Page 178 - Human Inspired Dexterity in Robotic Manipulation

176 Human Inspired Dexterity in Robotic Manipulation

Table 9.2 Nominal desired grasping force and gains for the simulations
10.0 N
f d
4.762
K p
0.238
K o
diag 1:003,0:651,0:735,0:278,0:177Þ 10 1 (Ns m/rad)
ð
C a
diag 0:606,0:687,0:786,0:642,0:198Þ 10 2 (Ns m/rad)
ð
C 1
diag 0:468,0:780,0:318,0:099Þ 10 2 (Ns m/rad)
ð
C 2
diag 0:648,0:780,0:318,0:099Þ 10 2 (Ns m/rad)
ð
C 3
T
x d ð 0:100,0:500,0:700Þ (m)
2 3
0:88 0:32 0:34
R d
0:34 0:94 0:00
4 5
0:32 0:12 0:94
Table 9.3 Initial conditions of the simulations
0 (rad/s)
_ q
T
q a ð 0:183, 1:369,1:898,1:343, 0:787Þ (rad)
T
q 01 ð 1:007,0:235, 0:771,1:338,0:328Þ (rad)
T
q 02 ð 0:242, 0:733,1:122,0:754Þ (rad)
T
q 03 ð 2:019, 0:924,0:912,1:088Þ (rad)
0 (m/s)
_ x
T
x ð 0:158,0:501,0:681Þ (m)
ω 0 (rad/s)
2 3
1:00 0:00 0:00
R
4 0:00 1:00 0:00 5
0:00 0:00 1:00
Figs. 9.4 and 9.5 show the transient responses of the x component of the
measured x and of θ z , which is the measured rotational angle around the
z-axis expressed in terms of XYZ Euler angles, respectively. In these figures,
represent the transient responses of x and θ z when the pro-
x new and θ z new
rep-
posed control inputs u p (t) and u o (t) are utilized, whereas x pre and θ z pre
resent the transient responses of x and θ z when the previously proposed
(t) are utilized. When the proposed method
(t) and u o real
control inputs u p real
is used, the oscillation is reduced, and the convergence rate is faster com-
pared with the case in which the previous method is used, even with the
low-sampling rate and long-time delays.
Figs. 9.6 and 9.7 show the behavior of the positions and orientations of
the measured- and virtual-object frames when the control inputs u p tðÞ and