Collision prediction and termination time determination method in stool dragon motion

Abstract

The invention relates to the technical field of collision prediction and motion control of multi-object motion, in particular to a method for collision prediction and termination time determination in stool dragon motion, which comprises the following steps: by establishing a motion model and a collision prediction model of a stool dragon, solving by using a numerical simulation method to obtain the position and speed of each section of stool; and the collision occurrence moment is predicted to determine the entry termination moment of the dragon dance team. According to the method, the collision moment can be accurately predicted, and the ending moment when the dragon dance team is entered is determined, so that the safety and the ornamental value of performance are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of collision prediction and motion control of multi-object motion, and in particular to a method for collision prediction and termination moment determination in a bench dragon motion. Background Art

[0002] In the field of multi-object motion control, especially in traditional cultural activities, such as bench dragon performances, it usually involves multiple participants holding long benches and coordinating movements to form the shape of a dragon for performance. This form of performance requires participants to perform precise coordination and control in a limited space to avoid collisions and ensure the smoothness and viewing experience of the performance.

[0003] Traditional dragon dance performances rely mainly on the experience and intuition of the participants to control movement and avoid collisions, but this approach has certain limitations. First, due to the lack of precise prediction and control methods, it is difficult to fully guarantee safety during the performance. Second, the viewing experience of the performance is limited by the individual skills and coordination abilities of the participants, making it difficult to achieve a highly consistent and precise performance effect. Summary of the invention

[0004] The purpose of the present invention is to solve the shortcomings existing in the prior art, and to propose a method for collision prediction and termination time determination in the movement of a bench dragon. The method can accurately predict the collision moment and determine the termination time of the dragon dance team to improve the safety and viewing experience of the performance.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for predicting collisions and determining the end time of a bench dragon movement is disclosed. The motion model and collision prediction model of the bench dragon are established, and the position and speed of each bench section are solved by a numerical simulation method. The time of collision is predicted to determine the end time of the dragon dance team.

[0007] Preferably, the motion model includes the motion equations of the dragon head, dragon body and dragon tail;

[0008] (1) The motion position model of the faucet front handle, including the equidistant spiral parameter equation of the Archimedean spiral in polar coordinates ρ = ρ0 + a·θ, and the equation in the rectangular coordinate system obtained based on the coordinate conversion relationship between the polar coordinate system and the rectangular coordinate system According to θ=ωt, the formula ρ=ρ0+a·θ can be rewritten as Wherein, ρ0 is the starting radius of the spiral, a is the growth coefficient, θ represents the angle between the line connecting the point and the center of the spiral and the x-axis, which is the polar angle in the polar coordinate system, ρ is the distance between the point and the center of the circle, which is expressed as the polar diameter in the polar coordinate system, p is the pitch, x and y are the horizontal and vertical coordinates in the rectangular coordinate system with the center of the spiral as the origin, w is the angular velocity of the faucet front handle movement, and t is the movement time;

[0009] (2) Motion model of the faucet handle after any n time intervals: At the initial moment, the position coordinates of the faucet handle are calculated to be (x0, y0); according to the formula ρ = ρ0 + a·θ, the time interval Δt is taken, and the motion model is discretized. The polar coordinates of the faucet handle after Δt are calculated to be expressed as: in, ρ0 is the starting radius of the spiral, θ0 is the polar angle at the initial moment, p is the pitch, Δt is the time interval, ν is the linear velocity, which represents the rate of change of the radial distance over time, w is the angular velocity, which represents the rate of change of the angle over time, and h is the radial distance. By recursion, the polar coordinates of the faucet handle after any n time intervals Δt can be expressed as:

[0010]

[0011] The coordinates converted into the rectangular coordinate system are expressed as:

[0012]

[0013] a is the growth coefficient, ρ0 is the starting radius of the spiral, Δt is the time interval, ν is the linear velocity, which represents the rate of change of radial distance over time, ρ n ,θ n is the polar diameter and polar angle of the faucet handle after any n time intervals, ρ n-1 ,θ n-1 is the polar diameter and polar angle of the faucet handle after any n-1 time intervals, x n ,y n Respectively represent the horizontal and vertical coordinates of the faucet front handle in the rectangular coordinate system after any n time intervals;

[0014] (3) The location of the dragon’s body and tail

[0015] Take two points on the spiral as the front and back handles of a bench. The distance between the two points is the distance between the two holes and is known. The angle between the front and back handles and the line connecting the center of the spiral is calculated by the cosine theorem of the triangle, thus obtaining the recursive formula between the two points, and then the positions of the front and back handles of the dragon body and tail are obtained; according to the coordinate formula in the rectangular coordinate system, we have:

[0016]

[0017] Among them, x i ,y i are the horizontal and vertical coordinates of the front handle of the i-th bench in the rectangular coordinate system, ρ i is the polar diameter of the front handle of the i-th bench, θ i is the polar angle of the front handle of the i-th bench, x i+1 ,y i+1 are the horizontal and vertical coordinates of the front handle of the i+1th bench in the rectangular coordinate system, ρ i+1 is the polar diameter of the front handle of the i+1th bench, θ i+1 is the polar angle of the front handle of the i+1th bench;

[0018] According to the cosine theorem of a triangle, the distance between the two points is equal to the distance d between the two holes of the bench. i , we get the equation:

[0019]

[0020] Among them, θ is the angle between the two fixed handles on the bench and the line connecting the coordinate origin, the polar angle of the front handle, and ρ i+1 is the diameter of the front handle of the i+1th bench, ρ i is the diameter of the front handle of the i-th bench, d i is the distance between the two handles on the i-th bench,

[0021] Using the coordinate formula and the spiral equation, solving this equation can get the angle θ, and thus get the position coordinates of the next handle. Still using the idea of ​​recursion, we can get the coordinates of all the dragon bodies and tails.

[0022] Among them, the movement speed, such as Fig.14 As shown in the figure, for a certain handle of a certain section of the dragon body, for the position (x t ,y t ) and the position at time t+1 (x t+1 ,y t+1 ), the forward speed of the handle can be calculated based on the rate of change of the handle position; for a handle n, its position (x n ,y n ) is:

[0023]

[0024] They represent the position coordinates x of handle n at time t. n and n The rate of change over time, that is, the components of velocity in the x and y directions, x t ,y tare the horizontal and vertical coordinates of handle n at time t, x t+1 ,y t+1 are the horizontal and vertical coordinates of handle n at time t+1;

[0025] Using the formula for the rate of change of the bench handle position, we can get the speed of the nth bench as:

[0026]

[0027] v n (t) represents the forward velocity of handle n at time t, which is the magnitude of the velocity vector, calculated by the square root of the sum of the squares of the velocity components in the x and y directions;

[0028] The speed of the dragon head's front handle and the position of each bench relative to the dragon head's front handle are used to iterate and calculate the speed of the entire dragon dance team.

[0029] Preferably, the numerical simulation method is a fourth-order Runge-Kutta method with high accuracy, and its truncation error is O(h 5 ), its classic fourth-order Runge-Kutta calculation formula is:

[0030]

[0031] Among them, any value y(n) is determined by the sum of the current value y(n-1) and the change per unit time; the change per unit time is the product of the time interval h and the approximate slope. For any time, the estimated slope is the weighted average of the following slopes:

[0032] K1: slope at the time starting point;

[0033] K2: The slope of the midpoint in time. According to the Euler method, the slope K1 is used to approximate y at point The value of

[0034] K3: midpoint slope in time, using slope K2 to approximate the y value;

[0035] K4: End point slope, using K3 to approximate the y value.

[0036] Preferably, the collision prediction model predicts the moment of collision by calculating the distance between the apex of the faucet and the line connecting the centers of the adjacent outer circle bench handles;

[0037] Collision conditions: Calculate the distances from the four vertices of the faucet to the straight line at different times to determine whether a collision will occur. The minimum time for a collision to occur is the end time of the disk entry.

[0038] Establish collision model: Figure 4As shown in the figure, analysis shows that when the distance between the vertex P and the straight line where the points X and Y are located is half the width of the board, the dragon head will collide with the dragon body section. Therefore, when the distance between the four points of the dragon head M, N, P, Q and the straight line where the two small holes on each dragon body section of the outer circle are located is d>d l When the distance between one point and the straight line satisfies d = d l The moment of , is the end time of the dragon dance team's entry;

[0039] Let the coordinates of point X be (x1, y1) and the coordinates of point Y be (x2, y2). Since the X and Y points of the bench are both on the equidistant spiral, the slope of the straight line XY always exists. Therefore, let the equation of the straight line where points X and Y are located be:

[0040]

[0041] x, y is a vertex on the rectangular bench (such as Figure 4 x1 and y1 are the horizontal and vertical coordinates of a fixed hole on the bench, and x2 and y2 are the horizontal and vertical coordinates of another fixed hole on the bench;

[0042] According to the solution of the above vertex coordinates, let the coordinates of point P be (x′, y′), and use the distance formula from point to line to get the distance d:

[0043]

[0044] d is a vertex on the rectangular bench (such as Figure 4 The distance from point P in the horizontal center line of the bench to the straight line between two points X and Y, where x and y are the vertices of the rectangular bench (such as Figure 4 x1 and y1 are the horizontal and vertical coordinates of a fixed hole on the bench, and x2 and y2 are the horizontal and vertical coordinates of another fixed hole on the bench;

[0045] Preferably, the termination time is determined based on the predicted collision time, giving the collision condition:

[0046] d≤d l

[0047] d is a vertex on the rectangular bench (such as Figure 4 The distance from point P) to the straight line between two points X and Y on the horizontal center line of the bench, d l Half the length of the board width;

[0048] Calculate the distances from the four vertices of the faucet to the straight line at different times to determine whether a collision will occur. The minimum time at which a collision occurs is the end time of the disk entry.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] The present invention can accurately predict the collision moment and determine the termination moment of the dragon dance team's winding, so as to improve the safety and viewing experience of the performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a schematic diagram of the bench dragon movement of the present invention;

[0052] Figure 2 A flow chart for constructing the movement model of the bench dragon of the present invention;

[0053] Figure 3 This is a convergence analysis diagram of the numerical simulation algorithm of the present invention for solving the movement model of the bench dragon;

[0054] Figure 4 A schematic diagram of the faucet collision prediction of the present invention;

[0055] Figure 5 The position of the dragon dance team at the moment of collision and a partial enlarged view of the present invention;

[0056] Figure 6 The distance d from the apex of the faucet to the straight line of the small hole of the adjacent outer circle bench l Schematic diagram of its relationship with other dragon bodies and time;

[0057] Figure 7 This is a schematic diagram of a U-turn space according to a second embodiment of the present invention;

[0058] Figure 8 It is a schematic diagram of collision under the minimum pitch of the present invention;

[0059] Fig. 9 is the relationship between the pitch and the pole diameter of the present invention;

[0060] Fig.10 To invent the top view of the dragon's body and tail;

[0061] Fig.11 It is a top view of the dragon body and dragon tail of the present invention;

[0062] Fig.12 It is a front view of the bench of the present invention;

[0063] Fig.13 It is a schematic diagram of two points on the spiral line of the bench of the present invention;

[0064] Fig.14 It is a schematic diagram of speed calculation of the present invention. DETAILED DESCRIPTION

[0065] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings, so that those skilled in the art can better understand the advantages and features of the present invention, thereby making a clearer definition of the protection scope of the present invention. The embodiments described in the present invention are only a part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present invention.

[0066] The invention discloses a method for predicting collision and determining the termination time in the movement of a bench dragon, and performs adjustment and control according to different lengths, speeds, winding directions and winding methods of the bench dragon.

[0067] Embodiment 1

[0068] A bench dragon is made up of 223 benches, of which the first section is the dragon head, the next 221 sections are the dragon body, and the last section is the dragon tail. The length of the dragon head is 341cm, the length of the dragon body and the dragon tail is 220cm, and the width of all benches is 30cm. There are two holes on each bench, with a hole diameter of 5.5cm, and the center of the hole is 27.5cm away from the nearest board head (see Fig.10 and Fig.11 ). Two adjacent benches are connected by handles (see Fig.12 ).

[0069] Figure 4 The diagram shows the collision between the vertex of the dragon head and the outer dragon body. Analysis shows that when the distance between the vertex P and the straight line where points X and Y are located is half the width of the board, that is, 15 cm, the dragon head will collide with the dragon body section. Therefore, when the distance d between the four vertices M, N, P, and Q of the dragon head and the straight line where the two small holes on each section of the outer dragon body are located is l >15cm, the benches will not collide; when the distance between one point and the straight line satisfies d l =15cm, that is the end time of the dragon dance team's entry.

[0070] Let the coordinates of point X be (x1, y1) and the coordinates of point Y be (x2, y2). Since the X and Y points of the bench are both on the equidistant spiral, the slope of the straight line XY always exists. Therefore, let the equation of the straight line where points X and Y are located be:

[0071]

[0072] According to the solution of the above vertex coordinates, let the coordinates of point P be (x′, y′), and use the distance formula from point to line to get the distance d l :

[0073]

[0074] Give the collision conditions:

[0075] d l ≤0.15

[0076] Calculate the distances from the four vertices of the faucet to the straight line at different times to determine whether a collision will occur. The minimum time at which a collision occurs is the end time of the disk entry.

[0077] Solution process

[0078] In order to obtain the end time of winding, according to the established model, it is necessary to judge the distance between the four vertices of the dragon head and the straight lines where the two small holes of each dragon body section of the adjacent outer circle are located. In order to obtain more comprehensive and complete data, the present invention adopts a traversal search method for solving.

[0079] Step 1 Initialize parameters: Use the parameters given in the question to assign values ​​to the variables, take the time step as 0.01, and discretize the continuous motion process.

[0080] Step 2 Calculate the movement position: Use the bench dragon movement model to calculate the position of each point in the movement.

[0081] Step 3: Calculate the equation of the straight line: Based on the calculated position coordinates of the handle center, calculate the equation of the straight line for the points on the adjacent outer circle of the faucet.

[0082] Step 4 Calculate the collision time: During the movement of the dragon head, calculate the positions of the four vertices of the dragon head according to the calculated positions of the front and rear handles of the dragon head, and then traverse and calculate the distances between the four points and the outer circle straight line respectively. The first moment when the distance is less than 0.15 is the end time of the dragon dance team's entry.

[0083] Since the position of each point is calculated by numerical simulation, there is an error between the obtained result and the analytical solution. Here, convergence analysis is still performed to prove whether the numerical simulation method is feasible by judging whether the required result converges. The results are shown in the figure. Figure 3 shown.

[0084] Figure 6 The distance d from the faucet vertex to the adjacent outer circle bench hole is given l The relationship with other dragon bodies and time. The points in the figure represent the distance d at this time. l <0.15, which means that the dragon head at this position will collide with this section of the dragon body.

[0085] At the moment of collision, i.e., t=412.33, the position and velocity data of the front handle of the dragon head and the subsequent front handles of the 1st, 51st, 101st, 151st, and 201st sections of the dragon body and the rear handle of the dragon tail are as follows:

[0086] Table 1 Position and speed of some handles at the moment of collision

[0087] Position x(m) Position y(m) Speed ​​(m / s) Faucet 1.093036 2.016887 1.000000 Section 1 Dragon Body -1.753613 1.651519 0.988753 Chapter 51 Dragon Body 1.139799 4.368929 0.974193 Chapter 101 Dragon Body -0.389627 -5.893857 0.971896 Chapter 151 Dragon Body 1.114593 -6.937478 0.970958 Chapter 201 Dragon Body -7.870762 -1.376091 0.970448 Dragon Tail (Back) 0.810186 8.339761 0.97029

[0088] Embodiment 2

[0089] Based on the first embodiment, this embodiment proposes that the dragon dance team should not only coil into but also be in a circular area with a diameter of 9 meters (see Figure 7 ) to determine the minimum pitch to avoid collisions among the dragon dance team during movement.

[0090] Determine the minimum pitch that allows the faucet front handle to spiral into the boundary of the turning space without collision, and add the following single-objective optimization model:

[0091] Decision variables

[0092] Pitch of an equidistant spiral:

[0093] p

[0094] Objective Function

[0095] The goal is to minimize the pitch, that is:

[0096] min p

[0097] Constraints

[0098] As the pitch decreases, according to the established collision model, the faucet collision time will be advanced, and the polar diameter at the time of collision will increase. Therefore, it is necessary to meet the requirement that when the faucet collides, the front handle of the faucet has been coiled into the turning area, that is:

[0099]

[0100] In summary, the optimization model is:

[0101] min p

[0102]

[0103] Solution of the model

[0104] 1) Particle swarm optimization algorithm with penalty term

[0105] For single-objective optimization models, particle swarm optimization algorithm is usually used.

[0106] The particle swarm optimization algorithm is a random search algorithm that simulates biological activities and swarm intelligence in nature and has good search and optimization capabilities. In order to obtain more accurate results and avoid falling into local optimality, the present invention uses a particle swarm optimization algorithm with a penalty term to solve the problem. The specific steps are as follows:

[0107] 1) Initialize the particle swarm and give parameter values, including the swarm size N, particle position x i and speed v i .

[0108] 2) Calculate the fitness value f(t) of each particle.

[0109] 3) The fitness value f(t) and the individual extreme value p best (i) Comparison. If f(t)>p best (i), then replace p with f(t) best (i).

[0110] 4) The fitness value f(t) and the global extreme value g best Compare. If f(t)>g best , then replace g with f(t) best .

[0111] 5) Determine whether the particle is out of bounds: If the particle violates the constraint, use the penalty term to adjust its fitness.

[0112] 6) Iteratively update the particle's velocity v i and position x i .

[0113] 7) Perform boundary condition processing.

[0114] 8) Determine whether the algorithm termination condition is met: if so, end the algorithm and output the optimization result; otherwise return to step 2).

[0115] 2) Solution steps

[0116] Step 1 Initialization settings: Assign values ​​to variables using the parameters in the question.

[0117] Step 2: Set the objective function and constraints: Take the minimum pitch as the objective function and use the model in Problem 2 as the constraints of the single-objective optimization model.

[0118] Step 3 uses the particle swarm optimization algorithm with a penalty term to solve: set the particle population size to 20, the number of iterations to 150, the range of the decision variable pitch p to (0.2~0.55), and the minimum pitch is obtained by the algorithm.

[0119] Solution

[0120] According to the above solution steps, the minimum pitch is 0.37. The schematic diagram of the position of the bench dragon at the time of collision under this pitch is as follows: Figure 8 shown.

[0121] Model checking

[0122] Since the particle swarm algorithm itself is prone to fall into the local optimum, the nearby pitches are taken for testing based on the minimum pitch obtained by solving.

[0123] The screw pitches are taken as 0.36, 0.37, 0.38, 0.39, 0.4 and 0.43 respectively, and are brought into the collision model to calculate the polar diameter at the time of collision. By judging the polar diameter at the time of collision and the radius of the turning space, it is determined whether the wheel can successfully enter the boundary of the turning space. The specific results are as follows: Fig. 9 shown.

[0124] from Fig. 9 It can be seen that when the pitch is 0.37m, the polar diameter when the collision occurs is the smallest, which proves that when the pitch is the minimum 0.37, the front handle of the faucet can follow the spiral line into the boundary of the turning space.

[0125] In summary, the present invention can accurately predict the collision moment and determine the end moment of the dragon dance team's coiling, so as to improve the safety and viewing experience of the performance.

[0126] The description and practice disclosed in the present invention are easy to think and understand for ordinary technicians in the technical field, and several improvements and modifications can be made without departing from the principles of the present invention. Therefore, modifications or improvements made without departing from the spirit of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. A method for predicting collision and determining the termination time in a bench dragon movement, characterized in that: By building a motion model and collision prediction model for the bench dragon, numerical simulation methods are used to solve the position and speed of each bench section, and the moment of collision is predicted to determine the end time of the dragon dance team's rotation.

2. The method for predicting collision and determining the end time in the movement of a bench dragon according to claim 1, characterized in that: The motion model includes the motion equations of the dragon head, dragon body and dragon tail; (1) The motion position model of the faucet front handle, including the equidistant spiral parameter equation of the Archimedean spiral in polar coordinates ρ = ρ0 + a·θ, and the equation in the rectangular coordinate system obtained based on the coordinate conversion relationship between the polar coordinate system and the rectangular coordinate system According to θ=ωt, the formula ρ=ρ0+a·θ can be rewritten as Among them, ρ0 is the starting radius of the spiral, a is the growth coefficient, θ represents the angle between the line connecting the point and the center of the spiral and the x-axis, which is the polar angle in the polar coordinate system, ρ is the distance between the point and the center of the circle, which is expressed as the polar diameter in the polar coordinate system, p is the pitch, x and y are the horizontal and vertical coordinates in the rectangular coordinate system with the center of the spiral as the origin, ω is the angular velocity of the faucet front handle movement, and t is the movement time; (2) Motion model of the faucet handle after any n time intervals: At the initial moment, the position coordinates of the faucet handle are calculated to be (x0, y0); according to the formula ρ = ρ0 + a·θ, the time interval Δt is taken, and the motion model is discretized. The polar coordinates of the faucet handle after the first time interval Δt are calculated to be expressed as in, ρ0 is the starting radius of the spiral, θ0 is the polar angle at the initial moment, p is the pitch, Δt is the time interval, v is the linear velocity, which represents the rate of change of the radial distance over time, w is the angular velocity, which represents the rate of change of the angle over time, and h is the radial distance. By recursion, the polar coordinates of the faucet handle after any n time intervals Δt are expressed as: The coordinates converted into the rectangular coordinate system are expressed as: a is the growth coefficient, ρ0 is the starting radius of the spiral, Δt is the time interval, v is the linear velocity, which represents the rate of change of radial distance over time, ρ n ,θ n is the polar diameter and polar angle of the faucet handle after any n time intervals, ρ n-1 ,θ n-1 is the polar diameter and polar angle of the faucet handle after any n-1 time intervals, x n ,y n Respectively represent the horizontal and vertical coordinates of the faucet front handle in the rectangular coordinate system after any n time intervals; (3) The location of the dragon’s body and tail Take two points on the spiral as the front and back handles of a bench. The distance between the two points is the distance between the two holes and is known. The angle between the front and back handles and the line connecting the center of the spiral is calculated by the cosine theorem of the triangle, thus obtaining the recursive formula between the two points, and then the positions of the front and back handles of the dragon body and tail are obtained; according to the coordinate formula in the rectangular coordinate system, we have: Among them, x i ,y i are the horizontal and vertical coordinates of the front handle of the i-th bench in the rectangular coordinate system, ρ i is the polar diameter of the front handle of the i-th bench, θ i is the polar angle of the front handle of the i-th bench, x i+1 ,y i+1 are the horizontal and vertical coordinates of the front handle of the i+1th bench in the rectangular coordinate system, ρ i+1 is the polar diameter of the front handle of the i+1th bench, θ i+1 is the polar angle of the front handle of the i+1th bench; According to the cosine theorem of a triangle, the distance between the two points is equal to the distance d between the two holes of the bench. i , we get the equation: Among them, θ is the angle between the two fixed handles on the bench and the line connecting the coordinate origin, ρ i+1 is the diameter of the front handle of the i+1th bench, ρ i is the diameter of the front handle of the i-th bench, d i is the distance between the two handles on the i-th bench, Using the coordinate formula and the spiral equation, solve the equation to get the angle θ, and then get the position coordinates of the next handle. Still using the recursive idea, get the coordinates of all the dragon bodies and tails. Among them, the movement speed, for a certain handle of a certain section of the dragon body, for the position at time t (x t ,y t ) and the position at time t+1 (x t+1 ,y t+1 ), the forward speed of the handle is calculated according to the rate of change of the handle position; for a handle n, its position (x n ,y n ) is: They represent the position coordinates x of handle n at time t. n and n The rate of change over time, that is, the components of velocity in the x and y directions, x t ,y t are the horizontal and vertical coordinates of handle n at time t, x t+1 ,y t+1 are the horizontal and vertical coordinates of handle n at time t+1; Using the formula for the rate of change of the bench handle position, we can get the speed of the nth bench as: v n (t) represents the forward velocity of handle n at time t, which is the magnitude of the velocity vector, calculated by the square root of the sum of the squares of the velocity components in the x and y directions; The speed of the dragon head's front handle and the position of each bench relative to the dragon head's front handle are used to iterate and calculate the speed of the entire dragon dance team.

3. The method for predicting collision and determining the end time in the movement of a bench dragon according to claim 1, characterized in that: The numerical simulation method is the fourth-order Runge-Kutta method, and the fourth-order Runge-Kutta calculation formula is: Among them, any value y(n) is determined by the sum of the current value y(n-1) and the change per unit time; the change per unit time is the product of the time interval h and the approximate slope. For any time, the estimated slope is the weighted average of the following slopes: K1: slope at the time starting point; K2: The slope of the midpoint in time. According to the Euler method, the slope K1 is used to approximate y at point The value of K3: midpoint slope in time, using slope K2 to approximate the y value; K4: End point slope, using K3 to approximate the y value.

4. The method for predicting collision and determining the end time in the movement of a bench dragon according to claim 1, characterized in that: The collision prediction model predicts the moment of collision by calculating the distance between the apex of the faucet and the center line of the adjacent outer circle bench handles; Collision conditions: Calculate the distances from the four vertices of the faucet to the straight line at different times to determine whether a collision will occur. The minimum time for a collision to occur is the end time of the disk entry. Establish a collision model: When the distance between the vertex P and the straight line where the points X and Y are located is half the width of the board, the faucet will collide with the dragon body section; therefore, when the distance between the four vertices M, N, P, Q of the faucet and the straight line where the two small holes on each dragon body section of the outer circle are located is d>d l When the distance between one point and the straight line satisfies d = d l The moment of , is the end time of the dragon dance team's entry; Let the coordinates of point X be (x1, y1) and the coordinates of point Y be (x2, y2). Since the X and Y points of the bench are both on the equidistant spiral, the slope of the straight line XY always exists. Therefore, let the equation of the straight line where points X and Y are located be: x, y are the horizontal and vertical coordinates of a vertex on the rectangular bench, x1, y1 are the horizontal and vertical coordinates of a fixed hole on the bench, and x2, y2 are the horizontal and vertical coordinates of another fixed hole on the bench; According to the solution of the above vertex coordinates, let the coordinates of point P be (x′, y′), and use the distance formula from point to line to get the distance d: d is the distance from a vertex on the rectangular bench to the straight line where two points X and Y on the horizontal center line of the bench are located, x and y are the horizontal and vertical coordinates of a vertex on the rectangular bench, x1 and y1 are the horizontal and vertical coordinates of a fixed hole on the bench, and x2 and y2 are the horizontal and vertical coordinates of another fixed hole on the bench.

5. The method for predicting collision and determining the end time in the movement of a bench dragon according to claim 4, characterized in that: The termination time is determined based on the predicted collision time, giving the collision condition: d≤d l d is the distance from a vertex on the rectangular bench to the straight line between the two points X and Y on the horizontal center line of the bench. l Half the length of the board width; Calculate the distances from the four vertices of the faucet to the straight line at different times to determine whether a collision will occur. The minimum time at which a collision occurs is the end time of the disk entry.

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