Five-segment S-curve flexible acceleration and deceleration control method, system and medium based on sine function

Abstract

The present invention discloses a five-segment S-curve flexible acceleration and deceleration control method, system and medium based on a sine function, which obtains the running distance, acceleration time and uniform speed time input by the user; calculates the maximum jerk, proportionality coefficient and maximum speed in the uniform speed stage according to the running distance, acceleration time and uniform speed time; constructs an acceleration and deceleration function control curve according to the maximum jerk, proportionality coefficient, maximum speed in the uniform speed stage, speed function and position function, so as to plan the position instruction; monitors the difference between the position instruction and the target position, and terminates the operation when the position instruction is equal to the target position to obtain the planned motion trajectory. The algorithm can take into account the execution efficiency of the code while ensuring the stability of the position motion, so as to achieve stable operation and efficient code. Moreover, the algorithm of the present invention can be applied in discrete systems, which can ensure smooth transition in each motion stage and meet the requirements of flexible acceleration and deceleration control.

Description

Technical Field

[0001] The present invention relates to the field of industrial automation control technology, and in particular to a five-segment S-curve flexible acceleration and deceleration control method, system and medium based on a sine function. Background Art

[0002] With the continuous development of science and technology, motion control systems are increasingly used in aerospace, chemical, industrial control and other fields. Due to the limited stress and load of the mechanical system, it is required to minimize the impact on the mechanical system. To achieve smooth and efficient control, the acceleration and deceleration control algorithm is an indispensable part. In the field of industrial automation control, the position S curve is a common acceleration and deceleration algorithm choice.

[0003] The position S-curve is a commonly used trajectory planning algorithm, which is widely used in the field of industrial automation. It is used in the control system to control the system from the current position to the given target position. The S-curve is a smooth curve that provides a "shock-controlled" acceleration and deceleration. Its characteristics are continuous speed / acceleration during the control process, which can achieve a smooth transition of the position curve, thereby reducing the vibration and shock of the system and improving the stability and accuracy of the system.

[0004] However, the existing position S-curve acceleration and deceleration control algorithm has some shortcomings: for example, the speed, acceleration or jerk value is not smooth, which leads to greater impact and vibration during operation; in addition, while improving stability, it will make the existing algorithm calculation more complicated and time-consuming, reduce the code execution efficiency, affect the switching frequency of power devices, and thus affect the overall real-time performance of the system. In short, it is difficult to balance the operation stability and algorithm complexity. Summary of the invention

[0005] The main purpose of the present invention is to provide a five-segment S-curve flexible acceleration and deceleration control method, system and medium based on a sine function, which can simultaneously take into account the execution efficiency of the code while ensuring the smoothness of position movement, so as to achieve stable operation and efficient code.

[0006] To achieve the above object, the present invention proposes a five-segment S-curve flexible acceleration and deceleration control method based on a sine function, which is applied to a motion control system and comprises the following steps:

[0007] Get the running distance, acceleration time, and uniform speed time input by the user;

[0008] The maximum jerk, the proportionality coefficient, and the maximum speed in the uniform speed stage are calculated according to the running distance, the acceleration time, and the uniform speed time;

[0009] An acceleration / deceleration function control curve is constructed according to the maximum jerk value, the proportional coefficient, the maximum speed in the uniform speed stage, the speed function, and the position function, so as to plan the position instruction;

[0010] The difference between the position command and the target position is monitored, and when the position command is equal to the target position, the operation is terminated to obtain the planned motion trajectory.

[0011] The step of constructing the acceleration / deceleration function control curve according to the maximum jerk value, the proportional coefficient, the maximum speed in the uniform speed stage, the speed function, and the position function comprises:

[0012] The speed curve is planned according to the maximum jerk value, the proportionality coefficient, the maximum speed in the uniform speed stage, the speed function, and the position function. According to the speed curve, the position curve is obtained by discrete integration of the speed.

[0013] The step of constructing the acceleration / deceleration function control curve according to the maximum jerk value, the proportional coefficient, the maximum speed in the uniform speed stage, the speed function, and the position function also includes:

[0014] When the remaining running distance is greater than the running distance in the acceleration phase, the position command is planned according to the speed function, where the remaining running distance is the distance between the current position feedback and the target position;

[0015] When the remaining running distance is less than or equal to the running distance in the acceleration stage, the remaining running distance is substituted into the position function, and the equation is solved using the Newton iteration method to obtain the remaining running time and the corresponding speed. The speed is used for discrete integration to plan the position instruction.

[0016] Wherein, the motion control system is a discrete system.

[0017] The five sections of the S-curve include: an acceleration section, a deceleration section, a constant speed section, an acceleration and deceleration section, and a deceleration and deceleration section, wherein the acceleration stage time is equal to the deceleration stage time.

[0018] Among them, the jerk curve is a sine curve, the jerk curve is continuous, the acceleration curve is continuous and smooth, the velocity curve is continuous and smooth, and the displacement curve is continuous and smooth. At the beginning and end of acceleration and deceleration, the velocity, acceleration, and jerk are all zero, and each motion stage has a smooth transition.

[0019] The present invention also proposes a five-segment S-curve flexible acceleration and deceleration control system based on a sine function. The system includes a memory and a processor. A computer program is stored in the memory. When the computer program is executed by the processor, the five-segment S-curve flexible acceleration and deceleration control method based on a sine function as described above is implemented.

[0020] The present invention also proposes a computer storage medium having a computer program stored thereon. When the computer program is executed by a processor, the five-segment S-curve flexible acceleration and deceleration control method based on a sine function as described above is implemented.

[0021] The present invention proposes a five-segment S-curve flexible acceleration and deceleration control method, system and medium based on a sine function, by obtaining the running distance, acceleration time and uniform speed time input by the user; according to the running distance, acceleration time and uniform speed time, the maximum jerk, proportional coefficient and maximum speed of the uniform speed stage are calculated; according to the maximum jerk, proportional coefficient, maximum speed of the uniform speed stage, speed function and position function, an acceleration and deceleration function control curve is constructed to plan the position instruction; the difference between the position instruction and the target position is monitored, and the operation is terminated when the position instruction is equal to the target position to obtain the planned motion trajectory. The five-segment S-curve flexible acceleration and deceleration control algorithm based on the sine function can simultaneously take into account the execution efficiency of the code while ensuring the stability of the position motion, so as to achieve stable operation and efficient code. In addition, industrial control systems such as robots, controllers and servos are all discrete systems, and the operation mode of the control system is basically to run the main control program once at a fixed time interval. The function expression of the position S curve is generally a function equation under time continuity, which cannot be directly used in a discrete system. The present invention simultaneously proposes an implementation method of the five-segment S-curve flexible acceleration and deceleration control algorithm in a discrete system. The five-segment S-curve flexible acceleration and deceleration control algorithm can ensure the continuity of the jerk curve, the continuous and smooth acceleration curve, the continuous and smooth velocity curve, and the continuous and smooth displacement curve. At the beginning and end of acceleration and deceleration, the velocity, acceleration, and jerk are all zero, and each motion stage has a smooth transition, meeting the requirements of flexible acceleration and deceleration control. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is the existing seven-segment S-curve acceleration and deceleration relationship diagram;

[0023] Figure 2 It is a flow chart of the five-segment S-curve flexible acceleration and deceleration control method based on the sine function of the present invention;

[0024] Figure 3 This is a five-segment S-curve flexible acceleration and deceleration control relationship diagram of the present invention;

[0025] Figure 4 It is a complete flow chart of the five-segment S-curve flexible acceleration and deceleration control method based on the sine function of the present invention. DETAILED DESCRIPTION

[0026] It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0027] As mentioned above, the position S-curve is a commonly used trajectory planning algorithm, which is widely used in the field of industrial automation and is used in control systems to control the system from the current position to a given target position. The S-curve is a smooth curve, which is characterized by continuous speed / acceleration during the control process, which can achieve a smooth transition of the position curve, thereby reducing the vibration and impact of the system and improving the stability and accuracy of the system.

[0028] The more commonly used position S-curve acceleration and deceleration control algorithms include: trapezoidal acceleration and deceleration control algorithm, seven-segment S-curve acceleration and deceleration control algorithm (such as Figure 1 As shown), cubic S-curve acceleration and deceleration control algorithm, sine curve acceleration and deceleration control algorithm, etc. The trapezoidal acceleration and deceleration algorithm is simple to plan and easy to implement. The algorithm takes less time, but there is a sudden change in acceleration, which will produce greater shock and vibration. Therefore, high-performance motion control systems do not use this acceleration and deceleration algorithm. It is only suitable for occasions with high requirements for code execution efficiency, not for occasions with high requirements for motion stability. The stability of the seven-segment S-curve acceleration and deceleration and cubic S-curve acceleration and deceleration control algorithms is better than that of the trapezoidal acceleration and deceleration, but there is a sudden change in jerk during the entire algorithm operation, resulting in uneven acceleration, which will cause greater shock and vibration, and have a certain impact on the motion stability. The jerk and acceleration curves of the sine curve acceleration and deceleration algorithm are smooth and continuous, which solves the problem of discontinuous jerk curves. Compared with the acceleration and deceleration control algorithms such as trapezoidal, S-type, cosine, and cubic S-curve, it reduces motion shock and improves stability; but what follows is that there are many algorithm classifications, complex calculations, and long algorithm time consumption, which affects the real-time performance of the system.

[0029] In view of the above problems, the present invention proposes a five-segment S-curve flexible acceleration and deceleration control algorithm based on a sine function. Under the premise of ensuring the smoothness of position movement, the algorithm can simultaneously take into account the execution efficiency of the code, so as to achieve stable operation and efficient code. In addition, industrial control systems such as robots, controllers, and servos are all discrete systems, and the control system operation mode is basically to run the main control program once at a fixed time interval. The function expression of the position S curve is generally a function equation under time continuity, which cannot be directly used in a discrete system. The present invention simultaneously proposes an implementation method of the five-segment S-curve flexible acceleration and deceleration control algorithm in a discrete system.

[0030] Reference Figure 2 The present invention proposes a five-segment S-curve flexible acceleration and deceleration control method based on a sine function, which is applied to a motion control system and comprises the following steps:

[0031] Step S1, obtaining the running distance, acceleration time, and uniform speed time input by the user;

[0032] Step S2, calculating the maximum jerk, the proportionality coefficient, and the maximum speed in the uniform speed stage according to the running distance, the acceleration time, and the uniform speed time;

[0033] Step S3, constructing an acceleration / deceleration function control curve according to the maximum jerk, the proportional coefficient, the maximum speed in the uniform speed stage, the speed function, and the position function, so as to plan the position instruction;

[0034] Step S4, monitoring the difference between the position command and the target position, and terminating the operation when the position command is equal to the target position to obtain the planned motion trajectory.

[0035] The step of constructing the acceleration / deceleration function control curve according to the maximum jerk value, the proportional coefficient, the maximum speed in the uniform speed stage, the speed function, and the position function comprises:

[0036] The speed curve is planned according to the maximum jerk value, the proportionality coefficient, the maximum speed in the uniform speed stage, the speed function, and the position function. According to the speed curve, the position curve is obtained by discrete integration of the speed.

[0037] The step of constructing the acceleration / deceleration function control curve according to the maximum jerk value, the proportional coefficient, the maximum speed in the uniform speed stage, the speed function, and the position function also includes:

[0038] When the remaining running distance is greater than the running distance in the acceleration phase, the position command is planned according to the speed function, where the remaining running distance is the distance between the current position feedback and the target position;

[0039] When the remaining running distance is less than or equal to the running distance in the acceleration stage, the remaining running distance is substituted into the position function, and the equation is solved using the Newton iteration method to obtain the remaining running time and the corresponding speed. The speed is used for discrete integration to plan the position instruction.

[0040] Wherein, the motion control system is a discrete system.

[0041] The five sections of the S-curve include: an acceleration section, a deceleration section, a constant speed section, an acceleration and deceleration section, and a deceleration and deceleration section, wherein the acceleration stage time is equal to the deceleration stage time.

[0042] Among them, the jerk curve is a sine curve, the jerk curve is continuous, the acceleration curve is continuous and smooth, the velocity curve is continuous and smooth, and the displacement curve is continuous and smooth. At the beginning and end of acceleration and deceleration, the velocity, acceleration, and jerk are all zero, and each motion stage has a smooth transition.

[0043] The five-segment S-curve flexible acceleration and deceleration control algorithm based on the sine function of the present invention can simultaneously take into account the execution efficiency of the code while ensuring the stability of the position movement, so as to achieve stable operation and efficient code. In addition, industrial control systems such as robots, controllers, and servos are all discrete systems, and the control system operation mode is basically to run the main control program once at a fixed time interval. The function expression of the position S curve is generally a function equation under time continuity, which cannot be directly used in a discrete system. The present invention simultaneously proposes an implementation method of the five-segment S-curve flexible acceleration and deceleration control algorithm in a discrete system. The five-segment S-curve flexible acceleration and deceleration control algorithm can ensure that the acceleration curve is continuous, the acceleration curve is continuous and smooth, the speed curve is continuous and smooth, and the displacement curve is continuous and smooth. At the beginning and end of the acceleration and deceleration, the speed, acceleration, and jerk are all zero, and each movement stage has a smooth transition, meeting the requirements of flexible acceleration and deceleration control.

[0044] The scheme of the present invention is described in detail below:

[0045] In the present invention, the basic principle and model of the five-segment S-curve flexible acceleration and deceleration control are as follows:

[0046] The five-segment S-curve flexible acceleration and deceleration control relationship diagram is as follows Figure 3 As shown, the jerk is defined as a sine curve, jmax is the maximum jerk, t is the time coordinate; Vs is the initial speed of the movement, Ve is the end speed of the movement, Vmax is the maximum speed, L is the path segment length, tk (k = 0, 1, 2, 3, 4, 5) is the time node, and Tk (k = 1, 2, 3, 4, 5) is the movement time of each movement stage, Tk = tk-tk-1. Figure 3 It can be seen that the five-segment S-curve flexible acceleration and deceleration control algorithm consists of five curves, namely: acceleration segment (0-t1), deceleration segment (t1-t2), uniform speed segment (t2-t3), acceleration and deceleration segment (t3-t4), deceleration and deceleration segment (t4-t5). In order to make the acceleration and speed at the starting point and the end point of the movement zero, the acceleration stage time and the deceleration stage time must be equal, so Vs=Ve=0, T1=T2, and similarly T4=T5.

[0047] Among them, the five-segment S-curve flexible acceleration and deceleration control algorithm can ensure the continuity of the jerk curve, the continuous and smooth acceleration curve, the continuous and smooth velocity curve, and the continuous and smooth displacement curve. At the beginning and end of acceleration and deceleration, the velocity, acceleration, and jerk are all zero, and each motion stage has a smooth transition, meeting the requirements of flexible acceleration and deceleration control.

[0048] from Figure 3It can be seen from the figure that the change law of each motion variable of the five-segment S-curve flexible acceleration and deceleration control algorithm can be used to derive the specific function model of the motion curve. The relevant function equation can be derived from the original sine curve of the jerk and the integral relationship between the jerk, acceleration, velocity and displacement:

[0049]

[0050]

[0051]

[0052] Assume jmax as the maximum jerk value, k1 as the proportional coefficient, and define the jerk curve function j(t) as:

[0053]

[0054] By integrating the jerk, we can get the acceleration curve function a(t):

[0055]

[0056] By integrating the acceleration, we can get the velocity curve function v(t):

[0057]

[0058] By integrating the velocity, we can get the displacement curve function s(t):

[0059]

[0060] from Figure 3 It can be seen that when t = t1, j(t1) = 0, that is, sin(k1T1) = 0. Therefore, the relationship between the acceleration time T1 and the proportional coefficient k1 should satisfy:

[0061] k1T1=π (1)

[0062] The maximum speed Vmax in the uniform speed stage can be obtained from the speed function v(t):

[0063]

[0064] The running distance Sa in the acceleration phase (T1, T2) can be obtained from the position function s(t):

[0065]

[0066] From the symmetry between the acceleration stage and the deceleration stage, we know that the running distance in the deceleration stage is equal to the running distance in the acceleration stage, so we can get:

[0067] L = 2 * Sa + Vmax * T3 (4)

[0068] From formulas (1), (2), (3), and (4), the following formula can be obtained:

[0069]

[0070] From the analysis of the formula, it can be seen that only by determining the running distance L, the acceleration time T1, and the constant-speed time T3 can V be obtained. max , j max , K1. According to V max , j max , K1, and by referring to the jerk, acceleration, velocity, and displacement function models and calculation formulas, a complete acceleration and deceleration function control curve can be constructed, and the desired running trajectory can be planned.

[0071] In the solution of the present invention, the implementation process of the five-segment S-curve flexible acceleration and deceleration control in a discrete system is as follows:

[0072] The overall idea of the implementation is that the user first inputs three variables, namely the running distance L, the acceleration time T1, and the constant-speed time T3, to determine the S-shaped running trajectory. From the calculation of the three variables, V max , j max , K1 can be obtained. According to V max , j max , K1 and the velocity function v(t) and position function s(t), the velocity curve is planned, and then the position curve can be obtained through the discrete integration of the velocity.

[0073] The planning process is divided into two stages:

[0074] 1. When the remaining running distance is greater than Sa, the position command is planned according to the velocity function v(t) when 0 < t < 2T1;

[0075] 2. When the remaining running distance is less than Sa, the remaining running distance is substituted into the position function when 0 < t < 2T1, and the Newton iteration method is used to solve the equation to obtain the remaining running time t and the corresponding velocity v(t), and the position command is planned by discrete integration of the velocity.

[0076] In the discrete system, before the curve starts to run, it is necessary to substitute the values of the three variables of the running distance L, the acceleration time T1, and the constant-speed time T3 into formula (5) to calculate V max , j max , K1. In addition, the running frequency of the discrete system is Freq, and the running interval time is Interval (Interval = 1 / Freq).

[0077] Stage 1: The process when the remaining distance is greater than Sa

[0078] When the remaining running distance (the distance between the current position feedback and the target position) is greater than Sa, the operation is in the acceleration phase (T1, T2), and the continuous-time domain formula for speed is

[0079]

[0080] where k1T1 = π, that is, in the discrete system, θ(k1t) needs to increase from 0 to 2π within 2T1 time. Angle increment:

[0081]

[0082] When starting to run, according to the speed formula V(t), substitute θn(k1t), j max , K1. θn starts from 0, and each time it is calculated, it increases by Δθ. When the calculated speed Vn reaches V max and then remains at V max . Then the calculated discrete speeds V1, V2... Vn will conform to the speed curve change law in the continuous-time domain. Multiply the discrete speed Vn by the interval time Interval and continuously accumulate it as the position command Posref. If the system runs according to the position command, it will obtain a position S curve that meets the requirements. Among them, the calculation formula for the position command Posref is as follows:

[0083]

[0084] Stage 2: The process when the remaining distance is less than or equal to Sa

[0085] When the remaining distance is less than or equal to Sa, the deceleration process will start. The deceleration process will calculate the corresponding speed in real time according to the remaining distance. It can be seen from Figure 3 that the acceleration phase (T1, T2) and the deceleration phase (T3, T4) are symmetric, and the acceleration running distance will be the same as the deceleration running distance. The deceleration process can be regarded as the reverse process of acceleration. When the remaining running distance is less than Sa, substitute the remaining running distance S(t k ) into the position function when 0 < t < 2T1, and use the Newton iteration method to solve the equation to obtain the remaining running time t k and the corresponding speed V(t k )(that is, f′(t k ), and then use the speed and the running interval Interval to perform discrete integration to generate the position command Posref. During the entire running process, the difference between the position command and the target position is monitored in real time. When the position command is equal to the target position, the operation ends. The position function f(t) and its derivative f′(t) used for the iteration method calculation are as follows.

[0086]

[0087] The basic idea of ​​Newton's iteration method is to use the tangent line of a function to approximate the root of an equation. Assuming that the equation to be solved is f(x)=0, starting from an initial approximate solution x0, the root of the equation can be estimated using the tangent line of the function f(x) at x=x0. The slope of the tangent line is f'(x0), so the intersection of the tangent line and the x-axis is a new approximate solution. By continuously iterating this process, the root of the equation can be approximated. The recursive formula of Newton's iteration method is as follows: k -x k-1 The iteration stops when the error is less than Interval / 10.

[0088]

[0089] The complete process of the five-segment S-curve flexible acceleration and deceleration control process of the present invention is as follows: Figure 4 shown.

[0090] The present invention also proposes a five-segment S-curve flexible acceleration and deceleration control system based on a sine function. The system includes a memory and a processor. A computer program is stored in the memory. When the computer program is executed by the processor, the five-segment S-curve flexible acceleration and deceleration control method based on a sine function as described above is implemented.

[0091] The present invention also proposes a computer storage medium having a computer program stored thereon. When the computer program is executed by a processor, the five-segment S-curve flexible acceleration and deceleration control method based on a sine function as described above is implemented.

[0092] The present invention proposes a five-segment S-curve flexible acceleration and deceleration control method, system and medium based on a sine function, by obtaining the running distance, acceleration time and uniform speed time input by the user; according to the running distance, acceleration time and uniform speed time, the maximum jerk, proportional coefficient and maximum speed of the uniform speed stage are calculated; according to the maximum jerk, proportional coefficient, maximum speed of the uniform speed stage, speed function and position function, an acceleration and deceleration function control curve is constructed to plan the position instruction; the difference between the position instruction and the target position is monitored, and the operation is terminated when the position instruction is equal to the target position to obtain the planned motion trajectory. The five-segment S-curve flexible acceleration and deceleration control algorithm based on the sine function can simultaneously take into account the execution efficiency of the code while ensuring the stability of the position motion, so as to achieve stable operation and efficient code. In addition, industrial control systems such as robots, controllers and servos are all discrete systems, and the operation mode of the control system is basically to run the main control program once at a fixed time interval. The function expression of the position S curve is generally a function equation under time continuity, which cannot be directly used in a discrete system. The present invention simultaneously proposes an implementation method of the five-segment S-curve flexible acceleration and deceleration control algorithm in a discrete system. The five-segment S-curve flexible acceleration and deceleration control algorithm can ensure the continuity of the jerk curve, the continuous and smooth acceleration curve, the continuous and smooth velocity curve, and the continuous and smooth displacement curve. At the beginning and end of acceleration and deceleration, the velocity, acceleration, and jerk are all zero, and each motion stage has a smooth transition, meeting the requirements of flexible acceleration and deceleration control.

[0093] The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Equivalent structures or equivalent process changes made by the scheme using the contents of the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A five-segment S-curve flexible acceleration and deceleration control method based on a sine function, the method being applied to a motion control system, characterized in that: The method comprises the following steps: Get the running distance, acceleration time, and uniform speed time input by the user; The maximum jerk, the proportionality coefficient, and the maximum speed in the uniform speed stage are calculated according to the running distance, the acceleration time, and the uniform speed time; An acceleration / deceleration function control curve is constructed according to the maximum jerk value, the proportional coefficient, the maximum speed in the uniform speed stage, the speed function, and the position function, so as to plan the position instruction; Monitor the difference between the position command and the target position, and terminate the operation when the position command is equal to the target position to obtain the planned motion trajectory; The step of constructing an acceleration / deceleration function control curve according to the maximum jerk value, the proportional coefficient, the maximum speed in the uniform speed stage, the speed function, and the position function comprises: A speed curve is planned according to the maximum jerk value, the proportionality coefficient, the maximum speed in the uniform speed stage, the speed function, and the position function, and a position curve is obtained by discrete integration of the speed according to the speed curve; The step of constructing an acceleration / deceleration function control curve according to the maximum jerk value, the proportional coefficient, the maximum speed in the uniform speed stage, the speed function, and the position function also includes: When the remaining running distance is greater than the running distance in the acceleration phase, the position command is planned according to the speed function, where the remaining running distance is the distance between the current position feedback and the target position; When the remaining running distance is less than or equal to the running distance in the acceleration stage, the remaining running distance is substituted into the position function, and the equation is solved using the Newton iteration method to obtain the remaining running time and the corresponding speed. The speed is used for discrete integration to plan the position instruction.

2. The method according to claim 1, characterized in that The motion control system is a discrete system.

3. The method according to claim 1, characterized in that The five-segment S-curve includes, in sequence: an acceleration segment, a deceleration segment, a uniform speed segment, an acceleration / deceleration segment, and a deceleration / deceleration segment, wherein the acceleration phase time is equal to the deceleration phase time.

4. The method according to claim 3, characterized in that The jerk curve is a sine curve. The jerk curve is continuous, the acceleration curve is continuous and smooth, the velocity curve is continuous and smooth, and the displacement curve is continuous and smooth. At the beginning and end of acceleration and deceleration, the velocity, acceleration, and jerk are all zero, and each motion stage has a smooth transition.

5. A five-segment S-curve flexible acceleration and deceleration control system based on a sine function, characterized in that: The system includes a memory and a processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, a five-segment S-curve flexible acceleration and deceleration control method based on a sine function as described in any one of claims 1 to 4 is implemented.

6. A computer storage medium, characterized in that: The computer storage medium stores a computer program, which, when executed by a processor, implements a five-segment S-curve flexible acceleration / deceleration control method based on a sine function as described in any one of claims 1 to 4.

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