IEEE Robotics & Automation Magazine - March 2016 - 79

Torque-Stiffness-Controlled Dynamic
Walking Robot
Based on the concept of torque-stiffnesscontrolled dynamic walking, we design and
construct a planar robot with a similar mechanical structure and a control mode as
the simulated model mentioned above. The
robot prototype has flat feet and compliant
joints (see Figure 10). Both the legs are constructed in pairs for lateral stability. The
weight of the robot is 5.1 kg. The fully extended leg length is 0.55 m, and the foot has
a length of 0.13 m and a height of 0.06 m.
The maximum contraction length of the leg
is 0.05 m, and the width of the robot is 0.30
m. As indicated in [28], for bipedal walking,
the dynamical effects in the lateral plane

have a marginal influence on the dynamics in the sagittal
plane. Thus, we used a sagittal walking robot to study the
principles of torque-stiffness-controlled dynamic walking.
The hip and ankle joints are equipped with mechanically
adjustable compliance and controllable equilibrium position
actuators (MACCEPAs), which can realize the independent
control of equilibrium position and stiffness [7]. The MACCEPA consists of two servomotors and an elastic element
such as a spring. The equilibrium position of the joint is controlled by one servomotor, while the joint stiffness can be adjusted through tuning the pretension of the spring by
controlling the other servomotor. Therefore, the equilibrium
position and the stiffness of the joint can be controlled by the
two servomotors, respectively. We employ a telescopic structure at the knee to avoid foot scuffing during swing phases.

Froude Number (-)

0.22
0.2
0.18
0.16
0.14
0.12

Method-I
Method-II
Method-III
Desired Speed

0.1
0.08

1
0.017
0.011
0.018

4
6
8
Step Number

2
3
4
5
6
7
8
9
0.008 0.015 0.024 0.021 0.024 0.027 0.021 0.011
0.009 0.013 0.016 0.012 0.012 0.013 0.022 0.020
0.016 0.016 0.019 0.016 0.014 0.008 0.014 0.014
(a)

0.7
Normalized Step Length (-)

oscillatory behaviors. In Method-II, the actual speed matches
the desired speed in most cases. When the trajectory of the desired speed has a large change, the actual speed shows some
overshoot and time delay. Method-III combines the characteristics of the above two methods. Consequently, in speed tracking, torque control can help implement immediate speed
variation when the tendency of the desired speed has a large
change, while stiffness control shows benefits in accuracy and
smoothness when the desired speed keeps the same trend.
For the analysis of adaptability, we use the maximum allowable ground disturbance of the biped to evaluate the disturbance rejection as the walker travels on an uneven floor. There
is a sudden decrease of ground height during stable periodic
walking. When the heel-strike has not occurred as former
steps, the walker performs an unstable phase. The walker with
high ability of disturbance rejection can
overcome the perturbation and return to
periodic walking, while poor disturbance
rejection leads to falling.
The results of maximum allowable
ground disturbance for varied neural signals
u e and u s in simulations are shown in Figure 9. The largest ground height variation
the walker can overcome is 5.3% leg length
at u e = 0.19 and u s = 31. The overall performance with a small u e is poor ^u e =
0.13). The explanation is that a large u e results in a large step length. The biped tends
to incline further forward when reaching
the new floor with a decreased ground
Step Number
height, and, thus, the motion cycles with
Method-I
large step lengths overcome the disturbance
Method-II
Method-III
easier. For a given u e , there exists an optimal
u s , which means an optimal stiffness for
disturbance rejection. For a large u e , the optimal u s decreases with increasing u e ,
which suggests the importance of coordination between joint torque and joint stiffness.

0.6
0.5
0.4
0.3
0.2
Method-I
Method-II
Method-III

0.1
0

Step Number
(b)
Figure 11. The speed control of the robot prototype with three different methods.
(a) The speed variation. (b) The step length variation. The speed is measured by
the dimensionless Froude number Fr. The step length is normalized by the leg
length. The gray dotted-dashed line in (a) indicates the target speed. The solid lines
represent the mean speed or step length of each step measured over ten trials from
the real robot ! the standard deviation of those measurements. The desired Fr is
changed from 0.11 to 0.18 at the end of the second step. Method-I, Method-II, and
Method-III represent changing only u e0 , changing only u 0s , and changing both u e0
and u 0s , respectively. A table of standard deviations is listed in (a).

march 2016

IEEE ROBOTICS & AUTOMATION MAGAZINE

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