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
- 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: 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)
- 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 158 and 159:
¯x(k + 1) = ((¯xr(k + 1)) T , ¯x
- 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