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14 12 10 8 6 4 2 0 −2 −4 FINAL MAP: INVERSE−DEPTH Delayed (two observations) F36 F37 F28 F42 F43 F27 F38 F13 F44 F7 F8 F9 F18 F10 F11 F39 F12 F1 F2 F26 F34 F33 F32 F31 F40 F35 F41 F3 F4 F29 F30 F22 F20 F23 F14 F5 F6 −5 0 5 10 15 F25 F24 F21 F19 F17 F16 F15 14 12 10 8 6 4 2 0 −2 −4 FINAL MAP: INVERSE−DEPTH Delayed Feature not aligned F28 F27 F26 F25 F24 F23 F34 F17 F33 F40 F32 F31 F30 F29 F22 F35 F36 F37 F38 F41 F42 F43 F44 F7 F8 F9 F10 F18 F11 F39 F12 F1 F2 F3 F4 F5 F6 −5 0 5 10 15 F21 F20 F19 F16 F15 F14 F13 14 12 10 8 6 4 2 0 −2 −4 FINAL MAP: INVERSE−DEPTH Delayed (Finite <strong>de</strong>pth) F36 F37 F42 F43 F38 F44 F8 F7 F39 F1 F2 F3 −5 0 5 10 15 F34 F35 F28 F27 F33 F40 F41 F32 F26 F31 F25 F4 F24 F17 F29 F30 F22 F16 F5 F21 F20 F19 F23 F15 F14 F13 F18 F9 F10 F11 F12 % final divergence number of steps to initialize features 100 4 3 2 1 0 80 60 40 20 0 Final divergence id−l id−u xy−f 0.1250.25 0.5 step size 1 % consistent features 100 80 60 40 20 0 Map consistency id−l id−u xy−f 0.1250.25 0.5 step size 1 Feature initialization step id−l id−u xy−f 0.1250.25 0.5 step size 1 % features used per step 100 80 60 40 20 0 Feature usage id−l id−u xy−f 0.1250.25 0.5 step size 1 % steps divergence % consistent features per step 100 80 60 40 20 0 100 80 60 40 20 0 0.1250.25 0.5 step size 1 F6 Trajectory divergence id−l id−u xy−f Map consistency per step id−l id−u xy−f 0.1250.25 0.5 step size 1 x dmin = 0.5m
14 12 10 8 6 4 2 0 −2 −4 FINAL MAP: INVERSE−DEPTH Delayed (two observations) F36 F37 F28 F42 F43 F27 F38 F13 F44 F7 F8 F9 F18 F10 F11 F39 F12 F1 F2 F26 F34 F33 F32 F31 F40 F35 F41 F3 F4 F29 F30 F22 F20 F23 F14 F5 F6 −5 0 5 10 15 F25 F24 F21 F19 F17 F16 F15 14 12 10 8 6 4 2 0 −2 −4 FINAL MAP: INVERSE−DEPTH Delayed Feature not aligned F28 F27 F26 F25 F24 F23 F34 F17 F33 F40 F32 F31 F30 F29 F22 F35 F36 F37 F38 F41 F42 F43 F44 F7 F8 F9 F10 F18 F11 F39 F12 F1 F2 F3 F4 F5 F6 −5 0 5 10 15 F21 F20 F19 F16 F15 F14 F13 14 12 10 8 6 4 2 0 −2 −4 FINAL MAP: INVERSE−DEPTH Delayed (Finite <strong>de</strong>pth) F36 F37 F42 F43 F38 F44 F8 F7 F39 F1 F2 F3 −5 0 5 10 15 F34 F35 F28 F27 F33 F40 F41 F32 F26 F31 F25 F4 F24 F17 F29 F30 F22 F16 F5 F21 F20 F19 F23 F15 F14 F13 F18 F9 F10 F11 F12 % final divergence number of steps to initialize features 100 4 3 2 1 0 80 60 40 20 0 Final divergence id−l id−u xy−f 0.1250.25 0.5 step size 1 % consistent features 100 80 60 40 20 0 Map consistency id−l id−u xy−f 0.1250.25 0.5 step size 1 Feature initialization step id−l id−u xy−f 0.1250.25 0.5 step size 1 % features used per step 100 80 60 40 20 0 Feature usage id−l id−u xy−f 0.1250.25 0.5 step size 1 % steps divergence % consistent features per step 100 80 60 40 20 0 100 80 60 40 20 0 0.1250.25 0.5 step size 1 F6 Trajectory divergence id−l id−u xy−f Map consistency per step id−l id−u xy−f 0.1250.25 0.5 step size 1 x dmin = 0.5m
Page 1 and 2: R. Aragüés (1980, Zaragoza) recei
Page 4: R. Aragüés (1980, Zaragoza) recei
Page 8: 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: % final divergence number of steps
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
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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
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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
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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
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−2 −2.5 −3 −3.5 −4 Centr.
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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
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P(k + 1|k) = I Si Si = 1 +
Page 158 and 159:
¯x(k + 1) = ((¯xr(k + 1)) T , ¯x
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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) =
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F 16 r1
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14 12 10 8 6 4 2 0 −2 λ * (L) Es
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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
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