IEEE Robotics & Automation Magazine - June 2013 - 80

Supporting Leg (Left)

8
6

Gain = 0 Gain = 0.9

X (m)

4
2

Gain = 1.5

0
−2
−4
−6

Supporting Leg (Right)

−8
−10
5.5

6.5
7
Time (s)

7.5

Figure 12. Medial-lateral displacement of the robot's COM
(Style 5). The green horizontal line at the top represents the
trajectory of the supporting left leg, while the purple line with dots
at the bottom represents the trajectory of the right supporting leg.

least energy consumption is beyond the scope of this article. It
is possible that there are other sets of equations that could lead
to even more efficient walking than the one presented here.
(Recall that the coefficients of the spinal equations are the
same.) Since this article focuses on answering the question of
whether having an articulated spine could lead to more efficient walking and given that a drop in energy consumption of
26.5% is considered to be satisfactory, we have sufficient results
to demonstrate our concept and settled with (2)-(5). Future
study could include developing locomotion controllers that
take upper and lower body movements, as well as energy efficiency, into account during the pattern generation stage.
Normally, a ZMP-based walking pattern generator, such as
the one presented in [34], is planned by giving referential ZMP
inputs. Then, researchers are able to obtain the joint motions
for stable walking. One might suspect that any empirically
tuned upper body motion might cause the robot to fall down.
However, the simulations conducted in this study showed that
the pattern generator proposed by Takanishi can cope with

100

Left Ankle Roll Axis (LAK_R)

Torque (N $ m)

50
Gain = 0.9
0

Gain = 1.5

−100

6.5
7
Time (s)

7.5

Figure 13. Torque at the left ankle joint (third walk cycle, Style 5).

IEEE ROBOTICS & AUTOMATION MAGAZINE

june 2013

Conclusions
This article has shown that by adding articulated spinal joints
in the torso, it is possible for a robot to walk at a higher energy
efficiency than its conventional rigid-torso counterpart. This
is accomplished by using the actuated spinal joints to reduce
the movement of the COM. Consequently, the torque at the
waist and leg joints is reduced, and the energy consumption is
lowered. In our study, when the spine of the robot is allowed
to bend, the robot consumed 26.5% less energy than when its
spine was one rigid body trunk. Interestingly, this happens
when the robot is walking with swaying hips. Our work
suggests that it is beneficial for the next generation of humanoid robots to have an articulated spine [33].
References

Gain = 0

−50

−150
5.5

this issue to a certain extent. During the pattern generation
stage, the algorithm computes the approximate compensatory
motion of the simplified and linearized (rather than the exact)
robot model. The pattern generator repeatedly calculates and
checks if the computed moment errors between the planned
and calculated ZMP are less than that of the acceptable threshold set by the user of the pattern generator [3], [4]. Such flexibility in the pattern generator allows the robot to walk even
with some deviations in the torso movements.
In our study, we observed that while walking, the robot
was able to maintain balance across the range of spine curvature gains under investigation. Dynamic balance was further
confirmed by verifying that the ZMP stayed within the support polygon formed by the feet and the ground. Note that
when we increased the gain further, the robot fell only when
the upper torso movements were so large that even humans
would have fallen. It might be possible that Takanishi's pattern
generator could be modified to handle more real-time trunk
deviations for more unrealistically large upper body movements. Such a modified pattern generator would change the
motion of the leg joints according to spinal motion.
Finally, we considered the energy consumption of a robot
similar to the one used in this study but without spinal joints.
The total weight of this robot was calculated by subtracting
the weight of SEG1, SEG2, and SEG3 (Table 1) from the total
weight of the spine robot. This robot was 15% lighter than the
original simulated robot model, and it required 161.13 J to
complete the same walking task. Recall that the original
model, walking with Style 5 spine movement, consumed
145.83 J and compare this with the rigid-torso case that
required 202.61 J, and consider the implications.

[1] A. D. Kuo, "Choosing your steps carefully: Trade-offs between economy
and versatility in dynamic walking bipedal robots," IEEE Robot. Automat.
Mag., vol. 14, pp. 18-29, June 2007.
[2] F. Yamasaki, K. Endo, M. Asada, and H. Kitano, "An energy-efficient walking
for a low-cost humanoid robot PINO," AI Mag., vol. 23, no. 1, pp. 60-61, 2002.
[3] Y. Ogura, T. Kataoka, K. Shimomura, H. Lim, and A. Takanishi, "A novel
method of biped walking pattern generation with predetermined knee joint
motion," in Proc. IEEE/RSJ Int. Conf. Intelligent Robots Systems, 2004,
pp. 2831-2836.

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