The algorithms used by schedulers depend on the complexity of the schedule and constraints for each problem. The 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. The optimal position of the attack station should be the blocking area (saddle-shaped area) and the hanging area (circular arc area in the middle). The 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. The 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. The 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 conditions, 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. The 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 characteristics 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. The 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 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 empirical 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 optimize the positioning of doubles in training and actual combat, it is very important to model and analyze the positioning of doubles, theoretically explore the most reasonable positioning and movement of doubles, and avoid the existing errors. Therefore, based on the mathematical model [16–19], the following research is carried out on the optimization 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. The 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. This 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 between the running speed of the players’ forward net footwork 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 difficulty 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. The magnitude of this required speed is a measure of difficulty. 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. The 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.