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Research Article
Algorithmic Study on Position and Movement Method of
Badminton Doubles
Yu Xie ,
1
Xiaodong Xie ,
1
Huan Xia ,
1
and Zhe Zhao
2
1
Physical Education Institute, Hunan University, Changsha 410082, China
2
Physical Education Institute, Hunan Normal University, Changsha 410012, China
Correspondence should be addressed to Zhe Zhao; 16334@hunnu.edu.cn
Received 27 September 2021; Accepted 16 December 2021; Published 10 January 2022
Academic Editor: Punit Gupta
Copyright ©2022 Yu Xie et al. is is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
e algorithms used by schedulers depend on the complexity of the schedule and constraints for each problem. e position and
movement of badminton players in badminton doubles competition is one of the key factors to improve the athletes’ transition
efficiency of offense and defense and the rate of winning matches and to save energy consumption. From the perspective of basic
theory, the author conducts research on the position and movement of badminton doubles. Based on the numerical analysis
method, the optimal model of standing position and direction composed of 7 nonlinear equations is established. In addition, the
final of 10 matches of the super series of the world badminton federation in 2019 was selected as the sample of speed parameters.
With the help of MATLAB mathematical analysis software, the numerical model established by the least square method was
adopted to optimize the specific standing position and walking model. Ultimately, the optimal solution has been obtained, which
can be represented on a plane graph. e optimal position of the attack station should be the blocking area (saddle-shaped area)
and the hanging area (circular arc area in the middle). e optimal defensive positioning should be left defensive positioning area
(left front triangle area) and right defensive positioning area (right front triangle area), which is consistent with our current
experience and research results. e research results use mathematical tools to calculate the accurate optimal position in doubles
matches, which has guiding significance to the choice of athletes’ position and walking position in actual combat and can also be
used as a reference for training, providing a certain theoretical basis for the standing and walking of badminton doubles
confrontation. e data collection and operation methods in this study can provide better calculation materials for artificial
intelligence optimization and fuzzy operation of motion displacement, which is of great significance in the field of motion,
simulation, and the call of parametric functions.
1. Introduction
As a sport of both recreational fitness and competition, the
amount of exercise of badminton can be independently
chosen by the participants according to their own condi-
tions, and the requirements for equipment and venues can
be high or low. And because the noncontact confrontation
reduces the possibility of injury and physical requirements, it
has been widely popularized in all parts of the world and has
become an Olympic competition [1]. According to the
number of participants, the badminton events can be divided
into singles, doubles, and three against three. e singles
events have high physical requirements [2–4], while the
doubles events emphasize more on tactics [5, 6], which is
essentially an accelerated version of doubles.
In badminton doubles tactics, standing and walking are
the basis, which are related to the cooperation between two
people and the reasonable distribution of areas [7]. Athletes’
technique ability not only needs to have their own char-
acteristics but also must keep strong backcourt tactics ability
before, during, and at the same time [8] because, in the game,
every detail might affect the competition results; it also
makes athletes need to have strong ability of details. e
footwork of badminton is an important part of the players’
technical and tactical abilities, among which backtracking is
the last step of the footwork of badminton, and backtracking
connects with the starting link of the next footwork [9].
Reasonable positioning and walking in doubles make the
division of labor of teammates clear, makes the preparation
of athletes more reasonable, reduces the unnecessary
Hindawi
Scientific Programming
Volume 2022, Article ID 6422442, 9 pages
https://doi.org/10.1155/2022/6422442
running of athletes in the confrontation, saves physical
energy, and increases the efficiency of scoring. Quite a few
scholars [8–13] have carried out research and discussion on
the positions and moves of doubles and reached some
consensus. Gawin [10] analyzed the match data and made
statistics on what kind of movement mode in doubles is
beneficial to gain the advantage in the serve. Zhu qiang et al.
[14] used the method of literature review, observation and
interview, etc., to discuss the position of attack and defense
switch in badminton doubles. Lin [15] also used similar
research methods to analyze and discuss Yang wang Xiao li’s
position in 10 doubles matches from 2013 to 2014.
It can be seen that, in addition to forming some em-
pirical consensus, there have also been some relevant studies
on the positioning and movement of doubles. Partial least
squares correlation analysis (PLSCA) (Abdi and Williams,
2013; Weaving et al., 2019) [16] was used to investigate the
composite relationship between perceived wellness status
and technical-tactical performance for both the forwards’
and backs’ positional groups as per previous methods [17]
(Emmonds et al., 2020). However, the conclusions of these
studies are all qualitative and empirically based, which may
be practical but not rigorous. In order to scientifically op-
timize the positioning of doubles in training and actual
combat, it is very important to model and analyze the po-
sitioning of doubles, theoretically explore the most rea-
sonable positioning and movement of doubles, and avoid the
existing errors. erefore, based on the mathematical model
[16–19], the following research is carried out on the opti-
mization of badminton doubles’ position and movement, in
order to provide some theoretical basis on this issue.
2. The Positioning Model of Doubles Based on
the Analytic Method
2.1. e Basic Idea of Model Building. In a badminton match,
when a player of his own side hits the ball, the time it takes
for the ball to fly from his own field to the field of his
opponent is the time for the player of his own side to stand.
Similarly, after the opponent hits the ball, the time for the
ball to fly from his court to his opponent’s court is the time
for his opponent to start and hit the ball. is is the basic
rhythm of badminton.
As can be seen from Figure 1, the time required for the
ball to fly from one side of the field to different areas of the
opposite side of the field is different, that is, the time from
starting to hitting is different for the incoming ball from
different landing points. For example, the split lob is faster
and shorter than the high ball, so the player who wants to
catch the ball should start and run to the right hitting area in
a shorter time. Of course, there is a certain difference be-
tween the running speed of the players’ forward net foot-
work and the running speed of the players’ backward
retreats’ footwork. To sum up, ignoring the secondary
influencing factors, the players should have a corresponding
optimal positioning point for the position of the ball when
facing the opponent’s shot. From this positioning point, it
should be equally difficult for them to return several furthest
corners of the area they are responsible for. In order to get
this position, the emphasis is on the evaluation of the dif-
ficulty of connecting each ball at the farthest corner. As the
ball travels from the opposing field to each of these farthest
corners, it corresponds to the distance the player must run
and the time he has to start to hit the ball, which is the
amount of speed the player must put into catching the ball.
e magnitude of this required speed is a measure of dif-
ficulty. So, the optimal positioning should allow the player at
that point to run at the two farthest corners of the net at the
same speed. e two farthest corners of the baseline should
run at the same speed. Moreover, the running speed towards
the furthest corner of the net and the furthest corner of the
baseline should satisfy the proportional relation between the
running speed of the net footwork and the running speed of
the back-and-back footwork.
2.2. Badminton Court Coordinate System Creation. In order
to calculate the distance better, an optimization model is
established based on the analytical method in this paper.
erefore, the analytical coordinate system of the site
should be built first to obtain the coordinate values of each
key point. One end of the center line of the net is taken as
the origin of the coordinate system. e X-axis is along the
long side of the court, while the Y-axis bisects the opposite
side of the court along the direction of the net, as shown in
Figure 2.
In Figure 2, the X-axis represents the longitudinal dis-
tance in the direction of the badminton court sideline, the Y-
axis represents the transverse distance in the direction of the
center line, and the intersection of one side sideline and the
middle is the origin. Doubles position is the end of the
movement to the position, the starting point to hit the ball,
and the basis of other doubles tactics. erefore, each po-
sition corresponds to the position of the ball when an op-
ponent hits the ball. In order to better illustrate the
optimization process, the ball is located at the corner of the
opponent’s baseline (G spot in Figure 2) as an example; see
Figure 2, for the coordinates of the two players’ position
points (points J and K on Figure 2) and the farthest corner
points (points A, B, C, D, E, and F on Figure 2) in the area
they are responsible for (CD is the dividing line of the area).
Considering that when the opponent hits the ball from the
baseline and ignores the situation that the ball rolls over the
net with a small probability, the ball should not fall into the
area surrounded by the two sideline of the line AE, the field,
and the net line (Y-axis), so there is no distribution of points
needing to catch the ball in this area. At this point, there are
seven unknown coordinate parameters, including the two-
axis coordinates x1 and y1 at point J, the two-axis coordi-
nates x2 and y2 at point K, the two-axis coordinates mand n
at point C, and the y-coordinate pat point D, where the
coordinates x1 and y1 and x2 and y2 of J are exactly the
coordinate values to be obtained.
2.3. Optimization Model Creation. As shown in Figure 2, the
ball falls from point G to A, B, or C. Points B, D, and F
correspond to the point where the ball clicks back from G.
e horizontal component of the average flying speed of the
2Scientific Programming
ball when hitting the ball is m/s. e average speed of
returning the ball after receiving the ball is m/s. According to
the physical relationship between flight distance, flight
speed, and flight time, the time (unit: s) of the ball from point
G to points A, B, C, D, E and F is
tGA �7.7/Vds,(1)
tGB �13.4/Vhc,(2)
tGC ��������������������
(6.7+m)2+(6.1−n)2
Vds
,(3)
tGD ���������������
13.42+(6.1−p)2
Vhc
,(4)
tGE ����������
7.22+6.12
Vds
�9.4
Vds
,(5)
e w tGF �����������
13.42+6.12
Vhc
�14.7
Vhc
.(6)
Assuming that the opponent hits the ball at the exact
time when the receiver starts, then according to the physical
relationship between running distance, running speed, and
running time, the running speed required by the player at
point J to catch the ball at A, B, C, and D is
Vn
JA ���������������������
x1−1.0
2+6.1−y1
2
tGA
,(7)
Vb
JB ���������������������
6.7−x1
2+6.1−y1
2
tGB
,(8)
Vn
JC �������������������
x1−m
2+y1−n
2
tGC
,(9)
0(0.5, 0.0) (6.7, 0.0)
(6.7, p)
(6.7, 6.1)(1.0, 6.1)
(–6.7, 6.1)
(x1, y1)
(x2, y2)
(m, n)
GA
C
EF
D
B
J
K
x (m)
y (m)
Figure 2: Analytical coordinate system of badminton doubles court and station.
Badminton flight path
Run the line
Figure 1: Badminton flight and running circuit diagram.
Scientific Programming 3
Vb
JD ��������������������
6.7−x1
2+y1−p
2
tGD
.(10)
e running speeds required by players at point K to
catch the ball at four points C, D, E, and F are
Vn
KC �������������������
x2−m
2+n−y2
2
tGC
,(11)
Vb
KD ��������������������
6.7−x2
2+p−y2
2
tGD
,(12)
Vn
KE ��������������
x2−0.5
2+y2
2
tGE
,(13)
Vb
KF ��������������
6.7−x2
2+y2
2
tGF
.(14)
In order to simplify the calculation, at the same time,
according to the split in the following section hanging ball
when the average speed of horizontal component of the
ball when the ball hits the back of the level of the average
speed component, athletes do back to the bottom line of
footwork when running with speed and athletes to the net
do online gait as running speed of the related research
(specific data discussed in Section 3), the ratio of discovery
can be approximately considered as the constant value,
which is
Vhc
Vds
�K1,(15)
Vn
Vb�K2.(16)
According to the basic idea in Section 2.1, when the
athletes at point J and at point K meet the requirements of
equation (16), the speed required to catch the ball at the
farthest corner point should be in the optimal position:
Vn
JA �K2Vb
JB �Vn
JC �K2Vb
JD,(17)
Vn
KC �K2Vb
KD �Vn
KE �K2Vb
KF.(18)
By substituting equations (1)∼(15) into equations (17)
and (18), we can obtain
13.4��������������������
x1−1.0
2+6.1−y1
2
�7.7K1K2��������������������
6.7−x1
2+6.1−y1
2
,(19)
��������������������
x1−1.0
2+6.1−y1
2
·�������������������
(6.7+m)2+(6.1−n)2
�7.7������������������
x1−m
2+y1−n
2
,(20)
��������������������
x1−1.0
2+6.1−y1
2
·��������������
13.42+(6.1−p)2
�7.7K1K2�������������������
6.7−x1
2+y1−p
2
,(21)
9.4K1K2�������������������
6.7−x2
2+p−y2
2
��������������
x2−0.5
2+y2
2
·��������������
13.42+(6.1−p)2
,(22)
9.4������������������
x2−m
2+n−y2
2
��������������
x2−0.5
2+y2
2
·�������������������
(6.7+m)2+(6.1−n)2
,(23)
14.7�������������
x2−0.5
2+y2
2
�9.4K1K2�������������
6.7−x2
2+y2
2
.(24)
Since point C is located on the point line AE, it should be
satisfied:
n�12.2m−6.1.(25)
3. Model Parameters and Solutions
3.1. Model Parameters: Speed Parameters. In order to sim-
plify and solve the established optimization model, this
paper tests the horizontal component of the average flying
speed of the ball when splitting the crane, the horizontal
component of the average flying speed of the ball when
hitting the backcourt ball, the running speed when the player
makes a backward step to the In this paper, and the final
videos of 10 matches of the world badminton federation
super series in the recent year were selected as the statistical
space to conduct sample statistics of various speed pa-
rameters. e source of the matches is shown in Table 1. A
total of 668 effective sum ratio data and 382 effective sum
ratio data were obtained, and their distribution is shown in
Figure 3.
rough fitting, it can be approximated to a fixed value
of 0.7657 and a fixed value of 1.3026. In equations (19)∼(25)
of the optimization model, it is always multiplied, so it can be
regarded as a parameter.
3.2. Model Solution. Models (19)–(25) are for nonlinear
equations, and the equation number equals the number of
variables (which can be regarded as known quantity), so a
4Scientific Programming
given interval may have a solution. Now, the fsolve function
of MATLAB mathematical software is used for trial calcu-
lation and solution. According to the help file of MATLAB,
the fsolve function is to use the least square method to solve
the nonlinear equations, and the general solution formula is
X�FSOLVE(FUN,X0,OPTIONS),(26)
Where FUN is the nonlinear system of equations requiring
solution. For this paper, equations (19)∼(25) are the non-
linear system and the initial value of the variable. Because the
solution process has a certain dependence on the numerical
value, in this paper, the understanding range is roughly
calculated according to the experience. en, we set the
initial value. OPTIONS represents the structure created for
OPTIMSET, which is the default value for this optimization
parameter.
In the input equations (19)∼(25) and the estimated initial
values of each parameter, the number of cycles is set to 1000
generations. e final results of each parameter are shown in
Table 2. e various errors corresponding to the solutions
obtained through numerical iteration are shown in Table 3.
Put the result back into the field map, and Figure 4(a) can
be obtained. e point of the left field is the position of the ball
when the opponent hits the ball. e point on the right side of
the field is the optimal station point of the two players of the
team based on the optimization of analytical method. By the
same method, the optimal solution of the position required by
Table 1: Model data source statistics table.
Event name Category Contestant e number of
data
Yubo Cup Final 2018 Women’s
doubles Yuki Fukushima Katsuka Hiroda vs. Zonko pan Ravinda 69
2018 World Championships Men’s doubles Li Junhui/Liu Yuchen vs. Jiamura Kenshi/Yueda Qigu 77
2018 World Championship
Final
Women’s
doubles
Yoshiyuki Fukushima/Hiroda Katsuhwa vs. Maayu Matsumoto
Naga 66
2018 World Badminton Final Women’s
doubles Takahashi Lihua/Matsuomi Sasaki vs. Li Shaoxi/Shen Shengzan 65
2019 Sudiman Cup Final Men’s doubles Li Junhui/Liu Yuchen vs. Watanabe Yuda/Endo Dayou 72
2018 World Badminton Final Women’s
doubles Takahashi Lihua/Matsuomi Sasaki vs. Li Shaoxi/Shen Shengzan 65
2019 World Championship
Final Men’s doubles Setiawan/Ahsan vs. Tomoki Zhuo/Kobayashi 59
2018 World Championship
Final
Women’s
doubles
Yoshiyuki Fukushima/Hiroda Katsuhwa vs. Maayu Matsumoto/
Naga 66
2019 World Women’s
doubles
Badminton final Mayou Matsumoto/Nagawara vs. chen Morin/Jia
Yifan 64
2019 World Championship
Final
Women’s
doubles Mayou Matsumoto/Nagawara/Yuki Fukushima/Kohwa Hiroda 71
1.5
1.0
0.5
K1
0.0
0 100 200 300 400 500 600 700
K1 = 0.7657
(a)
1.8
1.6
1.4
K2
1.0
1.2
0 100
K2 = 1.3026
200 300 400
(b)
Figure 3: Velocity parameter distribution diagram. (a) K
1
distribution diagram. (b) K
2
distribution diagram.
Table 2: Results obtained from equations (19)∼(25) (unit: m).
x1y1x2y2m n p
Results 2.8661 4.6844 2.6353 1.9088 0.7839 3.4636 2.9784
Scientific Programming 5
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Figure 4: Results of optimal positioning when the ball is at each key point in the opposite side field area. (a) Scenario 1. (b) Scenario 2.
(c) Scenario 3. (d) Scenario 4. (e) Scenario 5. (f ) Scenario 6. (g) Scenario 7. (h) Scenario 8.
Table 3: Errors of equations (19)∼(25) corresponding to solutions.
Equation (19) (20) (21) (22) (23) (24) (25)
Error −8.74E-07 −1.18E-07 −9.76E-07 8.91E-07 −1.37E-07 −9.30E-07 8.26E-14
6Scientific Programming
the opponent when the ball is at the other key points of the
opponent’s court can be calculated, as shown in Figures 4(b)∼
4(h). All the obtained optimized station positions and the
results obtained according to the symmetry relation are
collected in the same figure, as shown in Figure 5. e points in
the left and right field areas of the same color correspond to the
position of the ball and the corresponding relationship between
the positions of the square and the station.
Figure 5: Summary of optimized station positioning results.
H1
H1
H2
Figure 6: Station area and rotation path.
Scientific Programming 7
4. Analysis and Discussion
In Figures 4 and 5, the X-axis represents the longitudinal
distance in the direction of the badminton court sideline, the
Y-axis represents the transverse distance in the direction of
the center line, and the intersection of one side sideline and
the middle is the origin. e different color dots sign the
footfall dots and the directions. ree spline curves were
used to connect the stations of each side in the center and
right field in Figure 4 to obtain two offensive areas (red area)
and two defensive areas (blue area), as shown in Figure 6.
ere are two offensive areas; one is in the front of the
field, in the actual combat process, which should be re-
sponsible for the front of the net, so it can be called the net
position area; the other is in the back court, in the actual
combat process, which should be responsible for the back
court attack, so it can be called the killing and hanging
station area. e two defensive areas are located in the left
and right field, respectively, which can be called the left
guard area and the right guard area (in real combat rotation,
players should try their best to move in a straight line to
reduce the distance of moving, so they should use a straight
line to connect the boundaries of the offensive area and the
defensive area). e rotation path in Figure 6 can be ob-
tained. In the actual combat process, the so-called offensive
to defensive and defensive to offensive are the two players
who continue to choose a reasonable position between the
offensive zone and the defensive zone through these paths.
Based on the analytical method, we obtain Figure 6, which is
obtained by the optimization study of such a stance area and
rotary path graph; you can connect the attack area and
defensive area and their rotary path as a special “movement.”
Using the running circle, we can guide the positioning and
walking training of doubles players and even put the running
circle on the field, so as to develop the fixed thinking and
concept of positioning and field of doubles players. In this
way, the possible errors of positioning or moving can be
reduced due to panic in high-speed doubles competition.
is study is based on the mathematical analysis method
to optimize the position of doubles, and a running circle is
preliminary calculated. For example, consider that, in
practice, when players hit the ball at the baseline, they often
choose to kill the ball vigorously instead of hitting it to the
far corner of their own side. When the player receives the
ball in front of the court, he can use a certain arm span and
racket length; the center of gravity does not move to the
position of the ball. It also takes time for the athlete to start
the turn from the position. Taking the secondary influencing
factors into account will be the next step for more deepening
the research on the optimization of the target on the basis of
the overall train of thought. It is assumed that when the
above factors are taken into account, the resulting running
circle may be the result of a backward shift (as shown in
Figure 7(a)) or a longitudinal stretch (as shown in
Figure 7(b)) compared with the current one. ese as-
sumptions need to be further studied to confirm whether
they are reasonable. is kind of data has the position
characteristics of relatively optimized fuzzy algorithm. ese
features can provide reference for data collection and feature
analysis of subsequent sports competitions of multiple
athletes. After collecting the location data of multiple
multievent competitions, the database can optimize the
multipoint fuzzy computing of computer cloud, so as to
obtain a better model.
5. Conclusion
Based on the analytical method, this paper establishes the
optimal model of badminton doubles position, obtains the
relevant speed parameters through statistical analysis, then
solves the model by numerical method, and draws the
following conclusions.
(1) Based on the analytical method, an optimization
model is established. By inputting reasonable speed-
related parameters, the specific points of the optimal
positions of the two players in badminton doubles
can be solved.
(2) e specific distribution of these optimal stations
constitutes four regions, namely, the area of net
closing (the saddle-shaped area in the front), the area
of killing and hanging (the circular arc area in the
middle), the area of left guard (the triangle area in the
left front), and the area of right guard (the triangle
area in the right front).
(3) e rotation path can be obtained by connecting the
boundary between the offensive zone and the de-
fensive zone. e two players can constantly choose a
reasonable position between the offensive zone and
the defensive zone through the rotation path to
realize the switch from offense to defense and from
defense to offense.
(4) e offensive zone and the rotation paths that
connect them combine to form a running circle,
which can be used to guide doubles players in po-
sitioning training.
(5) As a model of multiplayer sports, this study can
provide more detailed data and statistics. e re-
search also provides a reference model for the col-
lection and calculation of multievent and
multiproject secretaries of subsequent cloud
H1
H1
(a) Backward translation (b) Longitudinal lengthening
Figure 7: Conjecture of running circle results when more factors
are considered. (a) Backward translation. (b) Longitudinal
lengthening.
8Scientific Programming
computing, to obtain the optimization of algorithm
and model.
Data Availability
e datasets used and/or analyzed during the current study
are available from the corresponding author upon reason-
able request.
Conflicts of Interest
e authors declare that there are no conflicts of interest
with respect to the research, authorship, and/or publication
of this article.
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Scientific Programming 9
