locomotion of a quadruped robot using cpg
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7/25/2019 Locomotion of a Quadruped Robot Using CPG
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Locomotion
of
a
Quadruped Robot
Using
CPG
Takayuki
ISHII,
Seiji MASAKADOand
K a m o
ISHII
Dept. of Brain Science and Engineering, Kyush u Institute ofTechnolo gy
Kitakyushu, Fukuoka
8084196
JAPAN
E-mail:
ishii@hrain.kyutech.ac.jp
Abst ract - It is well known that the rhythm generator
mechanism called Central Pattern Gene rato r (CPG)
controls rhythmic activities, such as locnmotion,
respiration, heart heat, etc in biological systems, and
various neuron models are proposed. The CPC has
attractive features such that (i)it generates periodical
signals persistently, @)return to the original oscillation
if
disturbances are removed, (i) the mathematical
conditions for oscillation are proved, and so
on.
In this
paper, a CPG network, which consists of the Matsuoka
model neurons, is introduced to realize the locomotion
of a quadruped walking robot and the response to
disturbances is discussed. The outputs of neurons are
utilized as the target angles of corresponding joints and
the efficiency of the proposed method is examined
through experiments with a qua druped walking robot.
1.
INTRODUCTION
Legged robots are expected
as
attractive tools to
transport in various environment such as rough terrain,
nuclear reactors, etc [ I]. The mobile capabilities of human
beings or deers in mountains attract us
in
spite
of
the
difficulties of contml and show
the
possibility of motion
control strategy imitating the processing of nervous
control mechanism.
The
rhythm generator mechanism called Central Pattern
Generator (CPG) [2][3] has been proven to be involved in
rhythmic activities, such
as
locomotion, respiration,
heartbeat, etc. Locomotion employing CPG attracts the
attention because the motion of each joint can be modeled
as the interaction between a nervous system and a
mechanical system.
The
CPG is a model to represent the
mutual inhibition among neurons, such that a neuron's
excitation suppresses other neurons' excitations. Matsuoka
[4]
proposed a mathematical model, and showed some
mathematical conditions of mutual inhabitation networks
represented by a continuous-variable neuron model that
make oscillations. Taga et. a1.[5] proposed the principle of
adaptive control of locomotion system, where nervous,
musculo-skeletal, and sensory systems behave
cooperatively to adapt to unpredictable environments.
In
this paper, a CPG network, which consists of the
Matsuoka model neurons, is introduced to realize
locnmotion
of
a quadruped walking robot and responses to
disturbances are discussed. The outputs of neurons are
utilized as the target of each joint angle, and the efficiency
of the proposed method is examined through experiments
with a quadruped walking robot.
11. CENTRAL PATTERN GENERATOR
CPG is the biological rhythmic system, and consists of
neural oscillators where
a
mutual inhibition among
neurons is modeled such that a neuron's excitation
suppresses others neurons' excitations. Beers et. al [6]
shows that the six legged robot takes reflective action
with a small number of instruction signal and simple
sensor inputs by imitating the nervous system of
cockroach. It is shown that CPG, which generates the
walk rhythm of a vertebrate, exists in a spine, and walk is
autonomously generated in the neuron system of
comparatively a low level below the midbrain [7][8].
In this paper, the mathematical model
of
CPG
proposed by Matsuoka[4]
is
introduced into
the
locomotion of a quadruped robot.
The
model among n
neurons with adaptation is expressed in continuous-
variable form as shown in I) .
7 i =
- , - / ~ : - ~ ~ ~ ? * ~ , , . ~ ~ ~ ~ d ,
1 )
,
r i
- r,
. .
.
=
intixi< .
us
Here, is a potential
of
the
neuron, v
is the variable that
represents the degree of the adaptation, T. T and
j?
are
parameters that specify the time course
of
the adaptation,
the wg indicates the strength of the inhibitory connection
between
the
neurons.
uo
is
an external input with a
constant rate, and feed; is a feed back signal. The
mathematical conditions to generate oscillations are
analyzed precisely in the reference [4]. The attractive
feature is that a CPG can adapt to extraneous signals from
the sensory system, the nervous system and unpredictable
environment, and the outputs of CPG return to the
rhythmical oscillation with the same frequency. A neural
oscillator[5] is illustrated in Fig.
I .
A neural oscillator
Fe
*,
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0 -2.0
-1.0
0 -1.0 0
-1.0 0
-
- 2 . 0
0
0
-1.0
0
-1.0
0
-1.0
-1.0 0 0
- 2 . 0 - 1 . 0
0 -1.0
0
0 - 1 . 0 - 2 . 0
0
0 -1.0
0
-1.0
-1.0
0
-1.0
0
0
- 2 . 0 - 1 . 0
0
0 -1.0 0 -1.0-2.0 0 0 -1.0
-1.0
0
-1.0 -1.0
0
-2.0
0
-1.0
0 -1.0 0 -1.0
-2.0
w. .
=
Fig. 2. Wave gait diagram ofduty factor 0.75.
I S i O
#
P f m r m
.......................
co,din.,ilUr
cOffiaQc-1
...................
Wiuiilx
CoKirirnt:-2
Fig. 3. The CPG network for walk gait of a quadmped
walking robot.
, .......... .........
i
m
t l
U
m
-.I.
Fig. 4. The output of the CPG network. The four neural
oscillators fire successively.
The numbers
,2
correspond to the neurons of left fore leg
(LEGI), 3,4 for the right fore leg (LEGZ),
5 6
far the left
rear leg
LEG3),
and
7 ,
8
for the right rear leg (LEG4),
respectively. The w12 is the weight between the extensor
neuron and the flexor neuron of LEG1 and w13 is the
weight between the extensor neuron of LEG1 and the
extensor neuron of LEGZ. If the w is positive, the
connection excites the other neuron, and if negative, the
connection suppresses the other. Zero means no
connection.
C.
Duty factor and walk phase
In order to generate a stable walk similar with wave gait,
the signal in Fig. 4 are utilized as the switching signal to
change legs from the supported leg phase to the swing leg
phase, and vise versa. If the corresponding signal is larger
than a certain threshold, the
leg
becomes in the swing
phase, and if smaller, the leg becomes in the supported
phase. By changing this threshold, walk gait in various
duty factors can be realized. The precise procedure of
walk gait generation for a quadruped walking robot is
described in the followings.
First, it supposed that one cycle consists of 200 steps. It
divides into the number
of
steps
of
a support leg and the
3 1 x 0
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B 0.5
1- B
B
VB= -V , (4)
0.6 0 7 0.75 0.8
0.9
Changing duty factor while walking can control the
walking speed. However, the robot becomes unstable if
the duty factor is changed rapidly. For example, a horse
changes walk gait according to walk speed and the change
of walk gait is completed within one cycle from a certain
walk gait
tu
another.
In
this research, the transition of walk
gait is realized within one walk cycle by changing the
threshold Th as shown in the following equation.
Th,, = Thvjd Th, hdd)'T
5 )
Here, Th,, is the new gait, Thholds the old gait and Tis the
period of one walk cycle.
E. Adaptation to disturbances
The generation of walk gait and the gait-transition can he
realized by employing the periodical signal
of
the CPG
network. The feature that the CPG network generates
oscillation signal robustly against disturbances, which is
one of interesting feature of CPG network,
is
utilized to
realize an adaptive walking.
The flow chart to deal with the disturbance on foot, the
contact to uneven ground, is shown in Fig. 5 . The
algorithm supposes that a contact of object occurs before
the scheduled time
to
contact the ground. If the touch
sensor of each foot reacts, a feedback signal is given
to
the
Feed, in
I) .
The trajectory of a leg which had a contact signal is shown
in Fig.6. A leg follows the trajectory
I )
to S ) , if there is
no disturbance. If the robot recognizes a level difference in
( 6 ) ,
the
Feed,
makes the leg change
f
he swing phase
to the support phase. If the output of CPG becomes larger
Feed =
- Oufppuf;
( 6 )
Th
0
Fig. 5 . Flow chart for adaptation to disturbances
0.11 0.25 0.3 0.38 0.5
Fig. 6. Trajectory ofleg.
than threshold at 7), it changes
to
the swing phase
between (8) to
9).
Then if there
is
no level difference, a
leg will return
to
I ) and takes the basic trajectory. Since
the mutual control combination of the CPG network, the
output of corresponding leg becomes, and the outputs of
other CPG become larger than threshold compulsorily, this
causes the support phase of other legs longer.
IV.
XP RIM NTS
The following three points are discussed in generating
walk gait of a quadruped robot.
The robot can walk, while it had kept the
posture stable.
The robot can change to various walk gaits
according to a situation.
The robot can be adapted tu disturbance.
(i)
(ii)
(iii)
A.Quadruped walking robot
A quadruped walking robot [9]
is
shown in Fig.
7.
As the
mechanical part, the TITAN-VI11 is introduced and each
leg has 3 DOF. As the sensors, a silicon retina sensor
[IO]
is mounted as the vision system
on
the top of robot, a
touch sensor is attached on each foot, and an attitude
sensor fur rolling, pitching, and heading is in the center of
body. The robot weights about 20 kg and the size
is
approximately
60 x 60
x
50
cm.
Fig. 8 shows the hardware architecture. In this research,
DIA hoards and the serial port are used tu control actuators.
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The target angles of each joint and pan-tilt camera system
are transmined through the DIA board into the DC motor
driver, and from serial port to a servo motor control driver,
respectively. And rolling, pitching and heading angles are
measured with TCMZ sensor and obtained through a serial
port. The image of silicon retina is captured with a image
processing board IP5000, and the touch signals are from a
PI0 board. Fig.9 shows the software architecture. The
RTLinuxver.2.2 (http:llw.rtlinux.org/) is used as the
realtime operating system for the software development.
The RTLinux
is
one of the real-time operating system and
can be available as the Open Source Software. The APIs to
handle the
IiO
data, scheduling and hardware interrupt are
prepared, therefore, the hardware level programming of
the robot is suitable. The low level software such as
sensing, actuation and control are developed as the real-
time threads (kernel module) because this process should
be scheduled in real-time. The image processing is carried
out as the normal Linux process (user program). The data
transmission to each leg of the robot that needs a real-time
control is overated on
the kemel side. and, additionallv, it
Fig. 7. A quadruped walking
robot
Fig.8. Hardware architecture of a quadmped walking
robot.
Fig.9. Software architecture of a quadruped walking
robot.
develops
as
a program
on
the user side. Moreover, the data
of the user program is exchanged for the kernel module
through FIFO and Shared-Memory.
B.
Experimental results
Walk gait in various duty factors can be realized using the
signal from the CPG network, and the relation between
duty factor and speed is investigated. The times to walk 2
[m] long are measured at duty factor 0.75, 0.85, 0.75 ->
0.85 and 0.85 -> 0.75, respectively.
In
the third and fourth
experiments, the duty factor
is
changed after I[m] walk.
The walk time in each duty factor is shown in Table 2.In
the experiments, one cycle time is fixed to 4 [sec],
therefore the robot moves faster when the duty factor is
small.
Table 2. Speed change with various duty factors.
-Change speed by changing duty factor
I
time(sec)
I
46.508
I
53.221
I
49.085 49.845
I
-Adaptation to disturbances
In order to investigate the efficiency of the proposed
method, the experiments are carried out that the robot
carries over a bump with height of 20 [mm] in front of the
left leg (LEGI).
In
the normal condition, the robot lifts up
legs 50 [mm].
Fie.10 shows the outout of the CPG network. In the
points of LEG1 (blue line) indicated with red circles, the
touch sensor of the LEG1 reacted to the bump and
feedback signals are given to the CPG network. Therefore,
the output signals corresponding to LEG1 become small
,......... ~~ ..............................
:-,..
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and other signals are excited. The
Z
position of each foot
is shown in Fig. 11 In the normal state, the Z position is
250 [mm] in the body coordinate. And the Z position of
LEG1 keeps small values while carrying over the bump,
and that of LEG3 becomes small successively. The rolling
and pitching angles of center of body using proposed
method are shown in Fig. 12. Fig. 13 is the resulton
condition that the feedback signals are
not
given to the
CPG network. Comparing the rolling angle with and
without feedback signals, the offset can be observed in
Fig.l3(a). In spite that the robot leans positive direction
around x-axis in the experiment without feedback signal,
the robot keeps the stability utilizing feedback signals. As
for pitching angle, the same results can be observed. The
average and distribution
of
rolling and pitching angle
while the robot having ridden on a bump is shown in Table
3.
It
is shown that the proposed method works as we
expected and keeps the robot stable.
...
.
uw
(a) Rolling angle
* I
..... _ ,
..
..............................
1 1.
OM
5
U
.
*.>
z
a
i:
U
.)I.-
M
.e, i . . . . . . . . I
...... .
I .
Epr
(b) Pitching angle
Fig.12. The experimental results with feedback signals.
1V.
CONCLUSIONS
In this paper, the generation of walk gait using the
Central Pattern Generator (CPG) is proposed and the
efficiency of the adaptation method against disturbances is
examined through the experiments.
Consequently, the walk gait for a quadruped robot can be
generated in various duty factors using CPG. And it is
shown that the walk gait can be changed smoothly by
changing threshold. Furthermore, it is shown that the robot
can keep the posture stable using feedback signal from
touch sensors while carrying over a bump. The CPG
network works as we expected.
In this paper, we discussed a walk gait to a convex
environment. The CPG network should be extended to the
various environments. Moreover, the feedback signal from
vision sensors is under consideration.
References
[I] S.Song, K.J.Waldron, Machines That Walk, The
Adaptive Suspension Vehicle, MIT Press, 1989
[2] G.S.Stent, W.B.Jr.Kristan, W.D.Friesen, C.A.A. Ort,
M.Poon and R.L.Carabrese, Neuronal Generation of the
Leech Swimming Movement, Science, Vol.2W, pp.1348-
1357, 1978
[3] J.T.Bachanam and S.Grillner, Newly Identified
Glutamate Interneurons and Their Role in Locomotion in
Lamprey Spinal Cors Science, Vo1.236, pp. 312-314,
1987
[4] K.Matsuoka: Sustained Oscillations Generated by
Mutually Inhibiting Neurons with Adaptation Biological
Cybemetics Vo1.52 pp.367-376,1985
[ 5 ] G.Taga, Y.Yamaguchi and H.Shimizu: Self-organized
. . . . . . . .
I.,
,
,.
....
......
I_
I
.. i
................................................................................................
c
(a) Rolling angle
. I ... ... ... .. ............... .............. ...... ....
uy
(b) Pitching angle
Fig.
13.
Experimental results without feedback
signals.
3183
Authorized licensed use limited to: Khajeh Nasir Toosi University of Technology. Downloaded on December 21, 2009 at 05:41 from IEEE Xplore. Restrictions apply.
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7/25/2019 Locomotion of a Quadruped Robot Using CPG
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control of bipedal locomotion by neural oscillators in
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[6] RD.Beer, H.J.Chil and L.S.Sterling: An Artificial
1nsectAmerican Scientist Vo1.79 pp.444452, 1991
[7] M.L.Shik and G.N.Orlovsky: Neurophysiology of
Locomotor Automatism Physiol. Review 56, pp.465-501,
1976
[8]
S.Grillner Control of locomotion in bipeds, tetrapods
and
fish
In Handbook of Physiology, volume I I ,
American Physiol. Society, Bethesda,
MD,
pp.1179-1236,
1981
[9] T.Ishii, K.Ishii, Geneartion
of
Walk Gait for the
Quardruped Robot Using Neural Oscillator, Proc. of RSJ
Conf. 2002, 1119,2M)2,pp.
70-71, 2002
[ O ]
K.Shimonomura, . Kame&, K.1shii and T.Yagi, A
Novel Robot Vision Employing a Silicon Retina, Journal
ofRohotics and Mechatoronics, vol. 13. No.4, pp.614-620,
2001
Appeudir
-
Example ofneura l oscillators
The neural oscillators with two to five neurons are
examined.Here T=12.0 T=l.O ~=2.5 andu0=l.O.
The weighting parameters
wv
are set to the same values
for
inhibition. The zero means
no
connection between
neurons.
(i) Two neurons
pp1138-1145,1991
w. .
=
I
.............................................................
. ......
r...w>:
...-i/
.. .
- 0 -1.5
0
-1.5-
-1.5 0 -1.5
0
0
-1.5 0 -1.5
-1.5
0 1.5
0
Fig.A-I. CPG with two neurons.
(ii) Three neurons
-2.5 -2.5
-2.5 -2.5
. . .
-.-.-I
. . . . . . . . . . . .
. .
......
-2.5
0
-2.5 -2.5
I
- 2 . 5 - 2 . 5 0 -2.5
-2.5 -2.5 - 2 . 5
0
w =
Fig.A-2. CPG with three neurons.
wv
=
3184
-2.5
0
-2.5 -2.5 -2.5
-2.5
-2.5
0
-2.5 -2.5
-2.5
-2.5
-2.5 0
-2.5
(iii) Four neurons a)
-.-
Fig. A-5 CPG with five neurons
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