Method for re-optimizing S-shaped speed curve

Abstract

The present invention relates to the field of automated detection technology, and specifically to a method for re-optimizing an S-shaped speed curve, caching and marking motion parameter limit control values ​​for an S-shaped speed curve that meets conditions; reversely searching for a mark position of the motion parameter, finding the last variable that has been reached and tentatively optimizing it: initializing and replacing the limit control value of the current variable, and re-planning the S-shaped speed curve; using the re-planned S-shaped speed curve and the corresponding motion parameter limit control constraints as a reference, proofreading and testing all motion parameter limit control values ​​in the curve, if an S-shaped speed curve that meets conditions can be obtained, the testing ends; otherwise, looping and testing all motion parameters until a more time-optimal S-shaped speed curve is obtained. The present application can re-optimize a multi-segment merged S-shaped speed curve, obtain a more time-optimal speed plan, improve processing efficiency, shorten processing time, and can be achieved without the user having to adjust any parameters.

Description

Technical Field

[0001] The invention relates to the field of automatic recognition technology, and in particular to a method for re-optimizing an S-shaped speed curve. Background Art

[0002] The non-smooth acceleration and deceleration in the feed motion is an important cause of the impact and vibration of the machine tool. The S-curve acceleration and deceleration algorithm currently used in high-end CNC systems has a continuous change curve of speed and acceleration, which is a popular speed control algorithm in current CNC machining.

[0003] However, the traditional S-curve acceleration and deceleration control algorithm has the following disadvantages: the acceleration curve basically changes continuously, but the jerk curve changes in steps. The jerk has sudden changes at its starting and end points and at the turning points of positive and negative values. The acceleration is not smooth at each turning point and there are inflection points, which cause impact and vibration of the CNC machine tool, thereby affecting the processing quality.

[0004] The invention patent with patent number CN114035513B provides a forward planning method and device for an S-shaped velocity curve, a storage medium and a computing device, and discloses that when multiple tool paths need to be merged for planning, the acceleration / jerk / jerk of the merged motion constraints generally needs to meet the requirements of not being greater than the corresponding limitations of all segments and the corresponding limitations at each connection point, that is, the minimum value of the corresponding limitations. This ensures that the acceleration / jerk / jerk of the merged S-shaped velocity curve all meet the motion constraints of each segment and the connection between segments.

[0005] However, the current control algorithm for merging and planning S-shaped curves cannot estimate the specific segments of the merged S-shaped velocity curve in which each motion segment is located. Therefore, it can only determine the control limits of the synthesized motion parameters (speed, acceleration, jerk, and jerk) based on the minimum values ​​of the corresponding motion segments. As a result, the planned velocity curve is relatively conservative and the resulting processing time is relatively long, which is not conducive to improving efficiency.

[0006] Based on the problems in the prior art, the present invention provides a method for re-optimizing an S-shaped speed curve. Summary of the invention

[0007] The purpose of the present invention is to provide a method for re-optimizing an S-shaped speed curve so as to solve the technical problem that the algorithm for S-shaped curve planning in the prior art determines the limit control value of the synthesized motion parameter corresponding to the minimum value on each motion segment, resulting in a conservative planned speed curve and a long processing time.

[0008] The technical solution of the present invention is: a method for re-optimizing an S-shaped speed curve, comprising:

[0009] S1. For the planned S-shaped speed curves that are merged into multiple segments, the speed curve is cached and the motion parameters are saved, and the limit control values ​​of the motion parameters are marked, wherein the motion parameters that reach the limit control value are marked as 1, and those that do not reach the limit control value are marked as 0;

[0010] S2, reversely search the flag bit in the motion parameter limit control variable to find out whether the variable that has reached the limit control value exists. If not, it indicates that the optimization is over; if so, execute the next step S3, and reset the flag bit corresponding to the variable to 0 to prevent repeated search;

[0011] S3. According to the trial order, the variable that reaches the limit control value is tested, and the current variable is set as the target variable. After the target variable is successfully tested, a new limit control value is replaced for the target variable, and the start and end speeds are kept unchanged, and the S-shaped speed curve is re-planned;

[0012] S4, applying the segmentation of the S-shaped velocity curve in the trial stage to each motion segment of the merged segment, and calculating the maximum motion parameter limit control value in each motion segment, and the motion parameter limit control value at the motion segment connection point;

[0013] S5. If the control limit value of the target variable is higher than the original control limit value on a certain motion segment, or higher than the original control limit value at a certain motion segment connection point, then obtain the original control limit values ​​of the corresponding variables at all the exceeded limits, and replace the control limit value of the target variable with the minimum value of each original control limit value at the exceeded limit, then return to step S3 to perform trial optimization again;

[0014] S6. If the control limit values ​​of the target variable are not higher than the original control limit values ​​on all motion segments and the original control limit values ​​at the connection points of all motion segments, then check in turn whether the control limit values ​​of other motion parameters are also not higher than the original control limit values ​​on all motion segments and the original control limit values ​​at the connection points of all motion segments; if not, this trial optimization fails and returns to step S2; if yes, the trial optimization is successful and a more time-optimal S-shaped velocity curve is obtained.

[0015] Preferably, the specific process of testing the target variable in step S3 is:

[0016] Initialize the original cached S-shaped speed curve to obtain the initialization limit control value of the target variable;

[0017] Determine the relationship between the initialization limit control value and the current limit control value of the target variable;

[0018] If the initialization limit control value is greater than the current limit control value of the target variable, it indicates that the trial is successful, and the current limit control value of the target variable is replaced with the initialization limit control value, and step S3 is executed; if the initialization limit control value is equal to the current limit control value of the target variable, it indicates that there is no room for optimization, then return to step S2, switch the next motion parameter variable to become the target variable, and try again.

[0019] Preferably, the initialization limit control value is determined only by the limit control of the local corresponding motion segment that reaches the limit control in the current S-shaped velocity curve, rather than taking the corresponding minimum value of all motion segments participating in the merger; for the same motion parameter variable, when multiple motion segments reach the limit control value, the minimum value of all limit control values ​​is selected as the initialization limit control value of the same motion parameter variable, and the selected initialization limit control value is not less than the current limit control value.

[0020] Preferably, before executing step S1, the operations performed include:

[0021] First, determine whether the current S-shaped speed curve has been optimized. If so, exit;

[0022] Otherwise, it is determined whether the current S-shaped velocity curve is obtained by combining several motion segments. If not, the process is exited; if yes, the process executes step S1.

[0023] Preferably, the motion parameters include velocity v, acceleration a, jerk j, and jerk s;

[0024] The contents of the data cache include the shape of the S-shaped velocity curve, the velocity v, acceleration a, jerk j, jerk s of the corresponding node on the S-shaped velocity curve, and the planning time t required to complete the given fixed trajectory according to the S-shaped velocity curve;

[0025] The motion parameter control constraints meet the following conditions: , , , .

[0026] Preferably, in step S4, the condition for applying the segmentation of the S-shaped speed curve in the trial phase to each motion segment of the merged segment is that the planning time of the re-planned S-shaped speed curve in the trial phase is not less than the planning time cached in step S1, otherwise, return to step S2, if yes, it is deemed that the condition is met and execute step S4.

[0027] Preferably, in step S2, the operation of reversely searching the flag bit in the motion parameter to find whether the variable reaching the limit control value exists determines the order of executing the tentative optimization operation on the target variable;

[0028] If the optimization is tried in the order of which of the four variables, velocity, acceleration, jerk and acceleration, reaches the control limit value first, then in step S1, for the variable currently being judged, the variable that reaches the control limit value is marked as 1, and the variable that does not reach the control limit value is marked as 0.

[0029] Preferably, after obtaining the optimized S-shaped speed curve, it is used as the current S-shaped speed curve, and steps S1-S6 are re-executed to perform verification and re-optimization until it cannot be optimized any further.

[0030] Preferably, after all the trials are completed, the finally obtained S-shaped velocity curve that meets the constraints and the corresponding motion parameter data are saved, which is the optimized velocity curve; and the merged segment in the S-shaped velocity curve is marked as having been re-optimized to prevent the process from being repeated during peripheral iterations; if the segment structure of the S-shaped velocity curve changes or the start and end speeds change during the peripheral iteration process, the mark automatically becomes invalid, and steps S1-S6 still need to be re-executed for re-optimization.

[0031] Compared with the prior art, the advantages of the present invention are:

[0032] (1) The present invention iteratively optimizes the S-shaped curve of the merger of multiple motion segments: the variables that reach the limit control value in the motion parameter limit control value (VAJS) are marked, and the variables that reach the limit control value are tentatively optimized in sequence. The limit control value used for the tentative optimization is determined by the motion segment in the current S-shaped velocity curve where the target variable touches the limit control value, rather than taking the corresponding minimum value of all the motion segments involved in the merger. In this way, the limit control value used for the tentative optimization of the present invention is equivalent to a subset of the corresponding minimum values ​​of all the motion segments involved in the merger in the prior art. Therefore, a larger limit control value can be obtained for trial, thereby improving processing efficiency.

[0033] Moreover, since the motion limit control amount of the local motion segment among all motion segments is used as the benchmark for optimization and adjustment, it can be used as an "anchor point" to estimate the correspondence of each motion segment on the S-shaped speed curve before and after the merging. The optimization trend of the S-shaped speed curve is clearer, and the selectable optimization limit control value is higher, which helps to reduce the number of iterations and shorten the processing time.

[0034] (2) Through the algorithm provided by the present invention, the S-shaped speed curve of the combined multi-segment motion is re-optimized, and a high-order 15-segment S-shaped speed curve planning can be achieved. During the trial optimization process, the speed, acceleration, and jerk are kept continuously controllable, and the jerk is controllable. A speed planning with better time optimization is obtained, which can improve the processing efficiency and shorten the processing time. This can be achieved without the user having to adjust any parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0036] Figure 1 The figure is a flow chart of the method for re-optimizing the S-shaped speed curve according to the present invention. DETAILED DESCRIPTION

[0037] The present invention is further described in detail below in conjunction with specific embodiments:

[0038] In the prior art, the machining tool path of a machine tool is optimized and controlled by an S-curve acceleration and deceleration speed control algorithm.

[0039] Usually, an S-shaped velocity curve refers to a curve whose velocity at the starting and ending points is a corresponding known value, and the acceleration and jerk are required to be 0. If a motion can be accelerated or decelerated from the starting speed to the end speed, and the maximum speed, maximum acceleration and jerk of the whole process meet the motion limit parameters, then the segment is called S-shaped planning; otherwise, the segment is called non-S-shaped planning. For the latter, the higher endpoint speed needs to be lowered to convert it from non-S-shaped planning to S-shaped planning; or it can be merged with the adjacent segment motion and then try S-shaped planning.

[0040] Generally, a complete S-shaped acceleration / deceleration curve includes seven velocity curve segments, namely, acceleration segment, uniform acceleration segment, deceleration segment, uniform velocity segment, acceleration / deceleration segment, uniform deceleration segment and deceleration / deceleration segment. If the jerk is to be continuous and the snap is controllable, a higher-order 15-segment S-shaped velocity curve is required.

[0041] However, before planning the 7-segment S-shaped speed curve, it is impossible to estimate which specific segments of the combined S-shaped speed curve each motion segment is in, so the combined motion parameter (speed, acceleration, jerk) limit control value can only be agreed upon based on the minimum value of each motion segment, resulting in a conservative planned speed curve and a long processing time, which is not conducive to improving efficiency. In the process of optimizing the global 15-segment or even more S-shaped speed curve, higher-order jerk acceleration needs to be considered, and there are fewer optimization solutions.

[0042] The present application discloses a method for re-optimizing an S-shaped speed curve, and the applicable conditions are:

[0043] The global 15-segment S-shaped speed curve requires that the speed, acceleration, and jerk throughout the entire process are both continuous and controlled. The jerk does not require to be continuous, but the absolute value must be controlled.

[0044] The tool path controlled by the optimization method satisfies:

[0045] Input: Several continuous tool paths can be combined to plan an S-shaped velocity curve (with 0 acceleration at the start and end). The trajectory of each tool path is fixed, the maximum VAJS limit is known, and the maximum VAJS limit of the connection point between segments has been calculated.

[0046] Output: Keep the start and end speeds unchanged, search for an S-shaped speed curve with better time, and ensure that VAJS on each participating tool path and related connection points does not exceed the specified limit value.

[0047] The method process is summarized as follows:

[0048] Determine whether the corresponding variable in the motion parameter is reached on the current S-shaped velocity curve, and set the mark bit 0 or 1 to avoid repeated trial of the same motion parameter variable; for the variable that reaches the motion parameter limit control value on the S-shaped velocity curve, reverse search the mark bit to find the variable that has reached the limit control value and perform a motion parameter limit control trial optimization operation on it; after trial optimization of each variable of the motion parameter corresponding to the S-shaped velocity curve, if the motion constraints are still met and an optimized S-shaped velocity curve is obtained, it indicates that the optimization is completed.

[0049] First of all, it should be noted that the motion parameters involved in this application include the velocity v, acceleration a, jerk j, jerk s of the corresponding nodes on the S-shaped velocity curve, and the planning time t required to achieve the jerk s.

[0050] The motion parameter control constraints meet the following conditions: , , , .

[0051] For the convenience of description, in some contents, the motion parameters: velocity v, acceleration a, jerk j, and jerk s are simply referred to as “VAJS”.

[0052] Detailed, such as Figure 1 As shown, the present application provides a method for re-optimizing an S-shaped speed curve, which is applicable to re-optimizing a planned S-shaped speed curve of multiple segments, and the S-shaped speed curve of a single segment motion is already optimal. The method includes the following steps:

[0053] Step 1: Determine whether the current S-shaped speed curve has been optimized. If yes, exit; otherwise, proceed to the next step.

[0054] Step 2: Determine whether the current S-shaped speed curve is a combination of multiple motions. If not, it indicates that the curve is already the most optimized S-shaped speed curve, then exit; otherwise, proceed to the next step.

[0055] Step 3: Cache the S-shaped speed curve that meets the execution conditions of step 2; and mark the limit control for the motion parameters on the S-shaped speed curve.

[0056] And determine whether the variable corresponding to the motion parameter (abbreviated as "VAJS") is reached on the curve. The variable that is reached is marked as 1, otherwise it is marked as 0.

[0057] This application only adjusts the variables that have reached the control limit value in order to obtain a curve with a better time. This is because if the control limit value on the generated S-shaped speed curve does not reach the control limit value, no further trial will be made, because no matter how much the limit value is increased, the shape of the newly generated S-shaped speed curve cannot be changed, that is, a better time result cannot be obtained. However, if the value of the amount that has reached the control limit value is tested to see if it can be increased, there is a chance to obtain an S-shaped speed curve with a better time.

[0058] Step 4: In the VAJS limit control variable, reversely search the mark bit to find the last variable that has been reached. If it does not exist, it indicates that the trial is completed, and go to step 10; otherwise, reset the mark bit corresponding to this variable to 0 to prevent subsequent repeated trials, and execute the next step.

[0059] Among them, the operation of reversely searching the flag bit in the motion parameter to find out whether the variable that reaches the limit control value exists determines the order in which the target variable performs the trial optimization operation.

[0060] The motion parameters include: velocity v, acceleration a, jerk j, jerk s, and the planning time t required to achieve the jerk s.

[0061] In one embodiment and other embodiments, the variables that reach the control limit among the four variables of "VAJS" are optimized in reverse order of "VAJS". Then, in step 3, for the currently determined variable, the variable that reaches the control limit is marked as 1, and the variable that does not reach the control limit is marked as 0. The above steps 2-10 are performed for the variable marked as 1.

[0062] In another or other embodiments, if the planning time t corresponding to the motion segment is sorted from large to small, and the time taken for "VAJS" to reach the peak on the speed curve is sorted from large to small, the corresponding control limit is sequentially executed according to the sorting steps 2-10 to perform trial optimization. Then, in step 3, for the currently judged variable, the planning time corresponding to the limit value remains unchanged, and the planning time mark corresponding to the control limit variable that has not reached the limit value or has been tried is set to 0, and the mark position of the control limit variable after the trial is recorded in an array. When all the elements in the array are 0, it indicates that the trial is over.

[0063] Step 5: Try to use a larger value for the control limit variable. Initialization control limit value: It is determined only by the sub-motion segment that touches the control limit in the current S-shaped velocity curve, rather than taking the corresponding minimum value of all motion segments involved in the merger. That is to say, for the same motion parameter variable, when multiple motion segments reach the control limit value, take the minimum value of the original control limit values ​​of all motion segments as the initialization control limit value of the variable, so that the new control limit value obtained is not less than the current control limit value. If it is equal, that is, there is no optimization space, go to step 4 and switch to the next variable that reaches the control limit value for optimization trial; otherwise, go to the next step.

[0064] Step 6: After replacing with the new limit control, keep the start and end speeds unchanged and re-plan the S-shaped speed curve. If the planned time is not less than the planned time saved in step 3, go to step 4; otherwise, go to the next step.

[0065] Step 7: The new S-shaped velocity curve is divided and applied to each motion segment therein, and the maximum motion parameter in each motion segment and the motion parameters at the connection points between the motion segments are calculated.

[0066] Step 8: First check whether the limit control value is higher than the original limit control value on each segment and the original limit control value at each connection point. If there is an excess, take the minimum value of the original limit control value at each excess point, replace the trial limit control value with this value, and go to step 6.

[0067] Step 9: Check whether other control limits are higher than the corresponding control limits in each segment and at the connection point. If not, it means that a more optimal S-shaped speed curve is obtained, and go to step 3; if so, this trial fails, and go to step 4 to try the next control limit variable.

[0068] Step 10: After all the trials are completed, the speed curve saved in step 3 is restored, which is the optimized speed curve, and the merged segment is marked as having been re-optimized to prevent the process from being repeated during peripheral iterations.

[0069] When the S-shaped speed curve, the structure within the segment changes, or the starting and ending speeds change, the mark will automatically become invalid; when the mark is read as valid, it can return quickly.

[0070] The method steps provided above are explained using the "global 15-segment S-shaped speed curve" as an example, and are also applicable to higher-order or lower-order S-shaped speed curves. For example, the lower-order "global 7-segment S-shaped speed curve" only contains VAJ limit control, and the principle is similar to the above algorithm, except that the trial variable lacks the "jerk acceleration".

[0071] The S-shaped curve planning process refers to the invention patent with patent number CN112650145B, which provides an S-shaped speed curve adaptive merging evaluation method and discloses an S-shaped curve planning method, including:

[0072] If the current S-shaped speed curve cannot be S-shaped planned (that is, the trajectory length is not enough to achieve the change of the S-shaped speed curve), then under the condition of "the processing time evaluation value is less than the sum of the two time evaluation values ​​before the merger", the adjacent S-shaped speed curves are continuously merged to transform the non-S-shaped plan into the S-shaped plan.

[0073] The present application provides a method for re-optimizing the S-shaped speed curve, which can re-optimize the S-shaped speed curve of multiple motion segments to obtain a more time-optimized speed planning, improve processing efficiency, shorten processing time, and can be achieved without the user having to adjust any parameters. In addition, the present invention realizes the global 15-segment S-shaped speed curve planning, which can achieve a speed curve with continuously controllable speed, acceleration, and jerk, and controllable jerk.

[0074] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with this technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the scope of protection of the present invention. For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is limited by the attached claims rather than the above description, and it is intended to include all changes within the meaning and scope of the equivalent elements of the claims in the present invention.

Claims

1. A method for re-optimizing an S-shaped speed curve, characterized in that: include: S1. For the planned S-shaped speed curves merged in multiple sections, the speed curve is cached and the motion parameters are saved, and the limit control values ​​of the motion parameters are marked, wherein the motion parameters reaching the limit control value are marked as 1, and those not reaching the limit control value are marked as 0; S2, reversely search the flag bit in the motion parameter limit control variable to find out whether the variable that has reached the limit control value exists. If not, it indicates that the optimization is over; if so, execute the next step S3, and reset the flag bit corresponding to the variable to 0 to prevent repeated search; S3. According to the trial order, the variable that reaches the limit control value is tested, and the current variable is set as the target variable. After the target variable is successfully tested, a new limit control value is replaced for the target variable, and the start and end speeds are kept unchanged, and the S-shaped speed curve is re-planned; S4, applying the segmentation of the S-shaped velocity curve in the trial stage to each motion segment of the merged segment, and calculating the maximum motion parameter limit control value in each motion segment, and the motion parameter limit control value at the motion segment connection point; S5. If the control limit value of the target variable is higher than the original control limit value on a certain motion segment, or higher than the original control limit value at a certain motion segment connection point, then obtain the original control limit values ​​of the corresponding variables at all the exceeded limits, and replace the control limit value of the target variable with the minimum value of the original control limit values ​​at the exceeded limits, and return to step S3 to perform trial optimization again; S6. If the control limit values ​​of the target variable are not higher than the original control limit values ​​on all motion segments and the original control limit values ​​at the connection points of all motion segments, then check in turn whether the control limit values ​​of other motion parameters are also not higher than the original control limit values ​​on all motion segments and the original control limit values ​​at the connection points of all motion segments; if not, this trial optimization fails and returns to step S2; if yes, the trial optimization is successful and a more time-optimal S-shaped velocity curve is obtained.

2. The method for re-optimizing an S-shaped speed curve according to claim 1, characterized in that: The specific process of testing the target variable in step S3 is as follows: Initialize the original cached S-shaped speed curve to obtain the initialization limit control value of the target variable; Determine the relationship between the initialization limit control value and the current limit control value of the target variable; If the initialization limit control value is greater than the current limit control value of the target variable, it indicates that the trial is successful, and the current limit control value of the target variable is replaced with the initialization limit control value, and step S3 is executed; if the initialization limit control value is equal to the current limit control value of the target variable, it indicates that there is no room for optimization, then return to step S2, switch the next motion parameter variable to become the target variable, and try again.

3. The method for re-optimizing an S-shaped speed curve according to claim 2, characterized in that: The initialization limit control value is determined only by the limit control value of the local corresponding motion segment that reaches the limit control in the current S-shaped velocity curve, rather than taking the corresponding minimum value of all motion segments participating in the merger; for the same motion parameter variable, when multiple motion segments reach the limit control value, the minimum value of all limit control values ​​is selected as the initialization limit control value of the same motion parameter variable, and the selected initialization limit control value is not less than the current limit control value.

4. The method for re-optimizing an S-shaped speed curve according to claim 1, characterized in that: Before executing step S1, the operations performed include: First, determine whether the current S-shaped speed curve has been optimized. If so, exit; Otherwise, it is determined whether the current S-shaped velocity curve is obtained by combining several motion segments. If not, the process is exited; if yes, the process executes step S1.

5. The method for re-optimizing an S-shaped speed curve according to claim 2, characterized in that: The motion parameters include velocity v, acceleration a, jerk j, and jerk s; The contents of the data cache include the shape of the S-shaped velocity curve, the velocity v, acceleration a, jerk j, jerk s of the corresponding node on the S-shaped velocity curve, and the planning time t required to complete the given fixed trajectory according to the S-shaped velocity curve; The motion parameter control constraints meet the following conditions: , , , .

6. The method for re-optimizing an S-shaped speed curve according to claim 1, characterized in that: In the step S4, the condition for applying the segmentation of the S-shaped speed curve in the trial phase to each motion segment of the merged segment is that the planning time of the re-planned S-shaped speed curve in the trial phase is not less than the planning time cached in step S1, otherwise, return to step S2, if yes, it is deemed that the condition is met and execute the step S4.

7. The method for re-optimizing an S-shaped speed curve according to claim 2, characterized in that: In step S2, the operation of searching the flag bit in the motion parameter in reverse order to find whether the variable reaching the limit control value exists determines the order of executing the tentative optimization operation on the target variable; If the optimization is tried in the order of which of the four variables, velocity, acceleration, jerk and acceleration, reaches the control limit value first, then in step S1, for the variable currently being judged, the variable that reaches the control limit value is marked as 1, and the variable that does not reach the control limit value is marked as 0.

8. The method for re-optimizing an S-shaped speed curve according to claim 2, characterized in that: After the optimized S-shaped speed curve is obtained, it is used as the current S-shaped speed curve, and steps S1-S6 are re-executed to perform verification and re-optimization until it cannot be optimized any further.

9. The method for re-optimizing an S-shaped speed curve according to claim 2, characterized in that: After all the trials are completed, the final S-shaped velocity curve that meets the constraints and the corresponding motion parameter data are saved, which is the optimized velocity curve; and the merged segment in the S-shaped velocity curve is marked as having been re-optimized to prevent the process from being repeated during the peripheral iteration; if the segment structure of the S-shaped velocity curve changes or the start and end speeds change during the peripheral iteration process, the mark will automatically become invalid and steps S1-S6 need to be re-executed for re-optimization.

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