S-curve acceleration and deceleration planning method, system and storage medium

Abstract

The present application discloses an S-curve acceleration and deceleration planning method, system and storage medium. When the method is executed, initial parameters of the S-curve are obtained; the initial parameters include an initial velocity and a final velocity; a first critical length and a second critical length are calculated based on the initial parameters; the first critical length is the path length from the initial velocity to the final velocity; the second critical length is the path length corresponding to the non-uniform speed section of the motion process; a target motion process is determined based on the first critical length, the second critical length and the initial parameters, and a set of equations corresponding to the target motion process is obtained based on the target motion process and the initial parameters; the set of equations is solved to obtain the running time corresponding to the target motion process to complete the S-curve acceleration and deceleration planning, and the running time corresponding to the target motion process is obtained by solving the set of equations, with short calculation time, high efficiency and convenience for real-time calculation.

Description

Technical Field

[0001] The present application relates to the field of motion control of numerical control systems, and in particular to an S-curve acceleration and deceleration planning method, system and storage medium. Background Art

[0002] In CNC motion control systems, the acceleration and deceleration control algorithm directly affects the real-time performance, stability and processing accuracy of the motion control system. The acceleration and deceleration control algorithm is used to reasonably plan the displacement, velocity, acceleration and jerk curve of the processing trajectory segment, and to achieve flexible control of the system during the start, stop, acceleration and deceleration stages, avoiding the system from losing step, vibration, overtravel and other phenomena, and ensuring the high-speed and stable operation of the system. In CNC motion control systems, the S-curve acceleration and deceleration control algorithm is a more commonly used algorithm.

[0003] In the related art, when solving the S-type acceleration and deceleration control algorithm, a numerical analytical solution is usually performed through the bisection method or the Newton iteration method. However, the bisection method and the Newton iteration method take a long time and are not convenient for real-time calculation. Summary of the invention

[0004] The present application aims to solve at least one of the technical problems existing in the prior art. To this end, the present application proposes an S-curve acceleration and deceleration planning method, system and storage medium, which can obtain a set of equations about the running time of each curve segment of the target motion process, and then solve the set of equations to obtain the running time of each segment of the target motion process, which is short in calculation time and convenient for real-time calculation.

[0005] The first embodiment of the present application provides an S-curve acceleration and deceleration planning method, including:

[0006] Obtaining initial parameters of the S-curve; the initial parameters include an initial velocity and a final velocity;

[0007] A first critical length and a second critical length are calculated based on the initial parameters; wherein the first critical length is the path length from the initial velocity to the final velocity; and the second critical length is the path length corresponding to the non-uniform speed section of the motion process;

[0008] According to the first critical length, the second critical length and the initial parameters, a target motion process is determined, and according to the target motion process and the initial parameters, a set of equations corresponding to the target motion process is obtained; wherein the motion process includes at least one of the following: an acceleration segment, a uniform acceleration segment, a deceleration segment, a uniform speed segment, an acceleration and deceleration segment, a uniform deceleration segment, and a deceleration and deceleration segment;

[0009] The equation group is solved to obtain the running time corresponding to the target motion process.

[0010] According to the S-curve acceleration and deceleration planning method of the embodiment of the present application, there are at least the following beneficial effects: when the S-curve acceleration and deceleration planning method of the embodiment of the present application is executed, the initial parameters of the S-curve are obtained; the initial parameters include the initial velocity and the final velocity; the first critical length and the second critical length are calculated according to the initial parameters; the first critical length is the path length from the initial velocity to the final velocity; the second critical length is the path length corresponding to the non-uniform speed section of the motion process; according to the first critical length, the second critical length and the initial parameters, the target motion process is determined, and according to the target motion process and the initial parameters, a group of equations corresponding to the target motion process is obtained; the group of equations is solved to obtain the running time corresponding to the target motion process to complete the S-curve acceleration and deceleration planning, and the running time corresponding to the target motion process is obtained by solving the group of equations, the calculation time is short, the efficiency is high, and it is convenient for real-time calculation.

[0011] According to some embodiments of the first aspect of the present application, calculating the first critical length and the second critical length according to the initial parameters includes:

[0012] The first critical length is calculated according to a first formula; wherein the initial parameters also include maximum acceleration and maximum jerk, and the first formula is:

[0013] L1=L a (Vs,Ve)=L d (Ve,Vs),

[0014]

[0015] Wherein, L1 represents the first critical length, V S represents the initial velocity, Ve represents the final velocity, A represents the maximum acceleration, J represents the maximum jerk, L a (Vs, Ve) represents the path length from the initial velocity to the final velocity, L d (Ve, Vs) represents the path length of deceleration from the final velocity to the initial velocity;

[0016] The second critical length is calculated according to a second formula; wherein the initial parameters also include a maximum driving speed, and the second formula is:

[0017] L2=L a (Vs,Vm)+L d (Vm,Ve)

[0018] Wherein, L2 represents the second critical length, Ve represents the final velocity, and V S represents the initial velocity, Vm represents the maximum driving speed, L a(Vs, Vm) represents the path length from the initial velocity to the maximum driving velocity, L d (Vm, Ve) characterizes the path length of deceleration from the maximum driving speed to the final speed.

[0019] According to some embodiments of the first aspect of the present application, the initial parameters further include an actual path length;

[0020] The target motion process is determined according to the first critical length, the second critical length and the initial parameters, and a set of equations corresponding to the target motion process is obtained according to the target motion process and the initial parameters, including:

[0021] When L≤L1 and Vs≤Ve, if Ve-Vs>A 2 / J and L>S 13 , determine that the target motion process only includes a jerk segment, a uniform acceleration segment, and a deceleration segment, and obtain a first set of equations according to the target motion process; wherein the first set of equations is:

[0022]

[0023]

[0024] Wherein, T1 represents the running time of the acceleration segment, T2 represents the running time of the uniform acceleration segment, T3 represents the running time of the deceleration segment, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, S 13 Characterization

[0025]

[0026] The path length of the motion process;

[0027] When L≤L1 and Vs≤Ve, if Ve-Vs≤A 2 / J or L≤S 13 , it is determined that the target motion process only includes the acceleration segment and the deceleration segment, and a second set of equations is obtained according to the target motion process; wherein the second set of equations is:

[0028] T1=T3,

[0029] JT1 3 +2Vs·T1-L=0.

[0030] Wherein, T1 represents the running time of the acceleration segment, T3 represents the running time of the deceleration segment, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, S 13 Characterization

[0031]

[0032] The path length of the motion process.

[0033] According to some embodiments of the first aspect of the present application, the target motion process is determined according to the first critical length, the second critical length and the initial parameters, and the set of equations corresponding to the target motion process is obtained according to the target motion process and the initial parameters, including:

[0034] When L≤L1 and Vs>Ve, if Vs-Ve>A 2 / J and L>S 57 , determine that the target motion process only includes an acceleration / deceleration segment, a uniform deceleration segment, and a deceleration / deceleration segment, and obtain a third equation group according to the target motion process; wherein the third equation group is:

[0035]

[0036]

[0037] Wherein, T5 represents the running time of the acceleration / deceleration section, T6 represents the running time of the uniform deceleration section, T7 represents the running time of the deceleration / deceleration section, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, S 57 Characterization

[0038]

[0039] The path length of the motion process;

[0040] When L≤L1 and Vs>Ve, if Vs-Ve≤A 2 / J or L≤S 57 , determine that the target motion process only includes the acceleration and deceleration segment and the deceleration and deceleration segment, and obtain the fourth set of equations according to the target motion process; wherein the fourth set of equations is:

[0041] T5=T7,

[0042] -JT5 3+2Vs·T5-L=0.

[0043] Wherein, T5 represents the running time of the acceleration / deceleration section, T7 represents the running time of the deceleration / deceleration section, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, S 57 Characterization

[0044]

[0045] The path length of the motion process.

[0046] According to some embodiments of the first aspect of the present application, the target motion process is determined according to the first critical length, the second critical length and the initial parameters, and the set of equations corresponding to the target motion process is obtained according to the target motion process and the initial parameters, including:

[0047] When L≥L2, if Vm-Vs>A 2 / J and Vm-Ve>A 2 / J, determine that the target motion process includes an acceleration segment, a uniform acceleration segment, a deceleration segment, a uniform speed segment, an acceleration / deceleration segment, a uniform deceleration segment, and a deceleration / deceleration segment, and obtain a fifth set of equations according to the target motion process; the fifth set of equations is:

[0048]

[0049]

[0050]

[0051] When L≥L2, if Vm-Vs≤A 2 / J and Vm-Ve≤A 2 / J, determining that the target motion process only includes an acceleration segment, a deceleration segment, a uniform speed segment, an acceleration / deceleration segment, and a deceleration / deceleration segment, and obtaining a sixth set of equations according to the target motion process;

[0052] The sixth set of equations is:

[0053]

[0054]

[0055]

[0056] When L≥L2, if Vm-Vs≤A 2 / J and Vm-Ve>A 2 / J, determine that the target motion process only includes a positive jerk segment, a negative jerk segment, a constant velocity segment, a positive acceleration and deceleration segment, a negative acceleration and deceleration segment, and a negative jerk segment, and obtain a seventh system of equations according to the target motion process; the seventh system of equations is:

[0057]

[0058]

[0059]

[0060] When L≥L2, if Vm - Vs > A 2 / J and Vm - Ve ≤ A 2 / J, determine that the target motion process only includes a positive jerk segment, a constant acceleration segment, a negative jerk segment, a constant velocity segment, a positive acceleration and deceleration segment, and a negative jerk segment, and obtain an eighth system of equations according to the target motion process; the eighth system of equations is:

[0061]

[0062]

[0063]

[0064] Among them, T1 represents the running time of the positive jerk segment, T2 represents the running time of the constant acceleration segment, T3 represents the running time of the negative jerk segment, T4 represents the running time of the constant velocity segment, T5 represents the running time of the positive acceleration and deceleration segment, T6 represents the running time of the negative acceleration and deceleration segment, T7 represents the running time of the negative jerk segment, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L2 represents the second critical length, Vm represents the maximum driving velocity, L a (Vs, Vm) represents the path length from the initial velocity V S accelerating to the maximum driving velocity Vm, L d (Vm, Ve) represents the path length from the maximum driving velocity Vm decelerating to the final velocity Ve.

[0065] According to some embodiments of the first aspect of the present application, the determining the target motion process according to the first critical length, the second critical length and the initial parameters, and obtaining the system of equations corresponding to the target motion process according to the target motion process and the initial parameters includes:

[0066] When L1 < L < L2 and Vs ≤ Ve and Ve - Vs > A 2 / J, if Vm - Ve > A 2 / J and L > S 12357 , it is determined that the target motion process only includes a positive jerk segment, a constant acceleration segment, a negative jerk segment, a positive deceleration segment, a constant deceleration segment, and a negative deceleration segment. According to the target motion process, a ninth set of equations is obtained, and the ninth set of equations is as follows:

[0067]

[0068]

[0069]

[0070] where T1 represents the running time of the positive jerk segment, T2 represents the running time of the constant acceleration segment, T3 represents the running time of the negative jerk segment, T5 represents the running time of the positive deceleration segment, T6 represents the running time of the constant deceleration segment, T7 represents the running time of the negative deceleration segment, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, L2 represents the second critical length, Vm represents the maximum driving velocity, S 12357 represents when

[0071]

[0072] the path length of the motion process;

[0073] When L1 < L < L2 and Vs ≤ Ve and Ve - Vs > A 2 / J, if Vm - Ve ≤ A 2 / J or L ≤ S 12357 , it is determined that the target motion process only includes the positive jerk segment, the constant acceleration segment, the negative jerk segment, the positive deceleration segment, and the negative deceleration segment. According to the target motion process, a tenth set of equations is obtained, and the tenth set of equations is as follows:

[0074]

[0075]

[0076] T7 = T5,

[0077]

[0078] where T1 represents the running time of the positive jerk segment, T2 represents the running time of the constant acceleration segment, T3 represents the running time of the negative jerk segment, T5 represents the running time of the positive deceleration segment, T7 represents the running time of the negative deceleration segment, A represents the maximum acceleration, J represents the maximum jerk, VS V_s represents the initial velocity, V_e represents the final velocity, L represents the actual path length, L1 represents the first critical length, L2 represents the second critical length, V_m represents the maximum driving velocity, and S 12357 represents when

[0079]

[0080] the path length of the motion process.

[0081] According to some embodiments of the first aspect of the present application, determining the target motion process according to the first critical length, the second critical length and the initial parameters, and obtaining the corresponding system of equations of the target motion process according to the target motion process and the initial parameters further includes:

[0082] When L1 < L < L2 and V_s ≤ V_e and V_e - V_s < A 2 / J, if V_m - V_s ≤ A 2 / J, it is determined that the target motion process only includes the positive acceleration increasing section, the negative acceleration increasing section, the positive deceleration section, and the negative deceleration section, and the eleventh system of equations is obtained according to the target motion process. The eleventh system of equations is:

[0083] T1 = T3, T5 = T7,

[0084] V_s + J·T1 2 = V_e + J·T5 2 ,

[0085] 2V_s·T1 + J·T1 3 + 2V_e·T5 + J·T5 3 = L.

[0086] Wherein, T1 represents the running time of the positive acceleration increasing section, T3 represents the running time of the negative acceleration increasing section, T5 represents the running time of the positive deceleration section, T7 represents the running time of the negative deceleration section, J represents the maximum positive jerk, A represents the maximum acceleration, V S represents the initial velocity, V_e represents the final velocity, V_m represents the maximum driving velocity, L represents the actual path length, L1 represents the first critical length, and L2 represents the second critical length.

[0087] According to some embodiments of the first aspect of the present application, determining the target motion process according to the first critical length, the second critical length and the initial parameters, and obtaining the corresponding system of equations of the target motion process according to the target motion process and the initial parameters further includes:

[0088] When L1 < L < L2 and V_s ≤ V_e and V_e - V_s < A2 / J and Vm - Vs > A 2 / J, if Vm - Ve > A 2 / J and L ≤ S 1357 , determine that the target motion process only includes the jounce segment, the positive acceleration segment, the negative acceleration segment, the deceleration segment, and the negative deceleration segment, and obtain the eleventh set of equations according to the target motion process;

[0089] When L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J and Vm - Vs > A 2 / J, if Vm - Ve > A 2 / J and S1357 < L ≤ S12357, determine that the target motion process only includes the jounce segment, the uniform acceleration segment, the negative acceleration segment, the deceleration segment, and the negative deceleration segment, and obtain the tenth set of equations according to the target motion process;

[0090] When L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J and Vm - Vs > A 2 / J, if Vm - Ve > A 2 / J and L > S 12357 , determine that the target motion process only includes the jounce segment, the uniform acceleration segment, the negative acceleration segment, the deceleration segment, the uniform deceleration segment, and the negative deceleration segment, and obtain the ninth set of equations according to the target motion process;

[0091] When L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J and Vm - Vs > A 2 / J, if Vm - Ve ≤ A 2 / J and L ≤ S 1357 , determine that the target motion process only includes the jounce segment, the negative acceleration segment, the deceleration segment, and the negative deceleration segment, and obtain the eleventh set of equations according to the target motion process;

[0092] When L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J and Vm - Vs > A 2 / J, if Vm - Ve ≤ A 2 / J and L > S 1357 , determine that the target motion process only includes the jounce segment, the uniform acceleration segment, the negative acceleration segment, the deceleration segment, and the negative deceleration segment, and obtain the tenth set of equations according to the target motion process;

[0093] where, J represents the maximum jounce acceleration, A represents the maximum acceleration, V Srepresents the initial velocity, Ve represents the final velocity, Vm represents the maximum driving velocity, L represents the actual path length, L1 represents the first critical length, L2 represents the second critical length, S 12357 Characterization

[0094]

[0095] The path length of the motion process;

[0096] S 1357 Characterization

[0097]

[0098] The path length of the motion process.

[0099] The second aspect of the present application provides an S-curve acceleration and deceleration planning system, including:

[0100] at least one memory;

[0101] at least one processor;

[0102] at least one program;

[0103] The program is stored in the memory, and the processor executes at least one program to implement:

[0104] An S-curve acceleration and deceleration planning method as described in any one of the embodiments of the first aspect of the present application.

[0105] In a third aspect, an embodiment of the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer-executable signal, and the computer-executable signal is used to execute:

[0106] An S-curve acceleration and deceleration planning method as described in any one of the embodiments of the first aspect of the present application.

[0107] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] The present application is further described below with reference to the accompanying drawings and embodiments, wherein:

[0109] Figure 1 This is a flowchart of the steps of the S-curve acceleration and deceleration planning method in some embodiments of the present application;

[0110] Figure 2 A schematic diagram of an S-curve motion process of some embodiments of the present application;

[0111] Figure 3This is a flowchart of the steps of the S-curve acceleration and deceleration planning method in some embodiments of the present application;

[0112] Figure 4 This is a flowchart of the steps of the S-curve acceleration and deceleration planning method in some embodiments of the present application;

[0113] Figure 5 This is a flowchart of the steps of the S-curve acceleration and deceleration planning method in some embodiments of the present application;

[0114] Figure 6 This is a flowchart of the steps of the S-curve acceleration and deceleration planning method in some embodiments of the present application;

[0115] Figure 7 This is a flowchart of the steps of the S-curve acceleration and deceleration planning method in some embodiments of the present application. DETAILED DESCRIPTION

[0116] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application, and cannot be understood as limiting the present application.

[0117] In the description of the present application, it should be understood that descriptions involving orientation, such as up, down, front, back, left, right, etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present application.

[0118] In the description of this application, "several" means more than one, "more" means more than two, "greater than", "less than", "exceed", etc. are understood to exclude the number itself, and "above", "below", "within", etc. are understood to include the number itself. If there is a description of "first" or "second", it is only used for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0119] In the description of this application, unless otherwise clearly defined, terms such as setting, installing, connecting, etc. should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in this application based on the specific content of the technical solution.

[0120] In the description of the present application, the description with reference to the terms "one embodiment", "some embodiments", "illustrative embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials, or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0121] Reference Figure 1 In a first aspect, an embodiment of the present application provides an S-curve acceleration and deceleration planning method, including but not limited to step S100, step S200, step S300, and step S400.

[0122] Step S100, obtaining initial parameters of the S-curve; the initial parameters include initial velocity and final velocity;

[0123] Step S200, calculating a first critical length and a second critical length according to the initial parameters; the first critical length is the path length from the initial velocity to the final velocity; the second critical length is the path length corresponding to the non-uniform velocity section of the motion process;

[0124] Step S300, determining a target motion process according to the first critical length, the second critical length and the initial parameters, and obtaining a set of equations corresponding to the target motion process according to the target motion process and the initial parameters;

[0125] Step S400, solving the equation group to obtain the running time corresponding to the target motion process.

[0126] According to the S-curve acceleration and deceleration planning method of the embodiment of the present application, there are at least the following beneficial effects: when the S-curve acceleration and deceleration planning method of the embodiment of the present application is executed, the initial parameters of the S-curve are obtained; the initial parameters include an initial velocity and a final velocity; the first critical length and the second critical length are calculated according to the initial parameters; the first critical length is the path length from the initial velocity to the final velocity; the second critical length is the path length corresponding to the non-uniform speed section of the motion process; according to the first critical length, the second critical length and the initial parameters, the target motion process is determined, and according to the target motion process and the initial parameters, a group of equations corresponding to the target motion process is obtained; the group of equations is solved to obtain the running time corresponding to the target motion process to complete the S-curve acceleration and deceleration planning, and the running time corresponding to the target motion process is obtained by solving the group of equations, the calculation time is short, the efficiency is high, and it is convenient for real-time calculation.

[0127] It is understandable that the S-curve acceleration and deceleration planning method of the embodiment of the present application can be applied to the numerical control motion control system. By planning the S-curve acceleration and deceleration, the displacement, velocity, acceleration and jerk curve of the processing trajectory segment are reasonably planned, and the system is flexibly controlled during the start, stop, acceleration and deceleration motion stages to avoid the system from losing step, vibration, overtravel and other phenomena, and ensure the high-speed and stable operation of the system. Moreover, in this field, it is impossible to convert the S-curve acceleration and deceleration algorithm into a rational equation when solving it, so it can only be solved by numerical analysis. When using numerical analysis to solve it, the commonly used dichotomy method and Newton iteration method are time-consuming and not convenient for real-time calculation. The S-curve acceleration and deceleration planning method of the embodiment of the present application solves the equation group to obtain the running time of each segment of the target motion process, which has high accuracy, short calculation time, high efficiency and is convenient for real-time calculation.

[0128] It is understandable that, referring to Figure 2 Generally speaking, the S-curve acceleration and deceleration process can be divided into 7 stages: acceleration stage, uniform acceleration stage, deceleration stage, uniform speed stage, acceleration and deceleration stage, uniform deceleration stage, and deceleration and deceleration stage. Figure 2 In the equation, T1 represents the running time of the acceleration segment, T2 represents the running time of the uniform acceleration segment, T3 represents the running time of the deceleration segment, T4 represents the running time of the uniform speed segment, T5 represents the running time of the acceleration and deceleration segment, T6 represents the running time of the uniform deceleration segment, and T7 represents the running time of the deceleration and deceleration segment. j(t) represents the acceleration, a(t) represents the acceleration, v(t) represents the velocity, s(t) represents the displacement, and v s Characterizes the initial velocity, v e Characterizes the terminal velocity, V max represents the maximum driving speed, and L represents the actual path length. Assume that the time taken for the motor acceleration curve to reach the maximum value from 0 and to reach 0 from the maximum value is equal, and this time is defined as a characteristic time constant t of the system. m , Figure 2 A max =D max During the target motion, when the acceleration reaches its maximum value, During the target motion, when the acceleration cannot reach the maximum value, T1=T3, T5=T7; where A represents the maximum acceleration and J represents the maximum jerk.

[0129] It can be understood that the calculation formula of acceleration j(t) is:

[0130]

[0131] The calculation formula of acceleration a(t) is:

[0132]

[0133] The calculation formula of velocity v(t) is:

[0134]

[0135] The calculation formula of displacement s(t) is:

[0136]

[0137] Among them, v s represents the initial velocity; v e represents the final velocity; t k (k=1,2,...,7) represents the transition time of each stage; τ k (k=1,2,...,7) represents the local time coordinate, which indicates the time when the starting point of each stage is taken as the zero point; T k (k=1,2,...,7) represents the duration of each stage.

[0138] The calculation formula for the running time T4 of the uniform speed section is:

[0139]

[0140] The acceleration zone specifically includes the acceleration section, the uniform acceleration section, and the deceleration section. The path length s of the acceleration zone a The calculation formula is:

[0141]

[0142] The deceleration zone specifically includes the acceleration and deceleration section, the uniform deceleration section, and the deceleration and deceleration section. The path length s of the deceleration zone is d The calculation formula is:

[0143]

[0144] Then the sum of the path length of the acceleration zone and the path length of the deceleration zone is s all The calculation formula is:

[0145] s all =s a +s d .

[0146] It is understandable that step S200 may include the following steps:

[0147] The first critical length is calculated according to the first formula; wherein the initial parameters also include the maximum acceleration and the maximum jerk, and the first formula is:

[0148] L1=L a (Vs,Ve)=L d (Ve,Vs)

[0149]

[0150] Among them, L1 represents the first critical length, V S represents the initial velocity, Ve represents the final velocity, A represents the maximum acceleration, J represents the maximum jerk, L a (Vs, Ve) represents the initial velocity V S The path length of acceleration to the final velocity Ve, L d (Ve,Vs) represents the final velocity V e The length of the path decelerated to the initial velocity Vs;

[0151] The second critical length is calculated according to the second formula; wherein the initial parameters also include the maximum driving speed, and the second formula is:

[0152] L2=L a (Vs,Vm)+L d (Vm,Ve)

[0153] Among them, L2 represents the second critical length, Ve represents the final velocity, and V S represents the initial velocity, Vm represents the maximum driving speed, L a (Vs,Vm) represents the initial velocity V S Path length for acceleration to maximum drive speed Vm, L d (Vm, Ve) represents the path length from the maximum driving speed to the final speed. a (Vs,Vm),L d (Vm,Ve),L a (Vs,Ve),L d The calculation formula of (Ve, Vs) is the same, L a (Vs,Vm),L d The specific calculation of (Vm, Ve) refers to the first formula. The second critical length is the path length corresponding to the non-uniform speed segment of the motion process, that is, the path length when the motion process does not include a uniform speed segment.

[0154] It is understood that the initial parameters also include the actual path length. Figure 3 , step S300 may include but is not limited to step S310 and step S311;

[0155] Step S310, when L≤L1 and Vs≤Ve, if Ve-Vs>A 2 / J and L>S 13 , determine that the target motion process only includes the acceleration segment, the uniform acceleration segment, and the deceleration segment, and obtain the first set of equations according to the target motion process; wherein the first set of equations is:

[0156]

[0157]

[0158] Among them, T1 represents the running time of the acceleration segment, T2 represents the running time of the uniform acceleration segment, T3 represents the running time of the deceleration segment, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, S 13 Characterization

[0159]

[0160] The path length of the motion process;

[0161] Step S311, when L≤L1 and Vs≤Ve, if Ve-Vs≤A 2 / J or L≤S 13 , it is determined that the target motion process only includes the acceleration segment and the deceleration segment, and the second set of equations is obtained according to the target motion process; wherein the second set of equations is:

[0162] T1=T3,

[0163] JT1 3 +2Vs·T1-L=0.

[0164] Among them, T1 represents the running time of the acceleration section, T3 represents the running time of the deceleration section, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, S 13 Characterization

[0165]

[0166] The path length of the motion process.

[0167] In step S310, since L≤L1 and Vs≤Ve, it can be determined that the target motion process does not include an acceleration / deceleration segment, a uniform deceleration segment, a deceleration / deceleration segment, and a uniform speed segment.

[0168]

[0169] T4=T5=T6=T7=0,

[0170] Then S can be calculated according to the calculation formula of displacement s(t): 13 , when the acceleration from the initial velocity to the final velocity can reach the maximum acceleration, and the actual path length is greater than S13 , that is, Ve-Vs>A 2 / J and L>S 13 , it can be determined that the target motion process includes a uniform acceleration segment. According to the path length s of the acceleration zone a The calculation formula of the first set of equations is obtained. By solving the root-finding formula of the quadratic equation, discarding the infeasible solution of T2, T2 can be obtained, and Since the target motion process only includes the acceleration segment, the uniform acceleration segment, and the deceleration segment, it can be obtained that T4=T5=T6=T7=0.

[0171] In step S311, since L≤L1 and Vs≤Ve, it can be determined that the target motion process does not include an acceleration / deceleration segment, a uniform deceleration segment, a deceleration / deceleration segment, and a uniform speed segment; and since Ve-Vs≤A 2 / J or L≤S 13 Therefore, it can be determined that the target motion process does not include the uniform acceleration segment, and thus it can be determined that the target motion process only includes the acceleration segment and the deceleration segment. According to the target motion process, according to the path length s of the acceleration zone a The calculation formula is used to obtain the second set of equations. The second set of equations is solved using Sheng Jin's formula for cubic equations, and the infeasible solutions are discarded. Since the target motion process only includes the acceleration segment and the deceleration segment, it can be obtained that T2=T4=T5=T6=T7=0.

[0172] It is understandable that, referring to Figure 4 , step S300 also includes but is not limited to step S312 and step S313.

[0173] Step S312: When L≤L1 and Vs>Ve, if Vs-Ve>A 2 / J and L>S 57 , determine that the target motion process only includes the acceleration and deceleration segment, the uniform deceleration segment, and the deceleration and deceleration segment, and obtain the third equation group according to the target motion process; wherein the third equation group is:

[0174]

[0175]

[0176] Among them, T5 represents the running time of the acceleration and deceleration section, T6 represents the running time of the uniform deceleration section, T7 represents the running time of the deceleration section, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, S 57 Characterization

[0177]

[0178] The path length of the motion process;

[0179] Step S313: When L≤L1 and Vs>Ve, if Vs-Ve≤A 2 / J or L≤S 57 , determine that the target motion process only includes the acceleration and deceleration segment and the deceleration and deceleration segment, and obtain the fourth set of equations according to the target motion process; wherein the fourth set of equations is:

[0180] T5=T7,

[0181] -JT5 3 +2Vs·T5-L=0.

[0182] Among them, T5 represents the running time of the acceleration and deceleration section, T7 represents the running time of the deceleration and deceleration section, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, S 57 Characterization

[0183]

[0184] The path length of the motion process.

[0185] In step S312, since L≤L1 and Vs>Ve, it can be determined that the target motion process does not include an acceleration segment, a uniform acceleration segment, a deceleration segment, and a uniform speed segment.

[0186] T1=T2=T3=T4=0,

[0187]

[0188] Then S can be calculated according to the calculation formula of displacement s(t): 57 , when the acceleration from the initial velocity to the final velocity can reach the maximum acceleration, and the actual path length is greater than S 57 , that is, Vs-Ve>A 2 / J and L>S 57 , it can be determined that the target motion process includes a uniform deceleration segment, and then it can be determined that the target motion process only includes an acceleration and deceleration segment, a uniform deceleration segment, and a deceleration and deceleration segment. According to the path length s of the deceleration zone d The calculation formula of the third equation group is obtained, and the root-finding formula of the quadratic equation is used to solve it. By discarding the infeasible solution, T6 can be obtained, and Since the target motion process is determined to include only the acceleration and deceleration segment, the uniform deceleration segment, and the deceleration and deceleration segment, it can be obtained that T1=T2=T3=T4=0.

[0189] In step S313, since L≤L1 and Vs>Ve, it can be determined that the target motion process does not include an acceleration segment, a uniform acceleration segment, a deceleration segment, and a uniform speed segment; and since Vs-Ve≤A 2 / J or L≤S 57 Therefore, it can be determined that the target motion process does not include a uniform deceleration segment, and further it can be determined that the target motion process only includes an acceleration and deceleration segment and a deceleration and deceleration segment. According to the path length s of the deceleration zone d The fourth set of equations is obtained by the calculation formula. The Sheng Jin formula of cubic equations is used to solve it. By discarding infeasible solutions, T5 can be obtained, and T5=T7. Since the target motion process only includes acceleration and deceleration segments and deceleration and deceleration segments, we can get T1=T2=T3=T4=T6=0.

[0190] It is understandable that, referring to Figure 5 Step S300 may also include but is not limited to step S320, step S321, step S322, and step S323.

[0191] Step S320, when L≥L2, if Vm-Vs>A 2 / J and Vm-Ve>A 2 / J, determine that the target motion process includes acceleration segment, uniform acceleration segment, deceleration segment, uniform speed segment, acceleration and deceleration segment, uniform deceleration segment, and deceleration and deceleration segment, and obtain the fifth set of equations according to the target motion process; the fifth set of equations is:

[0192]

[0193]

[0194]

[0195] Step S321, when L≥L2, if Vm-Vs≤A 2 / J and Vm-Ve≤A 2 / J, determine that the target motion process only includes the acceleration segment, the deceleration segment, the uniform speed segment, the acceleration and deceleration segment, and the deceleration and deceleration segment. The sixth set of equations is obtained according to the target motion process; the sixth set of equations is:

[0196]

[0197]

[0198]

[0199] Step S322, when L≥L2, if Vm-Vs≤A 2 / J and Vm-Ve>A 2 / J, determine that the target motion process only includes the acceleration segment, the deceleration segment, the uniform speed segment, the acceleration and deceleration segment, the uniform deceleration segment, and the deceleration and deceleration segment. The seventh equation group is obtained according to the target motion process; the seventh equation group is:

[0200]

[0201]

[0202]

[0203] Step S323, when L≥L2, if Vm-Vs>A 2 / J and Vm-Ve≤A 2 / J, determine that the target motion process only includes the acceleration segment, uniform acceleration segment, deceleration segment, uniform speed segment, acceleration and deceleration segment, and deceleration and deceleration segment. The eighth equation group is obtained according to the target motion process; the eighth equation group is:

[0204]

[0205]

[0206]

[0207] Wherein, T1 represents the running time of the acceleration segment, T2 represents the running time of the uniform acceleration segment, T3 represents the running time of the deceleration segment, T4 represents the running time of the uniform speed segment, T5 represents the running time of the acceleration and deceleration segment, T6 represents the running time of the uniform deceleration segment, T7 represents the running time of the deceleration and deceleration segment, A represents the maximum acceleration, J represents the maximum jerk, V represents the maximum acceleration, S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L2 represents the second critical length, Vm represents the maximum driving speed, L a (Vs,Vm) represents the initial velocity V S Path length for acceleration to maximum drive speed Vm, L d (Vm, Ve) represents the path length of deceleration from the maximum driving speed Vm to the final speed Ve.

[0208] In step S320, since L≥L2, Vm-Vs>A 2 / J and Vm-Ve>A 2 / J, therefore, it can be determined that the target motion distance includes the acceleration section, the uniform acceleration section, the deceleration section, the uniform speed section, the acceleration / deceleration section, the uniform deceleration section, and the deceleration / deceleration section; the fifth group of equations can be determined, and the running time of the acceleration section, the uniform acceleration section, the deceleration section, the uniform speed section, the acceleration / deceleration section, the uniform deceleration section, and the deceleration / deceleration section can be directly obtained from the fifth group of equations.

[0209] In step S321, since L ≥ L2, Vm - Vs ≤ A 2 / J and Vm - Ve ≤ A 2 / J, it can be determined that the target motion distance includes a positive jerk-up segment, a negative jerk-up segment, a constant-speed segment, a positive jerk-down segment, and a negative jerk-down segment; then the sixth set of equations can be determined, and the running times of the positive jerk-up segment, the negative jerk-up segment, the constant-speed segment, the positive jerk-down segment, and the negative jerk-down segment can be directly obtained from the sixth set of equations.

[0210] In step S322, since L ≥ L2, if Vm - Vs ≤ A 2 / J and Vm - Ve > A 2 / J, it is determined that the target motion process only includes a positive jerk-up segment, a negative jerk-up segment, a constant-speed segment, a positive jerk-down segment, a constant deceleration segment, and a negative jerk-down segment, and the seventh set of equations is obtained according to the target motion process.

[0211] In step S323, since L ≥ L2, if Vm - Vs > A 2 / J and Vm - Ve ≤ A 2 / J, it is determined that the target motion process only includes a positive jerk-up segment, a constant acceleration segment, a negative jerk-up segment, a constant-speed segment, a positive jerk-down segment, and a negative jerk-down segment, and the eighth set of equations is obtained according to the target motion process.

[0212] It can be understood that referring to Figure 6 , step S300 may further include but is not limited to step S330 and step S331.

[0213] Step S330, when L1 < L < L2 and Vs ≤ Ve and Ve - Vs > A 2 / J, if Vm - Ve > A 2 / J and L > S 12357 , it is determined that the target motion process only includes a positive jerk-up segment, a constant acceleration segment, a negative jerk-up segment, a positive jerk-down segment, a constant deceleration segment, and a negative jerk-down segment, and the ninth set of equations is obtained according to the target motion process. The ninth set of equations is:

[0214]

[0215]

[0216]

[0217] Among them, T1 represents the running time of the positive jerk-up segment, T2 represents the running time of the constant acceleration segment, T3 represents the running time of the negative jerk-up segment, T5 represents the running time of the positive jerk-down segment, T6 represents the running time of the constant deceleration segment, T7 represents the running time of the negative jerk-down segment, A represents the maximum acceleration, J represents the maximum jerk, V S$V_s$ represents the initial velocity, $V_e$ represents the final velocity, $L$ represents the actual path length, $L_1$ represents the first critical length, $L_2$ represents the second critical length, $V_m$ represents the maximum driving velocity, and $S$ 12357 represents when

[0218]

[0219] the path length of the motion process;

[0220] Step S331, when $L_1 < L < L_2$ and $V_s \leq V_e$ and $V_e - V_s > A$ 2 $ / J$, if $V_m - V_e \leq A$ 2 $ / J$ or $L \leq S$ 12357 , it is determined that the target motion process only includes the positive acceleration phase, the constant acceleration phase, the negative acceleration phase, the acceleration - deceleration phase, and the deceleration - deceleration phase. According to the target motion process, the tenth set of equations is obtained, and the tenth set of equations is:

[0221]

[0222]

[0223] $T_7 = T_5$,

[0224]

[0225] where $T_1$ represents the running time of the positive acceleration phase, $T_2$ represents the running time of the constant acceleration phase, $T_3$ represents the running time of the negative acceleration phase, $T_5$ represents the running time of the acceleration - deceleration phase, $T_7$ represents the running time of the deceleration - deceleration phase, $A$ represents the maximum acceleration, $J$ represents the maximum jerk, $V$ S represents the initial velocity, $V_e$ represents the final velocity, $L$ represents the actual path length, $L_1$ represents the first critical length, $L_2$ represents the second critical length, $V_m$ represents the maximum driving velocity, $S$ 12357 represents when

[0226]

[0227] the path length of the motion process.

[0228] In step S330, since $L_1 < L < L_2$, the velocity in the target motion process cannot reach the maximum driving velocity. Therefore, it can be determined that the target motion process does not include the constant velocity phase; when $V_s \leq V_e$, the velocity in the target motion process can increase from the initial velocity to reach the final velocity, and it is necessary to determine whether there is a constant acceleration phase. Since $V_e - V_s > A$ 2 $ / J$, it can be determined that the target motion process includes the constant acceleration phase; since $L > L_1$, it can be determined that the target motion process includes the acceleration - deceleration phase and the deceleration - deceleration phase. It is necessary to determine whether there is a constant deceleration phase in the target motion process. Let:

[0229]

[0230]

[0231] Then, S can be calculated according to the calculation formula of the displacement s(t). 12357 When the acceleration during the deceleration from the maximum driving speed to the final speed can reach the maximum acceleration and the actual path length is greater than S 12357 , that is, Vm - Ve > A 2 / J and L > S 12357 , it can be determined that the target motion process includes a constant deceleration section, and further it can be determined that the target motion process only includes a positive acceleration section, a constant acceleration section, a negative acceleration section, a positive deceleration section, a constant deceleration section, and a negative deceleration section. According to the target motion process, the ninth set of equations is obtained according to the calculation formula of the total path length s all of the acceleration region and the deceleration region. By using the root formula of the quadratic equation to solve and discarding the non - feasible solutions, the running times of the positive acceleration section, the constant acceleration section, the negative acceleration section, the positive deceleration section, the constant deceleration section, and the negative deceleration section can be obtained.

[0232] In step S331, since L1 < L < L2, the speed in the target motion process cannot reach the maximum driving speed, so it can be determined that the target motion process does not include a constant speed section; when Vs ≤ Ve, the speed in the target motion process can increase from the initial speed to reach the final speed, and it is necessary to determine whether there is a constant acceleration section. Since Ve - Vs > A 2 / J, it can be determined that the target motion process includes a constant acceleration section; and since Vm - Ve ≤ A 2 / J or L ≤ S 12357 , it can be determined that the target motion process does not include a constant deceleration section, and further it can be determined that the target motion process only includes a positive acceleration section, a constant acceleration section, a negative acceleration section, a positive deceleration section, and a negative deceleration section. According to the target motion process, the tenth set of equations is obtained according to the calculation formula of the total path length s all of the acceleration region and the deceleration region. By using Ferrari's method to solve the quartic equation and discarding the non - feasible solutions, the running times of the positive acceleration section, the constant acceleration section, the negative acceleration section, the positive deceleration section, and the negative deceleration section are obtained.

[0233] It can be understood that step S300 may further include step S340.

[0234] Step S340, when L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J, if Vm - Vs ≤ A 2 / J, it is determined that the target motion process only includes a positive acceleration section, a negative acceleration section, a positive deceleration section, and a negative deceleration section. According to the target motion process, the eleventh set of equations is obtained, and the eleventh set of equations is as follows:

[0235] T1 = T3, T5 = T7,

[0236] Vs + J·T1 2 = Ve + J·T5 2 ,

[0237] 2Vs·T1 + J·T1 3 + 2Ve·T5 + J·T5 3 = L.

[0238] Among them, T1 represents the running time of the positive jerk section, T3 represents the running time of the negative jerk section, T5 represents the running time of the acceleration and deceleration section, T7 represents the running time of the negative deceleration section, J represents the maximum jerk, A represents the maximum acceleration, V S represents the initial velocity, Ve represents the final velocity, Vm represents the maximum driving velocity, L represents the actual path length, L1 represents the first critical length, and L2 represents the second critical length.

[0239] In step S340, since L1 < L < L2, the velocity during the target motion process cannot reach the maximum driving velocity, so it can be determined that the target motion process does not include a constant velocity section; when Vs ≤ Ve, the velocity during the target motion process can increase from the initial velocity to reach the final velocity, and it is necessary to determine whether there is a uniformly accelerated section. Since Ve - Vs < A 2 / J, the maximum velocity during the target motion process cannot be determined, so it is necessary to determine whether the target motion process includes a uniformly accelerated section; and since Vm - Vs ≤ A 2 / J, when the target motion process does not include a uniformly accelerated section, it can be determined that the target motion process only includes the positive jerk section, the negative jerk section, the acceleration and deceleration section, and the negative deceleration section. According to the calculation formula of the total path length s all of the acceleration area and the deceleration area, the eleventh equation set is obtained. From the eleventh equation set, it is obtained that:

[0240] Vs = Ve - J(T1 2 - T5 2 ),

[0241] Ve = Vs + J·(T1 2 - T5 2 ).

[0242] Furthermore, substitute V S and Ve into 2Vs·T1 + J·T1 3 + 2Ve·T5 + J·T5 3 = L., and the third formula is obtained:

[0243] Vs·T1 + (Ve - J(T1 2 - T5 2))·T1 + Ve·T5 + (Vs + J·(T1 2 -T5 2 ))·T5 + J·T1 3 + J·T5 3

[0244] =(Vs + Ve)·(T1 + T5) + J·T1·T5·(T1 + T5)=L.

[0245] Let:

[0246] (T1 + T5)=m,

[0247] (T1 - T5)=n.

[0248] Then:

[0249]

[0250]

[0251] Substitute it into the third formula to get a quartic equation:

[0252]

[0253] Use Ferrari's method to solve the quartic equation to obtain the feasible solution m, and then obtain the running times of the positive acceleration phase, negative acceleration phase, positive deceleration phase, and negative deceleration phase.

[0254] It can be understood that referring to Figure 7 , step S300 may further include but is not limited to step S350, step S351, step S352, step S353, and step S354.

[0255] Step S350, when L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J and Vm - Vs > A 2 / J, if Vm - Ve > A 2 / J and L ≤ S 1357 , determine that the target motion process only includes the positive acceleration phase, negative acceleration phase, positive deceleration phase, and negative deceleration phase, and obtain the eleventh equation set according to the target motion process; in step S350, since L1 < L < L2, it can be determined that the target motion process does not include the uniform motion phase; since Vs ≤ Ve and Ve - Vs < A 2 / J, let:

[0256]

[0257] T2 = T4 = T6 = 0,

[0258]

[0259] It is possible to calculate and obtain S according to the calculation formula of displacement s(t). 1357 , if the acceleration during the period from the initial velocity to the maximum velocity and the deceleration from the maximum velocity to the final velocity can both reach the maximum acceleration, that is, Vm - Vs > A 2 / J, Vm - Ve > A 2 / J, and L ≤ S 1357 When it can be determined that the target motion process does not include a uniformly accelerated section and a uniformly decelerated section, and further it can be determined that the target motion process only includes a super-accelerated section, a decelerated-accelerated section, an accelerated-decelerated section, and a decelerated-decelerated section, the target motion process is the same as step S340. Therefore, the eleventh set of equations can be obtained, and by solving the eleventh set of equations, the running times of the super-accelerated section, the decelerated-accelerated section, the accelerated-decelerated section, and the decelerated-decelerated section can be obtained.

[0260] Step S351, when L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J and Vm - Vs > A 2 / J, if Vm - Ve > A 2 / J and S 1357 < L ≤ S 12357 , it is determined that the target motion process only includes a super-accelerated section, a uniformly accelerated section, a decelerated-accelerated section, an accelerated-decelerated section, and a decelerated-decelerated section, and the tenth set of equations is obtained according to the target motion process; in step S351, since L1 < L < L2, it can be determined that the target motion process does not include a constant-speed section. Since Vs ≤ Ve and Ve - Vs < A 2 / J, if Vm - Ve > A 2 / J and S 1357 < L ≤ S 12357 , then it can be determined that the target motion process includes a uniformly accelerated section and does not include a uniformly decelerated section. Further, it can be determined that the target motion process only includes a super-accelerated section, a uniformly accelerated section, a decelerated-accelerated section, an accelerated-decelerated section, and a decelerated-decelerated section, which is the same as the target motion process of step S331. Therefore, the tenth set of equations can be obtained, and by solving the tenth set of equations, the running times of the super-accelerated section, the uniformly accelerated section, the decelerated-accelerated section, the accelerated-decelerated section, and the decelerated-decelerated section can be obtained.

[0261] Step S352, when L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J and Vm - Vs > A 2 / J, if Vm - Ve > A 2 / J and L > S 12357 , it is determined that the target motion process only includes a super-accelerated section, a uniformly accelerated section, a decelerated-accelerated section, an accelerated-decelerated section, a uniformly decelerated section, and a decelerated-decelerated section, and the ninth set of equations is obtained according to the target motion process; in step S352, since L1 < L < L2, it can be determined that the target motion process does not include a constant-speed section. Since Vs ≤ Ve and Ve - Vs < A 2 / J, if Vm - Ve > A 2 / J and L > S 12357 , it can be determined that the target motion process includes a uniformly accelerated section and a uniformly decelerated section. Furthermore, it can be determined that the target motion process only includes a jerk-accelerated section, a uniformly accelerated section, a jerk-decelerated section, a jerk-slowed section, a uniformly decelerated section, and a negative-jerk decelerated section, which is the same as the target motion process in step S330. Therefore, the ninth set of equations can be obtained. By solving the ninth set of equations, the running times of the jerk-accelerated section, the uniformly accelerated section, the jerk-decelerated section, the jerk-slowed section, the uniformly decelerated section, and the negative-jerk decelerated section can be obtained.

[0262] Step S353, when L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J and Vm - Vs > A 2 / J, if Vm - Ve ≤ A 2 / J and L ≤ S 1357 , it is determined that the target motion process only includes a jerk-accelerated section, a jerk-decelerated section, a jerk-slowed section, and a negative-jerk decelerated section, and the eleventh set of equations is obtained according to the target motion process; in step S353, since L1 < L < L2, it can be determined that the target motion process does not include a constant-speed section. Since Vs ≤ Ve and Ve - Vs < A 2 / J, if Vm - Ve ≤ A 2 / J and L ≤ S 1357 , it can be determined that the target motion process does not include a uniformly accelerated section and a uniformly decelerated section. Furthermore, it can be determined that the target motion process only includes a jerk-accelerated section, a jerk-decelerated section, a jerk-slowed section, and a negative-jerk decelerated section. The target motion process is the same as that in step S340. Therefore, the eleventh set of equations can be obtained, and by solving the eleventh set of equations, the running times of the jerk-accelerated section, the jerk-decelerated section, the jerk-slowed section, and the negative-jerk decelerated section can be obtained.

[0263] Step S354, when L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J and Vm - Vs > A 2 / J, if Vm - Ve ≤ A 2 / J and L > S 1357 , it is determined that the target motion process only includes a jerk-accelerated section, a uniformly accelerated section, a jerk-decelerated section, a jerk-slowed section, and a negative-jerk decelerated section, and the tenth set of equations is obtained according to the target motion process; in step S354, since L1 < L < L2, it can be determined that the target motion process does not include a constant-speed section. Since Vs ≤ Ve and Ve - Vs < A 2 / J, if Vm - Ve ≤ A 2 / J and L > S 1357, it can be determined that the target motion process includes a uniformly accelerated section and does not include a uniformly decelerated section. Furthermore, it can be determined that the target motion process only includes a jounce acceleration section, a uniformly accelerated section, a deceleration acceleration section, a jerk deceleration section, and a deceleration deceleration section, which is the same as the target motion process in step S331. Therefore, the tenth set of equations can be obtained, and by solving the tenth set of equations, the running times of the jounce acceleration section, the uniformly accelerated section, the deceleration acceleration section, the jerk deceleration section, and the deceleration deceleration section can be obtained.

[0264] Among them, J represents the maximum jounce acceleration, A represents the maximum acceleration, V S represents the initial velocity, Ve represents the final velocity, Vm represents the maximum driving velocity, L represents the actual path length, L1 represents the first critical length, L2 represents the second critical length, S 12357 represents when

[0265]

[0266] the path length of the motion process;

[0267] S 1357 represents when

[0268]

[0269] the path length of the motion process.

[0270] It should be noted that steps S330 to S331, step S340, and steps S350 to S354 for planning the S-curve jerk-limited target motion process are all carried out under the conditions of L1 < L < L2 and Vs ≤ Ve. When L1 < L < L2, the target motion process is a reversible process, that is, the displacement from the initial velocity to first accelerate to a new maximum velocity and then decelerate to the final velocity is equal to the displacement from the final velocity to first accelerate to a new maximum velocity and then decelerate to the initial velocity. Therefore, the target motion process with L1 < L < L2 and Vs > Ve can be transformed into a motion process from the final velocity Ve to first accelerate and then decelerate to the initial velocity Vs. Finally, only the acceleration times of each section and the deceleration times of each section obtained by calculation need to be interchanged. The planning of the target motion process with L1 < L < L2 and Vs > Ve can refer to steps S330 to S331, step S340, and steps S350 to S354, and this application will not elaborate on it anymore.

[0271] In a second aspect, an embodiment of the present application provides an S-curve jerk-limited planning system, including:

[0272] at least one memory;

[0273] at least one processor;

[0274] at least one program;

[0275] The program is stored in the memory, and the processor executes at least one program to implement:

[0276] Such as the S-curve acceleration and deceleration planning method of any one of the embodiments of the first aspect of the present application.

[0277] The processor and the memory may be connected via a bus or other means.

[0278] The processor executes non-transient software instructions, commands and signals stored in the memory, thereby performing various functional applications and data processing, and the S-curve acceleration and deceleration planning method of the first aspect embodiment.

[0279] The non-transient software instructions and instructions required for implementing the S-curve acceleration and deceleration planning method of the embodiment of the present invention are stored in the memory. When executed by the processor, the channel screening method of the first embodiment of the present application or the S-curve acceleration and deceleration planning method of the embodiment of the present invention is executed, for example, the above-described Figure 1 Steps S100 to S500 of the method, Figure 3 Steps S310 to S311 of the method, Figure 4 In the method steps S312 to S313, Figure 5 Steps S320 to S323 of the method, Figure 6 Steps S330 to S331 of the method, Figure 7 Method steps S350 to S354 in.

[0280] It should be noted that the S-curve acceleration and deceleration planning system in the above-mentioned embodiment and the S-curve acceleration and deceleration planning method in the above-mentioned embodiment are based on the same inventive concept. Therefore, the corresponding content of the S-curve acceleration and deceleration planning method in the above-mentioned embodiment is also applicable to the S-curve acceleration and deceleration planning system in the above-mentioned embodiment, and has the same implementation principle and technical effect. In order to avoid redundant description, it will not be described in detail here.

[0281] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, i.e., may be located in one place, or may be distributed over multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0282] In a third aspect, an embodiment of the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer-executable signal, and the computer-executable signal is used to execute:

[0283] Such as the S-curve acceleration and deceleration planning method of any one of the embodiments of the first aspect of the present application.

[0284] The computer-readable storage medium stores computer-executable instructions, which are executed by a processor or a controller, for example, by a processor in the above embodiment, so that the above processor can execute the S-curve acceleration and deceleration planning method of the first aspect of the present application, for example, execute the above-described Figure 1 Steps S100 to S500 of the method, Figure 3 Steps S310 to S313 of the method, Figure 4 In the method steps S312 to S313, Figure 5 Steps S320 to S323 of the method, Figure 6 Steps S330 to S331 of the method, Figure 7 Method steps S350 to S354 in.

[0285] Through the description of the above embodiments, it will be appreciated by those skilled in the art that all or some of the steps and systems in the disclosed method above can be implemented as software, firmware, hardware and appropriate combinations thereof. Some physical components or all physical components can be implemented as software executed by a processor, such as a central processing unit, a digital signal processor or a microprocessor, or implemented as hardware, or implemented as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a readable medium, and the readable medium can include a computer storage medium (or a non-transitory medium) and a communication medium (or a temporary medium). As known to those skilled in the art, the term computer storage medium includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as a computer-readable signal, a data structure, an instruction module or other data). Computer storage media include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disk (DVD) or other optical disk storage, magnetic cassette, magnetic tape, disk storage or other magnetic storage device, or any other medium that can be used to store desired information and can be accessed by a computer. Furthermore, it is well known to those skilled in the art that communication media generally include computer readable signals, data structures, instruction modules, or other data in a modulated data signal such as a carrier wave or other transport mechanism, and may include any information delivery media.

[0286] The embodiments of the present application are described in detail above in conjunction with the accompanying drawings, but the present application is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in the relevant technical field without departing from the purpose of the present application. In addition, the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

Claims

1. A method for S-curve acceleration and deceleration planning, characterized in that: include: Get the initial parameters of the S-curve; The initial parameters include initial velocity and final velocity; A first critical length and a second critical length are calculated based on the initial parameters; wherein the first critical length is the path length from the initial velocity to the final velocity; and the second critical length is the path length corresponding to the non-uniform speed section of the motion process; According to the first critical length, the second critical length and the initial parameters, a target motion process is determined, and according to the target motion process and the initial parameters, a set of equations corresponding to the target motion process is obtained; wherein the motion process includes at least one of the following: an acceleration segment, a uniform acceleration segment, a deceleration segment, a uniform speed segment, an acceleration and deceleration segment, a uniform deceleration segment, and a deceleration and deceleration segment; Solving the set of equations to obtain the running time corresponding to the target motion process; The calculating the first critical length and the second critical length according to the initial parameters comprises: The first critical length is calculated according to a first formula; wherein the initial parameters also include maximum acceleration and maximum jerk, and the first formula is: L1=L a (Vs,Ve)=L d (Ve,Vs), Wherein, L1 represents the first critical length, V S represents the initial velocity, Ve represents the final velocity, A represents the maximum acceleration, J represents the maximum jerk, L a (Vs, Ve) represents the path length from the initial velocity to the final velocity, L d (Ve, Vs) represents the path length of deceleration from the final velocity to the initial velocity; The second critical length is calculated according to a second formula; wherein the initial parameters also include a maximum driving speed, and the second formula is: L2=L a (Vs,Vm)+L d (Vm,Ve) Wherein, L2 represents the second critical length, Ve represents the final velocity, and V S represents the initial velocity, Vm represents the maximum driving speed, L a (Vs, Vm) represents the path length from the initial velocity to the maximum driving velocity, L d (Vm, Ve) characterizes the path length of deceleration from the maximum driving speed to the final speed.

2. The S-curve acceleration and deceleration planning method according to claim 1, characterized in that: The initial parameters also include actual path length; The target motion process is determined according to the first critical length, the second critical length and the initial parameters, and a set of equations corresponding to the target motion process is obtained according to the target motion process and the initial parameters, including: When L≤L1 and Vs≤Ve, if Ve-Vs>A 2 / J and L>S 13 , determine that the target motion process only includes a jerk segment, a uniform acceleration segment, and a deceleration segment, and obtain a first set of equations according to the target motion process; wherein the first set of equations is: Wherein, T1 represents the running time of the acceleration segment, T2 represents the running time of the uniform acceleration segment, T3 represents the running time of the deceleration segment, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, S 13 Characterization The path length of the motion process; When L≤L1 and Vs≤Ve, if Ve-Vs≤A 2 / J or L≤S 13 , it is determined that the target motion process only includes the acceleration segment and the deceleration segment, and a second set of equations is obtained according to the target motion process; wherein the second set of equations is: T1=T3, Wherein, T1 represents the running time of the acceleration segment, T3 represents the running time of the deceleration segment, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, S 13 Characterization The path length of the motion process.

3. The S-curve acceleration and deceleration planning method according to claim 1, characterized in that: The target motion process is determined according to the first critical length, the second critical length and the initial parameters, and a set of equations corresponding to the target motion process is obtained according to the target motion process and the initial parameters, including: When L≤L1 and Vs>Ve, if Vs-Ve>A 2 / J and L>S 57 , determine that the target motion process only includes an acceleration / deceleration segment, a uniform deceleration segment, and a deceleration / deceleration segment, and obtain a third equation group according to the target motion process; wherein the third equation group is: Wherein, T5 represents the running time of the acceleration / deceleration section, T6 represents the running time of the uniform deceleration section, T7 represents the running time of the deceleration / deceleration section, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, S 57 Characterization The path length of the motion process; When L≤L1 and Vs>Ve, if Vs-Ve≤A 2 / J or L≤S 57 , determine that the target motion process only includes the acceleration and deceleration segment and the deceleration and deceleration segment, and obtain the fourth set of equations according to the target motion process; wherein the fourth set of equations is: T5=T7, Wherein, T5 represents the running time of the acceleration / deceleration section, T7 represents the running time of the deceleration / deceleration section, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, S 57 Characterization The path length of the motion process.

4. The S-curve acceleration and deceleration planning method according to claim 1, characterized in that: The target motion process is determined according to the first critical length, the second critical length and the initial parameters, and a set of equations corresponding to the target motion process is obtained according to the target motion process and the initial parameters, including: When L≥L2, if Vm-Vs>A 2 / J and Vm-Ve>A 2 / J, determine that the target motion process includes an acceleration segment, a uniform acceleration segment, a deceleration segment, a uniform speed segment, an acceleration / deceleration segment, a uniform deceleration segment, and a deceleration / deceleration segment, and obtain a fifth set of equations according to the target motion process; the fifth set of equations is: When L≥L2, if Vm-Vs≤A 2 / J and Vm-Ve≤A 2 / J, determining that the target motion process only includes an acceleration segment, a deceleration segment, a uniform speed segment, an acceleration / deceleration segment, and a deceleration / deceleration segment, and obtaining a sixth set of equations according to the target motion process; The sixth set of equations is: When L≥L2, if Vm-Vs≤A 2 / J and Vm-Ve>A 2 / J, determine that the target motion process only includes an acceleration segment, a deceleration segment, a uniform speed segment, an acceleration / deceleration segment, a uniform deceleration segment, and a deceleration / deceleration segment, and obtain a seventh set of equations according to the target motion process; the seventh set of equations is: When L≥L2, if Vm-Vs>A 2 / J and Vm-Ve≤A 2 / J, determine that the target motion process only includes an acceleration segment, a uniform acceleration segment, a deceleration segment, a uniform speed segment, an acceleration and deceleration segment, and a deceleration and deceleration segment, and obtain an eighth set of equations according to the target motion process; the eighth set of equations is: Wherein, T1 represents the running time of the acceleration segment, T2 represents the running time of the uniform acceleration segment, T3 represents the running time of the deceleration segment, T4 represents the running time of the uniform speed segment, T5 represents the running time of the acceleration / deceleration segment, T6 represents the running time of the uniform deceleration segment, T7 represents the running time of the deceleration / deceleration segment, A represents the maximum acceleration, J represents the maximum jerk, V represents the maximum acceleration, S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L2 represents the second critical length, Vm represents the maximum driving speed, L a (Vs, Vm) represents the initial velocity V S The path length for accelerating to the maximum driving speed Vm, L d (Vm, Ve) represents the length of the path from the maximum driving speed Vm to the final speed Ve.

5. The S-curve acceleration and deceleration planning method according to claim 1, characterized in that: The target motion process is determined according to the first critical length, the second critical length and the initial parameters, and a set of equations corresponding to the target motion process is obtained according to the target motion process and the initial parameters, including: When L1 < L < L2 and Vs ≤ Ve and Ve - Vs > A 2 / J, if Vm - Ve > A 2 / J and L > S 12357 , it is determined that the target motion process only includes a positive acceleration section, a constant acceleration section, a negative acceleration section, a positive deceleration section, a constant deceleration section, and a negative deceleration section. According to the target motion process, a ninth set of equations is obtained, and the ninth set of equations is as follows: Wherein, T1 represents the running time of the acceleration segment, T2 represents the running time of the uniform acceleration segment, T3 represents the running time of the deceleration segment, T5 represents the running time of the acceleration / deceleration segment, T6 represents the running time of the uniform deceleration segment, T7 represents the running time of the deceleration / deceleration segment, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, L2 represents the second critical length, Vm represents the maximum driving speed, S 12357 Characterization The path length of the motion process; When L1 < L < L2 and Vs ≤ Ve and Ve - Vs > A 2 / J, if Vm - Ve ≤ A 2 / J or L ≤ S 12357 , it is determined that the target motion process only includes the positive acceleration phase, the constant acceleration phase, the negative acceleration phase, the positive deceleration phase, and the negative deceleration phase. According to the target motion process, the tenth set of equations is obtained, and the tenth set of equations is as follows: T7=T5, Wherein, T1 represents the running time of the acceleration segment, T2 represents the running time of the uniform acceleration segment, T3 represents the running time of the deceleration segment, T5 represents the running time of the acceleration / deceleration segment, T7 represents the running time of the deceleration / deceleration segment, A represents the maximum acceleration, J represents the maximum jerk, V S represents the initial velocity, Ve represents the final velocity, L represents the actual path length, L1 represents the first critical length, L2 represents the second critical length, Vm represents the maximum driving speed, S 12357 Characterization The path length of the motion process.

6. The S-curve acceleration and deceleration planning method according to claim 5, characterized in that: The step of determining the target motion process according to the first critical length, the second critical length and the initial parameters, and obtaining the set of equations corresponding to the target motion process according to the target motion process and the initial parameters, further includes: When L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J, if Vm - Vs ≤ A 2 / J, it is determined that the target motion process only includes the positive acceleration phase, the negative acceleration phase, the positive deceleration phase, and the negative deceleration phase, and an eleventh equation set is obtained according to the target motion process. The eleventh equation set is as follows: T1=T3,T5=T7, Wherein, T1 represents the running time of the acceleration segment, T3 represents the running time of the deceleration segment, T5 represents the running time of the acceleration / deceleration segment, T7 represents the running time of the deceleration / deceleration segment, J represents the maximum jerk, A represents the maximum acceleration, V S represents the initial velocity, Ve represents the final velocity, Vm represents the maximum driving velocity, L represents the actual path length, L1 represents the first critical length, and L2 represents the second critical length.

7. The S-curve acceleration and deceleration planning method according to claim 6, characterized in that: The step of determining the target motion process according to the first critical length, the second critical length and the initial parameters, and obtaining the set of equations corresponding to the target motion process according to the target motion process and the initial parameters, further includes: When L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J and Vm - Vs > A 2 / J, if Vm - Ve > A 2 / J and L ≤ S 1357 , it is determined that the target motion process only includes the positive acceleration section, the negative acceleration section, the positive deceleration section, and the negative deceleration section, and the eleventh equation set is obtained according to the target motion process; When L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J and Vm - Vs > A 2 / J, if Vm - Ve > A 2 / J and S1357 < L ≤ S12357, it is determined that the target motion process only includes the positive acceleration increasing section, the uniform acceleration section, the negative acceleration increasing section, the positive deceleration section, and the negative deceleration section, and the tenth set of equations is obtained according to the target motion process; When L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J and Vm - Vs > A 2 / J, if Vm - Ve > A 2 / J and L > S 12357 , it is determined that the target motion process only includes a positive acceleration phase, a constant acceleration phase, a negative acceleration phase, a positive deceleration phase, a constant deceleration phase, and a negative deceleration phase, and the ninth set of equations is obtained according to the target motion process; When L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J and Vm - Vs > A 2 / J, if Vm - Ve ≤ A 2 / J and L ≤ S 1357 , it is determined that the target motion process only includes the positive acceleration phase, the negative acceleration phase, the positive deceleration phase, and the negative deceleration phase, and the eleventh equation set is obtained according to the target motion process; When L1 < L < L2 and Vs ≤ Ve and Ve - Vs < A 2 / J and Vm - Vs > A 2 / J, if Vm - Ve ≤ A 2 / J and L > S 1357 , it is determined that the target motion process only includes the jerk - increasing acceleration section, the uniform acceleration section, the jerk - decreasing acceleration section, the acceleration - decreasing deceleration section, and the deceleration - decreasing deceleration section, and the tenth equation set is obtained according to the target motion process; Wherein, J represents the maximum jerk, A represents the maximum acceleration, V S represents the initial velocity, Ve represents the final velocity, Vm represents the maximum driving velocity, L represents the actual path length, L1 represents the first critical length, L2 represents the second critical length, S 12357 Characterization The path length of the motion process; S 1357 Characterization The path length of the motion process.

8. An S-curve acceleration and deceleration planning system, characterized in that: include: at least one memory; at least one processor; at least one program; The program is stored in the memory, and the processor executes at least one program to implement: The S-curve acceleration and deceleration planning method according to any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer-executable signal, and the computer-executable signal is used to execute: The S-curve acceleration and deceleration planning method according to any one of claims 1 to 7.

Images