Fifteen-segment sine S-curve planning method, storage medium

Abstract

The present invention relates to the field of motion control technology, and specifically relates to a fifteen-segment sine S-curve planning method and a storage medium, including the following steps: The front end and the end of the stroke are respectively divided into a starting stage and an in-place stage. The starting stage includes a jerk segment, a constant acceleration segment, a deceleration acceleration segment, and a constant speed segment. The in-place stage includes a constant speed segment, a jerk segment, a constant acceleration segment, and a deceleration acceleration segment. The middle segment is divided into a seven-segment sine S-curve planning stage; the preset time and distance parameters are respectively used to back-calculate the speed when entering the constant speed segment of the starting stage V 2 and the speed when entering the constant speed segment of the in-place stage V 1 , and the middle segment is planned with a seven-segment sine S-curve with an initial speed of V 2 and a final speed of V 1 . This solution effectively reduces the torque required in the starting stage of the motor and the residual oscillation when the motor decelerates and stops, and improves the production efficiency and in-place accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of motion control, and particularly to a fifteen-segment sine S-curve planning method and a storage medium. Background Art

[0002] For the seven-segment sine S-curve planning currently used in the market, most of them plan the entire motion with an initial velocity and a final velocity of 0, and do not make any treatment for the motor startup and arrival moments. This is suitable for most application scenarios, but it is lacking for high-speed and high-inertia-ratio loads. For example, Patent (Publication No. CN114879609A) discloses a jerk-continuous trigonometric function curve planning method and system, and a chip mounter. The method includes the following steps: dividing the curve planning into an acceleration section, a constant-speed section, and a deceleration section, and further dividing the acceleration section and the deceleration section into a jerk section, a uniform acceleration section, and a decelerated acceleration section; setting and initializing the motion parameters of the curve planning; defining the ratio of the average acceleration of the deceleration section to the acceleration section as the softening factor, and defining the ratio of the maximum acceleration to the average acceleration within the deceleration section or the acceleration section as the acceleration coefficient; calculating the time nodes of each stage of the curve planning according to the motion parameters, the softening factor, and the acceleration coefficient; and updating the state of each stage of the curve planning according to the time nodes. Combining the characteristics of the continuous second derivative of the trigonometric function, a jerk-continuous S-curve planning is designed, which effectively reduces the motion impact, ensures the stable arrival time, and has simple operations. Another example is Patent (Publication No. CN114740806A) which discloses an S-curve planning method and system compatible with updating the target position during motion. The method includes the following steps: dividing the curve planning into 7 stages; setting and initializing the motion parameters of the curve planning; calculating the direct deceleration distance in the curve planning according to the motion parameters, and determining whether direct deceleration is possible; calculating the acceleration time and acceleration distance to accelerate to the maximum speed based on the determination result; calculating the time points of each stage according to the acceleration time and acceleration distance; detecting in real time whether there is a new target position. If not, updating the state of each stage of the curve planning according to the time points; if so, returning to the initial step to re-plan. The present invention supports curve planning with an initial velocity, is compatible with directly re-planning the position curve after the target position changes during the motion process, and effectively improves the production efficiency. However, the seven-segment sine S-curve planning ensures the continuity of acceleration and jerk, but does not deal with the startup and arrival stages. In high-speed and high-load scenarios, it is usually necessary to reduce the deceleration to ensure smooth arrival.

[0003] The seven-segment S-shaped curve planning requires reaching the maximum acceleration at the initial stage of motion. At this time, the torque and current that the motor needs to apply are extremely large. In the case where the rated electrical parameters of some motors are small, it is very likely that the motor position and speed error will be too large due to insufficient applied torque, resulting in error reporting and overcurrent reporting. In the motion stage structure, due to the existence of high-inertia loads, reducing the deceleration is usually used to achieve smooth motor positioning and reduce oscillation. However, this will cause an extension of the motion time and affect work efficiency. But high deceleration is likely to cause oscillation when the motor reaches the position, and the position shows a sinusoidal back-and-forth oscillation process. Therefore, in the prior art, without reducing the acceleration, deceleration, and motion time as much as possible, there is a lack of a solution to reduce the torque required in the motor startup stage and reduce the position error; or, reduce the residual oscillation in the motor positioning stage and improve the positioning accuracy. Summary of the Invention

[0004] The object of the present invention is to overcome the problems existing in the prior art. The object of the present invention is to provide a fifteen-segment sine S-shaped curve planning method and a storage medium.

[0005] To achieve the above object, in the first aspect of the present invention, a seven-segment sine S-shaped curve planning optimization method is provided. A curve planning for the positioning stage is added at the end of the stroke, which sequentially includes a constant-speed segment and a deceleration segment. Preset time and distance parameters and inversely calculate the speed V to enter the constant-speed segment 1 , and perform a seven-segment sine S-shaped curve planning for the stroke before the end with the final speed being V 1 to reduce the residual oscillation at the end.

[0006] Preferably, the presetting of the time and distance parameters and the inverse calculation of the speed V to enter the constant-speed segment 1 are specifically as follows: Preset the end distance as S, the total end movement time as T, and the constant-speed segment movement time as T 1 , and calculate the speed V 1 The formula is as follows:

[0007] Preferably, the deceleration segment is sequentially divided into a jerk segment, a constant acceleration segment, and a deceleration acceleration segment. The speed V(t) curve planning for the positioning stage is:

[0008]

[0009] The acceleration α(t) curve planning for the positioning stage is:

[0010]

[0011] where α m = 2*α 1 / (β + 1), α 1 = V 1 / (T - T 1), β is the multiple of the motion time of the uniform acceleration section to the motion time of the deceleration section, 0 < β < 1; w is the angular velocity constant, t is the real-time time of the curve planning in the in-place stage, t 1 = T 1 , t 2 = T 1 + T α , t 3 = T 1 + T α + T b , t 4 = T 1 + T α + T b + T c , T α 、T b 、T c are the motion times of the jerk section, the uniform acceleration section and the deceleration section respectively.

[0012] The second aspect of the present invention provides a seven-segment sine S-shaped curve planning optimization method. A starting stage curve planning is added to the starting end of the stroke, which successively includes an acceleration section and a uniform speed section. Preset time and distance parameters and back-calculate the speed V 2 at which to enter the uniform speed section. The subsequent stroke after the starting end is planned with a seven-segment sine S-shaped curve at an initial speed of V 2 to reduce the starting error.

[0013] Preferably, the presetting of the time and distance parameters and the back-calculation of the speed V 2 to enter the uniform speed section are specifically as follows: Preset the starting end distance as S 2 , the total motion time of the starting end as T 2 , the motion time of the uniform speed section as T 3 , and calculate the speed V 2 using the following formula:

[0014] Preferably, the acceleration section is successively divided into a jerk section, a uniform acceleration section and a deceleration section. The curve planning of the starting stage speed V1(t) is:

[0015] The curve planning of the starting stage acceleration α1(t) is:

[0016]

[0017] Wherein, α m1 = 2 * α 2 / (β 1 + 1), α 2 = V 2 / (T 2 - T 3 ), β1 is the multiple of the time of the uniform acceleration section to the time of the acceleration section, 0 < β 1 < 1; w is the angular velocity constant, t is the real-time time of the start-up phase curve planning, t 5 = T 3 t 6 = T 3 + T d t 7 = T 3 + T d + T e t 8 = T 3 + T d + T e + T f T d T e T f are the motion times of the jerk section, the uniform acceleration section and the deceleration section respectively.

[0018] The third aspect of the present invention provides a fifteen-segment sine S-shaped curve planning method, including the following steps:

[0019] The front end and the end of the stroke are respectively divided into a start-up phase and a in-place phase. The start-up phase includes a jerk section, a uniform acceleration section, a deceleration section and a constant speed section. The in-place phase includes a constant speed section, a jerk section, a uniform acceleration section and a deceleration section. The middle section is divided into a seven-segment sine S-shaped curve planning phase;

[0020] The preset time and distance parameters are respectively used to inversely calculate the speed V 2 entering the constant speed section of the start-up phase and the speed V 1 entering the constant speed section of the in-place phase. The middle section is planned with a seven-segment sine S-shaped curve with an initial speed of V 2 and a final speed of V 1 .

[0021] Preferably, the speed V(t) curve of the in-place phase is planned as:

[0022]

[0023] The acceleration α(t) curve of the in-place phase is planned as:

[0024]

[0025] where α m = 2 * α 1 / (β + 1), α 1 = V 1 / (T - T 1), β is the multiple of the motion time in the uniform acceleration section to the motion time in the deceleration section, 0 < β < 1; w is the angular velocity constant, t is the real-time time of the curve planning in the in-place stage, t 1 = T 1 t 2 = T 1 + T α t 3 = T 1 + T α + T b t 4 = T 1 + T α + T b + T c t α T b T c are the motion times of the jerk section, the uniform acceleration section and the deceleration section respectively.

[0026] Preferably, the curve planning of the starting stage speed V1(t) is:

[0027]

[0028] The curve planning of the starting stage acceleration α1(t) is:

[0029]

[0030] where α m1 = 2 * α 2 / (β 1 + 1), α 2 = V 2 / (T 2 - T 3 ), β 1 is the multiple of the motion time in the uniform acceleration section to the motion time in the acceleration section, 0 < β 1 < 1; w is the angular velocity constant, t is the real-time time of the curve planning in the starting stage, t 5 = T 3 t 6 = T 3 + T d t 7 = T 3 + T d + T e t 8 = T 3 + T d + T e + T f t d T e T fThey are respectively the motion times of the jerk section, the constant acceleration section, and the deceleration section.

[0031] The fourth aspect of the present invention provides a machine-readable storage medium, on which instructions are stored, and the instructions are used to cause the machine to execute the above-mentioned seven-segment sine S-shaped curve planning optimization method, and / or cause the machine to execute the above-mentioned fifteen-segment sine S-shaped curve planning method.

[0032] Through the above technical solutions, the following technical effects are achieved: On the basis of the seven-segment sine S-shaped curve planning, the existing curve planning logic is optimized, the curve planning in the motor starting stage is added, and the problem that the motor and the driver are prone to error reporting under the extremely high peak torque in the starting stage of driving a small motor with a high-quality load is processed, effectively reducing the torque required in the motor starting stage, and ensuring the operation efficiency as much as possible at high speeds and accelerations; and, the curve planning in the motor in-place stage is added, and the problem that residual oscillations are likely to occur during in-place of a high-speed and high-quality load, resulting in slow convergence speed, is processed, effectively reducing the residual oscillations when the motor decelerates and stops, cutting the energy of the structural system through the end buffer to improve the motor in-place accuracy, reducing the in-place residual oscillation time, and improving the production efficiency and in-place accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic diagram of the seven-segment sine S-shaped curve planning of the prior art solution;

[0034] Figure 2 It is a schematic diagram of the optimized seven-segment sine S-shaped curve planning in Embodiment 1 of the present invention;

[0035] Figure 3 It is a schematic diagram of the optimized seven-segment sine S-shaped curve planning in Embodiment 2 of the present invention;

[0036] Figure 4 It is a schematic diagram of the optimized fifteen-segment sine S-shaped curve planning in Embodiment 3 of the present invention;

[0037] Figure 5 It is a schematic diagram of the speed error and position error curves of the conventional seven-segment curve planning adopted in the test example of the present invention;

[0038] Figure 6 It is a schematic diagram of the in-place curve of the conventional seven-segment curve planning adopted in the test example of the present invention;

[0039] Figure 7 It is a schematic diagram of the speed error and position error curves planned by the solution in Embodiment 3 of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] The following is a detailed description of the specific implementation manners of the embodiments of the present invention in conjunction with the accompanying drawings. It should be understood that the specific implementation manners described herein are only used to illustrate and explain the embodiments of the present invention, and are not used to limit the embodiments of the present invention.

[0041] In the existing seven-segment sine S-curve planning, when the initial velocity and the final velocity are defaulted to 0, the curve is as Figure 1 shown, ensuring the continuity of acceleration and jerk. At the moment of reaching the end, the acceleration converges to 0, and the motor enters the tuning stage. However, the following problems will exist:

[0042] (1) Under a high-speed, high-quality and relatively rigid load, due to the influence of system inertia and the center of gravity of the structure, the motor's arrival curve sometimes shows a situation of slow sine convergence oscillation. Therefore, without changing the structural parameters and the motion time, it is necessary to consider adding logic for suppressing residual vibration in the three-loop controller, such as input shaping; or in order not to affect the efficiency as much as possible, it is necessary to reduce the deceleration value and reduce the energy when the system decelerates and stops. Suppressing the oscillation using the controller usually has obvious effects, but the system model will be relatively complex, and there will also be a lag;

[0043] (2) Under a high-acceleration and high-quality load, the motor usually needs to bear extremely high peak torque during the starting stage, which requires relatively high requirements for the motor and the drive system. During the starting stage, due to the influence of non-linear resistances such as system friction, during the process of the motor starting from rest, the torque applied by the motor is usually much larger than that during the running process. In servo system control, due to the lag of loop control, there are high position errors and speed errors during the starting stage, which may trigger an error report from the driver; in occasions that require frequent starting and stopping, the excessive peak current during the starting stage often brings extremely high motor temperature rise.

[0044] Embodiment 1

[0045] In order to overcome the above problem (1), the first aspect of the embodiments of the present invention provides an optimization method for seven-segment sine S-curve planning, adding a curve planning for the arrival stage at the end of the travel, including a constant-speed section and a deceleration section in sequence, presetting time and distance parameters and inversely calculating the speed V 1 to enter the constant-speed section, and planning a seven-segment sine S-curve for the travel before the end with the final speed being V 1 to reduce the residual oscillation at arrival.

[0046] The constant-speed section and the deceleration section at the end also adopt a sine-type S-curve to ensure the continuity of acceleration and jerk.

[0047] The calculation formula is as follows: The total motion travel is X, the designed motion distance of the constant-speed section + deceleration section at the end is S, the total motion time is T, and the motion time of the constant-speed section is T 1, the speed V at the entry into the uniform speed section is calculated by back-calculating the moving distance 1 and the average deceleration α in the deceleration section 1 Value:

[0048] S = V 1 * T 1 + V 1 *(T - T 1 ) / 2

[0049]

[0050] α 1 = V 1 / (T - T 1 )

[0051] Through the terminal speed V 1 and the average deceleration α 1 The position, speed, acceleration and jerk curves of the terminal motor movement can be planned. Assuming that the time of uniform deceleration in the acceleration process accounts for β times of the total deceleration time, then the peak deceleration α of the motor in this stage m is: α m = 2 * α 1 / (β + 1).

[0052] The time T of the deceleration-acceleration section a , the time T of the uniform deceleration section b , and the time T of the deceleration-deceleration section c are respectively:

[0053] T a = (1 - β)) * (T - T 1 ) / 2

[0054] T b = β(T - T 1 )

[0055] T c = (1 - β) * ((T - T 1 ) / 2.

[0056] The real-time deceleration value α(t) of the motor is calculated by the above parameters as:

[0057] where t 1 = T 1 , t 2 = T 1 + T α , t 3 = T 1 + T α + T b , t 4 = T 1 + Tα +T b +T c ,T α 、T b 、T c are the motion times of the jerk increasing section, the uniform acceleration section, and the jerk decreasing section respectively, and w is the angular velocity constant (the same hereinafter).

[0058] Furthermore, the velocity curve V(t) can be obtained as follows:

[0059]

[0060] The remaining stroke S 1 = X - S, and the position curve can be directly implemented using S(t + 1) = S(t) + V(t) * dt. Note that this displacement is based on S 1 This part of the stroke is planned and implemented with a seven-segment sine S-shaped curve, with an initial velocity of 0 and a final velocity of V 1 . The total is eleven segments in total. 1 .

[0061] It should be noted that the existing technology adopted in the embodiments of the present invention - the seven-segment sine S-shaped curve planning scheme is based on Patent CN114879609A or Patent CN114740806A.

[0062] On the basis of the seven-segment sine S-shaped curve planning with an initial velocity of 0 and a non-zero final velocity, an end uniform motion section and a deceleration section are added to correct it into an eleven-segment sine S-shaped curve planning. The curve is as follows Figure 2 shown, effectively dealing with the problem of the motor system reaching the position stage and reducing the residual oscillation at the end.

[0063] Embodiment 2

[0064] To solve the above problem (2), the embodiments of the present invention provide an optimization method for seven-segment sine S-shaped curve planning. A curve planning for the starting stage is added to the starting end of the stroke, which successively includes an acceleration section and a uniform motion section. Preset time and distance parameters are used to calculate the velocity V 2 entering the uniform motion section in reverse, and the stroke after the starting end is planned with a seven-segment sine S-shaped curve with an initial velocity of V 2 to reduce the starting error.

[0065] The uniform motion section and the deceleration section in the starting stage also adopt a sine S-shaped curve to ensure the continuity of acceleration and jerk.

[0066] The calculation formula is as follows: The total motion stroke is X, and the designed motion distance of the acceleration section + uniform motion section in the starting stage is S 2 , the total motion time is T 2 , and the motion time of the uniform motion section is T 3, the speed V at the entry into the uniform motion stage is calculated by back-calculating the moving distance 2 and the average acceleration a in the acceleration stage 2 value: α 2 = V 2 / (T 2 - T 3 ).

[0067] Based on the speed V at the uniform motion stage 2 and the average acceleration a 2 during the startup stage, the position, speed, acceleration, and jerk curves of the end motor can be planned. Assume that the time of uniform acceleration during the acceleration process accounts for β 1 times the total acceleration time. Then the peak acceleration α m1 of the motor in this stage is: α m1 = 2 * α 2 / (β 1 + 1).

[0068] The time T d in the jerk-up stage, the time T e in the uniform deceleration stage, and the time T f in the deceleration-down stage are respectively:

[0069] T d = (1 - β 1 ) * (T 2 - T 3 ) / 2

[0070] T e = β 1 * (T 2 - T 3 )

[0071] T f = (1 - β 1 ) * (T 2 - ·T 3 ) / 2.

[0072] By calculating the above parameters, the real-time acceleration value a1(t) of the motor is:

[0073]

[0074] Furthermore, the speed curve V1(t) can be obtained as:

[0075]

[0076] where β 1 is the multiple of the time of uniform acceleration during the acceleration stage, 0 < β 1 < 1; t is the real-time time of the curve planning in the startup stage, t 5 = T3 , t 6 = T 3 + T d , t 7 = T 3 + T d + T e , t 8 = T 3 + T d + T e + T f , T d , T e , T f are the motion times of the jerk segment, the constant acceleration segment, and the deceleration segment respectively.

[0077] The remaining stroke S 3 = X - S 2 , the position curve can be directly implemented using S(t + 1) = S(t) + V(t) * dt, moving from the 0 position to the S 2 position. S 3 This part of the stroke is planned and implemented with a seven-segment sine S-shaped curve, with an initial velocity of V 2 , and a final velocity of 0. A total of eleven segments.

[0078] Based on the seven-segment sine S-shaped curve planning with an initial velocity not equal to 0 and a final velocity of 0, an acceleration segment and a constant velocity segment are added to correct it into an eleven-segment sine S-shaped curve planning. The curve is as Figure 3 shown, effectively dealing with the start-up stage problem and reducing the peak torque of the motor.

[0079] Embodiment 3

[0080] To solve the above problems (1) and (2) simultaneously, an embodiment of the present invention provides a fifteen-segment sine S-shaped curve planning method, including the following steps:

[0081] The front end and the end of the stroke are respectively divided into a start-up stage and an in-place stage. The start-up stage includes a jerk segment, a constant acceleration segment, a deceleration segment, and a constant velocity segment. The in-place stage includes a constant velocity segment, a jerk segment, a constant acceleration segment, and a deceleration segment. The middle segment is divided into a seven-segment sine S-shaped curve planning stage;

[0082] The preset time and distance parameters are respectively inversely calculated to obtain the velocity V 2 entering the constant velocity segment of the start-up stage and the velocity V 1 entering the constant velocity segment of the in-place stage. The middle segment is planned with a seven-segment sine S-shaped curve with an initial velocity of V 2 and a final velocity of V 1 .

[0083] Based on the same inventive concept, the curve planning at the front end of the stroke in the embodiments of the present invention is the same as the solution in Embodiment 2, and the curve planning at the end of the stroke in the embodiments of the present invention is the same as the solution in Embodiment 1. On the basis of the seven-segment sinusoidal S-shaped curve planning with non-zero initial velocity and non-zero final velocity, an acceleration section, a constant velocity section, and a deceleration section are added and corrected into a fifteen-segment sinusoidal S-shaped curve planning, combined with the curve planning as shown in Figure 2 and the curve planning as shown in Figure 3 . The curve is as shown in Figure 4 , which effectively solves the problems in the starting stage, reduces the peak torque of the motor, adds a constant velocity section and a deceleration section at the end, solves the problems in the in-place stage of the motor system, and reduces the in-place residual oscillation.

[0084] Test example:

[0085] Testing is carried out based on the method of Embodiment 3.

[0086] Using the conventional seven-segment curve planning, under a certain speed, acceleration, and load, the speed error and position error curves of the motor during a 300-mm movement stroke are as shown in Figure 5 , and the in-place curve is as shown in Figure 6 .

[0087] As a comparison, testing is carried out using the solution of Embodiment 3 of the present invention. Under a certain speed, acceleration, and load, the position error and speed error curves of the motor during a 300-mm movement stroke are as shown in Figure 7 .

[0088] It can be seen that after adding the fifteen-segment type, with the same controller and under the full stroke, the maximum position error of the movement is reduced from 85 μm to 45 μm, and the maximum speed error is reduced from 18 mm / s to 11 mm / s, with a significant effect; in comparison of the in-place curves, the fifteen-segment type is more in line with the theoretical position curve than the seven-segment type, and the in-place performance is better.

[0089] Based on the same inventive concept, another embodiment of the present invention provides a machine-readable storage medium, on which instructions are stored. These instructions are used to cause a machine to execute the segmented sinusoidal S-shaped curve planning optimization method as in Embodiment 1, and / or to cause a machine to execute the segmented sinusoidal S-shaped curve planning optimization method as in Embodiment 2, and / or to cause a machine to execute the fifteen-segment sinusoidal S-shaped curve planning method as in Embodiment 3.

[0090] In summary, based on the seven-segment sine S-shaped curve planning, the technical solution of the present invention optimizes the existing curve planning logic, adds the curve planning in the motor starting stage, and addresses the problem that the motor and the driver are prone to error reporting under extremely high peak torque in the starting stage of driving a small motor with a high-quality load, effectively reducing the torque required in the motor starting stage and ensuring the operating efficiency as much as possible at high speeds and accelerations; and, adds the curve planning in the motor in-place stage, and addresses the problem that residual oscillations are likely to occur and the convergence speed is slow when a high-speed and high-quality load reaches the in-place position, effectively reducing the residual oscillations when the motor decelerates and stops, cutting the energy of the structural system through the end buffer method to improve the motor in-place accuracy, reducing the in-place residual oscillation time, and improving the production efficiency and in-place accuracy; it is achieved that there is no need to directly add the corresponding logic in the three-loop controller, the curve planning logic is simple to implement, and the parameters can also be adjusted arbitrarily.

[0091] The preferred embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited thereto. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solution of the present invention, including various specific technical features combined in any suitable manner. To avoid unnecessary repetition, the present invention will not separately describe various possible combination methods. However, these simple modifications and combinations should also be regarded as the content disclosed by the present invention and fall within the protection scope of the present invention.

Claims

1. A seven-segment sinusoidal S-curve planning optimization method, characterized in that: At the end of the stroke, a curve planning for the arrival stage is added, which includes a uniform speed section and a deceleration section in sequence, presets time and distance parameters, and reversely calculates the speed of entering the uniform speed section V 1 The distance before the end is the final speed. V 1 A seven-segment sinusoidal S-curve is planned to reduce the residual oscillation in place; the deceleration section is divided into an acceleration section, a uniform acceleration section and a deceleration section in sequence, and the acceleration α(t) curve in the in-place stage is planned as follows: Among them, α m =2*α1 / (β+1), α1= V 1 / ( TT 1 ), β is the multiple of the uniform acceleration period to the deceleration period, 0<β<1; w is the angular velocity constant, t is the real-time time of the curve planning of the arrival stage, t1=T1, t2=T1+T α , t3=T1+T α +T b , t4=T1+T α +T b +T c , T α , T b , T c They are the motion time of the acceleration segment, uniform acceleration segment and deceleration segment respectively.

2. The method according to claim 1, characterized in that The preset time and distance parameters are used to reversely calculate the speed of entering the uniform speed section V 1 Specifically: The preset end distance is S , the total end motion time is T, the uniform speed segment motion time is T1, calculate the speed V 1 The formula is as follows: .

3. The method according to claim 2, characterized in that The speed at the arrival stage V ( t ) The curve planning is: 。 4. A seven-segment sinusoidal S-curve planning optimization method, characterized in that: The starting stage curve planning is added at the starting end of the trip, including the acceleration section and the uniform speed section in sequence, presetting the time and distance parameters and inversely calculating the speed of entering the uniform speed section V 2 , the stroke behind the starting end is based on the initial speed V 2 A seven-segment sinusoidal S-curve is planned to reduce the startup error; the acceleration segment is divided into a jerk segment, a uniform acceleration segment, and a deceleration segment in sequence, and the acceleration α1(t) curve of the startup phase is planned as follows: Among them, α m1 =2*α2 / (β1+1), α2= V 2 / ( T 2 -T 3 ), β1 is the multiple of the uniform acceleration period to the acceleration period, 0<β1<1; w is the angular velocity constant, t is the real time of the curve planning in the startup phase, t5=T3, t6=T3+T d , t7=T3+T d +T e , t8=T3+T d +T e +T f , T d , T e , T f They are the motion time of the acceleration segment, uniform acceleration segment and deceleration segment respectively.

5. The method according to claim 4, characterized in that The preset time and distance parameters are used to reversely calculate the speed of entering the uniform speed section V 2 Specifically: The preset starting end distance is S 2 , the total motion time of the starting end is T2, the motion time of the uniform speed section is T3, and the calculated speed V 2 The formula is as follows: 。 6. The method according to claim 5, characterized in that The startup phase speed V1 ( t ) The curve planning is: .

7. A 15-segment sinusoidal S-curve planning method, characterized in that: The following steps are involved: The front end and the end of the stroke are divided into the starting stage and the arrival stage respectively. The starting stage includes the acceleration section, the uniform acceleration section, the deceleration section and the uniform speed section. The arrival stage includes the uniform speed section, the acceleration section, the uniform acceleration section and the deceleration section. The middle section is divided into a seven-segment sinusoidal S-curve planning stage. The preset time and distance parameters are used to calculate the speed of the uniform speed section in the startup phase. V 2 and the speed of the uniform speed section in the arrival phase V 1 The middle section takes the initial speed as V 2 The final speed is V 1 Conduct seven-segment sinusoidal S-curve planning. The acceleration α(t) curve of the arrival stage is planned as follows: Among them, α m =2*α1 / (β+1), α1= V 1 / ( TT 1 ), β is the multiple of the uniform acceleration period to the deceleration period, 0<β<1; w is the angular velocity constant, t is the real-time time of the curve planning of the arrival stage, t1=T1, t2=T1+T α , t3=T1+T α +T b , t4=T1+T α +T b +T c , T α , T b , T c are the motion time of the acceleration segment, uniform acceleration segment and deceleration segment respectively; The acceleration α1(t) curve of the startup phase is planned as: Among them, α m1 =2*α2 / (β1+1), α2= V 2 / ( T 2 -T 3 ), β1 is the multiple of the uniform acceleration period to the acceleration period, 0<β1<1; w is the angular velocity constant, t is the real time of the curve planning in the startup phase, t5=T3, t6=T3+T d , t7=T3+T d +T e , t8=T3+T d +T e +T f , T d , T e , T f They are the motion time of the acceleration segment, uniform acceleration segment and deceleration segment respectively.

8. The method according to claim 7, characterized in that The speed at the arrival stage V ( t ) The curve planning is: 。 9. The method according to claim 7, characterized in that: The startup phase speed V1 ( t ) The curve planning is: 。 10. A machine-readable storage medium having instructions stored thereon, the instructions being used to cause a machine to execute a method as described in any one of claims 1 to 3, and / or to cause a machine to execute a method as described in any one of claims 4 to 6, and / or to cause a machine to execute a method as described in any one of claims 7 to 9.

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