Human-Inspired Hyper Dynamic Manipulation
67
is generated by the absorber. The approximate equation of the elastic characteristic of the joint stops is shown in Equation (4.12).
τ
(θ ) = a + a
2
2
4
5
6
2stop _ char
2s
0
1 θ 2s + a 2 θ 2s + a 3 2
θ s + a 4 θ 2 2s + a 5 2
θ s + a 6 2
θ s
(4.12)
D 0 = 1 164
.
× 10, D 1 = −2 915
.
× 10, D 2 = 3 724
.
× 10
−1 , D 3 3 = −2 675
.
× 10
−2
D = 1 060
.
× 10
−3
−5
4
, D 5 = −2 141
.
× 10 , , D 6 = 1 715
.
× 10
−7
The action range of the joint stops is from θ 2V = 0 ⎡ ⎣ deg⎤ ⎦ to θ 2V = 20 ⎣ ⎡deg ⎦ ⎤ . The
role of the shock absorber is to absorb the collision between the arm and the
club, and the shock absorber used here can absorb a velocity difference up
to 9.3 rad/s.
Therefore, the passive torque in the wrist joint generated by the joint stops
can be represented by the following equation:
⎧τ 2minp , θ 2lb ≤ θ 2 ≤ θ 2min
⎪
⎪ ⎪
τ 2S = ⎨ 0,
θ θ 2 min < θ 2 < θ 2 max
(4.13)
⎪
⎩ ⎪ τ 2maxp , θ 2max ≤ θ 2 ≤ θ 2ub
where
τ
= τ
( 20
K
2minp
2stop _ char
− θ 2min − θ 2 )
τ
K
2maxp = −τ 2 st t op _ char ( 20 − θ 2 − θ 2max )
When the club rotates in the clockwise direction, the passive torque will be
generated after the club enters the action range of the joint stop from θ 2min to
θ 2lb . Likewise, when the club rotates in the counterclockwise direction, the
passive torque will be generated after the club enters the action range of the
joint stop from θ 2max to θ 2ub .
4.3 M ethod to Utilize Dynamically Coupled
Driving and Joint Stops
Some methods for controlling a manipulator with a passive joint using
dynamically coupled driving have been proposed (Arai and Tachi 1991; De
Luca and Oriolo 2002; Nakamura, Koinuma, and Suzuki 1996). The proposed
methods are interesting and effective for the manipulator with a complete
67
is generated by the absorber. The approximate equation of the elastic characteristic of the joint stops is shown in Equation (4.12).
τ
(θ ) = a + a
2
2
4
5
6
2stop _ char
2s
0
1 θ 2s + a 2 θ 2s + a 3 2
θ s + a 4 θ 2 2s + a 5 2
θ s + a 6 2
θ s
(4.12)
D 0 = 1 164
.
× 10, D 1 = −2 915
.
× 10, D 2 = 3 724
.
× 10
−1 , D 3 3 = −2 675
.
× 10
−2
D = 1 060
.
× 10
−3
−5
4
, D 5 = −2 141
.
× 10 , , D 6 = 1 715
.
× 10
−7
The action range of the joint stops is from θ 2V = 0 ⎡ ⎣ deg⎤ ⎦ to θ 2V = 20 ⎣ ⎡deg ⎦ ⎤ . The
role of the shock absorber is to absorb the collision between the arm and the
club, and the shock absorber used here can absorb a velocity difference up
to 9.3 rad/s.
Therefore, the passive torque in the wrist joint generated by the joint stops
can be represented by the following equation:
⎧τ 2minp , θ 2lb ≤ θ 2 ≤ θ 2min
⎪
⎪ ⎪
τ 2S = ⎨ 0,
θ θ 2 min < θ 2 < θ 2 max
(4.13)
⎪
⎩ ⎪ τ 2maxp , θ 2max ≤ θ 2 ≤ θ 2ub
where
τ
= τ
( 20
K
2minp
2stop _ char
− θ 2min − θ 2 )
τ
K
2maxp = −τ 2 st t op _ char ( 20 − θ 2 − θ 2max )
When the club rotates in the clockwise direction, the passive torque will be
generated after the club enters the action range of the joint stop from θ 2min to
θ 2lb . Likewise, when the club rotates in the counterclockwise direction, the
passive torque will be generated after the club enters the action range of the
joint stop from θ 2max to θ 2ub .
4.3 M ethod to Utilize Dynamically Coupled
Driving and Joint Stops
Some methods for controlling a manipulator with a passive joint using
dynamically coupled driving have been proposed (Arai and Tachi 1991; De
Luca and Oriolo 2002; Nakamura, Koinuma, and Suzuki 1996). The proposed
methods are interesting and effective for the manipulator with a complete