Table 3 Condition of the simulations

Roll

0

30

0

0

0

0

Pitch

0

0

0

30

0

0

Yaw

0

0

0

0

0

30

Nominal desired grasping force and gains

 Grasping force

\(f_{d}\)

1

(N)

 Gain for the object orientation control

\(K_{ri}\)

diag[3.5, 3.5, 3.5]

 Time delay

\(t_{\text {delay}}\)

50

(ms)

 Damping coefficient of joint1

\(B_{1}\)

diag[0.07, 0.07, 0.05, 0.04, 0.04]\(^{ {-2}}\)

(\({{\text{Ns}} \, {\text{m/rad}}}\))

 Damping coefficient of joint2

\(B_{2}\)

diag[0.07, 0.07, 0.05, 0.04, 0.04]\(^{{-2}}\)

(\({{\text{Ns}} \, {\text{m/rad}}}\))

 Damping coefficient of joint3

\(B_{3}\)

diag[0.07, 0.07, 0.05, 0.04, 0.04]\(^{{-2}}\)

(\({{\text{Ns}} \, {\text{m/rad}}}\))

Parameters of the robotic hand in simulation

 Length of link1

\(l_{1}\)

0.02

(m)

 Length of link2

\(l_{2}\)

0.03

(m)

 Length of link3

\(l_{3}\)

0.05

(m)

 Mass of link1

\(m_{1}\)

0.02

(kg)

 Mass of link2

\(m_{2}\)

0.03

(kg)

 Mass of link3

\(m_{3}\)

0.05

(kg)

 Inertia of link1

\(I_{1}\)

\(\text {diag(0.1042, 0.1042, 0.0063)}\times {10}^{ {-4}}\)

(\(\text {kg} \, \text {m}^{2}\))

 Inertia of link2

\(I_{2}\)

\(\text {diag(0.2250, 0.2250, 0.0375)}\times {10}^{{-5}}\)

(\(\text {kg} \,\text {m}^{2}\))

 Inertia of link3

\(I_{3}\)

\(\text {diag(0.6667, 0.6667, 0.2500)}\times {10}^{ {-6}}\)

(\(\text {kg} \, \text {m}^{2}\))

 Radius of fingertip

\(r_{i}\)

0.010

(m)

 Mass of object

M

0.050

(kg)

 Inertia of object

I

\(\text {diag(0.0716, 0.1127, 0.0823)}\times {10}^{{-4}}\)

(\(\text {kg} \, \text {m}^{2}\))