Page 177 - Human Inspired Dexterity in Robotic Manipulation

A Grasping and Manipulation Scheme 175

Table 9.1 Physical parameters for the simulations
Three-fingered hand-arm system

1st link length l a1 1.300 m l i1 0.300 m
2nd link length l a2 1.000 m l i2 0.200 m
3rd link length l a3 0.175 m l i3 0.140 m
1st center of mass l ga1 0.650 m l gi1 0.150 m
2nd center of mass l ga2 0.500 m l gi2 0.100 m
3rd center of mass l ga3 0.0875 m l gi3 0.070 m
1st mass m a1 1.300 kg m i1 0.250 kg
2nd mass m a2 1.000 kg m i2 0.150 kg
3rd mass m a3 0.400 kg m i3 0.100 kg
2
ð
1st inertia, I a1 diag 7:453,7:453,0:260Þ 10 1 (kg m )
2
ð
2nd inertia, I a2 diag 3:397,3:397,0:128Þ 10 1 (kg m )
2
ð
3rd inertia, I a3 diag 0:291,0:291,0:500Þ 10 1 (kg m )
2
ð
1st inertia, I i1 diag 7:725,7:725,0:450Þ 10 3 (kg m )
2
ð
2nd inertia, I i2 diag 2:060,2:060,0:120Þ 10 3 (kg m )
2
diag 0:538,0:538,0:031Þ 10 3 (kg m )
ð
3rd inertia, I i3
0.070 m
Fingertip radius, r i
5
1.000 10 N/m 2
Stiffness coefficient, k i
2 2 2
1.000 r Δr π Ns/m
Damping function, ξ i
i i
Object
Mass (m) 0.037 kg
0.092 m
Y 1
Y 2 0.048 m
0.048 m
Y 3
1.309 rad
θ t1
1.309 rad
θ t2
0.524 rad
θ t3
2
diag 1:273,0:193,1:148Þ 10 3 (kg m )
Inertia, I ð
N
T
X
ðtÞ¼ K o J ðtÞ f r x ðt t delay Þ r xd + r y ðt t delay Þ r yd
u o real Ωi
i¼1 (9.20)

+ r z ðt t delay Þ r zd g,
where the orientation of the measured-object frame is expressed in the form

of a rotational matrix, R tðÞ ¼ r x tðÞ,r y tðÞ,r z tðÞ 2 SOð3Þ. The sampling rate
was taken to be h ¼ 20 Hz, and the time delay due to the computational cost
of image processing and the latency of data communication was taken to be
t image ¼ 50 ms.