A method for estimating the spin of a table tennis ball based on its trajectory and applications thereof

Abstract

The application discloses a table tennis rotation estimation method based on a motion trajectory and application thereof, and the method comprises the following steps: 1, fitting the relationship between the Magnus force coefficient and the linear velocity and angular velocity of the ball; 2, based on the fitting relationship between the Magnus force coefficient and the linear velocity and angular velocity of the ball, a linear equation group of the direction of the angular velocity vector is constructed by using a new trajectory of the table tennis flight, and the direction angle of the table tennis rotation angular velocity vector is obtained by solving the linear equation group; 3, based on the direction of the table tennis rotation angular velocity vector, a nonlinear function of the rotation angular velocity module is constructed by using the new trajectory of the table tennis flight, and the minimum value of the nonlinear function is solved to obtain the module of the table tennis rotation angular velocity. The application can accurately estimate the rotation speed of the ball in flight, thereby improving the precision of the table tennis trajectory prediction.

Description

TECHNICAL FIELD

[0001] The application discloses a table tennis spin estimation method based on a motion trajectory and belongs to the technical field of robots. BACKGROUND

[0002] Table tennis is a national sport in China and has a great influence on China's sports industry. With the rise of new technologies such as computers, optics and automatic control, in addition to the traditional competitive mode of human vs. human, human vs. computer (VR game, human vs. robot) gradually enters our life, greatly enhancing the interest of table tennis. Therefore, how to combine the real table tennis movement with the virtual world as much as possible, how to efficiently perceive the motion properties of table tennis, and how to improve the effect of human-robot table tennis are urgent problems to be solved.

[0003] Spin is the essence of table tennis, and high-speed spin is unique to table tennis compared to other ball sports. Therefore, accurate spin estimation is the key to realizing human vs. computer. The flight trajectory of table tennis is related to the flight linear velocity, spin angular velocity, air resistance coefficient and Magnus force coefficient, and is highly nonlinear. The flight mode of the ball also determines the movement characteristics of the logo on the ball. How to accurately estimate the spin parameters of the ball using effective information (such as ball trajectory and ball logo) is a crucial step.

[0004] Although the existing method can solve the problem of spin estimation to some extent, it still has certain limitations, which are as follows:

[0005] 1. Spin estimation based on logo recognition relies heavily on long-focus lenses, high-frame-rate cameras and fast visual real-time processing, which requires high hardware requirements and needs to ensure that the ball is within the appropriate field of view of the camera, greatly increasing the workload.

[0006] 2. In the existing spin estimation based on motion trajectory, a common approach is to regard the air resistance coefficient (Cd) k d ) and the Magnus force coefficient (Cm) k m ) as pre-set constants. This has two limitations: a. k d , k m The air resistance coefficient and the Magnus force coefficient are related to air humidity, temperature, ball linear velocity and spin angular velocity, and directly setting them as constants cannot cover different ball speeds and different air temperatures; b. In fact k d , k mThe ratio of the ball's linear velocity to its rotational angular velocity has a non-linear relationship, so as the ball's linear velocity decreases during flight... k d , k m There will inevitably be changes, which does not conform to the assumption of a "constant".

[0007] A patent with publication number CN110941795A proposes a method for estimating the rotational angular velocity based on a random sample-consistency algorithm. This method first obtains the ball's trajectory through function fitting, then uses recursive least squares to obtain the ball's velocity and acceleration, calculates the unit vector of the Magnus force at each moment, and finally obtains the angular velocity of the ping-pong ball based on the sample-consistency algorithm. However, this method assumes that the Magnus force coefficient is known in advance and does not consider its variation with the ball's linear velocity and angular velocity, thus failing to guarantee the accuracy of the rotational estimation.

[0008] Existing patents with publication numbers CN110458281A (CN110458281B) provide a method for predicting the spin velocity of a ping-pong ball based on deep reinforcement learning. This method first normalizes the incoming ball position, then inputs the normalized sequence into a deep LSTM network, and finally inputs the resulting LSTM state vector into a spin estimation network to obtain the incident spin velocity. However, this method also fails to consider the influence of varying Magnus force coefficients on spin estimation, thus failing to guarantee the accuracy of spin estimation. Furthermore, this type of network-based method requires a large number of data samples, making the initial work complex and time-consuming. Summary of the Invention

[0009] To address the shortcomings of the prior art, this invention proposes a method for estimating the spin of a ping-pong ball based on its motion trajectory and its application, aiming to accurately estimate the ball's spin speed during flight, thereby improving the accuracy of ping-pong ball trajectory prediction.

[0010] To achieve the above-mentioned objectives, the following technical solution is adopted:

[0011] The present invention provides a method for estimating the spin of a ping-pong ball based on its motion trajectory, characterized in that the method comprises:

[0012] Step 1: Based on the aerodynamics of ping-pong ball flight, solve for several sets of ping-pong ball flight trajectories to obtain the air resistance coefficient, Magnus force coefficient, ball linear velocity, and acceleration of the ping-pong ball caused by Magnus force during the flight process. These are used to fit the relationship between the Magnus force coefficient and the ball linear velocity and angular velocity.

[0013] Step 1.1: Use a ball-launching machine to launch a ping-pong ball with an angular velocity of ω. During the flight of the ping-pong ball, use binocular vision at sampling intervals... T sBy sampling the ball's position coordinates, the trajectory of the ping-pong ball is obtained. w P( k ): k =1,2… n};in, k Indicates the number of sampling times. n This indicates the number of sampling points in a trajectory. w P( k ) indicates the first k The position vector of the ping-pong ball collected at each sampling time; and w P( k )= [ w x ( k ), w y ( k ), w z ( k )], w x ( k ), w y ( k ), w z ( k ) represent position vectors respectively w P( k In the world coordinate system x axis, y axis, z Components on the axis;

[0014] Step 1.2, through the analysis of... w x ( k ), w y ( k ), w z ( k A cubic polynomial fitting was performed to obtain the coordinates of the ping-pong ball and time as shown in equations (1), (2), and (3). t Continuity relationship:

[0015] w x ( t )= f x ( w x ( k ), t (1)

[0016] w y (t )= f x ( w y ( k ), t (2)

[0017] w z ( t )= f x ( w z ( k ), t (3)

[0018] In equations (1), (2), and (3), f x (•,•) 、f y (•,•) 、f z (•,•) represent the coordinates of the world coordinate system. x axis, y axis, z A cubic polynomial function on the axis with respect to the time variable t. w x (t), w y ( t ), w z ( t () represents the position vector of the ping-pong ball at time t in the world coordinate system after fitting. x axis, y axis, z The components of the axis;

[0019] By applying equations (1), (2), and (3) to find the relationship between... t The first and second derivatives, and let t = kT s Thus, we obtain the first equation as shown in equations (4) and (5). k The sphere's linear velocity in the world coordinate system at each sampling moment w v( k and acceleration w a( k ):

[0020] (4)

[0021] (5)

[0022] In equations (4) and (5), wv( k )=[ w v x ( k ), w v y ( k ), w v z ( k )], w a( k )=[ w a x ( k ), w a y ( k ), w a z ( k )], w v x ( k ), w v y ( k ), w v z ( k )for w v( k The components of the x, y, and z axes in the world coordinate system. w a x ( k ), w a y ( k ), w a z ( k )for w a( k The components of the x-axis, y-axis, and z-axis in the world coordinate system;

[0023] Step 1.3, use equations (6), (7), and (8) to solve for the first... k Air resistance coefficient of the ping-pong ball at each sampling time k D ( k ), the acceleration generated by the Magnus force in the world coordinate system w a M ( kMagnus force coefficient k m ( k ):

[0024] (6)

[0025] (7)

[0026] (8)

[0027] In equations (6) and (7), This represents the gravitational acceleration vector in the world coordinate system.

[0028] Step 1.4: Following the process in steps 1.1-1.3, collect data for different angular velocities, linear velocities, and emission directions. N Group the ping-pong ball trajectory and obtain the total number of ping-pong balls. k m ( k ) 、 w ω ( k ), w v ( k The set of ) : Y = {{ k m ( k j )} j}、X1={{ w ω ( k j )} j}、 X2={{ w v ( k j )} j}, j= 1,2 …N , k j = 1,2 …N j ,in, j Indicates the trajectory index. k j Indicates the first j The coordinate index of each trajectory, where Y is the index of the points containing the trajectory. A set of Magnus force coefficients, X1, X2 being a subset of... A set of angular velocities and linear velocities; and using X1 and X2 as independent variables and Y as dependent variable, a two-dimensional polynomial function is fitted to obtain the relationship shown in equation (9):

[0029] k m = f ( w v , w ω) (9).

[0030] Step 2: Based on the fitting relationship between the Magnus force coefficient and the ball's linear velocity and angular velocity, construct a system of linear equations for the direction of the angular velocity vector using the new trajectory of the ping-pong ball and solve them to obtain the direction angle of the ping-pong ball's rotational angular velocity vector.

[0031] Step 3: Based on the direction of the ping-pong ball's rotational angular velocity vector, construct a nonlinear function of the rotational angular velocity modulus using the new trajectory of the ping-pong ball's flight and solve for its minimum value to obtain the modulus of the ping-pong ball's rotational angular velocity.

[0032] The ping-pong ball spin estimation method described in this invention is also characterized in that step 2 includes:

[0033] Step 2.1, given a new trajectory T to be determined. d ={ w P d ( k d )|k d =1,2… N d}, w P d ( k d ) represents the first new trajectory to be determined. k d The position vector of the sphere in the world coordinate system at each sampling time. N d This represents the number of ping-pong ball coordinates contained in the new trajectory to be determined;

[0034] The velocity vector of the sphere in the world coordinate system at each sampling moment is calculated using equation (4). w v d ( k )=[ w v dx ( k ), w v dy ( k ), w v dz ( k Using equation (7), calculate the acceleration vector caused by the Magnus force in the world coordinate system.w a dM ( k )=[ w a dMx ( k ), w a dMy ( k ), w a dMz ( k )],in, w v dx ( k ), w v dy ( k ), w v dz ( k )for w v d ( k The components of the x, y, and z axes in the world coordinate system; w a dMx ( k ), w a dMy ( k d ), w a dMz ( k )for w a dM ( k The components of the x, y, and z axes in the world coordinate system;

[0035] Step 2.2, calculate the first position of the new trajectory to be determined according to equation (10). k d The transformation matrix between the relative coordinate system and the world coordinate system of the ping-pong ball at a given moment. w R dl ( k ):

[0036] (10)

[0037] In equation (10), R d11 ( k ), R d12 ( k ), R d21 ( k ), R d22 ( k ) is a matrixw R dl ( k The element in row 1, column 1, row 1, column 2, row 2, column 1, row 2, column 2;

[0038] Step 2.3: Calculate the left coefficient matrix L of the linear equation concerning the direction angle of the rotational angular velocity vector using equations (11) and (12), respectively. d and the right coefficient matrix R d :

[0039] (11)

[0040] (12)

[0041] Step 2.4, calculate the direction angle of the rotational angular velocity vector. :

[0042] a. Calculate using formula (13) θ d tangent value tan θ d :

[0043] tan θ d =(L d T L d ) -1 L d T R d (13)

[0044] b. Calculate the direction angle of the rotation direction vector using equation (14). :

[0045] (14)

[0046] Step 3 includes:

[0047] Step 3.1, based on the direction angle obtained in Step 2 Calculate the first using equation (15) k d angular velocity vector at each sampling time w ω d and velocity vector w v d ( k d The included angle θ dωv ( k d ):

[0048] (15)

[0049] In equation (15), w e dω Indicates and w ω d Unit vectors in the same direction, and we have:

[0050] (16)

[0051] Step 3.2, calculate the observed variable Y2 using equation (17):

[0052] (17)

[0053] Step 3.3: Solve for the magnitude of the rotational angular velocity vector by finding the minimum value of the function.

[0054] a. Let the independent variable X3 = [|| w v d ( k d )||| k d =1,2… N d ], X4=[ θ dωv ( k d )| k d =1,2… N d ];

[0055] b. Construct the fitting function using equation (18) y :

[0056] (18)

[0057] In equation (18), ||ω d || represents the undetermined coefficients for nonlinear regression;

[0058] c. Construct a nonlinear function using equation (19) and solve for the minimum value to obtain the modulus of the angular velocity of the ping-pong ball's rotation. :

[0059] (19).

[0060] In this embodiment, an electronic device includes a memory and a processor, characterized in that the memory is used to store a program that supports the processor in executing the ping-pong ball spin estimation method, and the processor is configured to execute the program stored in the memory.

[0061] In this embodiment, a computer-readable storage medium is provided, on which a computer program is stored, characterized in that the computer program is executed by a processor to perform the steps of the ping-pong ball spin estimation method.

[0062] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0063] 1. This invention solves the problem in the prior art that the air drag coefficient and Magnus force coefficient are treated as known constants in advance and the influence of the ball's linear velocity and angular velocity on these constants is not considered by solving the air drag coefficient and Magnus force coefficient in real time, thereby improving the accuracy of table tennis ball spin estimation.

[0064] 2. In step 1 of this invention, by using the characteristics of ball flight dynamics through the ball's trajectory, the air resistance coefficient and Magnus force coefficient are solved in real time, effectively avoiding the assumption that "the coefficients are constant" and avoiding the practice of "pre-calculating the air resistance coefficient and Magnus force coefficient based on the current air temperature and humidity" in previous patents, thereby improving the accuracy of ping-pong ball spin estimation.

[0065] 3. In step 1 of this invention, the functional relationship between the Magnus force coefficient, ball linear velocity, and rotational angular velocity, which are solved in real time, is fitted and used for spin estimation. This overcomes the problem in the prior art that "the relationship between the Magnus force coefficient and the ball angular velocity and linear velocity is not considered", thereby improving the accuracy of table tennis spin estimation. Attached Figure Description

[0066] Figure 1 This is a schematic diagram illustrating the world coordinate system, relative coordinate system, sphere linear velocity, and rotational angular velocity in an embodiment of the present invention;

[0067] Figure 2 This is a description of fitting in the embodiments of the present invention. k m A flowchart illustrating the relationship between angular velocity and linear velocity;

[0068] Figure 3 This is a flowchart describing the process of solving the direction of the rotational angular velocity vector in an embodiment of the present invention;

[0069] Figure 4 This is a schematic diagram illustrating the attitude relationship between the absolute coordinate system and the relative coordinate system in an embodiment of the present invention;

[0070] Figure 5 This is a flowchart describing the process of solving the rotational angular velocity vector magnitude in an embodiment of the present invention. Detailed Implementation

[0071] In this embodiment, a method for estimating the spin of a ping-pong ball based on its motion trajectory includes:

[0072] Step 1: Based on the aerodynamics of ping-pong ball flight, solve for several sets of ping-pong ball flight trajectories to obtain the air resistance coefficient, Magnus force coefficient, ball linear velocity, and acceleration of the ping-pong ball caused by Magnus force during the flight process. These are used to fit the relationship between the Magnus force coefficient and the ball linear velocity and angular velocity.

[0073] like Figure 1 Establishing a world coordinate system as shown O-xyz , y The axis is perpendicular to the width of the tabletop, parallel to the tabletop, and points away from the robot. z The axis is vertically upward, determined by the right-hand rule. x Axial direction.

[0074] The flight trajectory of a ping-pong ball is modeled using aerodynamics and Newton's second law. During flight, the ping-pong ball is mainly affected by gravity, air resistance, and Magnus force, resulting in the flight dynamics equation shown in equation (1):

[0075] w a = w g + k D || w v|| w v + k m w ω× w v (1)

[0076] In equation (1), w 'a' represents the acceleration of the ball in the world coordinate system. w g represents the gravitational acceleration vector in the world coordinate system. w v, w ω represents the linear velocity vector and angular velocity vector of the sphere in the world coordinate system. k D , k m These represent the air drag coefficient and the Magnus force coefficient, respectively.

[0077] Step 1.1: Collect several sets of ping-pong ball trajectories to generate sufficient data samples. The specific implementation method is as follows: Use a ball machine to launch a ping-pong ball with an angular velocity of ω. During the flight of the ping-pong ball, use binocular vision at sampling intervals... T s By sampling the ball's position coordinates, the trajectory of the ping-pong ball is obtained. w P( k ): k =1,2… n},in, kIndicates the number of sampling times. n This indicates the number of sampling points in a trajectory. w P( k ) indicates the first k The position vector of the ping-pong ball in the world coordinate system collected at each sampling time; and w P( k )= [ w x ( k ), w y ( k ), w z ( k )], w x ( k ), w y ( k ), w z ( k ) represent position vectors respectively w P( k In the world coordinate system x axis, y axis, z Components on the axis.

[0078] Step 1.2: To reduce the impact of noise from the binocular vision system on the ball's velocity and acceleration, this application employs a polynomial fitting method to fit the ball's coordinates at each sampling time, thereby achieving a filtering effect. Then, the ball's velocity and acceleration at each sampling time are calculated. Specifically, the steps involve... w x ( k ), w y ( k ), w z ( k A third-order polynomial fitting was performed to obtain the coordinates of the ping-pong ball and time as shown in equations (2), (3), and (4). t Continuity relationship:

[0079] w x ( t )= f x ( w x ( k ), t (2)

[0080] w y (t )= f x ( w y ( k ), t (3)

[0081] w z ( t )= f x ( w z ( k ), t (4)

[0082] In equations (2), (3), and (4), f x (•,•) ,f y (•,•) ,f z (•,•) represent the coordinates of the world coordinate system. x axis, y axis, z A cubic polynomial function on the axis with respect to the time variable t. w x (t), w y ( t ), w z ( t () represents the position vector of the ping-pong ball at time t in the world coordinate system after fitting. x axis, y axis, z The components of the axis.

[0083] By applying equations (2), (3), and (4), we can find the relationship between these equations and the equations. t The first and second derivatives, and let t = kT s Thus, we obtain the first equation as shown in equations (5) and (6). k The sphere's linear velocity in the world coordinate system at each sampling moment w v( k and acceleration w a( k ):

[0084] (5)

[0085] (6)

[0086] In equations (5) and (6), wv( k )=[ w v x ( k ), w v y ( k ), w v z ( k )], w a( k )=[ w a x ( k ), w a y ( k ), w a z ( k )], w v x ( k ), w v y ( k ), w v z ( k )for w v( k The components of the x, y, and z axes in the world coordinate system. w a x ( k ), w a y ( k ), w a z ( k )for w a( k The components of the x-axis, y-axis, and z-axis in the world coordinate system.

[0087] Step 1.3: To reduce the impact of noise from the binocular vision system on the ball's velocity and acceleration, this application uses a polynomial fitting method to fit the ball's coordinates at each sampling time, thereby achieving a filtering effect. Then, the ball's velocity and acceleration at each sampling time are solved. Specifically, equations (7), (8), and (9) are used to solve the equations for the first, second, and third sampling times, respectively. k Air resistance coefficient of the ping-pong ball at each sampling time kD ( k ), the acceleration generated by the Magnus force in the world coordinate system w a M ( k Magnus force coefficient k m ( k ):

[0088] (7)

[0089] (8)

[0090] (9)

[0091] Step 1.4, based on relevant theories of spherical flight fluid dynamics, k m Let be a function of the ball's linear velocity and angular velocity. To obtain the specific functional expression, this application adopts the following method: collect several sets of ball flight trajectories, and use equations (7), (8), and (9) to calculate the at each sampling time. k m ( k ), w v ( k )and Then, the function fitting method is used to approximate the result. and and The functional relationship is as follows: As shown in Figure 2, following steps 1.1-1.3, data with different angular velocities, linear velocities, and emission directions are collected. N Group the ping-pong ball trajectory and obtain the total number of ping-pong balls. k m ( k ) 、 w v( k ), w ω ( k The set of ) : Y = {{ k m ( k j )} j} and X1={{ w ω ( k j )} j}, X2={{ w v ( kj )} j}, j= 1,2 …N , k j = 1,2 …N j ,in, j Indicates the trajectory index. k j Indicates the first j The coordinate index of the trajectory, Y is the coordinate index of the point. A set of Magnus force coefficients, X1, X2 containing A set of angular velocities and linear velocities; and using X1 and X2 as independent variables and Y as dependent variable, a two-dimensional polynomial function is fitted to obtain the relationship shown in equation (10):

[0092] k m = f ( w v , w ω) (10)

[0093] Step 2, as shown in Figure 3, given an incoming ball trajectory, calculate the direction of its rotational angular velocity vector.

[0094] like Figure 1 The relative coordinate system shown is established on the sphere { Ox l y l z l}, Ox l Let the velocity vector of the ball be in the world coordinate system. x w Oy w Projection on a plane Oz l Vertically upwards, Oy l The direction is determined by the right-hand rule. According to equation (1), the magnitude of the Magnus force during the ball's flight is directly related to the angular velocity of the ball. Therefore, this application uses the direction of the Magnus force to derive the direction of the ball's rotation vector. The specific implementation method is as follows:

[0095] Step 2.1: Given the trajectory to be determined, calculate the ball's velocity, acceleration, and acceleration caused by the Magnus force at each sampling moment. The specific implementation is as follows: Given a new trajectory T to be determined... d ={ w P d ( kd )|k d =1,2… N d}, w P d ( k d ) represents the first new trajectory to be determined. k d The position vector of the sphere in the world coordinate system at each sampling time. N d This represents the number of ping-pong ball coordinates contained in the new trajectory to be determined.

[0096] The velocity vector of the sphere in the world coordinate system at each sampling moment is calculated using equation (5). w v d ( k )=[ w v dx ( k ), w v dy ( k ), w v dz ( k Using equation (8), calculate the acceleration vector in the world coordinate system caused by the Magnus force. w a dM ( k )=[ w a dMx ( k ), w a dMy ( k ), w a dMz ( k )],in, w v dx ( k ), w v dy ( k ), w v dz ( k )for w v d ( k The components of the x-axis, y-axis, and z-axis in the world coordinate system. w a dMx ( k ), w a dMy (k ), w a dMz ( k )for w a dM ( k The components of the x-axis, y-axis, and z-axis in the world coordinate system;

[0097] Step 2.2, due to the ball's relative position to the coordinate system during flight { Ox l y l z l The direction of} is constantly changing, therefore it is necessary to determine the direction of} at each sampling time. Ox l y l z l}and{ Ox w y w z w The transformation matrix of}. The specific implementation method is as follows: calculate the first} in the new trajectory to be determined according to equation (11). k d The transformation matrix between the relative coordinate system and the world coordinate system of the ping-pong ball at a given moment. w R dl ( k ):

[0098] (11)

[0099] In equation (11), R d11 ( k ), R d12 ( k ), R d21 ( k ), R d22 ( k ) is a matrix w R dl ( k The elements in the first row and first column, the first row and second column, the second row and first column, and the second row and second column of the matrix (11) are used; the derivation of equation (11) is as follows:

[0100] like Figure 4 As shown, establish a new coordinate system { Ox w ' y w ' zw The origin of this coordinate system is located at the center of the sphere. , Ox w ' , Oy w ' , Oz w The directions of ' are respectively with Ox w , Oy w , Oz w The directions are the same. Let the linear velocity of the ball be in the plane { x w ' Oy w The projection on '} , for exist Ox w ' , Oy w The projection on ', therefore we have { Ox l y l z l The three unit vectors of} that are in the same direction as the coordinate axes , , exist{ Ox w ' y w ' z w The coordinates in '} are:

[0101] (12)

[0102] (13)

[0103] (14)

[0104] Therefore:

[0105] (15)

[0106] Step 2.3, because Since this holds true, we can obtain equation (16):

[0107] (16)

[0108] Since in practice, the spin of table tennis balls is mainly topspin and backspin with a small amount of sidespin, If the above equation holds true, divide both sides by Thus, we obtain equation (17):

[0109] (17)

[0110] By combining equations (17) and (18) and (19), the left coefficient matrix L of the linear equation concerning the direction angle of the rotational angular velocity vector can be calculated. d and the right coefficient matrix R d :

[0111] (18)

[0112] (19)

[0113] Step 2.4: Calculate the direction angle of the rotational angular velocity vector using the ball's velocity and the acceleration caused by the Magnus force. The specific implementation method is as follows:

[0114] a. Calculated by (20) θ d tangent value tan θ d :

[0115] tan θ d =(L d T L d ) -1 L d T R d (20)

[0116] b. Calculate the direction angle of the rotation direction vector using equation (21). :

[0117] (twenty one).

[0118] Step 3, this application utilizes the information obtained in step 1.4 k m and , Based on the functional relationship, and using the direction of the rotational angular velocity vector obtained in step 2, the magnitude of the rotational angular velocity vector is solved by the acceleration caused by the Magnus force at each sampling moment.

[0119] Step 3.1, based on the direction angle obtained in Step 2 Calculate the first using equation (22) k d angular velocity vector at each sampling time w ωd and velocity vector w v d ( k d The included angle θ dωv ( k d ):

[0120] (twenty two)

[0121] In equation (22), w e dω Indicates and w ω d Unit vectors in the same direction, and we have:

[0122] (twenty three)

[0123] Step 3.2, calculate the observed variable Y2 using equation (24):

[0124] (twenty four)

[0125] Step 3.3: Solve for the magnitude of the rotational angular velocity vector by finding the minimum value of the function.

[0126] a. Let the independent variable X3 = [|| w v d ( k d )||| k d =1,2… N d ], X4=[ θ dωv ( k d )| k d =1,2… N d ];

[0127] b. Construct the fitting function using equation (25) y :

[0128] (25)

[0129] In equation (25), ||ω d || represents the undetermined coefficients for nonlinear regression;

[0130] c. Construct a nonlinear function using equation (26) and solve for the minimum value to obtain the modulus of the angular velocity of the ping-pong ball's rotation. :

[0131] (26)

[0132] The process in step 3 is as follows: Figure 5 As shown.

Claims

1. A method for estimating spin of a table tennis ball based on motion trajectory, characterized in that, The method comprises: Step 1, based on the air dynamics of table tennis flight, solving the trajectories of several groups of table tennis flight to obtain the air resistance coefficient, the Magnus force coefficient, the linear velocity of the table tennis, the acceleration of the table tennis caused by the Magnus force in the process of table tennis flight, for fitting the relationship between the Magnus force coefficient and the linear velocity and angular velocity of the table tennis; Step 1.1, a ping-pong ball with angular velocity ω is sent by a ball-throwing machine, and the position coordinates of the ping-pong ball are sampled at a sampling interval T s during the flight of the ping-pong ball by binocular vision : k = 1, 2…n}; wherein k represents the number of sampling times, n represents the number of sampling points in a trajectory, represents the position vector of the ping-pong ball collected at the kth sampling time; and = [ , , ], , , respectively represent the components of the position vector on the x-axis, y-axis and z-axis of the world coordinate system Step 1.2, the continuous relationship between the coordinates of the ping-pong ball and the time t is obtained by performing a cubic polynomial fitting on the data of the coordinates of the ping-pong ball and the time t as shown in formula (1), formula (2), and formula (3): , , ​ (1) (2) (3) (1), (2), (3) are cubic polynomial functions with respect to the time variable t on the x-axis, y-axis, z-axis of the world coordinate system, respectively, , , (1), (2), (3) are cubic polynomial functions with respect to the time variable t on the x-axis, y-axis, z-axis of the world coordinate system, respectively, , , denote the components of the position vector of the ping-pong ball at time t after fitting on the x-axis, y-axis, z-axis of the world coordinate system; By solving the first and second order derivatives of equation (1), equation (2), equation (3) with respect to t and setting t = kT s , the ball's linear velocity in the world coordinate system at the kth sampling time is obtained as shown in equation (4) and equation (5) and acceleration : (4) (5) In equations (4) and (5), =[ , , ], =[ , , ], , , for The components of the x-axis, y-axis, and z-axis in the world coordinate system. , , for The components of the x-axis, y-axis, and z-axis in the world coordinate system; Step 1.3, the air resistance coefficient of the ping-pong ball at the kth sampling time is solved by using formula (6), formula (7), and formula (8) respectively , the acceleration generated by the Magnus force in the world coordinate system , the Magnus force coefficient : (6) (7) (8) in formula (6), formula (7), w g represents the gravity acceleration vector in the world coordinate system; Step 1.

4. Collect N sets of Ping Pong trajectory with different angular velocities, different linear velocities, and different launch directions according to the process of Step 1.1-1.3 and obtain the set containing all , , , , , j = 1, 2…N, k j = 1, 2…N j , wherein j represents the trajectory index, k j represents the coordinate point index of the jth trajectory, Y is a set containing Magnetic force coefficients, X1, X2 is a set containing angular velocity, linear velocity; and perform two-dimensional polynomial function fitting on X1, X2 as independent variables and Y as dependent variable to obtain the relationship as shown in formula (9):​ (9) In formula (9), denotes the Magnus force coefficient; Step 2, based on the fitting relationship between the Magnus force coefficient and the linear velocity and angular velocity of the table tennis, constructing a linear equation set of the direction of the angular velocity vector using the new trajectory of the table tennis flight and solving it to obtain the direction angle of the rotational angular velocity vector of the table tennis; Step 3, based on the direction of the rotational angular velocity vector of the table tennis, constructing a nonlinear function of the modulus of the rotational angular velocity using the new trajectory of the table tennis flight and solving the minimum value to obtain the modulus of the rotational angular velocity of the table tennis.

2. The table tennis spin estimation method according to claim 1, characterized in that, The step 2 comprises: Step 2.1, given a new trajectory T to be solved d ={ |k d =1,2…N d}, represents the position vector of the ball in the world coordinate system at the k d th sampling time in the new trajectory to be solved, N d represents the number of ping pong ball coordinates contained in the new trajectory to be solved; The velocity vector of the sphere in the world coordinate system at each sampling moment is calculated using equation (4). =[ , , ] Calculate the acceleration vector caused by the Magnus force in the world coordinate system using equation (7). =[ , , ],in, , , for The components of the x-axis, y-axis, and z-axis in the world coordinate system; , , for The components of the x-axis, y-axis, and z-axis in the world coordinate system; Step 2.2, the conversion matrix of the relative coordinate system of the ping-pong ball in the new trajectory to be solved at the kth moment and the world coordinate system is calculated according to formula (10) d :​ (10) In formula (10), , , , is a matrix the elements of the first row, first column, the first row, second column, the second row, first column, and the second row, second column Step 2.

3. Calculate the left coefficient matrix L and the right coefficient matrix R with respect to the direction angle linear equation of the angular velocity vector direction angle using formula (11) and formula (12) respectively d and d : (11) (12) Step 2.

4. Calculate the azimuth angle of the angular velocity vector of rotation : a. Calculate θ by formula (13) d the tangent of : (13) b. Calculate the direction angle of the rotation direction vector by equation (14) : (14)。 3. The table tennis spin estimation method according to claim 2, characterized in that, The step 3 comprises: Step 3.1, the angle of direction according to the obtained in step 2 , the k d th sampling moment angular velocity vector and the velocity vector of the k th sampling moment are calculated by formula (15) : (15) In formula (15), denotes a unit vector in the same direction as denotes a unit vector in the same direction as (16) Step 3.2, calculating the observation variable Y2 using formula (17): (17) Step 3.3, solving the modulus of the rotational angular velocity vector by solving the minimum value of the function: a, let argument X3=[ |k d =1,2…N d ], X4=[ |k d =1,2…N d ]; b, constructing a fitting function y using formula (18): (18) In formula (18), are the pending coefficients for the non-linear regression; c. Constructing a non-linear function using equation (19) and solving for the minimum value to obtain the module of the spin angular velocity of the ping-pong ball : (19)。 4. An electronic device comprising a memory and a processor, characterized in that The memory is used for storing a program supporting the processor to execute the table tennis rotation estimation method in claim 1 or 2 or 3, and the processor is configured to execute the program stored in the memory.

5. A computer-readable storage medium having stored thereon a computer program, characterized in that The computer program is executed by the processor to execute the steps of the table tennis rotation estimation method in claim 1 or 2 or 3.

Images