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288 Autonomous Mobile Robots

The auxiliary signal u d is chosen as

u d1 −k u1 z 1 + h(Z 2 , t)
u d = =
u d2 −ρ 1 z 2 u d1 − k u2 z 3
where h(Z 2 , t) is chosen as

2
2
h(Z 2 , t) = (z + z ) sin t
2
3
It is easy to see that the selected h(Z 2 , t) satisfies Assumption 7.3.
In the simulation, the parameters of the system are assumed to be m 0 =
I 0 = 1.0, P = 0.1, L = 1.0, and L 1 = L 2 = 1, R 1 = R 2 = 1, K N1 = K N2 =
T
1, K a1 = K a2 = 1. The initial estimate ˆ θ(0) =[0.5, 0.5] which is different
from the true value. The design parameters are chosen as k u1 = 0.2, k u2 = 1.0,
ρ 1 = 1.0, = diag[10, 10], γ R = γ L = γ a = γ N = 1, and K e = diag[5, 5].

30

x 1 (rad) 20
10
0
0 5 10 15 20 25 30
Time (sec)

5
x 2 (m) 0

–5
0 5 10 15 20 25 30
Time (sec)

5

x 3 (m) 0

–5
0 5 10 15 20 25 30
Time (sec)

FIGURE 7.2 Responses of states x 1 , x 2 , and x 3 .

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c007” — 2006/3/31 — 16:43 — page 288 — #22