¯x(k + 1) = ((¯xr(k + 1)) T , ¯x1, ¯y1, . . . , ¯xm, ˆym) T = ((ˆxr(k) ⊕ x k k+1) T , ˆx1, ˆy1, . . . , ˆxm, ˆym) T , P(k + 1|k) = J1P(k)J T 1 + J2PodomJ T 2 , ⊕ ˆxr(k) x k k+1 ˆxr(k) ⊕ x k ⎡ ˆxk + xodom cos k+1 = ⎣ ˆ θk − yodom sin ˆ θk ˆyk + xodom sin ˆ θk + yodom cos ˆ ⎤ θk ⎦ , ˆθk + θodom J1 J2 J1 = blkDiag(j1, I), J2 = ((j2) T , 0) T ⎡ 1 0 −xodom sin j1 = ⎣ , ˆ θk − yodom cos ˆ θk 0 1 xodom cos ˆ θk − yodom sin ˆ ⎤ θk ⎦ , ⎡ cos j2 = ⎣ 0 0 1 ˆ θk − sin ˆ θk sin 0 ˆ θk cos ˆ θk 0 0 0 1 ⎤ ⎦ . ¯xi(k + 1) = (¯xi, ¯yi) T ¯xr(k + 1) = (¯xk+1, ¯yk+1, ¯ θk+1) T −(¯xi − ¯xk+1) sin hi(¯xr(k + 1), ¯xi(k + 1)) = atan2 ¯ θk+1 + (¯yi − ¯yk+1) cos ¯ θk+1 (¯xi − ¯xk+1) cos ¯ θk+1 + (¯yi − ¯yk+1) sin ¯ . θk+1 ∂hi Hi = 0 · · · 0 ∂¯xr(k+1) ∂hi ∂¯xr(k + 1) = ∂hi ∂hi ∂¯xk+1 ∂ ¯yk+1 ∂hi/∂ ¯ θk+1 = −1 ∂hi ∂¯xk+1 ∂hi ∂¯xi = − = ¯yk+1 − ¯yi ∂hi ∂ ¯ θk+1 (¯xk+1 − ¯xi) 2 2 , + (¯yk+1 − ¯yi) ¯yk+1 − ¯yi (¯xk+1 − ¯xi) 2 2 , + (¯yk+1 − ¯yi) ∂hi ∂¯xi(k+1) , ∂hi ∂¯yk+1 ∂hi ∂¯yi 0 · · · 0 , ∂hi ∂¯xi(k + 1) = = = − ∂hi ∂¯xi ∂hi ∂ ¯yi ¯xk+1 − xi (¯xk+1 − ¯xi) 2 2 , + (¯yk+1 − ¯yi) ¯xk+1 − ¯xi h H , (¯xk+1 − ¯xi) 2 2 , + (¯yk+1 − ¯yi) h = (h T 1 , . . . , h T n) T , H = (H T 1 , . . . , H T n) T .
ˆx(k + 1) = x(k + 1|k + 1) P(k + 1|k + 1) ˆx(k + 1) = ¯x(k + 1) + K(z − h), P(k + 1|k + 1) = (I − KH)P(k + 1|k), K = P(k + 1|k)H T S −1 , S = HP(k + 1|k)H T + R, ν = z − h S K z z = h ν ˆx(k + 1) = ¯x(k + 1) R σ 2 zI σz x = (xk+1, yk+1) f(x) f(x) = Tr(P(k + 1|k + 1)), P(k + 1|k + 1) x(0) = (xk, yk), ˙x = −∇f(x), x(0) = (xk, yk), x(t + 1) = x(t) − h∇f(x(t)), (xk, yk) x(t) x t ∇f(x(t) f x(t) h ˙x = 0 x(t + 1) − x(t)
- Page 1 and 2:
R. Aragüés (1980, Zaragoza) recei
- Page 4:
R. Aragüés (1980, Zaragoza) recei
- Page 8:
R. Aragüés (1980, Zaragoza) recei
- Page 12 and 13:
R. Aragüés (1980, Zaragoza) recei
- Page 14 and 15:
R. Aragüés (1980, Zaragoza) recei
- Page 16 and 17:
R. Aragüés (1980, Zaragoza) recei
- Page 18:
n n
- Page 21 and 22:
n n
- Page 23 and 24:
y 1000 500 −500 2000 1000 0 z
- Page 25 and 26:
• •
- Page 27 and 28:
• •
- Page 29 and 30:
k−
- Page 31 and 32:
•
- Page 33 and 34:
•
- Page 35 and 36:
(x, y)
- Page 37 and 38:
ρi = 0
- Page 39 and 40:
j xr zj
- Page 41 and 42:
xri i = 1, 2 zij j
- Page 43 and 44:
• (xr, yr,
- Page 45 and 46:
% final divergence number of steps
- Page 47 and 48:
14 12 10 8 6 4 2 0 −2 −4 FINAL
- Page 49 and 50:
14 12 10 8 6 4 2 0 −2 −4 FINAL
- Page 51 and 52:
i mi ∈ N i
- Page 53 and 54:
i Hi Hi
- Page 55 and 56:
Lchild i Li Lchild j
- Page 57 and 58:
i Li(0) = Li, I i G(0) = Σ
- Page 59 and 60:
ˆ Σi G (t)−Qi G (t)
- Page 61 and 62:
10 8 6 4 2 0 −2 −4 −6 −8
- Page 63 and 64:
10 8 6 4 2 0 −2 −4 −6 −8
- Page 66 and 67:
10 8 6 4 2 0 −2 −4 −6 −8
- Page 68 and 69:
n i, j r, s G
- Page 70 and 71:
i [I k j ]r,s [i k j ]r
- Page 72 and 73:
LW = diag(W 1) − W
- Page 74 and 75:
Y = P T ZP r S2 . . . Sn 0 P = 0
- Page 76 and 77:
exw(t) exw(t + 1) = A exw(t), exw(
- Page 78 and 79:
k1a k2b |k1a−k2b| ≤ max{k
- Page 80 and 81:
k x k ∗ = rr T u k = 1x k avg, w
- Page 82 and 83:
k − 1 k β k λ t
- Page 84 and 85:
i ∈ V
- Page 86 and 87:
A(t + kl) t k Ψ (t1 +
- Page 88:
15 10 5 0 −5 −10 −15 −5 0 5
- Page 91 and 92:
15 10 5 0 −5 −10 −15 −5 0 5
- Page 93 and 94:
i th f i r A, Ar,s [A]r,s
- Page 95 and 96:
msum |Fdis| = n i=1 mi = msum
- Page 97 and 98:
i, ti t, Xij(t) ∼ Xij(t
- Page 99 and 100:
i ∈ Vcom, r ∈ Si.
- Page 101 and 102:
3 < df = 7 f A 1 f A 2
- Page 103 and 104:
[ji]s,r (d) i f i r Cq
- Page 105 and 106:
f i r ∈ ˜ Si Xij ¯r ∈
- Page 107 and 108: f i r ∈ ˜ Si i f i r
- Page 109 and 110: , s ∈ C [C]r,s ≥ 0, C,
- Page 111 and 112: 1, . . . , rℓ, Cℓ.
- Page 113 and 114: 0 6 1 9 7 8 8 3 1 0 7 9 8 8 3 6 1 6
- Page 115 and 116: 10 8 6 4 2 0 −2 −4 −6 −8
- Page 117 and 118: Gdis
- Page 120 and 121: Gdis
- Page 122 and 123: i, j e, e ′ e i
- Page 124 and 125: 0 < θi < π i ∈ V
- Page 126 and 127: lim t→∞ T i G(t) = (R i ) T T
- Page 128 and 129: zθ ∈ Rm Σzθ ∈ Rm×m
- Page 130 and 131: ˆx a Va ˆ θa Va Υw = Σ
- Page 132 and 133: tmax ¯ θ a i tmax ¯
- Page 134 and 135: i ˆp a i = Υˆp a Va ˆpaV a =
- Page 136 and 137: ˆx a V
- Page 138 and 139: G a ∈ Ni i ∈ Va J
- Page 140 and 141: i ∈ V ˆx cen i (t)
- Page 142 and 143: ρ(J) = λeff(W) ||ecen(t)||2
- Page 144 and 145: 3 m G
- Page 146 and 147: 3.38 ◦ 1.87 ◦ x cm cm y
- Page 148 and 149: −2 −2.5 −3 −3.5 −4 Centr.
- Page 150 and 151: 35 30 25 20 15 10 5 0 0 200 400 600
- Page 152 and 153: 35 30 25 20 15 10 5 0 0 200 400 600
- Page 154 and 155: k k
- Page 156 and 157: P(k + 1|k) = I Si Si = 1 +
- Page 160 and 161: 8 6 4 2 0 −2 F1 Initial map −4
- Page 162 and 163: i 1 · · · m x 1 i fi1(x 1 i )
- Page 164 and 165: G n k k ∈ N i, j t
- Page 166 and 167: i xi(t) xj(t) (i)
- Page 168 and 169: i ˜ Cij(k) ˜ Cij(k) = 0
- Page 170 and 171: T = diam(G) βi(T ) i ∈ V
- Page 172 and 173: L V T L LVL = λL = diag(0, λ2(
- Page 174 and 175: ˙x(t) = −Lˆx(t) = u(t), ei(t) =
- Page 176 and 177: F 16 r1
- Page 178 and 179: 14 12 10 8 6 4 2 0 −2 λ * (L) Es
- Page 180 and 181: 60m × 45m
- Page 182 and 183: 15 10 5 0 −5 −10 −15 F23 −5
- Page 184 and 185: 4 2 0 3000 2000 1000 x 10 4 0 20 40
- Page 186 and 187: 23 22.5 22 0.5 −0.5 0 20 40 23 22
- Page 188 and 189: 1 7 16
- Page 190 and 191: 6 4 2 0 −2 k=1 k=2 k=3 k=4 k=5
- Page 192 and 193: 9 9 9
- Page 194 and 195: (C) msum
- Page 196 and 197: (c) msum
- Page 198 and 199: y −1000 500 2000 x
- Page 200 and 201: −200 200 400 0 R9 R7 R5 R2 R6 −
- Page 202: 2000 1000 0 −1000 −1000 0 1000
- Page 205 and 206: 2000 1000 0 −1000 −1000 0 1000
- Page 208 and 209:
2000 1000 0 −1000 −1000 0 1000
- Page 210 and 211:
2000 1000 0 −1000 −1000 0 1000
- Page 212 and 213:
2000 1000 0 −1000 −1000 0 1000
- Page 214 and 215:
2000 1000 0 −1000 −1000 0 1000
- Page 216 and 217:
O(n)
- Page 218 and 219:
p
- Page 220:
p
- Page 224 and 225:
60×45m