IEEE Robotics & Automation Magazine - June 2013 - 79

Time = 5.91 s

Time = 6.16 s

Time = 6.42 s

Time = 6.67 s

Time = 6.92 s

Figure 9. Snapshots of the robot walking efficiently with articulated spine motion (spine curvature gain 0.9, Style 5). The step length
is 100 mm.

also shown that the amount of energy saved for the roll-axis
hip joint motors is the greatest at gain 0.9.
Note that although both the vertical and lateral displacements of the COM at gain 1.5 are further reduced, the overall
energy consumption of the robot increases. This is because
although the COM is moving closer to the central line of
forward walking motion (the z axis), it is moving farther away
from the supporting leg. This leads to larger torque and more
energy consumption at the roll-axis ankle joints at higher
gains (compare Figures 12 and 13 with [33, Tables IV and V]).
Discussion
In this article, we used a systematic approach to find a set of
motion equations for the spine that leads to a reduction in

Waist Roll Axis (WST_R)

15

5

83.8

Gain = 0.9

0
Gain = 0

−5

Gain = 0

83.85

Y (cm)

Torque (N$m)

83.9

Gain = 1.5

10

Gain = 0.9

83.75
83.7
83.65

−10
−15
5.5

mechanical energy consumption by about a quarter. In our
study, we tried different combinations of signs and spine curvature gain factors and conducted a total of 197 different simulations. We compared the energy consumption resulting from
different styles of spinal movements during walking. We
observed that when the robot swung the upper torso to a higher
degree (e.g., Styles 4 and 7), much energy was required to complete the walking task. In contrast, when the robot swayed its
hips when it walked (Style 5), the walking became more efficient. Our approach could be applied to investigate the energy
efficiency of other robots developed by other research groups.
The focus of this article has been to show that by adding
actuated joints in the torso, the robot could walk with higher
energy efficiency. Finding the walking style that leads to the

83.6
6

6.5
7
Time (s)

7.5

8

Figure 10. Torque at the roll-axis waist joint (third walk cycle,
Style 5).

83.55
5.5

Gain = 1.5
6

6.5
7
Time (s)

7.5

8

Figure 11. Vertical displacement of the robot's COM (Style 5).

june 2013

*

IEEE ROBOTICS & AUTOMATION MAGAZINE

*

79



Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - June 2013

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