JFPS International Journal of Fluid Power System 13-3, 17/24, 2020JFPS International Journal of Fluid Power System 13-3, 17/24, 2020
Evaluation of Tracking Control for Hydraulic *Direct-drive System
Juri SHIMIZU**, Takuya OTANI***, Kenji HASHIMOTO****, Atsuo TAKANISHI***
Biped humanoid robots, whose size and output are equivalent to humans, have been developed. However, it is difficult to mount high-power large electrical motors with a mechanical transmission due to spatial limitations. Generally, hydraulic systems have a high energy density and excellent layout characteristics. This study proposes a hydraulic direct-drive (HDD) system using a single-rod cylinder for biped humanoid robots. The HDD system is based on meter-in control using pump- derived output flow and a meter-out control using a proportional valve. In this study, a bench was developed to evaluate the proposed HDD system, which can control the cylinder based on the pump flow rate. The proposed system was compared with a valve-based control system and an electro-hydrostatic actuator in terms of its responsiveness to step the velocity input and the sinusoidal position input. The results of this comparison demonstrate that the proposed system exhibits good velocity and position following capability.
Keywords: Hydraulics, Flow based control, Biped robot, Responsiveness
1. Introduction
and canes. To end this, user evaluations can be performed;
however, this approach has safety risks and presents problems
with reproducibility. Consequently, we developed a biped
humanoid robot that can be used to perform these evaluations.
Our developed robot, named WABIAN-2R (WAseda BIpedal
humANoid - No. 2 Refined), is fitted with a pelvis model and
it can execute a stretched knee gait1). As reported in recent
studies, our research team has been developing a robot that
can walk, hop, and run 2). To achieve this, the robot requires
high-power actuators. However, the installation of high-
power electric motors in human-sized robots is difficult due
to spatial limitations. To resolve this problem, this paper
proposes a method to induce a high torque with pelvic
oscillation and leg elasticity2).
To increase the output of an electrical motor, Urata et al.
demonstrated a technique that can improve the continuous
output torque using a liquid cooling system3). Other
researchers have proposed mounting two motors on the
* Manuscript received February 25, 2020 ** Waseda University and Hitachi, Ltd. (#41-304, 17 Kikui-cho, Shinjuku-ku, Tokyo, Japan)
driving axes of robots4),5). These approaches have provided
high-speed and high-torque joints in both legs and achieved a
high mobility for humanoids. However, in cyclic motions,
such as walking, running, and hopping, high-power actuators
are alternately required on the left and right legs but not
simultaneously. In conventional methods, the outputs of the
motors can be used only for one axis because the motors are
directly connected to the axes by a mechanical transmission.
Therefore, if the outputs of the driving sources for both legs
can be shared, the size of the motor can be further reduced.
In hydraulic systems, the outputs of the driving sources can
be shared. For example, Boston Dynamics developed Atlas6)
and Hyon et al. demonstrated the capabilities of a hydraulic
humanoid robot named TaeMu7). Khan et al. used an on-board
power pack in a hydraulic quadruped robot named MiniHyQ8).
In these robots, the power to be supplied to each axis can be
controlled via proportional valves. However, the use of valves
leads to energy losses.
reduce the hydraulic energy loss due to valves9),10). An
example of its application to a robot system is the electro-
hydrostatic actuator (EHA) proposed by Kaminaga et al.11).
However, it uses a through-rod cylinder, which is difficult to
mount.
E-mail: juri-shimizu1112@asagi.waseda.jp system for biped humanoid robots based on a displacement *** Waseda University
control system that uses a single-rod cylinder. The HDD **** Meiji University (1-1-1 Higashimita, Tama-ku, Kawasaki-shi, Kanagawa Japan) system achieved excellent energy savings, velocity
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JFPS International Journal of Fluid Power System 13-3, 17/24, 2020
followability, and nearly perfect position tracking12). In the
previous research, the current of the motor at a cylinder piston
speed of 3.0 mm/s was 11.4 A for valve-based control (VBC),
but 7.6 A for HDD. At a piston speed of 12.0 mm/s, VBC was
10.6 A and HDD was 9.7 A. It was also confirmed that the
energy consumption could be suppressed especially at low
speeds12). The motors in the system could be downsized by
sharing the outputs of the actuators of both legs. Based on a
simulation of the hopping movement, the motor power was
reduced by 35.6%13). However, the performance of the
proposed system for the target tragectory followability was
not compared with the previous system in the actual machine.
Biped robots are required to follow the target trajectory in
order to achieve stable biped locomotion. Especially when it
is used for the evaluation of products instead of a human being,
robots are required to follow a pre-planned trajectory. In this
study, to evaluate the responsiveness of the HDD, an
evaluation bench was constructed. The bench, the existing
VBC system, and the EHA were constructed by using the
same hydraulic equipment. The VBC and EHA were then
compared in terms of the responsiveness to the sinusoidal
position input.
The remainder of this paper is organized as follows. In
Section 3, the design of the HDD system for mounting and its
theoretical model are introduced. In Section 4, the
experimental setup, procedure, and the results are described.
Finally, the conclusions and the directions for future work are
presented in Section 5.
3.1 Description
A hydraulic system was designed that can independently
drive the axis of each joint. For the HDD system at each axis,
M Pump Unit (TFH-160)
Valve 1a Valve 1b
an actuator speed control was produced based on the pump
output flow to minimize the valve loss.
The difference between the proposed HDD and an EHA
with a single-rod cylinder is that the cylinder meter-out flow
is actively controlled. In a system such as a biped humanoid
robot in which the direction of the load on the cylinder
changes in a short cycle, meter-out flow control is required. In
a previous study that applied EHA to a biped humanoid robot,
this problem was solved via a closed-circuit system using a
through-rod cylinder 11). In contrast to this method, a feature
of the HDD is that a single-rod cylinder with high thrust is
used. In addition, the single-rod cylinder has the advantage
that the layout on the robot is uncomplicated because the
cylinder rod is retracted. However, compared to the closed-
circuit EHA, it has the disadvantage of having to control the
meter-out flow rate.
A cylinder meter-in flow control with an orifice is not
required at the HDD and EHA; thus, the transmission
efficiency between the pump output and the actuator output is
higher than that of the VBC in principle. The HDD has a
meter-out control, which results in more loss than the EHA.
However, the meter-out control is applied as a negative load,
and the effect of reducing the transmission efficiency is small.
A hydraulic system was designed for the HDD and the EHA.
Fig. 1 shows the proposed hydraulic circuit for one axis.
As illustrated in Fig. 1, the pump units are connected to the
cylinder via valves 1a and 1b, which are proportional valves.
A pump unit14) (TFH-160: Takako Industries, Japan) was
incorporated in the system. This device includes a pump, a
relief valve to protect the pump, and a check valve unit.
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JFPS International Journal of Fluid Power System 13-3, 17/24, 2020
Pump Unit (TFH-160)
Fig. 3 Flow-control mode.
The pump has two ports, and it can discharge from both
ports. Port A is connected to the cylinder rod side and port B
is connected to the cylinder cap side. The check valve unit has
two check valves, which are interconnected by a rod.
Therefore, this unit connects the lower pressure side of the
pump outlet to the tank. With this check valve unit, it becomes
possible to compensate for the difference in the flow rates of
the cylinder. If proportional valves 1a and 1b remain fully
open, it is possible to reproduce a general EHA circuit for the
single-rod cylinder. The circuit has two variable relief valves,
which can adjust the relief pressure.
In addition, a fixed-displacement axial piston pump was
selected because it exhibits a better volumetric efficiency than
a variable displacement pump. Moreover, a displacement
control unit is not needed in a fixed-displacement pump,
which makes it small and easily mountable. In this type of
pump, the flow rate can be controlled by regulating the
rotational speed of the pump. In this study, the pump and the
servomotor were connected, and the flow rate was controlled
by regulating the rotational speed of the motor.
A hydraulic system was designed for the VBC. Fig. 2
presents the proposed hydraulic circuit for one axis.
As displayed in Fig. 2, the pump units are connected to the
cylinder via valves 2a and 2b, which are proportional valves.
The valves have two ports. Valve 2a connects the cylinder rod
side to the pump outlet port and the cap side to the tank. The
instroke-direction velocity of the cylinder is controlled by
opening valve 2a. Valve 2b connects the cylinder cap side to
the pump outlet port and the rod side to the tank. The
outstroke-direction velocity of the cylinder is controlled by
opening valve 2b. The device can be made of only one
proportional valve; however, two independent proportional
valves were employed for the equipment used in this study.
This is to commonize the valve used in the experiment with
Fig. 1. The same valves used as valves 1a and 1b in Fig. 1 are
used as valves 2a and 2b in Fig. 2. When used as valves 1a
and 1b, the port on one side is plugged. The pump unit is the
same as that shown in Fig. 1. However, the rotation speed and
rotation direction remain constant, and the suction side is
connected to the tank and the outlet side to the cylinder. The
circuit has a variable relief valve. The valve is used to adjust
the relief pressure.
In the circuit presented in Fig. 3, the two flow-control
modes are selected depending on the external force acting on
the cylinder and the driving direction.
The first flow-control mode consists of a meter-in flow-
control mode with a positive load, in which the driving
direction of the cylinder and the direction of the external force
were opposite. Fig. 3(a) shows the meter-in flow-control. As
demonstrated in Fig. 3(a), the chamber of the cylinder
connected to the pump has a higher pressure. In this state, the
cylinder input flow rate is mostly the same as the pump-
derived output. Therefore, the pump can control the velocity
of the cylinder.
Based on the demand velocity of the cylinder VdC l, the
demand meter-in flow rate Q l
y
determined as follows:

where V yl is a positive value in outstroke, and a negative
value in instroke.
JFPS International Journal of Fluid Power System 13-3, 17/24, 2020
(a) Four-bar linkage mechanism (b) Parameters
(c) Mechanical load with weight
Fig. 4 Bench mechanical load.
Table 1 Hydraulic circuit model parameters. Pump displacement (cc/rev) 1.6 Pump relief pressure (MPa) 21 Cylinder stroke (mm) 132
Cylinder piston diameter (mm) 25 Cylinder rod diameter (mm) 16
Variable relief valve set pressure (MPa) 4.0 Hose inner diameter (mm) 3.6
Hose length (mm)
Pump to Valves 1a, 1b, 2a, 2b 100 Valves 1a, 1b, 2a, 2b to cylinder 1000
Valves 1a, 1b, 2a, 2b nominal flow rate (L/min/(MPa))
5/1
Experimental oil temperature (°C) 25 Flow coefficient 0.6
Density of fluid (kg/mm3) 850
Table 2 Four-bar linkage mechanism parameters. Length (mm) Mass (kg)
Link1 119.1 Main frame 4.2 Link2 112.9 Cylinder 2.0 XA 100.0 Link1 0.6 XB 68.5 Link2 0.4 ZB 400.0 ZC 342.9
In Equation (1), ACyl is the pressure receiving area of the
cylinder, which is defined as follows:
0

0
where ACylCap is the pressure receiving area of the cap side, and
ACylRod is the pressure receiving area of the rod side of the
cylinder.

where DP is the displacement of the pump, ω is the rotational
speed of the pump, and is the volumetric efficiency. In
this system, the pump was a fixed-displacement type. Its
derived output flow Q controlled based its Pump was on
rotational speed ω. Therefore, the demand pump rotational
speed required to generate the demand velocity of the
cylinder V yl can be determined from Equations (1) and (3). dC

The second control mode was a meter-out flow-control
mode with a negative load, in which the driving direction of
the cylinder and the direction of the external force were the
same. Fig. 3(b) shows the meter-out flow control; the pressure
in the chamber of the cylinder connected to valve 1 is high. In
this state, the output flow rate of the cylinder is mostly the
same as that of valve 1. Therefore, valve 1 can control the
velocity of the cylinder.
Based on the demand meter-in flow rate of the cylinder
QdC l , the demand meter-out flow rate of the cylinder Q yy in dC l
out can be determined as follows:

where is the pressure receiving area ratio, which can be
determined as follows:
0
In the meter-out flow-control mode, the velocity of the
cylinder is controlled by the flow rate of valve 1. The flow
rate of the valve Q can be modeled as follows: Va 1lve


where Cd is the flow coefficient, AValve 1 is the valve opening
area, PValve 1 in and PValve 1 out are the pressures at the input and
output ports of valve 1, respectively, and is the density of
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JFPS International Journal of Fluid Power System 13-3, 17/24, 2020
the fluid. In this study, petroleum fluid was used as the fluid
for the experiment. PValve1 out was almost zero, and PValve1 in
was mostly the same as the cylinder pressure at the meter-out
side. Q lveVa 1 was controlled based on its opening area AValve 1.
Therefore, the demand opening area required to
generate the demand velocity of the cylinder V l can be dCy
determined from Equations (5) and (7).

proposed system. WDPFA03 (WANDFLUH, Switzerland)
was adopted as valves 1a and 1b. Table 1 lists the hydraulic
parameters. SGM7J (YASKAWA, Japan) was used for
servomotor.
connected to the cylinder. A four-bar linkage mechanism was
used to secure a wide joint-driving range for the cylinder. Fig.
4 illustrates the mechanism and Table 2 lists their parameters.
4.2 Experimental Procedure
robot.
To evaluate the position control, the followability of the
HDD system for the sinusoidal position input was measured.
To control the proposed system, a feedforward control, which
was implemented based on Equations (1) to (8), was used. A
feedback control helped compensate for the error of the
feedforward control. Fig. 5 shows the block diagram of the
position control in the proposed system. The details of the
feedback control are presented below. In the figure, “Plant”
is the hydraulic system shown in Fig. 1 for HDD. The
rotational speed of the pump and the valve opening areas are
controlled in the hydraulics system.
In an actual hydraulic system, the required derived output
flow rate of the pump cannot be produced due to pump
leakage or a response delay. Furthermore, the required valve
flow rate is not produced because of valve leakage or response
delay. This flow rate error becomes a factor in calculating the
error of the velocity. To compensate for the steady error of the
velocity, the integral control of the velocity feedback is
Fig. 5 Block diagram of the HDD controller.
Fig. 6 Motion of the bench.
(a) Without weight.
Fig. 7 Velocity–time response for the step input.
effective. However, it is difficult to measure the piston
velocity directly; hence, the cylinder stroke was measured.
The integral value of the demand velocity is the demand
cylinder stroke . Therefore, the correction flow rate
is calculated based on the error between the demand
value of the cylinder stroke and the actual value .
The P controller was used to calculate the correction flow rate
.
The gain of the P controller was determined by trial and
error to minimize the target error of the velocity. The P gain
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JFPS International Journal of Fluid Power System 13-3, 17/24, 2020
(a) Sinusoidal response (0.2 Hz).
(b) Error (0.2 Hz)
(d) Error (0.5 Hz).
Fig. 8 Position–time response at different frequencies.
was set to 3000. With the corrected flow rate , can be calculated as follows:


Considering the corrected flow rate , can be
calculated as follows:


For the first evaluation, the response to the step input of the
target velocity of HDD and VBC was confirmed using the
constructed evaluation bench. As HDD and EHA have the
same meter-in control for the positive load, only HDD was
evaluated in the evaluation because the drive direction did not
change. The step response of the target velocity was evaluated
with and without a weight to confirm the effect of the external
force. In the case of having a weight, a 20 kg weight was
attached to the tip of the mechanical load, as shown in Fig. 4
(c).
For the next evaluation, the responsiveness of the three
systems to the target stroke was evaluated. In this report, the
target length of the cylinder is expressed in the form of a sine
wave. The amplitude was set to ± 25 mm, and the frequencies
were set to 0.2 and 0.5 Hz. The measurement was then
performed. For the HDD, the controller with the proportional
control added to the feed-forward control to compensate for
flow error was applied. The control, which is presented in Fig.
5, was also applied to the EHA; however, the proportional
valve was set to fully open. The proportional control based on
the cylinder length error was applied to the VBC system.
Fig. 6 displays the posture of the simulated load device
during the evaluation. The load fluctuates during driving
when the cylinder stroke LCyl varies with respect to the
sinusoidal wave, with a stroke of 0 mm at the position where
the cylinder is vertical.
4.3 Experimental Results
Fig. 7 shows the velocity response to a step input. The dead
time of the proposed HDD was 60 ms, while the conventional
VBC was 30 ms. VBC only opens the valve, whereas the
HDD that raises the pump rotational velocity has a longer
dead time than VBC.
Without weight, the time to reach 95% of the demand
velocity is 2100 ms for VBC and 220 ms for HDD. With a 20
kg weight, the time to reach 95% of the demand velocity is
3180 ms for VBC and 430 ms for HDD. In a VBC that
controls the opening area of a proportional valve only by
proportional control, the convergence speed drops
immediately before reaching the target velocity. However, in
the HDD that provides feedback for the measured stroke
amount and applies the integral control to the target velocity,
the convergence to the target is fast.
In the VBC, which controls the opening area of the
proportional valve based on the difference from the target
velocity, the convergence time increased by 1080 ms because
the cylinder pressure changed due to the disturbance by the
weight. However, in the HDD, the rotational velocity of the
pump was controlled; thus, it was only marginally affected by
the disturbance due to the weight, and the convergence time
increased by 210 ms.
Fig. 8 shows the measurement results of each condition and
the tracking error. As depicted in Figs. 8(a) and (b), the
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JFPS International Journal of Fluid Power System 13-3, 17/24, 2020
proposed HDD exhibits the minimum error at 0.2 Hz. In the
VBC with only the feedback control, a steady error occurred.
In the EHA, the error increased when the cylinder switched
from contraction to expansion. This is because the frame
freely falls because of its own weight when the driving
direction is switched. When the error increases, it behaves in
an oscillatory manner because the proportional control tries to
compensate for this error.
As demonstrated in Figs. 8(c) and (d), at 0.5 Hz, the HDD
and EHA have the same error. This is because the passage
flow rate of the proportional valve increases, and the opening
command of the proportional valve becomes close to fully
open. Moreover, the difference in the opening area of the
proportional valves decreases in the two systems.
The error further increased in the VBC. Instead of a steady
error, the error per se varies with the change in the cylinder
stroke. This is due to the delay of the proportional valve.
4.4 Discussion
responsiveness than a pump based control EHA and HDD.
However, in this study, HDD showed better response than
VBC. This result is because the same hydraulic equipment
was used for VBC and HDD.
In the VBC circuit constructed in this study, the relief valve
set pressure and pump discharge flow rate were determined
from the torque that the motor can output constantly and
stably and the pump displacement. In the HDD, the pump
discharge pressure is almost the same as the cylinder pressure,
which is sufficiently lower than the relief valve set pressure.
Therefore, the HDD has better responsiveness than the VBC
because it can output a higher pump discharge flow rate than
the VBC for the same motor output upper limit. In addition,
the HDD calculates the feedforward cylinder speed (pump
discharge flow rate) required to determine the command value,
whereas VBC controls the valve opening area via feedback
control by using PID control. Therefore, the convergence time
for the target speed is longer than that of the HDD. If a larger
hydraulic source than the HDD is used for the VBC, the VBC
may have better responsiveness; however, it is difficult to
mount the large hydraulic source on a mobile robot.
5. Conclusion and Future Work
This study constructed a bench device for an HDD system
that was used for a previously proposed biped humanoid robot
and the response characteristics were evaluated against a step
input and a sinusoidal input. When using the same
proportional valve, the proposed system exhibits a higher
target followability than the VBC. In addition, compared to
the EHA, which directly controls the flow rate via the pump,
the present system, which performs meter-out control via a
proportional valve, shows excellent follow-up performance,
particularly at low frequencies. In order to realize stable
bipedal motions by following a pre-planned trajectory, speed
response and followability to the target trajectory are required.
In this study, it was shown that HDD can be applied
effectively in a method to realize such motions. However, the
effectiveness of the method to control joint torque is not
shown.
In the future, we will evaluate the effectiveness of HDD for
force control, and the tracking performance under a load
assuming the operation of a biped humanoid robot. We also
plan to build a biped robot that incorporates the proposed
system and perform walking experiments. The robot will be
compared with a robot that incorporates VBC or EHA for
followability and energy consumption in the walking pattern.
It is expected that the proposed HDD will achieve better target
followability than VBC and EHA, in case using same
equipment that can be mounted on a mobile robot as shown in
this paper. In addition, previous studies have shown that HDD
can be expected to be more energy efficient than VBC. These
results indicate that HDD is a better system for bipedal
humanoid robots than VBC and EHA.
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