))dt = Z + ( J T c ^(t))dt (1.)! ; +! _q q D(q)q + D(q)q = J T c ^ (1.8)
8 8 1 LAGRANGE (1.5) (1.8) D(q) Jc T J c _q +^ = D(q)_q (1.9) ^ ^ =(J c D 1 J T c )1 J c _q (1.5) _q + _q + =: P _q ; P := (I n D 1 J T c (J cd 1 J T c )1 J c ) (1.51) P _q _q + (PP= P )
9 9 y (x ;y ) l mg (x 1;y 1) mg x 1.1: m l mx 1 = (1.5) my 1 = mg (1.5) mx = (1.5) my = mg (1.55) (x 1 x ) +(y 1 y ) = l (1.5) [(x 1 x )(y 1 y ) (x 1 x ) (y 1 y )] _x 1 _y 1 _x _y 5 = (1.5) m m m m 5 x 1 y 1 x y 5 + mg mg 5 = (x 1 x ) (y 1 y ) (x 1 x ) (y 1 y )] 5 (1.58) x 1 y 1 x 5 = y g 5 m g [(x 1 x )(y 1 y ) (x 1 x ) (y 1 y )] (x 1 x ) (y 1 y ) (x 1 x ) 5 (1.59) (y 1 y )] x 1 y 1 x y 5 = 8 (_x 1 _x )+(_y 1 _y )9 (1.)
10 1 1 LAGRANGE = m l 8 (_x 1 _x )+(_y 1 _y )9 (1.1) _y y 1 y = _y = 1 y 1 y ((x 1 x )_x 1 +(y 1 y )_y 1 (x 1 x )_x ) (1.) _x 1 _y 1 _x _y 5 = J _x 1 _y 1 _x 5 (1.) J := (x 1 x )=1 (y 1 y )=1 (x 1 x )=1 5 ; 1:=y 1 y (1.) 1 (x 1 x )=1 +mj T J_ 1 (y 1 y )=1 1 (x 1 x )=1 _x 1 _y 1 _x 5 = 5 m m m m 1 (x 1 x )=1 1 (y 1 y )=1 1 (x 1 x )= (x 1 x )=1 (y 1 y )=1 (x 1 x )=1 x 1 x y 1 y (x 1 x ) (y 1 y ) 1 5 x 1 y 1 x 5 5 (1.5) m 1+ (x1x) (x 1x )(y 1y ) (x1x) (y 1y ) (y 1y )(x 1 x ) (x1x) mj T J x 1 _y 1 _x 5 + (x 1 x ) 1 mg (1 + y1y 1 )mg (x 1x ) 1 mg 5 (1.) = (1.) y 1 y = _x x = x 1 + l cos (1.8) y = y 1 + l sin (1.9) _x = _x 1 l sin _ (1.) _y = _y 1 + l cos _ (1.1)
11 11 _x 1 _y 1 _x _y 5 = l sin 1 l cos 5 _x 1 _y 1 _ 5 (1.) m l sin l cos l sin l cos l 5 x 1 y m l cos _ l sin _ 5 + mg l cos mg 5 = (1.) (x g ;y g ) x 1 = x g l cos (1.) y 1 = y g l sin (1.5) Newton Euler ( ) m l 5 x g y g 5 + mg 5 = (1.) (x 1 ;y 1 ) (1.) (x 1 ;y 1 ) (_x 1+ ; _y 1+ ; _ + ) 1 1 _x 1+ _y 1+ _ + 5 = (1.) (_x 1 ; _y 1 ; _ ) ( 1 ; ) m ml sin m ml cos ml sin ml cos ml 5 _x 1+ _y 1+ _ + 5 = m ml sin m ml cos ml sin ml cos ml ( 1 ; ) 1 1+cos sin cos _x 1 = m sin cos 1+sin _y 1 5 _x 1 _y 1 _ (1.8) (1.9) ml sin _x 1+ +ml cos _y 1+ +ml _ + =[ 1] l cos l sin 5 m _x 1+ m _y 1+ (x 1 ;y 1 ) 5 = ml sin _x 1 +ml cos _y 1 +ml _ (1.8) 5 1
12 1 1 LAGRANGE
13 _x = f(x); x() = x (.1) x e f(x e )= (.) [Lyapunov ( )] x e Lyapunov (.1 ) 8 >; 9() > ; kx x e k <!kx(t) x e k < (.) Lyapunov x(t) x e [ ] Lyapunov 9 >; kx x e k <! lim t!1 kx(t) x e k = (.) x e x e x e [ ] 9 >;c>!kx(t) x e kce t kx x e k (.5) x [Lyapunov ] (.1) V (x) x e x e 1
14 1 x x x e x(t) x 1.1: 1. V (x) > ;V(x e )=. V (x) V _ (x) < (x = x e ) V (x) Lyapunov Lyapunov _x = ksin(x); k> (.) x e = Lyapunov V (x) = 1 x (.) V (x) > ( <x<;x= ) _V (x) =x _x = kxsin(x) < ( <x<;x= ) (.8) Lyapunov mx + c _x + kx = (.9) ms + cs + k = (.1) Routh Hurwitz m; c; k Lyapunov Lyapunov V (x) = 1 m _x + 1 kx (.11) x =[x; _x] T, x e =[; ] T V (x) > (x = x e ) V (x) _V (x) = _xmx + kx _x
15 (.1) _V (x) = _x(c _x kx)+kx _x = c _x (.1) x =[x; ] T V _ (x) = V (x) < (x = x e ) Lyapunov Lyapunov Lyapunov Lyapunov LaSalle [LaSalle ] (.1) V (x) x e x e 1. V (x) > ;V(x e )=. V (x) V _ (x)(x = x e ). V _ (x) x(t) =x e Lyapunov V _ (x) _x(t) (.1) (.1) x(t) (.1) kx = (.15) k > x = V _ x(t) = x e LaSalle x e Lyapunov _x = f(x; t); x() = x (.1) f(x e ;t)= (.1) [ K ] R + R + K 1. () =. (p) > 8 p >. Lyapunov [Lyapunov ( )] x e = ( )
16 1 1. K ; V (x; t) (kxk) V (x; t) (kxk) (.18). K _ V (x; t) _V (x; t) (kxk) (.19) K t Lyapunov.1. Barbalet() Lyapunov Lyapunov Lyapunov Barbalet f(t) 1. _ f! )= f t = 1 f(t) = log t. f t = 1 )= _ f! f(t) =exp(at) cos(exp(bt))(b >a>).. f(t) _ f ) f t = 1 Barbalet [] f(t) 8 R>; 9(R) > ;t 1 ;t ; jt 1 t j <)jf(t 1 ) f(t )j <R R t exp(t) Barbalet [Barbalet ] f t = 1 f _ f _! (t!1) [ ] f t = 1 f f _! (t!1) L p (; 1) = f(t) Z 1 jy( )j p d < 1 (.) L 1 (; 1) =ff(t) jess:supjf(t)j < 1for t (; 1)g (.1) Lebesgue() ess:sup sup sup H(s) strictly stable( ) H(1) = strictly proper( )
17 .1. 1 [ ] H(s) u L (; 1) Y (s) =H(s)U(s) (.) y y L (; 1) \ L 1 (; 1) _y L (; 1) Barbalet [ ] f f L (; R 1) f _ L 1 f f(t)! (t!1) t g(t) = jf( )j f _ L 1 Barbalet _g! f(t)
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19 1. PTP(Point ToPoint). CP (Continuous Path) PTP CP 1.. x d q d q x q x d PTP CP.1 x d q d i 1 i i 1 i (.1) ( )! m J m, m, K J m _! m + m! m = Kv i (.1) 19
20 Link i 1:n _q i, i z i1! m, m Joint i Link i-1 v.1: i 1 n! m = n _q i (.) n m = i (.) (.1) _q i n J m q + n m = nkv i (.) D(q)q + C(q; _q)_q + G(q) = i X j d ij q + h i (q; _q) = i (.5) h i (q; _q) f i (q; _q; q) = (.) (.5) X j=1;j=i d ij q j + h i (q; _q) (.) (d ii (q)+n J m )q i + n m _q i + f i (q; _q; q) =nkv (.) q(q ) d ii = d ii (q) (.8) n 1 d ii (q) d ii = ( d ii + n J m )q i + n m _q i = i f i (q; _q; q) (.9) f i
21 .. PD 1 f i (q; _q; q) v nk 1 n Jms +n m _q i 1 s q i.: f i nk d ii + n J m n (f i ) f i (q; _q; q) q q. PD PTP q q d = K d _q(t) K p (q(t) q d )+G(q) (.1) K d ;K p x = [q T ; _q T ] T x x d =[q T ; d T ] T LaSalle (.1) D(q)q + C(q; _q)_q + K d _q + K p (q q d )= (.11) q d e := q q d _q = _e; e =q (e; _e) D(e + q d )e + C(e + q d ; _e)_e + K d _e + K p e = (.1) q d q d (e; _e) (; ) Lyapunov V (e; _e) = 1 _et D(q)_e + 1 et K p e (.1) D(q) K p V (e; _e) > (e; _e = (; )) V _V = _e T D(q)q + 1 _et _D(q)_e + e T K p _e (.1) (.1) _V = _e T (C(e + q d ; _e)_e K d _e K p e)+ 1 _et _D(q)_e + e T K p _e (.15)
22 _V = 1 _et ( _ D(e + q d ) C(e + q d ; _e)) _e _e T K d _e (.1) D(e _ + q d ) C(e + q d ; _e) = D(q) _ C(q; _q) _V = _e T K d _e (.1) LaSalle _V = _e T K d _e (.18) K d _q q (.1) K p e = (.19) K p e = (e; _e) =(; ) V _ (.1) (e; _e) =(; ) K d ;K p q. x d (t) q d (t) q d (t) ( ) f x = f(q) (.) x d q d x s q s x s = f(q s ) (.1) x s x q f x s + x = f(q s + q) (.) x s + x f(q s )+J(q)q; J (.) q = J 1 x (.) x x d x -J 1 x _q d = J 1 (q d )_x d (.5)
23 .. ( ) _q = _q d Z t _x = J(q d )J d _x d ; x(t) =x s + _x d d (.) _q d _q _q d = J 1 (q)(_x d K p (x x d )) (.) _q J 1 (q)(_x d K p (x x d )) (.8) e := x x d _x = _x d K p (x x d ) (.9) _e + K p e = (.) K p. ( ) PD PTP CP = D(q)v + C(q; _q)_q + G(q) (.1) v D(q)q + C(q; _q)_q + G(q) =D(q)v + C(q; _q)_q + G(q) (.) D(q) q = v (q i = v i ;i=1; 111;n) (.) v q (. ) q q d e := q q d ; (e i = q i q di ) (.) v =q d K d _e K p e (.5) K d ;K p (.) e + K d _e + K p e = (.) V = 1 _et _e + 1 et K p e (.) Lyapunov
24 v D(q) D(q)q + C(q; _q)_q + G(q) = q; _q q C(q; _q)_q + G(q) I s.: K d = diag(k d1 ; 111;k dn );K p = diag(k p1 ; 111;k pn ) (.8) e i e i + k di _e i + k pi e i = (.9) = ^D(q)v + ^C(q; _q)_q + ^G(q) (.) ^ (.5) PID Z v =q d K d _e K p e K i e( )d (.1) K d ;K p ;K i d dt R ed e _e 5 = I I 5 R ed e _e 5 + I 5 v (.) J(q) x = f(q) (.) _x = J _q (.) x = J q + _ J _q (.5) _q = J 1 _q (.) q = J 1 (x _ J _q) (.)
25 .5. 5 J T D(q)J 1 x + J T (C(q; _q) J T D(q) _ J)J 1 _x + J T G(q) =J T (.8) D x (x) := J T D(q)J 1 (.9) C x (x; _x) := J T (C(q; _q) J T D(q) _ JJ 1 (.5) G x (x) := J T G(q) (.51) x := J T (.5) D x (x)x + C x (x; _x)_x + G x (x) = x (.5) x d e x := x x d (.5) x = D x (x)v x + C x (x; _x)_x + G x (x) (.55) v x = x d K dx _e x K p e x (.5) x d q d D x (x) M _ x C x ( ).5 (Variable Structure Control:VSC) (. ) (Sliding Mode Control:SMC) ; () sup (M(q)) (.5) q inf (M(q)) (.58) q = ^C(q; _q)_q + ^G(q) k(q; _q; q d )Sgn(S) (.59) Sgn(S) = ( S ksk ksk = ksk = (.)
26 x x x 1 x 1 x x 1.: S S(e; _e) := _e +e (.1) h(q; _q) kc(q; _q)_q + G(q) ^C(q; _q)_q + ^G(q)k =: k ~ hk h(q; _q) (.) k() k(q; _q; _q d ; q d )= h(q; _q) + + kq d k + k_ek (.) V (S) (Lyapunov ) V (S) := 1 ksk = 1 ST S (.) _V = ksk _ ksk = S T (D 1 (q)(u ~ h) q d +_e) (.5) _V = ks T D 1 S=kSk + S T (D 1~ h q d +_e) (.) k ksk + ksk( h + kq dk + k_ek) (.) = ksk (.8) ksk = ksk ksk (.9) ksk t + ksk() (.) t ksk()= ksk ksk = _e = e (.1)
27 .5. e S=kSk S=kSk S Sat(S) = (.) ksk +
28 8
29 .1 q R n c i (q) =; (i =1; 111;m) (.1) C(q) =;C R m (.) D(q)_q + h(q) = (.) (.) _C(q) =J c _q = (.) J J c _q q (.) c (.) (.5) D(q)_q + h(q) = + c (.) T c _q = (.) _q (.5) c = J T c ; Rm (.8) (.5) J c q + _ J c _q = (.9) (.) D(q) J T c (q) J c (q) q = h(q; _q) J _ c _q (.1) q, (.1) 9
30 . x C(x) = (.11) _x = E f E Rmn (.1) C(x) E f E p E p rank = n (.1) E f E p q x x = f(q) (.15) _x = J _q; (.1) _C(x) =! E f J _q = (.1) D(q)q + h(q; _q) = J T E T f (.18) E p _x _x p _x p = E p _x (.19) E _x = _x p ; E := E p E f (.) E x + _ E _x = I x p (.1) (.1) x = J q + _ J _q (.)
31 .. 1 (.1) I x p = EJ 1 (D 1 ( h J T E T f ) _ J _q)+ _ EJ _q (.) u 1 u x p = u 1 (.) = u (.5) (.) I u 1 = EJ 1 (D 1 ( h J T E T f u ) _ J _q)+ _ EJ _q (.) (JE 1 = D I! ) u 1 EJ q + h + J T E T u f (.) (.) I x p = I u 1 + EJD 1 J T E T f (u ) (.8) [ I] =E f JD 1 J T E T (u f ) (.9) E f E f JD 1 J T E T f u = (.8) x p = u 1 x p x d, e p := x p x d d, e f := d u 1 =x d K 1 e p K _e p ; K 1 > ; K > (.) Z t u = d K e f ()d; K > (.1)..1
32 Gc r f r f l rc (a) (b) Rcc.1: RCC F e J D(q)_q + h(q) = J T F e (.) J T D(q)J 1 x + J T (C(q; _q) J T D(q) _ J)J 1 _x + J T G(q) =J T F e (.) F e x; _x ( ) M m e + D m _e + K m e = F e (.) e = x x d x d F e (.) q x = M 1 (x m d D m _e K m e + F e ) (.5) (.) = J J T D(q)J 1 M 1 m (x d D m _e K m e + F e )+J T (C(q; _q) J T D(q) J)J _ 1 _x + J T G(q)+Fe (.) F e M 1(x m d D m _ek m e+ F e ) ()...1(a) (b) Rcc (RCC:Remote Compliance Center)
33 .. RCC (a) M _v + G = f c + f (.) I _! +! I! = c + r f (.8) v;! f c ; c Rcc M d _v d = f (.9) I d _! d +! d I d! d = r c f (.) v d ;! d Rcc f c ; c (.8) (.) c c = r f + r c f = l f (.1) v = v d +! d l (.) _v = _v d + _! d l +! d! d l (.) _v = _v d = M 1 d f (.) f c M 1 (f c + f G) =M 1 d f + _! d l +! d! d l (.5) f c = M(M 1 d f + _! d l +! d! d l) f + G (.) _! d = I 1 d (r c f! I d!) (.).. (VIM) (.5) (Virtual Reference) x r v x = v (.8) x e := x x r (.9)
34 e = v x r (.5) u := v x r d dt e _e e 5 = I I 5 e _e e 5 + I 5 _u (.51) x T =[e; _e T ; e T ] _u Z 1 J = x T Qx + _u T R _udt (.5) _u = Fx (.5) x() = R ed u(t) =F Z x = F e _e 5 (.5) e ( ) R ed v =x r F e _e 5 (.55)
35 5 ( ) F 1 (s) v (s) = H(s) v 1 (s) F (s) (5.1) H(s) F 1 (s) v 1 (s) F (s)+v (s) = S(s) F 1 (s)+v 1 (s) F (s) v (s) (5.) S(s) H(s) S(s) S(s) = 1 1 (H(s) I)(H(s)+I) 1 (5.) 5
36 5 V1 V F1 F 5.1. n- Z T F T (t)v(t)dt ; for 8 T (5.) (H 1 ) [ ] n- ks(s)k 1 1 (5.5) kxk L p ks(s)k 1 = sup max (S (!)S(j!)) = sup ksxk! kxk S (j!)=s T (j!); kxk = Z 1 x T (t)x(t)dt
37 5.1. [ ]( ) ks(s)k 1 kf + vk kf vk (5.) Z 1 <F;v>; <F;v>:= F T (t)v(t)dt (5.) 5.1. v (t) =v 1 (t T ) (5.8) F 1 (t) =F (t T ) (5.9) T F1(s) v (s) = H(s) = S(s) = e Ts e Ts e Ts e Ts tanh(ts) sech(ts) sech(ts) tanh(ts) v 1 (s) F (s) (5.1) (5.11) (5.1) S H 1 S T (j!)s(j!)= tan (!T)+sec (!T) jtan(!t)sec(!t) jtan(!t)sec(!t) tan (!T)+sec (!T) (5.1)! =(jtan(!t)j + jsec(!t)j) ; (jjtan(!t)jjsec(!t)jj) (5.1) q ks(s)k 1 =sup max (S T (j!)s(j!)) = sup jtan(!t)j + jsec(!t)j = 1 (5.15)!! 5.1. D(q)q + C(q; _q)_q + G(q) = (5.1) q : ( q T =[ 1 ; 111; n ] : D(q) : C(q; _q)_q : G(q) :
38 8 5 _ D(q) C(q; _q) (5.1) C(q; _q)( ) P P T = P (5.18) x F F x T Px = (5.19) = G(q)+F (5.) D(q)_v + C(q; v)v = F (5.1) _q := v F v V (q; v)( ) V (q; v) = 1 vt D(q)v (5.) V _V = v T (D _v + 1 D(q)v) _ V (q; v) (5.) = v T (F C(q; v)v + 1 D(q))v _ = v T F + 1 vt ( _ D(q) C(q; v))v = v T F T Z T v T Fdt = V (T ) V () V () (5.) (5.1) v D F C
39 (5.1 D m (q m ) v m _ + C m (q m ;v m )v m = F cm + F o (5.5) D s (q s )_ v s + C s (q s ;v s )v s = F cs F e (5.) F o : F e : 1. v s v m ( ). F o F e ( ) F cs : F cs = K v e + K p R edt; e := vm v s F cm : F cm = F cs PD v s = v m = F cs = F e F m = F cm F cm = F cs F m = F e F m ;F e ( ) Vm Vs e Dm Ds Kv Cm Fcm Fcs Cs Kp Fm Fe v m F c v sd (t) =v m (t T ) F md (t) =F cs (t T ) ( )
40 5 Vm Vsd Vs delay e Dm Ds Kv Cm Fcm Fmd Fcs Cs Kp Fm Fe Vm Vsd Fmd Fcs 5.1. F md (s) v m (s) F cs (s)+v sd (s) S(s) = = S(s) e st e st F md (s)+v m (s) F cs (s) v sd (s) (5.) S (j!)s(j!) = I ks(s)k 1 = 1 F md (t) = v m (t)+(f cs v sd )(t T ) v sd (t) = F cs (t)+(f md + v m )(t T ) T F md = F cs ;v sd = v m T ( T ) 5.1. F m ; F e D v (q v )_v v + C v (q v ;v v )v v + K v q v = F m F e (5.8) K v
41 Vm Vm Vsd Vsd + delay - Fmd Fcs Fmd + - Fcs Vv Dv Cv Kv -Vv Fm Fe
42 5 Dv Cv Kv Vs Vs em es Dm Ds Fm Fe Kv Kv Cm Fcm Fcs Cs Kp Kp Fm Fe
43 5.1.
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