An intelligent billiards training system

Abstract

The present invention discloses an intelligent billiards training system, which relates to the field of image processing technology. Through multi-sensor fusion technology such as depth camera, laser radar, high-speed camera, etc., it accurately constructs a three-dimensional model of the billiard table and the ball, making the training environment more realistic; the path simulation module can automatically calculate the best hitting angle and the best hitting force F, helping the trainee find the best offensive route and reducing the cost of trial and error. It can measure the friction coefficient of the table cloth in real time and perform trajectory correction based on the different materials of the table cloth friction to ensure that the calculated cue ball speed matches the actual situation and avoid trajectory deviation. If the trainee's hitting angle or force deviates from the optimal calculated value, the system can automatically correct it and provide optimization suggestions. The system can also monitor the standing posture, grip and body balance, and quantitatively evaluate the stability of the posture; the trainee can correct bad posture in a short time.

Description

Technical Field

[0001] The present invention relates to the technical field of image processing, in particular to an intelligent billiards training system. Background Art

[0002] Billiards training is a sport that requires extremely high precision. Its effectiveness is affected by a variety of factors, including the trainee's hitting force, hitting angle, the collision trajectory between the cue ball and the target ball, and the friction coefficient of the tablecloth. In traditional billiards training, trainees often rely on personal experience to practice, lacking quantitative indicators to evaluate the accuracy of their shots. Because trainees cannot accurately grasp the appropriate hitting force and angle, training efficiency is often low, making it difficult to achieve accurate shots. Furthermore, traditional training methods rely primarily on visual judgment and trial and error, lacking scientific error analysis and path optimization, making it difficult for trainees to systematically improve their skills.

[0003] While some existing billiards training devices offer some degree of trajectory analysis or video playback, they still have significant shortcomings. For example, most devices cannot accurately measure the strength of a player's strokes and lack the ability to dynamically adjust the friction coefficient of the tablecloth. This results in discrepancies between the simulated cue ball's trajectory and the actual trajectory. The friction coefficient of the tablecloth can vary slightly depending on the material used, and ignoring these details can lead to discrepancies between the simulated results and the actual strokes, affecting the player's judgment and further reducing the accuracy and effectiveness of training.

[0004] Furthermore, if the friction coefficient of the tablecloth is not accurately accounted for during simulation, the cue ball's trajectory may deviate significantly from reality, leading the trainee to make adjustments based on inaccurate data, exacerbating training errors. For example, in high-friction areas, the cue ball's velocity will decay more rapidly, while in low-friction areas, the cue ball may travel further. If the training system fails to accurately simulate these details, the trainee may mistakenly believe that the problem lies with their technique rather than the surface, and may incorrectly adjust the force or angle of their shot, compromising training effectiveness. Summary of the Invention

[0005] In view of the deficiencies of the prior art, the present invention provides an intelligent billiards training system to solve the problems mentioned in the background technology.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solutions: an intelligent billiards training system, comprising:

[0007] The 3D billiards scene modeling module uses a depth camera and lidar to acquire image and 3D data of the billiard table and balls, constructing a 3D model of the billiard table and projecting the trajectory of the cue ball and target ball each time the trainee hits the ball into the 3D model.

[0008] The path simulation module is used to simulate and analyze the best hitting angle of the cue ball when setting the target ball during training. and the initial velocity of the first cue ball ; and collect the friction coefficient of the tablecloth , the initial speed of the first cue ball Correct and convert to obtain the initial velocity of the second cue ball and hitting force F;

[0009] Error analysis module, used to collect the training strength of the trainer's training and training hitting angles and the best angle to hit the cue ball Compare and calculate the hitting force F to obtain the hitting force error and hitting angle error :when , the first warning signal is issued to remind the trainee that the hitting force is not up to standard; when , a second warning signal is issued to remind the trainee that the hitting angle is unqualified;

[0010] The trajectory intelligent monitoring module is used to establish a trajectory motion data set based on the actual and expected motion trajectories after each swing of the trainee. The trajectory motion data set is analyzed to obtain: the cue ball trajectory deviation coefficient , target ball motion deviation factor and the cue ball abnormal out-of-bounds factor , and comprehensively calculate the hitting trajectory accuracy coefficient , set the preset qualified threshold X, if < qualified threshold X, the third warning signal is triggered.

[0011] Preferably, the path simulation module includes an image acquisition unit and a simulation calculation unit;

[0012] The image acquisition unit is used to collect the coordinates of the i-th pocket on the billiard table, marked as , collect the current mother ball coordinates , the coordinates of the target ball And the radius R of the target sphere:

[0013] Collect the current rotation state and motion state of the cue ball, including spin, top spin and back spin;

[0014] The motion states include: stationary, rolling and sliding states;

[0015] The simulation calculation unit is used to project the target ball into the three-dimensional model when the trainer is training, and calculate the best hitting angle of the cue ball through the collision physics algorithm. , the initial speed of the first cue ball , the initial velocity of the second cue ball and hitting force F;

[0016] Best angle for hitting the cue ball The way to obtain is as follows:

[0017] S11. When the moving direction of the target ball and the i-th pocket is consistent, calculate the target ball's pocket vector :

[0018] ;

[0019] Where, represents the x-axis coordinate of the i-th pocket along the long side of the billiard table in the Cartesian coordinate system;

[0020] represents the y-axis coordinate of the i-th pocket along the short side of the billiard table in the Cartesian coordinate system;

[0021] represents the x-axis coordinate of the object ball along the long side of the billiard table in the Cartesian coordinate system;

[0022] represents the y-axis coordinate of the object ball along the long side of the billiard table in the Cartesian coordinate system;

[0023] S12, and calculate the i-th pocket direction angle of the target ball :

[0024] ;

[0025] S13. The cue ball needs to receive the contact point of the target ball in order to make the target ball move along the direction of the i-th pocket. First, calculate the coordinates of the collision point of the target ball. :

[0026] ;

[0027] ;

[0028] S14. Calculate the direction of the cue ball :

[0029] ;

[0030] S15. Calculate the best angle for hitting the cue ball to ensure correct collision with the target ball:

[0031] ;

[0032] Where, represents the x-axis coordinate of the cue ball along the long side of the billiard table in the Cartesian coordinate system;

[0033] Represents the y-axis coordinate of the cue ball along the long side of the billiard table in the Cartesian coordinate system.

[0034] Preferably, the initial speed of the first cue ball is and the initial velocity of the second cue ball The way to obtain is as follows:

[0035] S21. In order to pocket the target ball smoothly, it is necessary to calculate the force F of the cue ball. The force F of the cue ball is affected by the friction coefficient of the tablecloth. First, according to the law of conservation of momentum, the mass of the mother ball is collected. and target ball mass , when the mass of the cue ball and target ball mass When they are equal, calculate the initial speed of the first cue ball , the initial speed of the first cue ball The following formula should be satisfied:

[0036] ;

[0037] Where, is the target ball speed; and target ball mass When they are equal, that is, the initial velocity of the cue ball should be equal to the final velocity of the target ball, the cue ball stops completely after hitting the target ball, and the target ball moves in the direction of collision;

[0038] When the mass of the cue ball ≠Target ball mass When the initial speed of the first cue ball is The following formula should be satisfied:

[0039] ;

[0040] ;

[0041] Where, represents the velocity of the cue ball after collision;

[0042] S22, target ball speed Will be affected by the friction coefficient of the tablecloth And the movement distance is attenuated, the target ball speed is calculated by the following formula Make corrections to obtain the corrected target ball speed :

[0043] ;

[0044] Where, Indicates the friction coefficient of the tablecloth, including: nylon blended material μ = 0.03-0.05; competition-grade tablecloth containing 85-90% wool μ = 0.13-0.025; American eight-ball coarse wool, wool content between 50%-80% μ = 0.03-0.04; 91%-100% fine wool μ = 0.008-0.015; fancy nine-ball wool tablecloth μ = 0.01-0.02; is the distance from the target ball to the i-th pocket, Indicates the speed attenuation factor, the farther away, the greater the speed loss;

[0045] S23, based on the corrected target ball speed , the initial speed of the first cue ball Perform synchronous correction and calculate the initial velocity of the second cue ball using the following formula: , when the masses of the cue ball and the target ball are equal, the initial velocity of the second cue ball is Satisfies the following formula: ;

[0046] When the mass of the cue ball ≠Target ball mass When the initial velocity of the second cue ball is Satisfies the following formula: .

[0047] Preferably, the hitting force F is obtained as follows:

[0048] According to the initial velocity of the second cue ball , according to the impulse-momentum theorem and Newton's second law, it is converted into the hitting force F through the following formula: ;

[0049] Where t represents the contact time between the club head and the cue ball, the unit is S, and is set to 0.001s-0.005s.

[0050] Preferably, the error analysis module is used to install an angle sensor and a force sensor on the club to collect the training player's hitting force. and training hitting angles and the best angle to hit the cue ball Compare it with the hitting force F to calculate the hitting force error using the following formula and hitting angle error :

[0051] ;

[0052] ;

[0053] when , the first warning signal is issued to remind the trainee that the hitting force is not up to standard; when , indicating that the trainee hits the ball too hard, prompting the trainee to reduce the hitting force; when , indicating that the trainee hits the ball too lightly, prompting the trainee to increase the hitting force;

[0054] when , a second warning signal is issued to remind the trainee that the hitting angle is unqualified; when , prompting the trainee that the angle of the club head deviates to the left; when , prompting the trainee that the club head angle deviates to the right.

[0055] Preferably, the trajectory intelligent monitoring module includes a second acquisition unit and a second calculation unit;

[0056] The second acquisition unit is used to collect the actual motion trajectory and expected motion trajectory of the trainee after each swing, and establish a trajectory motion data set;

[0057] The second calculation unit is used to perform in-depth calculation and analysis based on the trajectory motion data set to calculate the cue ball trajectory deviation coefficient using the following formula: , target ball motion deviation factor and the cue ball abnormal out-of-bounds factor : ;

[0058] Where, Indicates the difference in the cue ball trajectory angle, It represents the lateral displacement of the cue ball during its linear motion. Indicates the deviation between the actual speed of the cue ball and the theoretical calculated speed. Indicates the deviation value of the forward or backspin state of the cue ball; Expressed as weight coefficient; ;

[0059] Where, Indicates the angle between the actual direction of the target ball and the expected direction. Indicates the distance error between the final stop position of the target ball and the target point. It represents the error between the actual speed of the target ball and the expected speed. Indicates the deviation of the target ball's rotation direction from the expected trajectory; Expressed as weight coefficient;

[0060] ;

[0061] Where, Indicates the closest distance between the cue ball and the edge of the table. Indicates the height of the cue ball jumping, Indicates the spin state deviation value of the cue ball; Expressed as a weight coefficient.

[0062] Preferably, the trajectory intelligent monitoring module further includes a first correlation unit and a first early warning unit;

[0063] The first associated unit is used to offset the cue ball trajectory coefficient , target ball motion deviation factor and the cue ball abnormal out-of-bounds factor After dimensionless processing, the hitting trajectory accuracy coefficient is calculated using the following related formula: : ;

[0064] Where, They are the cue ball trajectory deviation coefficients , target ball motion deviation factor and the cue ball abnormal out-of-bounds factor The weight coefficient of

[0065] The first warning unit is used to preset the qualified threshold X and the hitting trajectory accuracy coefficient Compared with the preset qualified threshold X, if the hitting trajectory accuracy coefficient If the threshold value is less than X, it means that the student's billiards training is unqualified, triggering the third warning signal and generating the first strategy, including adjusting the current training plan and adding 10%-20% club head angle training tasks. The club head angle training tasks include low-spin training, high-spin training, and side-spin training.

[0066] If the hitting trajectory accuracy coefficient ≥Qualified threshold X, indicating that the trainee has passed the billiards training and continues with the current training plan.

[0067] Preferably, the posture correction module is used to analyze the trainer's standing posture, grip method and body center of gravity distribution to analyze and calculate the standing posture stability factor , Grip stability factor and body balance factors ;

[0068] The posture correction module includes a pressure acquisition unit, a grip acquisition unit, and an inertia acquisition unit;

[0069] The pressure collection unit is used to install a pressure sensor on the ground mat to detect the pressure of the trainee's left foot and right foot pressure ;

[0070] Grip collection unit, used to install a grip pressure sensor at the club grip position to detect and obtain the actual grip pressure ; Inertial acquisition unit, used to install a posture sensor on the trainer's waist to collect the center of gravity position , front and rear tilt angle , and install an acceleration sensor on the trainee to monitor the body shaking speed in real time .

[0071] Preferably, the posture correction module further includes a first analysis unit, a second analysis unit and a third analysis unit;

[0072] The first analysis unit is used to extract the center of gravity position , the trainer's left foot pressure and right foot pressure , after dimensionless processing, the standing stability factor is calculated by the following formula : ;

[0073] Where, The total force on the body, , Indicates the maximum allowable offset distance of the center of gravity in standing position; ; Indicates the horizontal coordinate of the trainer's current center of gravity, Indicates the coordinates of the trainee's current center of gravity in the front and back directions; Indicates the horizontal coordinate of the center of gravity in the standard standing posture; Indicates the front-back coordinates of the center of gravity in a standard standing posture;

[0074] like , indicating that the trainee's center of gravity is biased to the right;

[0075] like , indicating that the trainee's center of gravity is biased to the left;

[0076] like , indicating that the trainee's current center of gravity is biased forward, causing forward leaning;

[0077] like , indicating that the trainee's current center of gravity is biased to the rear, causing backward leaning;

[0078] The second analysis unit is used to extract the actual grip pressure , and calculate the grip stability factor using the following formula : ;

[0079] Where, is the actual grip pressure, Indicates the optimal grip pressure, Indicates the maximum allowable grip pressure. Indicates the shaft angle deviation value when gripping the club. Indicates the maximum allowable grip angle deviation value;

[0080] The third analysis unit is used to extract the front and rear tilt angles and body sway speed , after dimensionless processing, the body balance factor is calculated by the following formula :

[0081] ;

[0082] Where, Indicates the maximum allowable tilt angle, Indicates the maximum allowed shaking speed.

[0083] Preferably, the posture correction module further includes a second associating unit and a second warning unit;

[0084] The second associated unit is used to extract the stance stability factor , Grip stability factor and body balance factors , after dimensionless processing, the posture standard index is obtained through the following associated formula : ;

[0085] Where, Stance stability factor , Grip stability factor and body balance factors The weight coefficient of

[0086] The second warning unit is used to preset the posture standardization threshold Z and set the posture standard index Compare with the posture standardization threshold Z to determine whether the trainee's posture is qualified, including:

[0087] If the standard index of posture < Posture standardization threshold Z, indicating that the trainee's posture is unqualified during billiards training, triggering the fourth warning signal and generating the second strategy, including: adjusting the current training plan, adjusting the standing posture, and adding 30s of standing balance training before each training. The standing balance training includes: single-leg standing training and core muscle training; adjusting the standing position, center of gravity distribution according to and Get closer and increase grip strength and stability training by 5%;

[0088] If the standard index of posture ≥Posture standardization threshold Z, indicating that the trainee's posture during billiards training is qualified and the trainee continues to carry out the current training plan.

[0089] The present invention provides an intelligent billiards training system. It has the following beneficial effects:

[0090] (1) This intelligent billiards training system uses multi-sensor fusion technology such as depth cameras, laser radar, and high-speed cameras to accurately construct a three-dimensional model of the billiard table and ball, making the training environment more realistic; the path simulation module can automatically calculate the optimal hitting angle and the optimal hitting force F, helping the trainee find the best attack route and reducing the cost of trial and error. It can measure the friction coefficient of the table cloth in real time and perform trajectory correction based on the different friction materials of the table cloth to ensure that the calculated cue ball speed matches the actual situation and avoid trajectory deviation. If the trainee's hitting angle or force deviates from the optimal calculated value, the system can automatically correct it and provide optimization suggestions.

[0091] (2) This intelligent billiards training system integrates a high-frame-rate motion capture device to capture the actual and expected motion trajectories after each swing of the trainee, and establishes a trajectory motion data set for subsequent calculation and analysis. Based on the trajectory motion data set, the cue ball trajectory deviation coefficient, target ball motion deviation factor, and cue ball abnormal out-of-bounds factor are calculated in depth, and the flight trajectory is analyzed in real time to identify abnormalities of fly balls and jump balls. The system can automatically match the optimal hitting trajectory and provide adjustment suggestions, effectively reducing errors caused by angle, speed, or rotation errors, allowing players to more accurately control the landing point of the ball and improve their performance.

[0092] (3) Through the pressure acquisition unit, grip acquisition unit and inertia acquisition unit, combined with the multi-factor calculation model, the trainee's standing posture stability, grip stability and body balance are accurately quantified and fed back in real time. The pressure acquisition unit detects the trainee's left and right foot pressures, and the standing posture stability factor is calculated based on the center of gravity position. , analyze the trainee's center of gravity shift; when the standing posture is not stable enough, the system automatically provides posture optimization suggestions, such as adjusting footwork placement and performing core stability training to help the trainee maintain the best standing position.

[0093] (4) This intelligent billiards training system obtains the actual grip pressure of the trainee through the grip acquisition unit and calculates the grip stability factor , real-time analysis of whether the grip strength and shaft angle meet the optimal standards; grip stability factor Too small or too large indicates that the grip strength or shaft angle deviation is large, which may affect the trajectory of the ball and requires targeted training (such as increasing grip strength adjustment exercises).

[0094] (5) This intelligent billiards training system monitors the trainee's front and back tilt angle and body shaking speed through an inertial acquisition unit and calculates the body balance factor. , real-time evaluation of the trainee's stability during the hitting process; the system will factor the stance stability , Grip stability factor and body balance factors Perform weighted calculation to obtain the posture standard index , used to comprehensively evaluate the trainee's posture qualification: if Z < the preset threshold Z, the system triggers the fourth warning signal and generates the second training strategy to correct the trainee's posture. Compared with the traditional training mode, it promotes accurate monitoring of stance, grip and body balance, and quantitatively evaluates posture stability; the trainee can correct bad posture in a short time and improve the stability of the shot; avoid posture deviation caused by different observation angles of the coach or the trainee's own lack of perception. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 The figure is a flow chart of an intelligent billiards training system according to the present invention. DETAILED DESCRIPTION

[0096] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0097] Example 1

[0098] See also Figure 1 The present invention provides an intelligent billiards training system, please refer to Figure 1 ,include:

[0099] The 3D billiards scene modeling module uses a depth camera and lidar to acquire image and 3D data of the billiard table and balls, constructing a 3D model of the billiard table and projecting the trajectory of the cue ball and target ball each time the trainee hits the ball into the 3D model.

[0100] The depth camera is used to obtain the spatial coordinate information of the billiard table and its surrounding environment in real time to form point cloud data;

[0101] Combined with RGB information, point cloud data is converted into a color 3D model, making the training environment more intuitive;

[0102] Adaptive deep learning algorithms are used to optimize edge detection to improve 3D modeling accuracy. High-precision laser radar is used to scan the surface of the pool table in detail. Combined with optical recognition algorithms, the edges of the pool table, pocket positions, and ball distribution are detected in real time, providing more accurate data support for subsequent trajectory simulation. A high-frame rate (over 1000fps) camera is used to record the movement trajectories of the cue ball and target ball in real time to ensure accurate data capture at the moment of impact. The movement paths of the cue ball and target ball are restored in real time in the 3D model through the trajector's each hit, combined with visual recognition technology and image processing technology. Spatial point cloud reconstruction technology is used to generate a high-precision pool table model, ensuring that the movement paths of all balls are based on a real-scale virtual environment.

[0103] The path simulation module is used to simulate and analyze the best hitting angle of the cue ball when setting the target ball during training. and the initial velocity of the first cue ball ; and collect the friction coefficient of the tablecloth , the initial speed of the first cue ball Correct and convert to obtain the initial velocity of the second cue ball and hitting force F;

[0104] Error analysis module, used to collect the training strength of the trainer's training and training hitting angles and the best angle to hit the cue ball Compare and calculate the hitting force F to obtain the hitting force error and hitting angle error :when , the first warning signal is issued to remind the trainee that the hitting force is not up to standard; when , a second warning signal is issued to remind the trainee that the hitting angle is unqualified;

[0105] The trajectory intelligent monitoring module is used to establish a trajectory motion data set based on the actual and expected motion trajectories after each swing of the trainee. The trajectory motion data set is analyzed to obtain: the cue ball trajectory deviation coefficient , target ball motion deviation factor and the cue ball abnormal out-of-bounds factor , and comprehensively calculate the hitting trajectory accuracy coefficient , set the preset qualified threshold X, if < qualified threshold X, the third warning signal is triggered.

[0106] In this embodiment, a multi-sensor fusion technology, including depth cameras, lidar, and high-speed cameras, accurately constructs a three-dimensional model of the pool table and ball, making the training environment more realistic. The path simulation module automatically calculates the optimal hitting angle and initial hitting speed, helping the trainee find the best attack path and reducing trial and error. It can also measure the tablecloth friction coefficient in real time and perform trajectory correction based on different areas of tablecloth friction, ensuring that the calculated cue ball speed matches the actual situation and avoiding trajectory deviation. If the trainee's hitting angle or force deviates from the optimal calculated value, the system can automatically correct it and provide optimization suggestions.

[0107] The system can detect the trainee's actual hitting force and angle, and compare them with the calculated optimal hitting force F and optimal hitting angle, and calculate the error:

[0108] If the hitting force error is ≠0, the first warning signal is triggered to remind the trainee to adjust the force.

[0109] If the hitting angle error is ≠0, a second warning signal is triggered to remind the trainee to adjust the angle.

[0110] Through the trajectory intelligent monitoring module, a trajectory motion data set is established, covering:

[0111] Cue ball trajectory deviation coefficient (detects whether the cue ball moves along the expected path);

[0112] Target ball motion deviation factor (calculate whether the target ball rolls in the expected direction);

[0113] Abnormal cue ball out-of-bounds factor (detects whether the cue ball is abnormally out-of-bounds);

[0114] The module calculates the accuracy coefficient of the hitting trajectory. If it falls below the set threshold X, a third warning signal is triggered, prompting the trainee to adjust their hitting method. This module can accumulate training data over time, analyze the trainee's technical stability, and provide targeted improvement suggestions.

[0115] The system records a player's historical batting data and supports slow playback and keyframe analysis, helping them review training details. It also provides personalized training plans tailored to their weaknesses. For example, if a player frequently experiences large force errors, the system can recommend precise force control training. If a player's angle control is unstable, it can recommend batting angle optimization training.

[0116] Example 2

[0117] This embodiment is explained in Example 1, please refer to Figure 1 ,Specifically, the path simulation module includes an image acquisition unit and a simulation ,computation unit;

[0118] The image acquisition unit is used to collect the coordinates of the i-th pocket on the billiard table, marked as , collect the current mother ball coordinates , the coordinates of the target ball And the radius R of the target sphere:

[0119] Collect the current rotation state and motion state of the cue ball, including spin, top spin and back spin;

[0120] The motion states include: stationary, rolling and sliding states;

[0121] The simulation calculation unit is used to project the target ball into the three-dimensional model when the trainer is training, and calculate the best hitting angle of the cue ball through the collision physics algorithm. , the initial speed of the first cue ball , the initial velocity of the second cue ball and hitting force F;

[0122] Best angle for hitting the cue ball The way to obtain is as follows:

[0123] S11. When the moving direction of the target ball and the i-th pocket is consistent, calculate the target ball's pocket vector : ;

[0124] Where, represents the x-axis coordinate of the i-th pocket along the long side of the billiard table in the Cartesian coordinate system;

[0125] represents the y-axis coordinate of the i-th pocket along the short side of the billiard table in the Cartesian coordinate system;

[0126] represents the x-axis coordinate of the object ball along the long side of the billiard table in the Cartesian coordinate system;

[0127] represents the y-axis coordinate of the object ball along the long side of the billiard table in the Cartesian coordinate system;

[0128] Target ball into pocket vector Indicates the direction of the target ball entering the i-th pocket;

[0129] S12, and calculate the i-th pocket direction angle of the target ball : ;

[0130] ;

[0131] The i-th pocket direction angle Describes how the object ball should move to properly enter the pocket.

[0132] S13. The cue ball needs to receive the contact point of the target ball in order to make the target ball move along the direction of the i-th pocket. First, calculate the coordinates of the collision point of the target ball. :

[0133] ;

[0134] ;

[0135] The object ball's collision point coordinates indicate the specific location where the cue ball must hit the object ball.

[0136] S14. Calculate the direction of the cue ball : ;

[0137] The direction of the cue ball Describes how the cue ball should move to accurately hit the object ball at the optimal contact point;

[0138] S15. Calculate the best angle for hitting the cue ball To ensure correct collision with the target ball, the expression is as follows: ;

[0139] Where, represents the x-axis coordinate of the cue ball along the long side of the billiard table in the Cartesian coordinate system;

[0140] Represents the y-axis coordinate of the cue ball along the long side of the billiard table in the Cartesian coordinate system.

[0141] In this embodiment, the best hitting angle of the cue ball is How should the trainee aim at the cue ball so that the target ball enters the pocket along the correct trajectory? What is the best angle for hitting the cue ball? The system automatically adapts to different target ball and pocket positions, improving training applicability. Combined with real-time trajectory feedback, training strategies can be adjusted to help participants master hitting techniques more quickly.

[0142] Example 3,

[0143] This embodiment is explained in Example 1, please refer to Figure 1 Specifically, the initial speed of the first cue ball is and the initial velocity of the second cue ball The way to obtain is as follows:

[0144] S21. In order to pocket the target ball smoothly, it is necessary to calculate the force F of the cue ball. The force F of the cue ball is affected by the friction coefficient of the tablecloth. First, according to the law of conservation of momentum, the mass of the mother ball is collected. and target ball mass , when the mass of the cue ball and target ball mass When they are equal, calculate the initial speed of the first cue ball , the initial speed of the first cue ball The following formula should be satisfied: ;

[0145] Where, is the target ball speed; and target ball mass When they are equal, that is, the initial velocity of the cue ball should be equal to the final velocity of the target ball, the cue ball stops completely after hitting the target ball, and the target ball moves in the direction of collision;

[0146] When the mass of the cue ball ≠Target ball mass When the initial speed of the first cue ball is The following formula should be satisfied:

[0147] ;

[0148] ;

[0149] Where, Represents the velocity of the cue ball after impact. When the cue ball is more massive than the target ball, the initial velocity of the cue ball will be slightly higher than the final velocity of the target ball to compensate for momentum loss. The velocities of the cue and target balls are averaged to maintain momentum conservation. If the target ball is more massive, the cue ball may rebound faster.

[0150] S22, target ball speed Will be affected by the friction coefficient of the tablecloth And the movement distance is attenuated, the target ball speed is calculated by the following formula Make corrections to obtain the corrected target ball speed :

[0151] ;

[0152] Where, Indicates the friction coefficient of the tablecloth, including: nylon blended material μ = 0.03-0.05; competition-grade tablecloth containing 85-90% wool μ = 0.13-0.025; American eight-ball coarse wool, wool content between 50%-80% μ = 0.03-0.04; 91%-100% fine wool tablecloth μ = 0.008-0.015; fancy nine-ball wool tablecloth μ = 0.01-0.02; is the distance from the target ball to the i-th pocket, Indicates the speed attenuation factor, the farther away, the greater the speed loss;

[0153] The following is the coefficient of friction of the tablecloth Example chart:

[0154]

[0155] When using a tablecloth with a high wool content (such as 91%-100% fine wool), the friction is lower and the target ball rolls farther;

[0156] When using a coarser wool tablecloth (such as 50%-80% American eight-ball tablecloth), the friction is greater and the target ball rolls attenuated faster.

[0157] In the actual hitting process, the target ball speed will be affected by the friction of the table cloth and will decay as the distance of the ball increases. It can improve calculation accuracy and prevent the target ball from being unable to enter the pocket due to excessive deceleration due to friction.

[0158] S23, based on the corrected target ball speed , the initial speed of the first cue ball Perform synchronous correction and calculate the initial velocity of the second cue ball using the following formula: , when the masses of the cue ball and the target ball are equal, the initial velocity of the second cue ball is Satisfies the following formula: ;

[0159] When the mass of the cue ball ≠Target ball mass When the initial velocity of the second cue ball is Satisfies the following formula: .

[0160] In this embodiment, in the billiards training system, in order to ensure that the target ball is pocketed smoothly, it is necessary to accurately calculate the impact force F of the cue ball and its initial velocity, and to correct the target ball velocity by taking into account the influence of tablecloth friction. Based on the law of conservation of momentum and the influence of friction, this system optimizes the motion trajectory of the cue ball and improves the accuracy of the shot. Based on the conservation of momentum, it ensures that the impact force F of the cue ball is just right to avoid shots that are too strong or too weak. The target ball velocity is corrected to make it more in line with the real environment, ensuring that the calculated results are consistent with the actual shot trajectory. The calculation formula can be automatically adjusted according to different tablecloth materials to improve applicability. It helps trainees find the most appropriate impact force and improves the success rate of pocketing the ball. Calculating the velocity of the cue ball after impact helps to formulate continuous offensive strategies and achieve advanced billiards tactical training.

[0161] Example 4

[0162] This embodiment is explained in Example 1, please refer to Figure 1 Specifically, the method for obtaining the hitting force F is:

[0163] According to the initial velocity of the second cue ball , according to the impulse-momentum theorem and Newton's second law, it is converted into the hitting force F through the following formula: ;

[0164] Where t represents the contact time between the club head and the cue ball, the unit is S, and is set to 0.001s-0.005s.

[0165] The mass of the cue ball of standard billiards is about 0.17kg-0.18kg (slightly different for American 8-ball, snooker, nine-ball, etc.).

[0166] Depends on your shot goals and tactical needs, such as:

[0167] A shot that requires a lot of force (such as hitting a long-distance target with force).

[0168] A shot that requires controlled force (such as a light push or a tight angle move).

[0169] Short contact time (0.001s-0.002s): produces stronger hitting force, suitable for powerful attacks, K balls, and long-distance shots.

[0170] Long contact (0.003s-0.005s): The hitting force is relatively small, suitable for soft positioning, close-to-cushion shots, etc.

[0171] In this embodiment, the initial velocity of the cue ball is converted into the force applied by the club head, helping the trainee determine the optimal force. The hitting force F can be combined with a camera tracking system or table sensors to measure the hitting force in real time and compare it with the theoretical calculated value to improve training accuracy.

[0172] Example 5

[0173] This embodiment is explained in Example 4. Please refer to Figure 1 Specifically, the error analysis module is used to install angle sensors and force sensors on the club to collect the training player's hitting force. and training hitting angles and the best angle to hit the cue ball Compare it with the hitting force F to calculate the hitting force error using the following formula and hitting angle error :

[0174] ;

[0175] ;

[0176] when ≠0, the first warning signal is issued to remind the trainee that the hitting force is not up to standard; when , indicating that the trainee hits the ball too hard, prompting the trainee to reduce the hitting force; when , indicating that the trainee hits the ball too lightly, prompting the trainee to increase the hitting force;

[0177] when ≠0, a second warning signal is issued to remind the trainee that the hitting angle is unqualified; when >0, it prompts the trainee that the angle of the club head deviates to the left; when <0, it prompts the trainee that the club head angle deviates to the right.

[0178] In this embodiment, the system utilizes an error analysis module. Using angle sensors and force sensors mounted on the cue, the system collects the user's hitting force and training angle in real time. This information is then compared with the theoretically calculated optimal cue ball hitting angle and hitting force F, calculating the hitting force error and hitting angle error, and providing targeted feedback and adjustments. Through real-time data comparison, the user can intuitively perceive their hitting errors and gradually adjust their hitting force and angle to improve accuracy. Using first and second warning signals, the user can immediately correct errors, preventing long-term incorrect posture from affecting their performance. The system can also record the user's historical hitting error data, analyze common problems (such as excessive force and angle deviation), and provide personalized training recommendations.

[0179] Example 6

[0180] If the initial velocity of the cue ball is too high, it may rebound abnormally after hitting the edge of the pool, or even fly off the table. If the cue head is tilted too much, it may cause the cue ball to jump excessively, increasing the risk of flying off the table. This is usually considered a serious mistake in billiards training.

[0181] This embodiment is explained in Example 1, please refer to Figure 1 ,Specifically, the trajectory intelligent monitoring module includes a second ,acquisition unit and a second computing unit;

[0182] The second acquisition unit is used to collect the actual motion trajectory and expected motion trajectory of the trainee after each swing, and establish a trajectory motion data set;

[0183] The second calculation unit is used to perform in-depth calculation and analysis based on the trajectory motion data set to calculate the cue ball trajectory deviation coefficient using the following formula: , target ball motion deviation factor and the cue ball abnormal out-of-bounds factor : ;

[0184] Where, Indicates the difference in the cue ball trajectory angle, It represents the lateral displacement of the cue ball during its linear motion. Indicates the deviation between the actual speed of the cue ball and the theoretical calculated speed. Indicates the deviation value of the forward or backspin state of the cue ball; Expressed as weight coefficient, and the sum of weights is 1;

[0185] ;

[0186] Where, Indicates the angle between the actual direction of the target ball and the expected direction. Indicates the distance error between the final stop position of the target ball and the target point. It represents the error between the actual speed of the target ball and the expected speed. Indicates the deviation of the target ball's rotation direction from the expected trajectory; Expressed as weight coefficient, and the sum of weights is 1;

[0187] ;

[0188] Where, Indicates the closest distance between the cue ball and the edge of the table. Indicates the height of the cue ball jumping, Indicates the spin state deviation value of the cue ball; Expressed as weight coefficient, and the sum of weights is 1.

[0189] Cue ball trajectory deviation coefficient Represents the degree of deviation of the cue ball trajectory;

[0190] Target ball motion deviation factor Represents the accuracy of the target ball's trajectory;

[0191] Abnormal out-of-bounds factor of the cue ball Indicates whether the cue ball jumps out of bounds abnormally.

[0192] In this embodiment, the actual and expected trajectory of each swing is collected and a trajectory motion dataset is created for subsequent calculation and analysis. Based on the trajectory motion dataset, the cue ball trajectory deviation coefficient, target ball motion deviation factor, and cue ball abnormal out-of-bounds factor are calculated to evaluate the quality and accuracy of the shot.

[0193] Example 7

[0194] This embodiment is explained in Example 1, please refer to Figure 1 ,Specifically, the trajectory intelligent monitoring module also includes a first ,association unit and a first warning unit;

[0195] The first associated unit is used to offset the cue ball trajectory coefficient , target ball motion deviation factor and the cue ball abnormal out-of-bounds factor After dimensionless processing, the hitting trajectory accuracy coefficient is calculated using the following related formula: : ;

[0196] Where, They are the cue ball trajectory deviation coefficients , target ball motion deviation factor and the cue ball abnormal out-of-bounds factor The weight coefficient of , and the weight sum is 1;

[0197] The first warning unit is used to preset the qualified threshold X and the hitting trajectory accuracy coefficient Compared with the preset qualified threshold X, if the hitting trajectory accuracy coefficient If the threshold value is less than X, it means that the student's billiards training is unqualified, triggering the third warning signal and generating the first strategy, including adjusting the current training plan and adding 10%-20% club head angle training tasks. The club head angle training tasks include low-spin training, high-spin training, and side-spin training.

[0198] If the hitting trajectory accuracy coefficient ≥Qualified threshold X, indicating that the trainee has passed the billiards training and continues with the current training plan.

[0199] This embodiment calculates the cue ball trajectory deviation coefficient, target ball motion deviation factor, and cue ball abnormal out-of-bounds factor to comprehensively measure a practitioner's shot trajectory deviation and accurately analyze shot quality. This allows practitioners to intuitively understand the deviation between the actual cue ball trajectory and the ideal trajectory, optimizing their shot strategy and improving shot accuracy. A dimensionless processing method is used to standardize multiple deviation data points, eliminating the influence of different physical quantities and enhancing the scientific nature of data analysis.

[0200] By calculating the accuracy coefficient of the striking trajectory and establishing quantifiable evaluation standards, the training process can be made more objective and accurate.

[0201] Set a warning threshold X. When the hitting trajectory accuracy coefficient is lower than the threshold, the system automatically triggers the third warning signal to remind the trainee to adjust the hitting method to prevent the formation of wrong habits.

[0202] Trainees can get targeted training suggestions in a timely manner to reduce bad batting habits caused by long-term incorrect training;

[0203] After the third warning signal is triggered, the system will automatically adjust the training plan, adding 10%-20% of club head angle training tasks, including special training such as low club, high club, and side spin, to specifically optimize the trainee's shot control ability.

[0204] Example 8

[0205] In billiards training, correct standing posture, grip and body center of gravity control are crucial to the accuracy and stability of the shot. However, under traditional training methods, it is often difficult for trainees to intuitively perceive their own posture deviations, leading to the following problems: the trainee may lose balance due to uneven distribution of the center of gravity on both feet, thereby affecting the stability of the shot. Gripping the club too tightly will limit the ability to control the club head, while gripping the club too loosely can easily cause the club head to deviate, affecting the trajectory and rotation control of the shot. When aiming or hitting the ball, the trainee's body may shake, causing the cue ball trajectory to deviate, especially when performing high, low or side-spin shots, affecting accuracy. Traditional training mainly relies on the coach's observation or the trainee's subjective feelings. It lacks data support, making it difficult to accurately identify posture errors and unable to formulate targeted corrective training plans.

[0206] This embodiment is explained in Example 1, please refer to Figure 1 Specifically, it also includes a posture correction module for analyzing the trainer's standing posture, grip method and body center of gravity distribution to analyze and calculate the standing posture stability factor , Grip stability factor and body balance factors ;

[0207] The posture correction module includes a pressure acquisition unit, a grip acquisition unit, and an inertia acquisition unit;

[0208] The pressure collection unit is used to install a pressure sensor on the ground mat to detect the pressure of the trainee's left foot and right foot pressure ;

[0209] Grip collection unit, used to install a grip pressure sensor at the club grip position to detect and obtain the actual grip pressure ;

[0210] Inertial acquisition unit, used to install a posture sensor on the trainer's waist to collect the center of gravity position , front and rear tilt angle , and install an acceleration sensor on the trainee to monitor the body shaking speed in real time .

[0211] The posture correction module further includes a first analyzing unit, a second analyzing unit, and a third analyzing unit;

[0212] The first analysis unit is used to extract the center of gravity position , the trainer's left foot pressure and right foot pressure , after dimensionless processing, the standing stability factor is calculated by the following formula : ;

[0213] Where, The total force on the body, , Indicates the maximum allowable offset distance of the center of gravity in standing position; , The closer it is to 1, the more stable the stance;

[0214] Indicates the horizontal coordinate of the trainer's current center of gravity, Indicates the coordinates of the trainee's current center of gravity in the front and back directions; Indicates the horizontal coordinate of the center of gravity in the standard standing posture; Indicates the front-back coordinates of the center of gravity in a standard standing posture;

[0215] like , indicating that the trainee's center of gravity is biased to the right;

[0216] like , indicating that the trainee's center of gravity is biased to the left;

[0217] like , indicating that the trainee's current center of gravity is biased forward, causing forward leaning;

[0218] like , indicating that the trainee's current center of gravity is biased to the rear, causing backward leaning;

[0219] The second analysis unit is used to extract the actual grip pressure , and calculate the grip stability factor using the following formula : ;

[0220] Where, is the actual grip pressure, Indicates the optimal grip pressure, Indicates the maximum allowable grip pressure. Indicates the shaft angle deviation value when gripping the club. Indicates the maximum allowable grip angle deviation value; The closer it is to 1, the more stable the trainer's grip is;

[0221] The third analysis unit is used to extract the front and rear tilt angles and body sway speed , after dimensionless processing, the body balance factor is calculated by the following formula : ;

[0222] Where, Indicates the maximum allowable tilt angle, Indicates the maximum allowed shaking speed. The closer it is to 1, the better the trainee's body balance is.

[0223] The posture correction module further includes a second associating unit and a second warning unit;

[0224] The second associated unit is used to extract the stance stability factor , Grip stability factor and body balance factors , after dimensionless processing, the posture standard index is obtained through the following associated formula : ;

[0225] Where, Stance stability factor , Grip stability factor and body balance factors The weight coefficient of , and the weight sum is 1;

[0226] The second warning unit is used to preset the posture standardization threshold Z and set the posture standard index Compare with the posture standardization threshold Z to determine whether the trainee's posture is qualified, including:

[0227] If the standard index of posture < Posture standardization threshold Z, indicating that the trainee's posture is unqualified during billiards training, triggering the fourth warning signal and generating the second strategy, including: adjusting the current training plan, adjusting the standing posture, and adding 30s of standing balance training before each training. The standing balance training includes: single-leg standing training and core muscle training; adjusting the standing position, center of gravity distribution according to and Get closer and increase grip strength and stability training by 5%;

[0228] If the standard index of posture ≥Posture standardization threshold Z, indicating that the trainee's posture during billiards training is in a qualified state and the trainee continues to carry out the current training plan.

[0229] In this embodiment, the pressure acquisition unit, the grip acquisition unit and the inertia acquisition unit are combined with a multi-factor calculation model to achieve accurate quantification and real-time feedback of the trainee's standing posture stability, grip stability and body balance. The pressure acquisition unit detects the trainee's left and right foot pressures, and the standing posture stability factor is calculated in combination with the center of gravity position. , analyze the trainee's center of gravity shift; when the standing posture is not stable enough, the system automatically provides posture optimization suggestions, such as adjusting footwork placement and performing core stability training to help the trainee maintain the best standing position.

[0230] The grip acquisition unit obtains the trainer's actual grip pressure and calculates the grip stability factor , real-time analysis of whether the grip strength and shaft angle meet the optimal standards; grip stability factor Too small or too large indicates that the grip strength or shaft angle deviation is large, which may affect the trajectory of the ball and requires targeted training (such as increasing grip strength adjustment exercises).

[0231] The inertial acquisition unit monitors the trainee's front and back tilt angles and body shaking speed to calculate the body balance factor , real-time evaluation of the trainee’s stability during hitting the ball;

[0232] Through the second associated unit, the system converts the stance stability factor , Grip stability factor and body balance factors Perform weighted calculation to obtain the posture standard index , used to comprehensively evaluate the trainee's posture qualification: If Z < the preset threshold Z, the system triggers the fourth warning signal and generates the second training strategy, including:

[0233] Add 30 seconds of standing balance training (single-leg standing training, core muscle training);

[0234] Adjust your stance to ensure a more balanced center of gravity distribution;

[0235] Improve grip strength and stability by 5% and enhance shaft control.

[0236] The posture correction scheme of the above embodiment promotes accurate monitoring of stance, grip, and body balance, and quantitative evaluation of posture stability, compared to traditional training modes. Trainees can correct bad postures in a short period of time and improve their shot stability. It also avoids posture deviations caused by different coach observation angles or the trainee's own lack of perception.

[0237] The threshold is set to facilitate comparison. The size of the threshold depends on the amount of sample data and the number of bases set by technicians in this field for each set of sample data; as long as it does not affect the proportional relationship between the parameter and the quantized value.

[0238] The above formulas are obtained by collecting a large amount of data and performing software simulation, and a formula close to the actual value is selected. The coefficients in the formula are set by those skilled in the art according to actual conditions. The above is only a preferred specific implementation method of the present invention, but the protection scope of the present invention is not limited to this. Any technician familiar with this technical field, within the technical scope disclosed by the present invention, can make equivalent replacements or changes based on the technical solution and inventive concept of the present invention, which should be covered by the protection scope of the present invention.

Claims

1. An intelligent billiards training system, characterized in that: include: The 3D billiards scene modeling module uses a depth camera and lidar to acquire image and 3D data of the billiard table and balls, constructing a 3D model of the billiard table and projecting the trajectory of the cue ball and target ball each time the trainee hits the ball into the 3D model. The path simulation module is used to simulate and analyze the best hitting angle of the cue ball when setting the target ball during the training process. and the initial velocity of the first cue ball ; And collect the friction coefficient of the tablecloth , the initial speed of the first cue ball Correct and convert to obtain the initial velocity of the second cue ball and hitting force F; The path simulation module includes an image acquisition unit and a simulation calculation unit; The image acquisition unit is used to collect the coordinates of the i-th pocket on the billiard table, marked as , collect the current mother ball coordinates , the coordinates of the target ball And the radius R of the target sphere: Collect the current rotation state and motion state of the cue ball, including spin, top spin and back spin; The motion states include: stationary, rolling and sliding states; The simulation calculation unit is used to project the target ball into the three-dimensional model when the trainer is training, and calculate the best hitting angle of the cue ball through the collision physics algorithm. , the initial speed of the first cue ball , the initial velocity of the second cue ball and hitting force F; The best hitting angle of the cue ball The way to obtain is as follows: S11. When the moving direction of the target ball and the i-th pocket is consistent, calculate the target ball's pocket vector : ; Where, represents the x-axis coordinate of the i-th pocket along the long side of the billiard table in the Cartesian coordinate system; represents the y-axis coordinate of the i-th pocket along the short side of the billiard table in the Cartesian coordinate system; represents the x-axis coordinate of the object ball along the long side of the billiard table in the Cartesian coordinate system; represents the y-axis coordinate of the object ball along the long side of the billiard table in the Cartesian coordinate system; S12, and calculate the i-th pocket direction angle of the target ball : ; S13. The cue ball needs to receive the contact point of the target ball in order to make the target ball move along the direction of the i-th pocket. First, calculate the coordinates of the collision point of the target ball. : ； ； S14. Calculate the direction of the cue ball : ; S15. Calculate the best angle for hitting the cue ball to ensure correct collision with the target ball: ; Where, represents the x-axis coordinate of the cue ball along the long side of the billiard table in the Cartesian coordinate system; represents the y-axis coordinate of the cue ball along the long side of the billiard table in the Cartesian coordinate system; Error analysis module, used to collect the training strength of the trainer's training and training hitting angles and the best angle to hit the cue ball Compare and calculate the hitting force F to obtain the hitting force error and hitting angle error :when , the first warning signal is issued to remind the trainee that the hitting force is not up to standard; when , a second warning signal is issued to remind the trainee that the hitting angle is unqualified; The trajectory intelligent monitoring module is used to establish a trajectory motion data set based on the actual and expected motion trajectories after each swing of the trainee. The trajectory motion data set is analyzed to obtain: the cue ball trajectory deviation coefficient , target ball motion deviation factor and the cue ball abnormal out-of-bounds factor , and comprehensively calculate the hitting trajectory accuracy coefficient , set the preset qualified threshold X, if If the qualified threshold value X is exceeded, the third warning signal is triggered.

2. The intelligent billiards training system according to claim 1, characterized in that: The initial speed of the first cue ball and the initial velocity of the second cue ball The way to obtain is as follows: S21. In order to pocket the target ball smoothly, it is necessary to calculate the force F of the cue ball. The force F of the cue ball is affected by the friction coefficient of the tablecloth. First, according to the law of conservation of momentum, the mass of the mother ball is collected. and target ball mass , when the mass of the cue ball and target ball mass When they are equal, calculate the initial speed of the first cue ball , the initial speed of the first cue ball The following formula should be satisfied: ; Where, is the target ball speed; and target ball mass When they are equal, that is, the initial velocity of the cue ball should be equal to the final velocity of the target ball, the cue ball stops completely after hitting the target ball, and the target ball moves in the direction of collision; When the mass of the cue ball ≠Target ball mass When the initial speed of the first cue ball is The following formula should be satisfied: ; Where, represents the velocity of the cue ball after collision; ; S22, target ball speed Will be affected by the friction coefficient of the tablecloth And the movement distance is attenuated, the target ball speed is calculated by the following formula Make corrections to obtain the corrected target ball speed : ； Where, Indicates the friction coefficient of the tablecloth, including: nylon blended material μ = 0.03-0.05; competition-grade tablecloth containing 85-90% wool μ = 0.13-0.025; American eight-ball coarse wool, wool content between 50%-80% μ = 0.03-0.04; 91%-100% fine wool μ = 0.008-0.015; fancy nine-ball wool tablecloth μ = 0.01-0.02; is the distance from the target ball to the i-th pocket, Indicates the speed attenuation factor, the farther away, the greater the speed loss; S23, based on the corrected target ball speed , the initial speed of the first cue ball Perform synchronous correction and calculate the initial velocity of the second cue ball using the following formula: , when the masses of the cue ball and the target ball are equal, the initial velocity of the second cue ball is Satisfies the following formula: ; When the mass of the cue ball ≠Target ball mass When the initial velocity of the second cue ball is Satisfies the following formula: .

3. The intelligent billiards training system according to claim 2, characterized in that: The method for obtaining the hitting force F is as follows: based on the initial velocity of the second cue ball , according to the impulse-momentum theorem and Newton's second law, it is converted into the hitting force F through the following formula: Where t represents the contact time between the club head and the cue ball, the unit is S, and is set to 0.001s-0.005s.

4. The intelligent billiards training system according to claim 3, characterized in that: The error analysis module is used to install an angle sensor and a force sensor on the club to collect the training player's training hitting force. and training hitting angles and the best angle to hit the cue ball Compare it with the hitting force F to calculate the hitting force error using the following formula and hitting angle error : ； ； when , the first warning signal is issued to remind the trainee that the hitting force is not up to standard; when , indicating that the trainee hits the ball too hard, prompting the trainee to reduce the hitting force; when , indicating that the trainee hits the ball too lightly, prompting the trainee to increase the hitting force; when , a second warning signal is issued to remind the trainee that the hitting angle is unqualified; when , prompting the trainee that the angle of the club head deviates to the left; when , prompting the trainee that the club head angle deviates to the right.

5. The intelligent billiards training system according to claim 1, characterized in that: The trajectory intelligent monitoring module includes a second acquisition unit and a second calculation unit; The second acquisition unit is used to collect the actual motion trajectory and expected motion trajectory of the trainee after each swing, and establish a trajectory motion data set; The second calculation unit is used to perform in-depth calculation and analysis based on the trajectory motion data set to calculate the cue ball trajectory deviation coefficient using the following formula: , target ball motion deviation factor and the cue ball abnormal out-of-bounds factor : ; Where, Indicates the difference in the cue ball trajectory angle, It represents the lateral displacement of the cue ball during its linear motion. Indicates the deviation between the actual speed of the cue ball and the theoretical calculated speed. Indicates the deviation value of the forward or backspin state of the cue ball; Expressed as weight coefficient; ； Where, Indicates the angle between the actual direction of the target ball and the expected direction. Indicates the distance error between the final stop position of the target ball and the target point. It represents the error between the actual speed of the target ball and the expected speed. Indicates the deviation of the target ball's rotation direction from the expected trajectory; Expressed as weight coefficient; ； Where, Indicates the closest distance between the cue ball and the edge of the table. Indicates the height of the cue ball jumping, Indicates the spin state deviation value of the cue ball; Expressed as a weight coefficient.

6. The intelligent billiards training system according to claim 5, characterized in that: The trajectory intelligent monitoring module also includes a first correlation unit and a first early warning unit; The first associated unit is used to offset the cue ball trajectory coefficient , target ball motion deviation factor and the cue ball abnormal out-of-bounds factor After dimensionless processing, the hitting trajectory accuracy coefficient is calculated using the following related formula: : ; Where, They are the cue ball trajectory deviation coefficients , target ball motion deviation factor and the cue ball abnormal out-of-bounds factor The weight coefficient of The first warning unit is used to preset the qualified threshold value X and set the hitting trajectory accuracy coefficient Preset qualified threshold X for comparison, if the hitting trajectory accuracy coefficient If the threshold value is less than X, it means that the student's billiards training is unqualified, triggering the third warning signal and generating the first strategy, including adjusting the current training plan and adding 10%-20% club head angle training tasks. The club head angle training tasks include low-spin training, high-spin training, and side-spin training. If the hitting trajectory accuracy coefficient ≥Qualified threshold X, indicating that the trainee has passed the billiards training and continues with the current training plan.

7. The intelligent billiards training system according to claim 1, characterized in that: Also includes: Posture correction module, used to analyze the trainer's standing posture, grip method and body center of gravity distribution, in order to analyze and calculate the standing posture stability factor , Grip stability factor and body balance factors ; The posture correction module includes a pressure acquisition unit, a grip acquisition unit and an inertia acquisition unit; The pressure collection unit is used to install a pressure sensor on the ground mat to detect the pressure of the trainee's left foot. and right foot pressure ; The grip collection unit is used to install a grip pressure sensor at the grip position of the golf club to detect and obtain the actual grip pressure. ; The inertial acquisition unit is used to install a posture sensor on the trainer's waist to acquire the center of gravity position. , front and rear tilt angle , and install an acceleration sensor on the trainee to monitor the body shaking speed in real time .

8. The intelligent billiards training system according to claim 7, characterized in that: The posture correction module further includes a first analyzing unit, a second analyzing unit and a third analyzing unit; The first analysis unit is used to extract the center of gravity position , the trainer's left foot pressure and right foot pressure , after dimensionless processing, the standing stability factor is calculated by the following formula : ; Where, The total force on the body, , Indicates the maximum allowable offset distance of the center of gravity in standing position; Indicates the horizontal coordinate of the trainer's current center of gravity, Indicates the coordinates of the trainee's current center of gravity in the front and back directions; Indicates the horizontal coordinate of the center of gravity in the standard standing posture; Indicates the front-back coordinates of the center of gravity in a standard standing posture; like , indicating that the trainee's center of gravity is biased to the right; like , indicating that the trainee's center of gravity is biased to the left; like , indicating that the trainee's current center of gravity is biased forward, causing forward leaning; like , indicating that the trainee's current center of gravity is biased to the rear, causing backward leaning; The second analysis unit is used to extract the actual grip pressure , and calculate the grip stability factor using the following formula : ; Where, is the actual grip pressure, Indicates the optimal grip pressure, Indicates the maximum allowable grip pressure. Indicates the shaft angle deviation value when gripping the club. Indicates the maximum allowable grip angle deviation value; The closer it is to 1, the more stable the trainer's grip is; The third analysis unit is used to extract the front and rear tilt angles and body sway speed , after dimensionless processing, the body balance factor is calculated by the following formula : ; Where, Indicates the maximum allowable tilt angle, Indicates the maximum allowed shaking speed.

9. The intelligent billiards training system according to claim 8, characterized in that: The posture correction module further includes a second associating unit and a second warning unit; The second associated unit is used to extract the standing stability factor , Grip stability factor and body balance factors , after dimensionless processing, the posture standard index is obtained through the following associated formula : ; Where, Stance stability factor , Grip stability factor and body balance factors The weight coefficient of The second warning unit is used to preset the posture standardization threshold Z and set the posture standard index Compare with the posture standardization threshold Z to determine whether the trainee's posture is qualified, including: If the standard index of posture < Posture standardization threshold Z, indicating that the trainee's posture is unqualified during billiards training, triggering the fourth warning signal and generating the second strategy, including: adjusting the current training plan, adjusting the standing posture, and adding 30s of standing balance training before each training. The standing balance training includes: single-leg standing training and core muscle training; adjusting the standing position, center of gravity distribution according to and Get closer and increase grip strength and stability training by 5%; If the standard index of posture ≥Posture standardization threshold Z, indicating that the trainee's posture during billiards training is qualified and the trainee continues to carry out the current training plan.

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