PFC Alvaro Bravo Sancho

8/17/2019 PFC Alvaro Bravo Sancho

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α

α

β

β


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α

α

α

α

β

β

β

β


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Capı́tulo1


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•

•

•

•

•


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Capı́tulo2


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q = [q 1, q 2, . . . , q i] q i ∈ R i = 1, . . . , D

=

R3x3 p3x1

f 1x3 w1x1

=

R3x3 p3x1

f 1x3

w1x1

R3x3 p3x1

=

R3x3 p3x1

0 1

=

θ j

d j

a j

α j

j = 1, . . . , D


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θ j x j−1 x j z j−1

d j

z j−1 x j z j−1

a j z j−1 x j

x j z j−1 z j

α j z j−1 z j x j

A j−1

j

=

cos θ j − cos α j sin θ j sin α j sin θ j a j cos θ j

sin θ j cos αi cos θ j − sin α j cos θ j a j sin θ j

0 sin α j cos α j d j

0 0 0 1

T 0n

f k(q ) = T 0n =

n

j=1

A j−1 j = A01A

12 . . . A

j−1 j . . . A

n−1n


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a j d j α j θ j

q

q = f −1k ( p, ϕ)

ϕ

q


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q


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{ q 1, . . . , q i, . . . , q NP } q i = (q 1,i, . . . , q j,i, . . . , q N,i)

i = 1, . . . , N P

( pi, ϕi) = f k( q i), ( pi, ϕi) ∈ C

pi ϕi f k

q j,i q i q

−

j ≤ q j,i ≤ q + j

q − j q

+ j j = 1, . . . , N

( pd, ϕd)

q i

E p =| pd − pi | E o =| ϕd − ϕi |

( pi, ϕi)


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f (q ) = w pE p + woE o

w p wo

q

q − j ≤ q j ≤ q + j


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Capı́tulo3


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f (x),

x ∈ C

x

x


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(x, g)

P (x, g) = (x1,g, . . . , xi,g, . . . , xNP,g)

xi,g

xi,g = (x1,i, . . . , x j,i, . . . , xD,i)

(x, 0) = (x1,0, . . . , xi,0, . . . , xNP,0)

xi,0 = {x j,i} = x−

j + rand j(0, 1)(x+ j − x

−

j ), = 1, . . . ,

rand j(0, 1)

[0, 1]

x j,i xi,0

xr1 xr2 xr3 r1 r2 r3

vi,g

vi,g = xr1,g +

(xr2,g − xr3,g)


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[0, 1+]

xr2,g − xr3,g

xr1

ui,g

(u, g)

ui,g

vi,g xi,g

ui,g = u j,i =

v j,i, rand j(0, 1) ≤ CR = jrand

x j,i,

∈ [0, 1]

rand j(0, 1) u j,i

vi,g xi,g

= jrand ui,g

vi,g

xi,g

vi,g

rand j(0, 1)

xi,g


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ui,g = u j,i =

v j,i, rand j(0, 1) ≤ C R

x j,i,

rand j(0, 1) > CR

(x, g)

(u, g)

xi,g ui,g

xi,g+1 = x j,i = u

i,g,

f (ui,g) ≤ f (xi,g)

xi,g,

(x, g + 1)


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D, gmax, N P , F ∈ (0, 1+), CR ∈ [1, 0], x

+ j yx

−

j

i ≤ N P ∧ j ≤ D

x j,i = x−

j + rand j(0, 1)(x+ j − x

−

j )

g ≤ gmax

i ≤ N P

r1, r2, r3 = round(rand(1, N P ))

jrand = round(rand(1, D))

j ≤ D

rand(0, 1) ≤ C R ∨ j = jrand

u j,i = x j,r1 + (x j,r2 − x j,r3)

u j,i = x j,i

f (ui,g) ≤ f (xi,g)

xi,g+1 = ui,g

xi,g+1 = xi,g

g = g + 1


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≤

≤

≤

≤

F crit

F crit =

1 − C R2

N P

∈ [0, 1]

(u, g)


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≤

≤

≤ ≤

•

x(r1,g)

x(best,g)

•

•

• vi,g = xr1,g + (xr2,g − xr3,g)

• vi,g = xbest,g + (xr2,g − xr3,g)

• vi,g = xbest,g + (xr2,g + xr3,g − xr4,g − xr5,g)

• vi,g = xr1,g + (xr2,g + xr3,g − xr4,g − xr5,g)

• vi,g = xi,g + (xbest,g − xi,g) + (xr2,g − xr3,g)


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(x, g)

P = (x1, . . . , xi, . . . , xNP ) f (xi) ≤ f (xi+1)

W ⊂

δ

W = (x1, . . . , xi, . . . , xδ),


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S ⊂ P

β

S = (x1, . . . , xi, . . . , xβ),

β δ δ =

N P ∗ DRATE

100

δ

Q

S

α

α = σ(λ)

Q = (x1, . . . , xi, . . . , xδ), xi = xs + α

λ

s

[1, β ]

W

Q

δ


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DRATE,α = σ(λ), β

P = {x1, . . . , xi, . . . , xN P }

f (xi) ≤ f (xi+1)

i ∈ [N P − δ + 1, N P ]

s = rand[1, β ]

Q = xs + α

f ( Q) < f ( W )

xi = Q


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Capı́tulo4


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ϕ

a j α j d j θ j

a1 θ1

a2 θ2

a3 θ3


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a1 a2 a3

x = a1cos(θ1) + a2cos(θ1 + θ2) + a3cos(θ1 + θ2 + θ3)

y = a1sin(θ1) + a2sin(θ1 + θ2) + a3sin(θ1 + θ2 + θ3)

ϕ = θ1 + θ2 + θ3

φ,θ,ψ


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a j α j d j θ j

θ1

a2 θ2

a3 d3 θ3

d4

θ4

θ5

θ6

a2 a3 d3 d4

T ( j−1)

j


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w p wo

1

Σai

1

2π

λKC P d

2π


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Σai λKC

P d

ϕ

ϕ

φ

θ

ψ

φ,θyψ

%


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M e ± ST De

M i ± ST Di


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%

±

E P ± ± ± ±

E O ± ± ± ±

E T ± ± ± ±

±

± ± ± ±

± ± ± ±

± ± ± ±


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%

±

E P ± ± ± ±

E O ± ± ± ±

E T ± ± ± ±

±

±

±

±

±

±

±

±

±

±

±

±

±


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%

±

E P ± ± ± ±

E O ± ± ± ±

E T ± ± ± ±

±


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±

±

±

±

±

±

±

±

±

±

±

±


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%

±


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E P ± ± ± ±

E O ± ± ± ±

E T ± ± ± ±

±

±

±

±

±

±

±

±

±

±

±

±

±


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∈ [0, 1]


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(u, g)

≤ ≤

≤ ≤

%

±

E P ± ± ± ±

E O ± ± ± ±

E T ± ± ± ±

±


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±

±

±

±

±

±

±

±

±

±

±

±


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%

±


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E P ± ± ± ±

E O ± ± ± ±

E T ± ± ± ±

±

±

±

±

±

±

±

±

±

±

±

±

±

PFC Alvaro Bravo Sancho

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