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n ∈ N n Gcom = (Vcom, Ecom) Vcom = {1, . . . , n} i j (i, j) ∈ Ecom Ni i Ni = {j | (i, j) ∈ Ecom}. i Si mi Si = {f i 1, . . . , f i mi }. Si Sj j ∈ Ni Si Robot C f C 1 f C 2 f B 2 Robot B f B 1 f D 1 X f D 2 Robot D f A 2 f A 1 Robot A A B C D A f A 1 f D 2 f B 1 B f B 1 f C 1 C f C 1 f D 1 f D 1 f D 2 i, j k r, r ′ , s, s ′ , r th
i th f i r A, Ar,s [A]r,s (r, s) Aij (i, j) Ik k × k 0k1×k2 k1 × k2 F Si Sj, ij ∈ Nmi×mj i 1 if fr and f j s are associated, [ij]r,s = 0 otherwise, r = 1, . . . , mi s = 1, . . . , mj F F Si F (Si, Si) = ii = I ij mi r=1 [ij]r,s ≤ 1 r = 1, . . . , mi s = 1, . . . , mj mj s=1 [ij]r,s ≤ 1, i j Si Sj F (Si, Sj) = ij = T (F (Sj, Si)) ji = T n n n F Si Sj i, j ∈ {1, . . . , n} Gcen = (Fcen, Ecen) Fcen f i r i = 1, . . . , n r = 1, . . . , mi f i r f j s [ij]r,s = 1
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R. Aragüés (1980, Zaragoza) recei
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n n
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n n
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y 1000 500 −500 2000 1000 0 z
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• •
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• •
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k−
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•
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•
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(x, y)
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ρi = 0
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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: 15 10 5 0 −5 −10 −15 −5 0 5
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)
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ρ(J) = λeff(W) ||ecen(t)||2
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3 m G
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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
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35 30 25 20 15 10 5 0 0 200 400 600
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k k
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P(k + 1|k) = I Si Si = 1 +
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¯x(k + 1) = ((¯xr(k + 1)) T , ¯x
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8 6 4 2 0 −2 F1 Initial map −4
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i 1 · · · m x 1 i fi1(x 1 i )
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G n k k ∈ N i, j t
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i xi(t) xj(t) (i)
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i ˜ Cij(k) ˜ Cij(k) = 0
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T = diam(G) βi(T ) i ∈ V
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L V T L LVL = λL = diag(0, λ2(
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˙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
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15 10 5 0 −5 −10 −15 F23 −5
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4 2 0 3000 2000 1000 x 10 4 0 20 40
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23 22.5 22 0.5 −0.5 0 20 40 23 22
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1 7 16
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6 4 2 0 −2 k=1 k=2 k=3 k=4 k=5
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9 9 9
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(C) msum
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(c) msum
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y −1000 500 2000 x
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−200 200 400 0 R9 R7 R5 R2 R6 −
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2000 1000 0 −1000 −1000 0 1000
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2000 1000 0 −1000 −1000 0 1000
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2000 1000 0 −1000 −1000 0 1000
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2000 1000 0 −1000 −1000 0 1000
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2000 1000 0 −1000 −1000 0 1000
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2000 1000 0 −1000 −1000 0 1000
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O(n)
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p
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p
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60×45m
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