IEEE Robotics & Automation Magazine - June 2013 - 78

Efficient Walking with Spinal Movement
and Swaying Hips
Figures 5 and 6 also show that at gain 0.9 when the spinal
movement is of Style 5, the robot requires the least energy to
complete a walk cycle. In other words, the robot is able to
walk the most efficiently when its spinal and waist joints are
governed by the set of motion equations corresponding to
Style 5. Compared with its rigid-torso counterpart, which
requires 202.61 J to finish a walk cycle, the robot only requires
145.83 J to complete the same task. The percentage drop in
energy consumption is 26.5%. In terms of the mechanical
COT (J $ N -1 $ m -1), the corresponding values for the rigid
and spinal cases are 0.858 and 0.647, respectively. Our results
showed that a robot with an articulated spine could walk at
higher energy efficiency than its rigid-torso counterpart.
Figures 8 and 9 show snapshots of the robot walking with
spine curvature gains 0 and 0.9, respectively. When the gain is
zero, the spine does not bend and the body trunk remains
straight above the stance leg. When we set the gain to 0.9, the
spine bends toward the swinging leg and the robot appears to
be walking with swaying hips [33]. This suggests that it is beneficial to include these features in the design of future robots.
Where Is Energy Saved?
To investigate where the energy is saved, we compared the
energy consumption of individual joints at various spine curvature gains when the spinal movement is of Style 5. Recall
that as the motion of the lower body is the same in all simulations, a change in the energy consumption of the motors in the
leg joints is caused by the style of spinal motion. In [33, Tables
IV and V], it is shown that compared with the rigid-torso
counterpart, all the leg joints consume less energy at gains 1 or

Time = 5.91 s

Time = 6.16 s

below. Our results showed that by adding spinal motion, it is
possible to reduce the energy consumption of the leg joints.
In [33, Table V], it is also shown that, unlike other leg
joints, the roll-axis ankle joints consume more energy than
their rigid-torso counterparts at gains between 1.1 and 1.5.
Moreover, the larger the gain, the more the energy is consumed. In other words, when the amount of lateral bending
in the spine increases, more energy from the roll-axis joints at
the ankles is required.
Note that the roll-axis joint at the waist (WST_R) is important because it connects the lower and upper body. Figure 10
shows that the torque at this joint is reduced when the spine
curvature gain is changed from 0 to 0.9. However, at gain 1.5,
the torque increases in the opposite direction.
Physical Interaction on Energy Saving
To understand the physical interaction that leads to efficient
walking, we compared the center of mass (COM) of the
robot at gains 0, 0.9, and 1.5. Figure 11 shows that as the gain
increases, the vertical displacement and the location of the
COM are both lowered. As the position of the COM corresponds to energy expenditure [39], such changes correspond
to lowering the energy consumption of the robot at gain 0.9.
Figure 12 shows that at gain 0.9, the medial-lateral movement of the robot's COM is less than that of the rigid-torso
case. This shows that bending the spine in the direction of
the swinging leg leads to a reduction in the COM's lateral
movement (see also Figures 4 and 9). Based on the premise
that the horizontal COM displacement is costly in terms of
energy consumption [39], [40], the smaller lateral and vertical displacements of the COM lead to less overall energy
consumption at gain 0.9 than at gain 0. In [33, Table V], it is

Time = 6.42 s

Time = 6.67 s

Time = 6.92 s

Figure 8. Snapshots of the robot walking with rigid torso (at spine curvature gain zero). The step length is 100 mm. Dots in red
represent the ZMP.

IEEE ROBOTICS & AUTOMATION MAGAZINE

june 2013

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