Method and device for processing displacement instruction with non-zero end point speed based on dynamic programming, processor and storage medium thereof

Abstract

The invention relates to a method for processing a displacement instruction with non-zero end point speed based on dynamic programming. The method comprises the following steps: judging whether two target speeds can form a target speed range or not; judging an inclusion relation among the starting point speed, the terminal point speed and the target speed range; determining a speed change direction; calculating the displacement Sse required for changing from the displacement starting point to the displacement ending point at the maximum jerk; judging the direction of the target speed used during movement; the whole-course displacement Ssvve is calculated; judging a speed change mode during movement; calculating a moving axis control parameter of each time period; and calculating the coordinates of all the moving axes in each time period. By the adoption of the method and device for processing the displacement instruction with the non-zero end point speed based on dynamic planning, the processor and the computer readable storage medium, fastest processing during turning interpolation is achieved, control is flexible, precision is high, processing is easy, the adaptability to changes of input parameters and instruction parameters is high, and the practical value is very high.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of numerical control machine tools, in particular to the field of interpolation, and more particularly to a method, device, processor and computer readable storage medium for processing displacement instructions with non-zero end point speed based on dynamic programming. BACKGROUND

[0002] The core of a numerical control machine tool is numerical control software, and the core of the numerical control software is interpolation, which determines the precision, smoothness and processing efficiency of a part processed by the numerical control machine tool. Single straight line interpolation, as a basis for interpolation technology, is of great importance. In the straight line interpolation algorithm, there are many restrictions on displacement instructions, and it is generally specified that the start point speed and the end point speed should be equal to zero, resulting in redundancy in processing time in some cases. It is desirable to find a proper algorithm to process displacement instructions with non-zero end point speed, so as to achieve faster processing speed and more flexible interpolation control. SUMMARY

[0003] The present application overcomes the shortcomings of the prior art and provides a method, device, processor and computer readable storage medium for processing displacement instructions with non-zero end point speed based on dynamic programming, which satisfies flexible control, small error and a wide range of applications.

[0004] To achieve the above-mentioned purpose, the method, device, processor and computer readable storage medium for processing displacement instructions with non-zero end point speed based on dynamic programming are as follows:

[0005] The method for processing displacement instructions with non-zero end point speed based on dynamic programming mainly comprises the following steps:

[0006] (1) comparing the set positive target speed with the negative target speed, if the positive target speed is greater than the negative target speed, it is considered that the two target speeds can form a target speed range; if the positive target speed is less than the negative target speed, it is considered that the two target speeds cannot form a target speed range, and the step is ended;

[0007] (2) comparing the start point speed Vs and the end point speed Ve of the set movement instruction with the target speed range, judging the inclusion relationship of the start point speed, the end point speed and the target speed range, if the end point speed simultaneously satisfies being less than the positive target speed Vu and being greater than the negative target speed Vd, the start point speed is compared with Vu and the negative target speed Vd to obtain the size relationship of the displacement start point speed Vs, the displacement end point speed Ve, the positive target speed Vu and the negative target speed Vd; otherwise, the step is ended;

[0008] (3) According to the inclusion relation of the start speed, the end speed and the target speed range, the speed change direction is determined;

[0009] (4) The displacement Sse required from the displacement start point to the displacement end point with the maximum jerk is calculated;

[0010] (5) The given displacement S is compared with Sse, if S is greater than Sse, it is considered that the positive direction target speed Vu is used in the movement; otherwise, it is considered that the negative direction target speed Vd is used in the movement;

[0011] (6) The total displacement Ssvve required from the start speed to the target speed Vu or Vd with the maximum jerk and then to the end speed with the maximum jerk is calculated;

[0012] (7) The given displacement S is compared with Ssvve, if S is greater than Ssvve, there is a speed constant change stage in the movement; otherwise, there is no speed constant change stage in the movement;

[0013] (8) According to the displacement, speed and acceleration relation, the movement axis control parameters of each time period are calculated;

[0014] (9) According to the movement axis control parameters of each time period, the coordinates of all movement axes of each time period are calculated.

[0015] Preferably, the step (2) specifically comprises the following steps:

[0016] (2.1) The size relation of the displacement end speed Ve, the positive direction target speed Vu and the negative direction target speed Vd is compared;

[0017] (2.2) It is judged whether the displacement end speed Ve satisfies the conditions of being less than the positive direction target speed Vu and being greater than the negative direction target speed Vd at the same time, if yes, step (2.3) is continued; otherwise, the step is ended;

[0018] (2.3) The size relation of the displacement start speed Vs, the positive direction target speed Vu and the negative direction target speed Vd is compared, if Vs is greater than Vu or less than Vd, it is considered that Vs is out of the given target speed range; otherwise, it is considered that Vs is in the given target speed range;

[0019] (2.4) The size relation of the displacement start speed Vs, the displacement end speed Ve, the positive direction target speed Vu and the negative direction target speed Vd is obtained.

[0020] Preferably, the step (5) specifically comprises the following steps:

[0021] (5.1) comparing the given displacement S with the size of displacement Sse required for changing from the displacement start point to the displacement end point with the maximum jerk variation, if S is greater than Sse, then continue step (5.2); otherwise, continue step (5.3);

[0022] (5.2) marking the target speed direction used in the movement as the positive direction, i.e. using the positive target speed Vu;

[0023] (5.3) marking the target speed direction used in the movement as the negative direction, i.e. using the negative target speed Vd.

[0024] Preferably, the step (6) specifically comprises the following steps:

[0025] (6.1) calculating the displacement time T1 required for changing from the start point speed to the target speed positive direction target speed Vu or negative direction target speed Vd according to the speed-time waveform;

[0026] (6.2) calculating the displacement Ssv from the start point speed to the target speed for the speed-time waveform by using the triangular area formula, wherein the sum of the target speed and the start point speed is the height and the displacement time T is the base;

[0027] (6.3) calculating the displacement time T2 required for changing from the target speed Vu or Vd to the end point speed according to the speed-time waveform;

[0028] (6.4) calculating the displacement Sve from the start point speed to the target speed for the speed-time waveform by using the triangular area formula, wherein the sum of the target speed and the end point speed is the height and the displacement time T2 is the base;

[0029] (6.5) adding Ssv and Sve to obtain the whole displacement Ssvve required for changing from the start point speed to the end point speed with the maximum jerk variation after changing from the start point speed to the target speed with the maximum jerk variation.

[0030] The device for processing displacement instruction with non-zero end point speed based on dynamic programming in the numerical control system, the main features of which are that the device comprises:

[0031] a processor configured to execute computer executable instructions;

[0032] a memory storing one or more computer executable instructions, which, when executed by the processor, implement each step of the method for processing displacement instruction with non-zero end point speed based on dynamic programming described above.

[0033] The processor for processing displacement instruction with non-zero end point speed based on dynamic programming in the numerical control system, the main feature of which is that the processor is configured to execute computer executable instructions, and when the computer executable instructions are executed by the processor, each step of the method for processing displacement instruction with non-zero end point speed based on dynamic programming is implemented.

[0034] The computer readable storage medium, the main feature of which is that the computer program is stored thereon, and the computer program can be executed by the processor to implement each step of the method for processing displacement instruction with non-zero end point speed based on dynamic programming.

[0035] The method, device, processor and computer readable storage medium for processing displacement instruction with non-zero end point speed based on dynamic programming adopted by the application ensure that the displacement from the target speed to the end point speed can always be partially offset by the displacement from the start point speed to the target speed by adopting the segmented planning mode, so that the sum of the two displacements conforms to the given displacement S, thereby realizing the setting of the non-zero end point speed of the displacement instruction. It is ensured that the jerk in one of the axis directions is always maintained to be maximum, thereby realizing the fastest machining during the turning interpolation. The application has the characteristics of flexible control, high precision, simple processing, strong adaptability to changes of input parameters and instruction parameters, and high practical value in the numerical control system, and meets the real-time requirements of the numerical control system. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 The flowchart for distinguishing different turning durations of the method for processing displacement instruction with non-zero end point speed based on dynamic programming of the application.

[0037] Figure 2 The curve diagram generated by the acceleration data obtained by the method for processing displacement instruction with non-zero end point speed based on dynamic programming of the application.

[0038] Figure 3 The curve diagram generated by the speed data obtained by the method for processing displacement instruction with non-zero end point speed based on dynamic programming of the application.

[0039] Figure 4 The trajectory curve diagram obtained by the method for processing displacement instruction with non-zero end point speed based on dynamic programming of the application.

[0040] Figure 5 The flowchart of the method for processing displacement instruction with non-zero end point speed based on dynamic programming of the application. DETAILED DESCRIPTION

[0041] In order to make the technical contents of the present application clearer, further description will be made in combination with specific examples.

[0042] The method for processing displacement instruction with non-zero end point speed based on dynamic programming of the present application includes the following steps:

[0043] (1) comparing the set positive direction target speed with the negative direction target speed, if the positive direction target speed is greater than the negative direction target speed, it is considered that the two target speeds can form a target speed range; if the positive direction target speed is less than the negative direction target speed, it is considered that the two target speeds cannot form a target speed range, and the step is ended;

[0044] (2) comparing the start point speed Vs and the end point speed Ve of the set displacement instruction with the target speed range, judging the inclusion relation of the start point speed, the end point speed and the target speed range, if the end point speed simultaneously satisfies less than the positive direction target speed Vu and greater than the negative direction target speed Vd, then the start point speed is compared with Vu and the negative direction target speed Vd, and the size relation of the displacement start point speed Vs, the displacement end point speed Ve, the positive direction target speed Vu and the negative direction target speed Vd is obtained; otherwise, the step is ended;

[0045] (3) determining the speed change direction according to the inclusion relation of the start point speed, the end point speed and the target speed range;

[0046] (4) calculating the displacement Sse required from the displacement start point to the displacement end point with maximum jerk change;

[0047] (5) comparing the size of the given displacement S with Sse, if S is greater than Sse, it is considered that the positive direction target speed Vu is used during the movement; otherwise, it is considered that the negative direction target speed Vd is used during the movement;

[0048] (6) calculating the total displacement Ssvve required from the start point speed to the target speed Vu or Vd with maximum jerk change and then to the end point speed with maximum jerk change;

[0049] (7) comparing the given displacement S with Ssvve, if S is greater than Ssvve, there is a speed uniform change stage during the movement; otherwise, there is no speed uniform change stage during the movement;

[0050] (8) calculating the movement axis control parameter of each time period according to the displacement, speed and acceleration relation;

[0051] (9) calculating the coordinates of all movement axes of each time period according to the movement axis control parameter of each time period.

[0052] As a preferred embodiment of the present application, the step (2) specifically includes the following steps:

[0053] (2.1) comparing the displacement end point speed Ve with the positive direction target speed Vu and the negative direction target speed Vd;

[0054] (2.2) judging whether the displacement end point speed Ve satisfies the condition of being less than the positive direction target speed Vu and greater than the negative direction target speed Vd at the same time, if yes, continuing step (2.3); otherwise, ending step;

[0055] (2.3) comparing the displacement start point speed Vs with the positive direction target speed Vu and the negative direction target speed Vd, if Vs is greater than Vu or less than Vd, it is considered that Vs is out of the given target speed range; otherwise, it is considered that Vs is in the given target speed range;

[0056] (2.4) obtaining the size relationship of the displacement start point speed Vs, the displacement end point speed Ve, the positive direction target speed Vu and the negative direction target speed Vd.

[0057] As a preferred embodiment of the present application, the step (5) specifically comprises the following steps:

[0058] (5.1) comparing the given displacement S with the displacement Sse required for changing from the displacement start point to the displacement end point with the maximum jerk, if S is greater than Sse, continuing step (5.2); otherwise, continuing step (5.3);

[0059] (5.2) marking the target speed direction used in moving as the positive direction, i.e. using the positive direction target speed Vu;

[0060] (5.3) marking the target speed direction used in moving as the negative direction, i.e. using the negative direction target speed Vd.

[0061] As a preferred embodiment of the present application, the step (6) specifically comprises the following steps:

[0062] (6.1) calculating the displacement time T1 required for changing from the start point speed to the target speed positive direction target speed Vu or negative direction target speed Vd according to the speed-time waveform;

[0063] (6.2) calculating the displacement Ssv from the start point speed to the target speed by using the triangular area formula for the speed-time waveform, wherein the sum of the target speed and the start point speed is taken as the height and the displacement time T is taken as the base;

[0064] (6.3) calculating the displacement time T2 required for changing from the target speed Vu or Vd to the end point speed according to the speed-time waveform;

[0065] (6.4) Calculate the displacement Sve from the start speed to the target speed using the formula for the area of a triangle, with the sum of the target speed and the end speed as the height and the displacement time T2 as the base;

[0066] (6.5) Add Ssv and Sve to obtain the total displacement Ssvve required from the start speed to the target speed with the maximum jerk and from the target speed to the end speed with the maximum jerk.

[0067] The device for processing displacement instructions with a non-zero end speed based on dynamic programming in the numerical control system of the present application, wherein the device comprises:

[0068] a processor configured to execute computer executable instructions;

[0069] a memory storing one or more computer executable instructions, which, when executed by the processor, implement each step of the method for processing displacement instructions with a non-zero end speed based on dynamic programming described above.

[0070] The processor for processing displacement instructions with a non-zero end speed based on dynamic programming in the numerical control system of the present application, wherein the processor is configured to execute computer executable instructions, which, when executed by the processor, implement each step of the method for processing displacement instructions with a non-zero end speed based on dynamic programming described above.

[0071] The computer readable storage medium of the present application, on which a computer program is stored, the computer program can be executed by a processor to implement each step of the method for processing displacement instructions with a non-zero end speed based on dynamic programming described above.

[0072] In the detailed description of the present application, the algorithm principle of the present application is as follows:

[0073] 1. Classification planning algorithm:

[0074] In order to achieve the above-mentioned goal, it is necessary to find the best displacement interpolation scheme in a single displacement instruction under the constraints of displacement, speed and acceleration.

[0075] The present application adopts the scheme of classification planning algorithm to distinguish the inclusion relationship of different start speed, end speed and target speed range, and the algorithm flow is as shown in Figure 1 The principle of the algorithm is as follows:

[0076] The positive direction target speed Vu or Vd used in the interpolation process is determined according to the inclusion relation of the start point speed, the end point speed and the target speed range, the speed change mode during displacement is determined by comparing the given displacement S with the size of See and comparing the given displacement S with the size of Ssvve, and then the corresponding interpolation period is calculated according to the different speed waveform conditions. In this way, the same mathematical model can cope with various scenarios, and the calculation is relatively simple and the response speed is fast.

[0077] According to the size comparison of the given displacement S and Ssvve, the speed change mode during displacement is determined, which specifically includes the following steps:

[0078] (6.1) The displacement time T1 required for changing from the start point speed to the target speed Vu or Vd is calculated according to the speed-time waveform;

[0079] (6.2) The displacement Ssv of changing from the start point speed to the target speed is calculated by using the triangular area formula for the speed-time waveform, with the sum of the target speed and the start point speed as the height and the displacement time T as the base;

[0080] (6.3) The displacement time T2 required for changing from the target speed Vu or Vd to the end point speed is calculated according to the speed-time waveform;

[0081] (6.4) The displacement Sve of changing from the start point speed to the target speed is calculated by using the triangular area formula for the speed-time waveform, with the sum of the target speed and the end point speed as the height and the displacement time T2 as the base;

[0082] (6.5) The displacement Ssvve required for changing from the start point speed to the target speed with the maximum jerk and then changing to the end point speed with the maximum jerk is obtained by adding Ssv and Sve.

[0083] In step (6.1), the total turning time T1 is calculated, which is specifically:

[0084] The total turning time T1 is calculated according to the following formula:

[0085] T1 = (A / jmax-1) + (ΔV / A);

[0086] In step (6.3), the total turning time T2 is calculated, which is specifically:

[0087] The total turning time T2 is calculated according to the following formula:

[0088] T2 = (A / jmax-1) + (ΔV / A);

[0089] Wherein, V is the target speed, ΔV is the speed difference between the target speed and the start point speed or the end point speed, Jmax is the maximum jerk, and A is the maximum acceleration.

[0090] The interpolation method mentioned in the method is:

[0091] Record the current time as t, the displacement as s, the velocity as v, the acceleration as a, and the J as the jerk in the axial direction, then:

[0092] t+=T;

[0093] s+=v×T;

[0094] Wherein, T is the interpolation time period.

[0095] If the current is in the uniform speed stage, v is unchanged, otherwise v+=a×T;

[0096] a has three cases according to different stages:

[0097] If in the acceleration increasing stage, a+=J×T;

[0098] If in the acceleration decreasing stage, a-=J×T;

[0099] Otherwise, a is unchanged.

[0100] The implementation results of the embodiment are as follows:

[0101] The method for processing displacement instructions with non-zero end point speed in the numerical control system based on dynamic programming, wherein the acceleration value generated by operation generates a curve after waveform as shown in Figure 2 .

[0102] The method for processing displacement instructions with non-zero end point speed in the numerical control system based on dynamic programming, wherein the velocity value generated by operation generates a curve after waveform as shown in Figure 3 .

[0103] The method for processing displacement instructions with non-zero end point speed in the numerical control system based on dynamic programming, wherein the displacement generated by operation is as shown in Figure 4 .

[0104] The specific implementation scheme of the embodiment can be referred to the related description in the above embodiment, which will not be repeated here.

[0105] It can be understood that the same or similar parts in the above embodiments can be mutually referred to, and the contents not described in detail in some embodiments can be referred to the same or similar contents in other embodiments.

[0106] It should be noted that in the description of the present application, the terms "first", "second", etc. are only for the purpose of description, and cannot be understood as indicating or implying relative importance. In addition, in the description of the present application, unless otherwise specified, the meaning of "a plurality of" is at least two.

[0107] Any procedural or methodological descriptions in flow charts or otherwise described herein can be understood to represent modules, segments, or portions of code that include executable instructions for implementing the specified logical functions or steps, and the scope of preferred embodiments of the present application includes additional implementations in which the functions are performed in an order different from that shown or discussed, including substantially simultaneously, in reverse order, or in an order that is otherwise considered to be equivalent by those skilled in the art of the embodiments.

[0108] It should be understood that portions of the present application can be realized with hardware, software, firmware or a combination thereof. In the foregoing embodiments, a number of the steps or methods can be realized as software or firmware to be executed by a suitable instruction-executing device as stored in a storage medium. For example, if realized with hardware, and as in another embodiment, any one or a combination of the following technologies known in the art can be used: discrete logic circuitry having logic gates for implementing logic functions on data signals, application specific integrated circuits having appropriate combinational logic gates, programmable gate arrays (PGA), field programmable gate arrays (FPGA), and the like.

[0109] Those skilled in the art of the present technology can understand that all or part of the steps carried out by the above-mentioned embodiments can be completed by programs instructing relevant hardware, and the corresponding programs can be stored in a computer-readable storage medium. When the program is executed, it includes one of the steps of the method embodiments or a combination thereof.

[0110] In addition, each functional unit in each embodiment of the present application can be integrated into one processing module, or each unit can exist physically separately, or two or more units can be integrated into one module. The above-mentioned integrated module can be realized in the form of hardware or in the form of a software functional module. If the integrated module is realized in the form of a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0111] The storage medium mentioned above can be a read-only memory, a magnetic disk or an optical disk, etc.

[0112] In the description of the present specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0113] The method, device, processor and computer readable storage medium of the application ensure that the acceleration of one of the axes is always maintained at a maximum, thereby achieving the fastest machining during turning interpolation, and have the characteristics of flexible control, high precision, simple processing, strong adaptability to changes in input parameters and instruction parameters, high practical value in a numerical control system, and compliance with the real-time requirements of the numerical control system.

[0114] In this specification, the application has been described with reference to its particular embodiments. It is clear, however, that various modifications and changes can be made without departing from the spirit and scope of the application. Therefore, the specification and drawings should be considered illustrative rather than restrictive.

Claims

1. A method of implementing displacement command processing with a non-zero end-point velocity based on dynamic programming, characterized by, The method comprises the following steps: (1) comparing the set positive direction target speed with the negative direction target speed, if the positive direction target speed is greater than the negative direction target speed, it is considered that the two target speeds can form a target speed range; if the positive direction target speed is less than the negative direction target speed, it is considered that the two target speeds cannot form a target speed range, and the step is ended; (2) comparing the start speed Vs and the end speed Ve of the set movement instruction with the target speed range, judging the inclusion relation of the start speed, the end speed and the target speed range, if the end speed simultaneously satisfies less than the positive direction target speed Vu and greater than the negative direction target speed Vd, the start speed Vs, the end speed Ve, the positive direction target speed Vu and the negative direction target speed Vd are continuously compared to obtain the size relation; otherwise, the step is ended; (3) determining the speed change direction according to the inclusion relation of the start speed, the end speed and the target speed range; (4) calculating the displacement Sse required for changing from the displacement start point to the displacement end point with the maximum jerk; (5) comparing the given displacement S with the size of Sse, if S is greater than Sse, it is considered that the positive direction target speed Vu is used during movement; otherwise, it is considered that the negative direction target speed Vd is used during movement; (6) calculating the total displacement Ssvve required for changing from the start speed to the target speed Vu or Vd with the maximum jerk and then changing to the end speed with the maximum jerk; (7) comparing the given displacement S with Ssvve, if S is greater than Ssvve, there is a speed uniform change stage during movement; otherwise, there is a speed uniform change stage during movement; (8) calculating the movement axis control parameter of each time period according to the displacement, the speed and the acceleration relation; (9) calculating the coordinates of all movement axes of each time period according to the movement axis control parameter of each time period.

2. The method of claim 1, wherein the displacement command processing is implemented based on dynamic programming to achieve a non-zero end-point velocity. The step (2) specifically comprises the following steps: (2.1) comparing the size relation of the displacement end speed Ve, the positive direction target speed Vu and the negative direction target speed Vd; (2.2) judging whether the displacement end speed Ve simultaneously satisfies less than the positive direction target speed Vu and greater than the negative direction target speed Vd, if yes, the step (2.3) is continued; otherwise, the step is ended; (2.3) comparing the size relation of the displacement start speed Vs, the positive direction target speed Vu and the negative direction target speed Vd, if Vs is greater than Vu or less than Vd, it is considered that Vs is out of the given target speed range; otherwise, it is considered that Vs is in the given target speed range; (2.4) obtaining the size relation of the displacement start speed Vs, the displacement end speed Ve, the positive direction target speed Vu and the negative direction target speed Vd.

3. The method of claim 1, wherein the displacement command processing is implemented based on dynamic programming to achieve a non-zero end-point velocity, and The step (5) specifically comprises the following steps: (5.1) comparing the given displacement S with the size of Sse required for changing from the displacement start point to the displacement end point with the maximum jerk, if S is greater than Sse, the step (5.2) is continued; otherwise, the step (5.3) is continued; (5.2) marking the target speed direction used during movement as the positive direction, i.e. using the positive direction target speed Vu; (5.3) marking the target speed direction used during movement as the negative direction, i.e. using the negative direction target speed Vd. (5.3) The target speed direction used when the marker is moving is negative, i.e. negative target speed Vd is used.

4. The method of claim 1, wherein the displacement command processing is implemented based on dynamic programming to achieve a non-zero end-point velocity, and The step (6) specifically comprises the following steps: (6.1) Calculate the displacement time T1 required to change from the start speed to the target speed positive direction target speed Vu or negative direction target speed Vd according to the speed-time waveform; (6.2) Calculate the displacement Ssv from the start speed to the target speed using the triangular area formula for the speed-time waveform, with the sum of the target speed and the start speed as the height and the displacement time T as the base; (6.3) Calculate the displacement time T2 required to change from the target speed Vu or Vd to the end speed according to the speed-time waveform; (6.4) Calculate the displacement Sve from the start speed to the end speed using the triangular area formula for the speed-time waveform, with the sum of the target speed and the end speed as the height and the displacement time T2 as the base; (6.5) Add Ssv and Sve to obtain the total displacement Ssvve required to change from the start speed to the end speed with maximum jerk.

5. An apparatus for processing a displacement command with a non-zero end point velocity based on dynamic programming in a numerical control system, characterized by, The apparatus comprises: a processor configured to execute computer executable instructions; a memory storing one or more computer executable instructions which, when executed by the processor, implement each step of the method of claim 1 to 4 for processing displacement instructions based on dynamic programming to achieve a non-zero end speed.

6. A processor for processing a displacement command with a non-zero end point velocity based on dynamic programming in a numerical control system, characterized by, The processor is configured to execute computer executable instructions which, when executed by the processor, implement each step of the method of claim 1 to 4 for processing displacement instructions based on dynamic programming to achieve a non-zero end speed.

7. A computer readable storage medium characterized by a computer program stored thereon, which can be executed by a processor to implement each step of the method of claim 1 to 4 for processing displacement instructions based on dynamic programming to achieve a non-zero end speed.

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