IEEE Robotics & Automation Magazine - June 2013 - 74
i3
i2
20
0
−20
i1
20
0
−20
WST
20
0
−20
20
0
−20
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
As shown in Figure 2, we initially
assumed that the articulated spinal
joints were nonbendable. Then, we
used the pattern generator presented
in [34] and [35] to generate control
inputs for the limbs. Next, to generate
motion for the spinal and waist joints,
we used
i 3 ^ t h = sign 3 $ gain $ Ref (t),
i 2 ^ t h = sign 2 $ gain $ Ref (t),
i 1 ^ t h = sign 1 $ gain $ Ref (t),
i WST ^ t h = sign wst $ gain $ Ref (t),
(2)
(3)
(4)
(5)
Time = 6.16 s
Time = 6.42 s
Time = 6.67 s
Time = 6.92 s
1.4
1.4
1.2
1.2
1.2
1.2
1.2
1
1
1
1
1
0.8
0.8
0.8
0.8
0.8
0.6
0.6
0.6
Y (m)
1.4
Y (m)
1.4
Y (m)
Y (m)
Time = 5.91 s
1.4
Y (m)
LAK_R
where Ref(t) represents the reference
signal used to generate control inputs
for the articulated spinal joints. For the
0
1
2
3
4
5
6
7
8
9
10
simulations presented in this article,
Time (s)
Ref(t) is the train of control signals
(generated by the pattern generator
Figure 3. Control inputs for the spinal joints (in degrees). In the top four panels,
mentioned above) used to turn the
horizontal lines in black represent the control inputs when the gain is zero. Solid curves
in red correspond to the control inputs when the gain is 0.9. The dash-dot curves in blue
roll-axis joint at the left ankle.
correspond to the control inputs when the gain is set to 1.5. In the bottom panel, LAK_R
i 3 (t), i 2 (t), i 1 (t), and i WST (t) coris the reference signal from the roll-axis motor in the left ankle joint.
respond to the control signals (in
degrees) for SEG3, SEG2, SEG1, and
WST,
respectively,
shown
in Figure 1.
movement is the same regardless of how the upper body
The
reason
we
selected
the case in which references
bends. This allows us to directly compare the effect of
for
all
the
spinal
joints
are
at
the same angle for the left
spinal motion on the energy consumption of individual
ankle
roll-axis
joint
is
that
during
walking, there are
leg joints.
10
0
−10
0.6
0.6
0.4
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
0.2
0
−0.2
0
X (m)
0
−0.2
0.2
0
X (m)
Gain 0
0.2
Gain 0.9
0
−0.2
0
X (m)
0.2
Gain 1.5
0
−0.2
0
X (m)
Left Leg
0.2
0
−0.2
0
X (m)
0.2
Right Leg
Figure 4. Sample snapshots of the robot walking with different spine curvature gain factors (one step in the third walk cycle, front
view). Dots represent the COM of the corresponding roll-axis joints. Note that the dot at the top in each panel represents the COM
of the neck joint, while the second dot from the bottom of each leg represents the COM of the shin. The open circles represent the
corresponding COM of the robot.
74
*
IEEE ROBOTICS & AUTOMATION MAGAZINE
*
june 2013
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