The optimal tracking control of the falling ball trajectory in football training is the basis for improving athletes' skills. Generally, the academic circle adopts the precision map trajectory tracking control method. At the same time, we combine the fuzzy control law to track the optimal drop point trajectory. This can improve the optimal drop ball positioning and dynamic follow-up control capabilities [1]. The optimal trajectory tracking control method of football training has received significant attention.

The optimal ball trajectory tracking methods for football training mainly include fuzzy tracking control method, SLAM tracking control method, adaptive dynamic following control method, and so on. Scholars established the constraint reference model of trajectory following control and combined template matching and grid matching methods to realize trajectory following control. In this way, the tracking control ability of the ball drop point trajectory in football training can be improved. However, the adaptive performance of the above methods for tracking the trajectory of the falling ball in football training is not good, and the time cost is too high. Therefore, this paper proposes a tracking method for the trajectory of the falling ball in football training based on fractional differential equations. We construct a constrained parameter model for trajectory tracking control of the falling ball in football training [2]. At the same time, we use fractional differential equations for optimal trajectory optimization control. At the same time, this paper adopts the multi-parameter dynamic following method to realize the trajectory tracking of the falling ball in football training. Finally, this paper conducts an experimental test analysis and draws a valid conclusion.

In this paper, the end position reference model is used to carry out the spatial planning and design of the football training drop point trajectory. The two-degree-of-freedom model is used for the spatial planning of the trajectory of the ball drop point in football training. We first use the attitude sensor to sample the flight trajectory information and mechanical information of the football training ball [3]. We construct the spatial planning model of the football training sphere's flight trajectory (Fig. 1).

We construct the kinematics model of the sphere based on the spatial position distribution model of the trajectory of the football training drop point. We use the end position reference model for the spatial planning and design of the football training drop point trajectory. Suppose the GPS to be converted is the point _{1}(_{2}(

We get adaptive learning weights in the plane Cartesian coordinate system:

Where _{1}(_{2}(_{t}^{T} is the spatial position state vector of the football training drop point. _{1}(_{2}(

We construct a flight kinematics model for the trajectory tracking of the ball in football training based on the control as mentioned above constraints of the trajectory tracking of the ball drop point [6]. We construct a linear control matrix of dynamic motion primitives for tracking the ball's trajectory in football training under a single degree of freedom. In this paper, the football training drop point trajectory track is divided by the segmented trajectory learning method [7]. We determine the primitive points of the abscissa of point A on both sides of the meridian. In this way, we get the optimization process of the trajectory of the football training drop point:

Where ^{T}

We construct a constrained parameter model for trajectory tracking control of the falling ball in football training. In this paper, the SLAM positioning method of a high-precision map is used to establish the grid structure model of the trajectory tracking of the falling ball. We analyze the latitude value of the distance between points

In this paper, the control model of the trajectory tracking of the ball drop point in football training is divided into a deterministic model and an uncertain model. We call them
_{c}_{c}

In this paper, the proportional-integral control is used for trajectory correction control to obtain the boundary conditions:

This paper uses a section of RTK-GPS data from the campus playground for steady-state tracking control. At this point, we obtain the sufficient conditions for the flight stability of the trajectory of the football training drop point:

When

We combine the Lyapunov stability principle for coordinate transformation. At this point, we set the Lyapunov function to be

Thus, a kinematic model for determining each GPS point on the trajectory is constructed. We get a time lag of _{s}_{c}_{CSA}

In this paper, the trajectory motion of the ball drop point in football training is regarded as a two-dimensional motion in the plane [9]. The football training sphere enters the initial value

In this paper, the optimal landing point ^{Λ}

Where ^{d}

In football training, the low-altitude landing point of the sphere satisfies the spatial distribution law of automatic optimization of inertial navigation. Suppose ^{*} is a limit point in the optimal solution set (_{k}

The experiment was designed using Matlab7. We realize the electronic sensor for collecting the flight attitude parameters of the football training sphere. In this paper, the ARM5.0 video acquisition instrument is used to capture the time-lapse of the football training drop point [10]. The time interval of data collection is 0.12s. The sampling frequency is 200KHz. The interference signal-to-noise ratio is -20dB. The minimum ground clearance is 3cm. The operating frequency is 1.2GHz. Set _{1} = 10

This paper proposes a tracking method for the trajectory of the falling ball in football training based on fractional differential equations. At the same time, we construct a constrained parameter model for trajectory tracking control of the ball drop point in football training. The grid structure model of the trajectory tracking of the falling ball is established using the high-precision map's SLAM positioning method. The optimal trajectory optimization control is carried out by using fractional differential equations. We use the multi-parameter dynamic following method to track the trajectory of the falling ball in football training. The research shows that this method has better adaptive performance in tracking the trajectory of the ball drop point in football training. The trajectory tracking has high precision and strong control ability. The model improves the football training effect.

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