Show PDF File - robotics - Universidad de Zaragoza

More documents

Recommendations

Info

i ˆp a i = Υˆp a Va ˆpaV a = B Σ−1 w w, ˆx a i ˆθ a i = M −1 i (fi(ˆp a V) + mi) , Mi fi(pa V (t)) mi M = blkDiag(M2, . . . , Mn) ˆq a Va ˆpaV a ˆqa Va = (ˆx a 2) T θˆ a 2, . . . , (ˆx a n) T T θˆ a n Υˆp a V a Υˆq a V a ˆpa i (t) i ∈ V a ˆp a i = [(ˆx a i ) T θˆ a i ] T ρ(M −1 (M − Υˆq a Va)) < 1 ρ(I − M −1 Υˆq a Va) < 1. λ(I − M −1Υˆq a Va) = 1 − λ(M −1Υˆq a Va) 0 < λ(M −1Υˆq a V 0 < λ(M −1Υˆq a V M −1 Υˆq a Va λ(M −1Υˆq a V λmin(M −1 ) λmax(Υˆq a Va ) 0 < λmin(M −1 ) λmax(Υˆq a Va ) 0 < λ(M −1Υˆq a Va) a) < 2. a) a) ≥ λ(M −1Υˆq a Va) < 2 Υˆq a Va adj(G) ⊗ I3 adj(G) I3 3 × 3 s = 1 adj(G)ij = 0 for |i − j| > s. Υˆq a V a s′ = 1 λmax(M −1 Υˆq a Va) < 2s′ = 2. ¯ θa V ˜ θa V
pi i xi i ∈ {1, . . . , n} p− xi ∈ R p xj −xi e = (i, j) ∈ E G = (V, E) i ze ∈ R p j ze = xj − xi + ve, ve ∼ N (0p×p, Σze) z ∈ R mp Σz ∈ R mp×mp m z = (z T 1 , . . . , z T m) T , Σz = blkDiag(Σz1, . . . , Σzm), G i Ni n z a ∈ V a = 1 ˆx a a = 0p a ˆx a V a ∈ R(n−1)p ˆx a V a = ((ˆxa 2) T , . . . , (ˆx a n) T ) T V a = V\{a} a ˆx a V a = Σˆx a V a (Aa ⊗ Ip) Σ −1 z z, Σˆx a V a = (A a ⊗ Ip)Σ −1 z (A a ⊗ Ip) T −1 , A a ∈ R (n−1)×m G a ˆx a V = (0Tp , (ˆx a Va)T ) T Σˆx a V = blkDiag 0p×p, Σˆx a Va a i Ni
Page 1 and 2:
R. Aragüés (1980, Zaragoza) recei
Page 4:
Page 8:
Page 12 and 13:
Page 14 and 15:
Page 16 and 17:
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 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
show all

Show PDF File - robotics - Universidad de Zaragoza

Create successful ePaper yourself

Delete template?

Save as template?