IEEE Robotics & Automation Magazine - March 2016 - 80

The leg may contract or stretch depending on the gait phase,
controlled by a servomotor equipped at the knee with a pinion-rack mechanism. In this article, we use the RX-64 servomotors (ROBOTIS Co., Ltd.) to implement the actuators.
The robot has five potentiometers to measure the joint angles. One potentiometer is at the hip to measure the relative
angle between the inner legs and the outer legs. The other
four potentiometers are
equipped at the four
Experimental results from
ankle joints to estimate
the ankle angles. Each
both simulations and the
foot has two switch sensors at the sole to detect
prototype indicate that
foot contact information,
with one positioned at the
either joint torque control
heel and the other positioned at the toe.
or joint stiffness control has
The robot is controlled
by the aforementioned
distinctive advantages in
CPG-based method. The
two signals u e0 and u s0 are
motion behavior modulation used to modulate the
walking behaviors. Tuning
such as speed control.
u e0 leads to the movement
of the servomotors for
equilibrium position control, while adjusting u s0 can change the pretension of the spring
at each joint, and thus control joint stiffness. The principles of
limb coordination and feedback are the same as those in the
simulated model as mentioned above. The closed-loop speed
control of the robot also employs the control laws shown in
(11) and (12). The parameter values and the expression of
feedback functions of the CPG model in the prototype can
also be found in the supplemental material for this article,
available in IEEE Xplore.
The effects of u e0 and u s0 in the real robot are consistent with
those in simulations [see Figure 5(c) and (d)]. The step frequen-

cy is influenced mainly by joint stiffness. In closed-loop speed
control, we also study the performance of the aforementioned
three methods: 1) Method-I (controls only u e0 with fixed u s0 ), 2)
Method-II (controls only u s0 with fixed u e0 ), and 3) Method-III
(controls both u e0 and u s0 ). In the experiments, the robot walks
at a speed of 0.26 m/s (Fr = 0.11) at the first two steps. From the
third step, the desired speed changes to 0.42 m/s (Fr = 0.18).
The mean Froude number and normalized step length of each
step measured over ten trials from the real robot ! the standard
deviation of those measurements are shown in Figure 11(a) and
(b), respectively. The speed variations and step length variations
of the three methods show similar tendencies to the simulation
results. Method-II and Method-III still achieve higher control
precision compared with Method-I. The locomotion of the real
robot involves a large disturbance from the environment, especially during transitions and fast walking with Method-I, as the
standard deviations have large values. The prototype can overcome a ground disturbance of 2.8 cm (5.1% leg length) at Fr =
0.14. The supplemental multimedia material of the article contains the video of walking on an uneven terrain and speed transition of a representative trial for each method.
In this article, we analyze the motion behavior modulation of dynamic walking with both controllable joint torque
and joint stiffness. The addition of adaptable stiffness extends the dimension of input in motion control (see Figure
12). Thus, the locomotion can be controlled over a broader
accessible range and in a more accurate way. The experimental results from both simulations and the prototype indicate
that either joint torque control or joint stiffness control has
distinctive advantages in motion behavior modulation such
as speed control. In joint torque control, the walking pattern
is adjusted toward the desired performance through directly
tuning the actuation, which exhibits fast response. In stiffness control, the intrinsic dynamics is adjusted to adapt to
the new limit cycle, and smooth pattern transitions are obtained with high control precision. In general, the combination of joint torque and joint stiffness adjustments achieves
the best performance, which
means that suitable portions
of external and internal conChange
trol are optimal.
Stiffness
Although a variety of conSmoothness
Accuracy
trol methods can be applied in
torque-stiffness-controlled dynamic walking, CPG-based
Optimal
control is especially suitable
due to the essential smoothFast
ness and the easy implementaResponse
tion of limb coordination. In
this article, applying CPGChange Torque
based control approach is similar to adding coupling
Figure 12. The comparison of three control methods during walking pattern transitions. Each axis
between the equilibrium posirepresents an input (joint torque or stiffness) of motion control. The advantage of torque control
is fast response, while stiffness control is beneficial to smoothness and accuracy. According to
tions/stiffnesses of different
the results in this article, the optimal method is the combination of torque control and stiffness
joints, based on the basic princontrol. The stickgrams of speed control with the three methods are shown in the plane. A
ciples of human-like walking
diagram of speed variation of each method is added to the corresponding stickgram.

IEEE ROBOTICS & AUTOMATION MAGAZINE

march 2016

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - March 2016