Application of Fuzzy Self-tuning PID Controller in
Soccer Robot
Yuzhi
Wu
Haihua
Faculty of Information Engineering
Jiaozuo University
Jiaozuo, Henan, 454003, China
lihongyun168@sina.com
Abstract-Moving and turning of robots quickly and
accurately should be ensured in games of robot soccer. However
conventional PID control usually uses fixed parameters in its
control processing, so it is hard to achieve satisfactory control
effect. Fuzzy control technique is applied to process of PID
parameters self-tuning, and control parameters are self-tuned
on-line according to different conditions in this proposed paper.
Compared with conventional PID controller, fuzzy self-tuning
PID controller can have more advantages, such as higher
flexibility ˈ control adaptability, better dynamic and static
performance. Its effectiveness and practicability are tested and
verified in MiroSot soccer robots designˊ
Keywords ˖ fuzzy control; PID control; PWM; MiroSot;
self-tuning
I.INTRODUCTION
Robot soccer has been an important experiment platform
of artificial intelligence study. Its system usually combines
environment
perception,
dynamic
decision-making,
communications subsystems and control subsystem, and the
last one is of particular importance [1]. Control subsystem
aims at controlling the motion and arbitrary turning of robots
quickly and accurately [2]. At present, conventional PID
controller uses fixed control parameters and has been applied
in industrial and soccer robot control field widely [3].
However it is hard to get satisfactory control effect for using
fixed parameters in its control processing. Fuzzy control is an
method to realize auto-control based on summarized operation
experience using inference rules similar to mankind
thought[4]. In this paper, fuzzy control technique is used in
Wang
Faculty of Information Engineering
Jiaozuo University
Jiaozuo, Henan, 454003, China
whh0101@sina.com
the process of PID parameters self-tuning and control
parameters are self-tuned on-line according to different
conditions. The experimental results indicate fuzzy control
can achieve better control effect compared with conventional
methods.
The organization of this paper is as follows: robot soccer
PID principle of control is presented in Section II and design
of fuzzy PID controller is described in Section III; in section
IV, application on MiroSot robot and the results analysis are
introduced; Section V contains the conclusion.
II.
PID CONTROL PRINCIPLE OF ROBOT
SOCCER
At present, soccer robots usually use conventional PID
controller to control its motion and turning.
As described above, for using fixed parameters
conventional PID controller may result in unexpected effects,
such as more overshoot, slow system response speed and
lager static error. Fuzzy PID controller improves those, which
is developed on the basis of the conventional PID controller
and realized by fuzzy inference. The purpose of fuzzy PID
control is to identify the fuzzy relationship between PID
parameters and system deviation. Decision-making is done
according to deviation E and its change rate Ec
correspondingly using fuzzy inference. So PID parameters
ratio coefficient Kp, integral coefficient Ki and differential
coefficient Kd are self-tuned on-line and sent to PID
controller, to get satisfactory control effect by PWM mode[4],
[6]. Its principle is shown in figure 1.
has been formed after years' research. Designing process is as
follows:
A. Fuzzy PID controller structure
The fuzzy controller is of two inputs and three outputs.
Inputs are deviation E and its change rate Ec, and outputs are
increment of PID parameters: ƸKp, ƸKi and ƸKd used for
setting PID parameters Kp, Ki and Kd on-line respectively
according to the fuzzy inference rules.
B. Decision of the membership function
Figure 1. fuzzy PID control
III. DESIGN OF FUZZY PID CONTROLLER
Fuzzy controller is designed on the basis of operation
experiences. A set of fixed steps designing fuzzy controller
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Both deviation E and its change rate Ec are divided into
seven fuzzy subset: {NB, NM, NS, ZR, PS, PM, PB}
(NB=Negative Big, NM=Negative Middle, NS=Negative
Small, ZR=Zero, PS=Positive Small, PM=Positive Middle,
PB= Positive Big) from the domain [-6,+6] ,quantized graded
into{-6, -5, -4, -3, -2, -1,0, 1, 2, 3, 4, 5, 6}. Fuzzy outputs:
ƸKp ƸKd and ƸKi are also defined seven fuzzy subsets:
{NB, NM, NS, ZR, PS, PM, PB}, from the domain [3, +3],
quantized graded into {-3, -2, -1, 0, 1, 2, 3}. And membership
functions of each fuzzy subset are determined by operating
experience. In this paper, normal functions are used as
membership functions of each fuzzy subset of fuzzy variable
E and Ec, is given in figure 2(a). And outputs: ƸKp, ƸKd
and ƸKi also use normal functions as membership functions,
which are shown in figure 2(b).
C. Fuzzy control rules
According to the impact of Kp, Ki and Kd on
characteristics of system outputs, following inference rules
are gotten [4]. When deviation E is high, take larger ƸKp and
smaller ƸKd to improve response speed and avoid
differential supersaturation resulted from transient
increasement deviation at the beginning. Differential
supersaturation may cause the control effect beyond the range
of allowable control. And integral effect should be restricted
to avoid larger overshoot. When deviation E is low, ƸKp and
ƸKi should take a little larger to improve control precision,
reduce static error and make system with better steady
performance. When deviation E is in middle values, ƸKp,
ƸKi and ƸKd should not take too large for a smaller
overshoot and keep the stability of robot, and in this case,
ƸKd impacts on the response speed mostly. Considering the
antijamming performance of system,ƸKd should take larger
or lower as Ec is larger or lower accordingly to avoid system
oscillation occurring around the predetermined values.
In summary, self-tuning control rules of PID parameters
ƸKp, ƸKi and ƸKd can be gotten as shown in following
tables [6].
b. ƸKp, ƸKi and ƸKd membership
function curve
a. E, Ec membership function curve
Fig. 2.
Membership functions curve
TABLE I INFERENCE RULES MATRIX USED TO
UPDATE THE PROPORTIONAL GAIN ƸKp OF THE PID
CONTROLLER
EC
E
NB
NM
NS
ZR
PS
PM
PB
NB
NM
NS
ZR
PS
PM
PB
PB
PB
PM
PM
PS
PS
ZR
PB
PB
PM
PM
PS
ZR
ZR
PM
PM
PM
PM
ZR
NS
NM
PM
PS
PS
ZR
NS
NM
NM
PS
PS
ZR
NM
NM
NM
NM
ZR
ZR
NS
NB
NB
NM
NB
ZR
ZR
NM
NB
NB
NB
NB
TABLE II INFERENCE RULES MATRIX USED TO
UPDATE THE INTEGRAL GAIN ƸKi OF THE PID
CONTROLLER
EC
E
NB
NM
NS
ZR
PS
PM
PB
NB
NM
NS
ZR
PS
PM
PB
NB
NB
NB
NB
NS
ZR
ZR
NB
NB
NS
NS
NS
ZR
ZR
NS
NS
NS
NS
ZR
PS
PS
NS
NS
NS
ZR
PS
PS
PS
NS
NS
ZR
PS
PS
PS
PB
ZR
ZR
PS
PB
PB
PB
PB
ZR
ZR
PS
PB
PB
PB
PB
TABLE III INFERENCE RULES MATRIX USED TO
UPDATE THE DIFFERENTIAL GAIN ƸKd OF THE PID
CONTROLLER
EC
E
NB
NM
NB
PS
NS
NM
PS
NS
NS
ZR
PS
PM
PB
NB
NB
NB
NS
PS
NB
NB
NS
NS
ZR
NS
ZR
NS
NB
NB
NS
NS
ZR
ZR
ZR
NS
NS
NS
NS
NS
ZR
PS
ZR
ZR
ZR
ZR
ZR
ZR
ZR
PM
PB
PS
PS
PS
PS
PS
PB
PB
PB
PB
PS
PS
PS
PS
PB
Total of fuzzy control rules is 49 and fuzzy control rulers
can be got from tables.
Kp0, Ki0 and Kd0 can be obtained by using formula Z-N
[5]. Outputs of fuzzy controller: ƸKp, ƸKi and ƸKd are
gotten correspondingly to self-tuning PID parameters on-line.
PID parameters are adjusted by using the following algorithm
[7], [8]:
Kp = Kp0 + a ×ƸKp
(1)
Ki = Ki0 + b ×ƸKi
(2)
Kd = Kd0 + c ×ƸKd
(3)
a, b and c are adjustment coefficients in formula (1) to (3),
and select different values according to different objects. In
the process of soccer robots matching, control system
accomplishes PID parameters self-tuning on-line by
processing the results of fuzzy logic inference rules, checking
tables and calculating corresponding PID parameters Kp, Ki
and Kd.
,9 APPLICATION ON MIROSOT ROBOT AND
ANALYSIS THE RESULTS
MiroSot soccer robot is driven by two 4.6W DC motors;
its rated speed and work voltage are 8200rpm and 6V
respectively. The motor output connects driving wheel by a
reducer of 7:1, and soccer robot weights 500 grams. The
above algorithm is applied in MiroSot soccer robot control
system and programmed by c language. System deviation E
and its change rate Ec represent the change of wheel speed
and its acceleration respectively. The lE and lEc express the
change of left wheel speed and its acceleration. The rE and
rEc express right wheel’s. Unit-step response curve of system
shows in figure 3. In testing, PC sends robot speed values (15,
25, 35, 0) through a wireless transmitting chip, and gets
feedback speed. Compared with target speed of upper PC, E
and Ec can be gotten. So controller of soccer robot can control
its moving and turning correctly using PID parameters Kp, Ki
and Kd obtained by the proposed algorithm.
Figure 3. Step System response curve
The results show that the system overshoot are reduced
significantly and its static and dynamic performance are
improved by using fuzzy parameters self-tuning PID control.
Response speed and control accuracy of target values also
exceed those using conventional PID control. In a word, this
method can meet the requirements of competition. Control
effect is shown in Table IV.
Table IV Control Comparison Table
Type
Control
Adjustment
time (ms)
Overshoot
Amount (%)
static error
(m / s)
Convention
al PID
30.38
40
0.016
Fuzzy PID
13.2
6.7
0.01
In this paper, fuzzy inference is applied to robot soccer
tuning PID parameters, and the controller has the merits of
both fuzzy controller and conventional PID controller. This
method makes use of expert experience in real-time PID
parameters tuning efficiently and retains advantage of simple
structure of conventional PID controller. Experimental results
show that the system adjustment time and overshoot decrease
significantly, and control performance is gotten much
improved after the method of fuzzy self-tuning parameters is
applied in conventional PID controller.
ACKNOWLEDGMENT
In addition, fuzzy PID control is applied in the soccer
robot motion control, avoiding artificial tuning of complicated
PID parameters for different friction coefficients and all kinds
of interference factors of competition fields. Adjusting PID
parameters on-line can achieve fast and accurate PID control
effects and reduce work of PID parameters optimization
greatly through fuzzy control procedures.
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