Speed planning and fixed cycle interpolation method based on normalized cycloid function

Abstract

The application discloses a speed planning and fixed cycle interpolation method based on a normalized cycloid function and relates to the technical field of automatic processing.The method comprises the following steps: a system collects CNC motion section parameters and determines a normalized cycloid speed function; a normalized cycloid function constraint conversion framework is formed; a working condition type is determined; different cycloid planning time constraint equations are respectively executed for different working condition types based on the same normalized cycloid function constraint conversion framework; path direction cumulative displacement is solved from a cycloid integral result based on the cycloid planning time constraint; the cumulative displacement is sampled according to a fixed interpolation cycle; and path direction displacement increments of each interpolation cycle are calculated; the path direction displacement increments are mapped into increments of each axis; and CNC executable interpolation sequences are output.The application can complete long and short stroke unified peak speed solving, integral cumulative displacement sampling, final cycle end point closing and abnormal degeneration processing, thereby solving the problem of landing of a cycloid trajectory from a theoretical formula to CNC industrial interpolation.

Description

Technical Field

[0001] This invention relates to the field of automated processing technology, specifically to a speed planning and fixed-period interpolation method based on a normalized cycloidal function. Background Technology

[0002] When executing a machining program, a CNC system typically analyzes the machining trajectory into multiple motion segments. Each motion segment usually includes several parameters such as path length, starting speed, ending speed, maximum allowable feed rate, maximum allowable acceleration, maximum allowable jerk, interpolation cycle, and path geometry information. In actual CNC system operation, a speed curve is generated based on the above parameters, and position increments or pulse commands are output using a fixed interpolation cycle. However, in the interpolation process, cycloidal formulas or theoretical curves alone cannot directly form a usable industrial interpolation method. Existing technologies lack a complete implementation method for planning interpolation links in CNC systems, that is, a complete industrial implementation process is lacking, from motion segment parameter input, dynamic constraint conversion, peak speed solution, unified processing of long and short strokes, analytical cumulative displacement sampling, discrete interpolation output to endpoint closure. Summary of the Invention

[0003] The purpose of this invention is to provide a velocity planning and fixed-period interpolation method based on a normalized cycloidal function to solve the problems raised in the prior art.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a velocity planning and fixed-period interpolation method based on a normalized cycloidal function, the method comprising:

[0005] Step 101: The system collects CNC motion segment parameters and determines the normalized cycloidal velocity function;

[0006] Step 102: Calculate the shape constraint coefficients based on the derivative of the normalized cycloid function, and convert the normalized cycloid function into engineering constraint parameters that can be directly corresponding to the machine tool, thus forming a normalized cycloid function constraint conversion framework.

[0007] Step 103: Determine the working condition type. Based on the same normalized cycloidal function constraint conversion framework, execute different cycloidal planning time constraint equations for different working condition types. After solving, different cycloidal planning time constraints are formed. The working condition types include long-stroke working conditions and short-stroke working conditions.

[0008] Step 104: Based on the time constraint of cycloidal planning, directly solve the cumulative displacement in the path direction from the cycloidal integral result, sample the cumulative displacement according to the fixed interpolation period, and calculate the displacement increment in the path direction for each interpolation period;

[0009] Step 105: Map the path direction displacement increment to each axis increment, wherein each axis increment includes the target position of each axis, the position increment of each axis, and the speed command or pulse command;

[0010] Step 106: Output the CNC executable interpolation sequence, which includes the path direction displacement increment and the increment of each axis per cycle.

[0011] According to the above technical solution, the CNC motion segment parameters include: the path length of the motion to be planned, the starting speed, the ending speed, the maximum allowable speed, the maximum allowable acceleration, the maximum allowable jerk, the interpolation period, and the path geometry information;

[0012] The path length includes the length of a straight line, the arc length of a circular arc, the arc length of a spline curve, or the equivalent path length obtained through preprocessing.

[0013] According to the above technical solution, the normalized cycloidal velocity function should meet the requirements of continuous boundary velocity and smooth transition, and the normalized cycloidal velocity function should be integrated once to form an integral function.

[0014] According to the above technical solution, the shape constraint coefficient includes a normalized maximum acceleration coefficient and a normalized maximum jerk coefficient. The normalized maximum acceleration coefficient is the maximum value of the absolute value of the first derivative of the normalized cycloidal velocity function, and the normalized maximum jerk coefficient is the maximum value of the absolute value of the second derivative of the normalized cycloidal velocity function.

[0015] According to the above technical solution, the process of converting the normalized cycloidal function into engineering constraint parameters that can be directly corresponding to the machine tool, forming a normalized cycloidal function constraint conversion framework, includes:

[0016] For a candidate peak velocity Vp, the system calculates the velocity change as follows: ΔVa = Vp - Vs, ΔVd = Vp - Ve; where ΔVa refers to the velocity change during the acceleration phase, ΔVd is the velocity change during the deceleration phase, Vs refers to the starting velocity, and Ve refers to the ending velocity.

[0017] Calculate the acceleration period time Ta and the deceleration period time Td: Ta = max(ΔVa·Ca / Amax, sqrt(ΔVa·Cj / Jmax)), Td = max(ΔVd·Ca / Amax, sqrt(ΔVd·Cj / Jmax));

[0018] Where Ca and Cj refer to the normalized maximum acceleration coefficient and the normalized maximum jerk coefficient, respectively; Amax refers to the maximum allowable acceleration; and Jmax refers to the maximum allowable jerk.

[0019] According to the above technical solution, the determination of the working condition type includes:

[0020] The system takes the maximum allowable speed as the candidate peak speed, and calculates the acceleration section displacement La, deceleration section displacement Ld and remaining constant-speed section displacement Lc: La=Ta·(Vs+Vp) / 2; Ld=Td·(Vp+Ve) / 2;

[0021] Lc=L-La-Ld;

[0022] Wherein, if Lc≥0, it is determined as a long-stroke working condition, the system takes Vp=Vmax, the constant-speed section time Tc=Lc / Vp, and the total planning time is: Ta+Tc+Td; wherein, Vmax refers to the maximum allowable speed;

[0023] If Lc<0, it is determined as a short-stroke working condition, the system searches for the candidate peak speed Vp1 in the interval [max(Vs,Ve), Vmax] to make La(Vp1)+Ld(Vp1) match the path length, wherein La(Vp1) and Ld(Vp1) respectively refer to the acceleration section displacement and deceleration section displacement at the candidate peak speed Vp1, and after the search is completed, the system sets Tc to zero, so as to obtain a cycloid planning result without a constant-speed section.

[0024] According to the above technical solution, the solving of the cumulative displacement in the path direction directly from the cycloid integration result based on the cycloid planning time constraint, and sampling the cumulative displacement according to a fixed interpolation period includes:

[0025] Constructing cumulative displacement functions for the acceleration section, constant-speed section and deceleration section:

[0026] For the acceleration section 0≤t≤Ta, let x=t / Ta, then: v(t)=Vs+(Vp-Vs)·g(x); s(t)=Vs·t+(Vp-Vs)·Ta·G(x);

[0027] For the constant-speed section Ta<t≤Ta+Tc, then: v(t)=Vp; s(t)=La+Vp·(t-Ta);

[0028] For the deceleration section Ta+Tc<t≤Ta+Tc+Td, let x=(t-Ta-Tc) / Td, then: v(t)=Vp-(Vp-Ve)·g(x); s(t)=La+Lc+Vp·(t-Ta-Tc)-(Vp-Ve)·Td·G(x);

[0029] Wherein, t is the time variable counted from the start point of the current planning section; v(t) is the instantaneous speed or feed speed in the path direction corresponding to time t; s(t) is the cumulative displacement in the path direction corresponding to time t; Vs is the start speed of the planning section; Vp is the peak speed; Ta is the time of the acceleration section; x=t / Ta is the normalized time of the acceleration section; g(x) is the normalized cycloid speed transition function; G(x) is the first integral function of g(x).

[0030] According to the above technical solution, calculating the path direction displacement increment for each interpolation cycle includes:

[0031] The cumulative displacement is sampled according to a fixed interpolation period. The system sets the kth sampling time as: tk=min(kT, Ta+Tc+Td);

[0032] Calculate the path direction displacement increment Δsk in the kth interpolation cycle: Δsk = s(tk) - s(tk-1).

[0033] According to the above technical solution, the mapping of the path direction displacement increment to each axis increment further includes:

[0034] For linear motion, the system distributes the path direction displacement increment according to the proportion of each axis direction; for circular, spline or other curved motion, the system converts the path direction displacement increment into the target position of each axis, the position increment of each axis, the velocity command or the pulse command according to the correspondence between the path geometric parameters and the arc length.

[0035] According to the above technical solution, it also includes:

[0036] If the interpolation period cannot be divided by the total planning time, then the last sampling time is taken as the total planning time, and the last displacement increment is taken as the difference between the target total length and the output cumulative length, so that the cumulative output length is equal to the target path length and the endpoint speed is consistent with the target endpoint speed.

[0037] Compared with the prior art, the beneficial effects of the present invention are: the present application can convert the normalized cycloidal function into engineering planning parameters that can match the maximum speed, maximum acceleration, maximum jerk, start and end speed, path length and interpolation period of CNC, and further complete the solution of unified peak speed for long and short strokes, integral cumulative displacement sampling, final cycle end point closure and abnormal degradation processing, thereby solving the problem of implementing the cycloidal trajectory from theoretical formula to CNC industrial interpolation.

[0038] In practical engineering, this invention can directly match machine tool dynamic constraints, establishing a correspondence between the cycloidal function and the maximum acceleration and maximum jerk, ensuring that the planning results meet machine tool constraints during the generation stage. It can uniformly handle long and short strokes; long strokes can reach the maximum allowable speed and include a constant speed segment; short strokes generate a cycloidal curve without a constant speed segment through adaptive peak speed search, avoiding switching between different speed models. Simultaneously, the cycloidal speed transition helps reduce acceleration and jerk impacts, thereby reducing machine tool vibration, impact, and servo following errors, improving machining stability, and enhancing the quality of high-speed precision machining.

[0039] This application also features engineering security and scalability, and can adapt to real-world industrial scenarios such as short distances, zero speed changes, low dynamic constraints, and mismatched interpolation cycles through abnormal degradation processing. Attached Figure Description

[0040] Figure 1 This is a flowchart of the velocity planning and fixed-period interpolation method based on the normalized cycloidal function of the present invention. Detailed Implementation

[0041] Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0042] Example: Figure 1 As shown, this invention provides a velocity planning and fixed-period interpolation method based on a normalized cycloidal function, the method comprising:

[0043] Step 101: The system collects CNC motion segment parameters and determines the normalized cycloidal velocity function;

[0044] Step 102: Calculate the shape constraint coefficients based on the derivative of the normalized cycloid function, and convert the normalized cycloid function into engineering constraint parameters that can be directly corresponding to the machine tool, thus forming a normalized cycloid function constraint conversion framework.

[0045] Step 103: Determine the working condition type. Based on the same normalized cycloidal function constraint conversion framework, execute different cycloidal planning time constraint equations for different working condition types. After solving, different cycloidal planning time constraints are formed. The working condition types include long-stroke working conditions and short-stroke working conditions.

[0046] Step 104: Based on the time constraint of cycloidal planning, directly solve the cumulative displacement in the path direction from the cycloidal integral result, sample the cumulative displacement according to the fixed interpolation period, and calculate the displacement increment in the path direction for each interpolation period;

[0047] Step 105: Map the path direction displacement increment to each axis increment, wherein each axis increment includes the target position of each axis, the position increment of each axis, and the speed command or pulse command;

[0048] Step 106: Output the CNC executable interpolation sequence, which includes the path direction displacement increment and the increment of each axis per cycle.

[0049] In this embodiment, the system collects the path length L, starting velocity Vs, ending velocity Ve, maximum allowable velocity Vmax, maximum allowable acceleration Amax, maximum allowable jerk Jmax, interpolation period T, and path geometry information of the motion to be planned. The path length L can be the length of a straight line, the arc length of a circular arc, the arc length of a spline curve, or an equivalent path length obtained through preprocessing.

[0050] In this embodiment, the system selects a normalized cycloidal velocity transition function g(x) that satisfies the requirements of continuous boundary velocity and smooth transition, where x∈[0,1]. g(x) adopts:

[0051] g(x)=xa·sin(2πx)-b·sin(4πx)

[0052] Where a and b are shape coefficients. The system also establishes an integral function G(x) for g(x), which is used to directly calculate the cumulative displacement along the path direction. This step allows for the creation of a differentiable, integrable, and sampleable normalized velocity transition function for CNC velocity planning.

[0053] The system determines the normalized maximum acceleration coefficient Ca and the normalized maximum jerk coefficient Cj based on the first and second derivatives of g(x):

[0054] Ca=max|g'(x)|, Cj=max|g''(x)|, x∈[0,1]

[0055] Further, the normalized cycloidal function is converted into engineering constraint parameters that can be directly corresponding to the machine tool, forming a normalized cycloidal function constraint conversion framework, including:

[0056] For a candidate peak velocity Vp, the system calculates the velocity change as follows: ΔVa = Vp - Vs, ΔVd = Vp - Ve; where ΔVa refers to the velocity change during the acceleration phase, ΔVd is the velocity change during the deceleration phase, Vs refers to the starting velocity, and Ve refers to the ending velocity.

[0057] Calculate the acceleration period time Ta and the deceleration period time Td: Ta = max(ΔVa·Ca / Amax, sqrt(ΔVa·Cj / Jmax)), Td = max(ΔVd·Ca / Amax, sqrt(ΔVd·Cj / Jmax));

[0058] Where Ca and Cj refer to the normalized maximum acceleration coefficient and the normalized maximum jerk coefficient, respectively; Amax refers to the maximum allowable acceleration; and Jmax refers to the maximum allowable jerk.

[0059] Perform long-range reachability assessment:

[0060] The system takes the maximum allowable speed as the candidate peak speed, and calculates the acceleration section displacement La, deceleration section displacement Ld and remaining constant-speed section displacement Lc: La=Ta·(Vs+Vp) / 2; Ld=Td·(Vp+Ve) / 2;

[0061] Lc=L-La-Ld;

[0062] Wherein, if Lc≥0, it is determined as a long-stroke working condition, the system takes Vp=Vmax, the constant-speed section time Tc=Lc / Vp, and the total planning time is: Ta+Tc+Td; wherein, Vmax refers to the maximum allowable speed;

[0063] If Lc<0, it is determined as a short-stroke working condition, and the adaptive solution of the short-stroke peak speed is performed. The system searches for the candidate peak speed Vp1 in the interval [max(Vs,Ve), Vmax], so that La(Vp1)+Ld(Vp1) matches the path length. Mathematically, the matching means that La(Vp1)+Ld(Vp1)=L; in specific engineering implementation, due to numerical search and floating-point errors, it normally satisfies |La(Vp1)+Ld(Vp1)-L|≤εL, where εL is a preset length tolerance. That is, the peak speed Vp1 is searched to make the sum of the acceleration section displacement and the deceleration section displacement equal to the target path length L or equal to the target path length L within the tolerance range. Wherein, La(Vp1) and Ld(Vp1) respectively refer to the acceleration section displacement and the deceleration section displacement at the candidate peak speed Vp1. After the search is completed, the system sets Tc to zero, so as to obtain the cycloid planning result without a constant-speed section. In this embodiment, both the long stroke and the short stroke can be processed in the same normalized cycloid constraint conversion framework, without the need for manual switching between multiple models such as trapezoid, triangle, and S-curve

[0064] Further, the accumulated displacement in the path direction is directly solved from the cycloid integration result based on the cycloid planning time constraint, and sampling the accumulated displacement according to a fixed interpolation cycle includes:

[0065] Constructing the accumulated displacement functions of the acceleration section, the constant-speed section and the deceleration section:

[0066] For the acceleration section 0≤t≤Ta, let x=t / Ta, then: v(t)=Vs+(Vp-Vs)·g(x); s(t)=Vs·t+(Vp-Vs)·Ta·G(x);

[0067] For the constant-speed section Ta<t≤Ta+Tc, then: v(t)=Vp; s(t)=La+Vp·(t-Ta);

[0068] For the deceleration section Ta+Tc<t≤Ta+Tc+Td, let x=(t-Ta-Tc) / Td,

[0069] Then v(t)=Vp-(Vp-Ve)·g(x); s(t)=La+Lc+Vp·(t-Ta-Tc)-(Vp-Ve)·Td·G(x);

[0070] Where t is the time variable starting from the beginning of the current planning segment; v(t) is the instantaneous velocity or feed rate in the path direction at time t; s(t) is the cumulative displacement in the path direction at time t; Vs is the velocity at the beginning of the planning segment; Vp is the peak velocity; Ta is the acceleration segment time; x = t / Ta is the normalized acceleration segment time; g(x) is the normalized cycloidal velocity transition function; and G(x) is the first integral function of g(x). In this embodiment, by using the cumulative displacement function, the system can directly obtain the sampleable path length from the cycloidal integral result, reducing the error caused by approximating the cycloidal curve to other velocity models.

[0071] Further calculate the path direction displacement increment for each interpolation cycle:

[0072] The cumulative displacement is sampled according to a fixed interpolation period. The system sets the kth sampling time as: tk=min(kT, Ta+Tc+Td);

[0073] Calculate the path direction displacement increment Δsk in the kth interpolation cycle: Δsk = s(tk) - s(tk-1).

[0074] The mapping of path direction displacement increments to axis increments also includes:

[0075] For linear motion, the system distributes the path direction displacement increment according to the proportion of each axis direction; for circular, spline or other curved motion, the system converts the path direction displacement increment into the target position of each axis, the position increment of each axis, the velocity command or the pulse command according to the correspondence between the path geometric parameters and the arc length.

[0076] If the interpolation period cannot be divided by the total planning time, then the last sampling time is taken as the total planning time, and the last displacement increment is taken as the difference between the target total length and the output cumulative length, so that the cumulative output length is equal to the target path length and the endpoint speed is consistent with the target endpoint speed.

[0077] When the input parameters do not meet the planning conditions, the speed change is zero, the maximum acceleration or maximum acceleration is too small, the search for peak speed fails, the interpolation period is too large, or the path mapping is abnormal, the system can adopt methods such as speed limiting, reducing peak speed, extending planning time, degenerating to zero uniform speed segment, degenerating to safe planning mode, or prompting the upper layer to replan, to ensure the safety and stability of the CNC control process.

[0078] The final output is a CNC-executable interpolation sequence. This interpolation sequence may include the path displacement increment per cycle, the position increment of each axis, the target position of each axis, the velocity reference value, the acceleration reference value, or the number of pulses. The output sequence meets the fixed interpolation cycle requirement and is consistent with the desired normalized cycloidal velocity planning result.

[0079] In one extended implementation, if there is a non-zero acceleration at the start or end of a motion segment, the system can use a generalized cycloidal planning template with a non-zero acceleration boundary for processing. This extended implementation is used to handle motion segments or sub-planning segments where the start velocity vs, end velocity ve, start acceleration as, and end acceleration ae are all known, enabling the standard zero-acceleration boundary cycloidal planning to be extended to a cycloidal planning that supports continuous acceleration transfer between segments.

[0080] The system first defines the normalized time τ = t / T, where τ ∈ [0,1] and T is the planning time to be determined; it defines the velocity increment Δv = ve - vs, the acceleration increment Δa = ae - as, and the average acceleration aavg = (as + ae) / 2, and defines parameters related to the time scale:

[0081] C(T) = Δv / T - aavg

[0082] The system constructs a generalized cycloidal acceleration function that satisfies the non-zero acceleration boundary:

[0083] a(t)=as+Δa / 2·(1-cos(πτ))+C(T)·(1-cos(2πτ))

[0084] The function satisfies a(0) = as and a(T) = ae. In the standard cycloidal programming part, g(x) is used as the normalized velocity transition function, and G(x) is the first integral of g(x); it is not an integral of g(x) multiple times. In the non-zero acceleration boundary extension implementation, the acceleration function a(t) is constructed first, then v(t) is obtained by a first integral, and s(t) is obtained by a second integral. When as = 0 and ae = 0, the above equation automatically degenerates into the standard cycloidal acceleration form:

[0085] a(t)=Δv / T·(1-cos(2πτ))

[0086] The system integrates the above acceleration function to obtain the velocity function:

[0087] v(t)=vs+T·[as·τ+Δa·(τ / 2-sin(πτ) / (2π))+C(T)·(τ-sin(2πτ) / (2π))]

[0088] Furthermore, by integration, the cumulative displacement function along the path direction is obtained:

[0089] s(t) = s0 + vs·t + T2 ·[as·τ 2 / 2+Δa·(τ 2 / 4+(cos(πτ)-1) / (2π 2 ))+C(T)·(τ 2 / 2+(cos(2πτ)-1) / (4π 2 ))]

[0090] Where s0 is the cumulative displacement at the starting point. The acceleration function can be obtained by differentiating the acceleration function:

[0091] j(t)=(π / T)·sin(πτ)·[Δa / 2+4·C(T)·cos(πτ)]

[0092] Therefore, the extended template automatically satisfies j(0)=0 and j(T)=0, which is beneficial for maintaining a smoother jerk transition between adjacent planning segments in CNC.

[0093] When solving for the minimum planning time, the system first performs a feasibility check to determine whether the endpoint accelerations meet the requirements:

[0094] |as|≤Amax,|ae|≤Amax;

[0095] If the endpoint acceleration exceeds the machine tool's maximum acceleration, the boundary state is infeasible. The system reduces the boundary velocity, adjusts the boundary acceleration, splits the planning segment, or degenerates into a safe speed-limited planning approach. If the endpoint acceleration satisfies the constraints, the system calculates the peak acceleration Apeak(T) and peak jerk Jpeak(T) at a given T, and determines:

[0096] Apeak(T)≤Amax and Jpeak(T)≤Jmax

[0097] For Apeak(T), the system can be rewritten as x = cos(πτ) to express the acceleration as follows:

[0098] a(x) = aavg + 2C - Δa / 2·x - 2C·x 2

[0099] Candidate points for acceleration extrema include endpoints τ=0, τ=1, and interior points:

[0100] xa = -Δa / (8C)

[0101] When C≠0 and |Δa|≤8|C|, the interior points are valid. The system compares the absolute values ​​of the endpoint accelerations and the interior extrema to obtain Apeak(T). For Jpeak(T), the system can transform the jerk peak search into the calculation of candidate points on x∈[-1,1], where the candidate points satisfy:

[0102] 16C·x 2 +Δa·x-8C=0

[0103] When C≠0, the candidate roots are:

[0104] xj±=(-Δa±sqrt(Δa 2 +512C 2 )) / (32C)

[0105] The system retains roots falling within [-1,1] and substitutes them into j(t) to calculate the peak value; when C=0, the system uses a degenerate expression:

[0106] Jpeak(T) = π·|Δa| / (2T)

[0107] In engineering implementation, the system can be solved by a one-dimensional search to find the minimum feasible time Tmin. The system constructs an initial lower bound:

[0108] T low =max(eps, |Δv| / Amax, π·|Δa| / (2Jmax))

[0109] Then let T high =max(2·T low , eps), if T high If it is not feasible, then continuously adjust T. high Double it until Apeak(T) high )≤Amax and Jpeak(T) high )≤Jmax. Then in [T low , T high Perform a binary search within the interval until the interval width is less than the preset tolerance tol, obtaining Tmin = T high This one-dimensional search only requires repeated calculation of the analytical peak, resulting in low computational cost, making it suitable for use in CNC background planning threads or look-ahead planning threads.

[0110] If the current problem involves known boundary states and a known path length L, then the system can be derived from the displacement relationships at t=T:

[0111] L=(vs+ve) / 2·T+(as-ae) / π 2 ·T 2

[0112] The system first calculates the T that matches the given L based on this relationship, and then checks whether the T satisfies the Amax and Jmax constraints. If it does not, it means that the combination of the current length and the non-zero acceleration boundary state is not feasible. The system can reduce vs or ve, adjust as or ae, add transition segments, split motion segments, or switch to safe planning mode.

[0113] If the current problem is the construction of an acceleration or deceleration segment template, the system can first calculate Tmin based on the given start and end velocities and accelerations, then calculate the required length of the template using the displacement formula, and use this length as the occupied length of the acceleration or deceleration segment in the long and short stroke peak velocity solution. For planning involving peak velocity Vp, the system can perform the above non-zero acceleration boundary solution for the acceleration segment from (vs,as) to (Vp,ap) and the deceleration segment from (Vp,ap) to (ve,ae), where ap can be zero, determined according to the continuity of adjacent segments, or determined through joint optimization.

[0114] During fixed-period interpolation output, the system still employs cumulative displacement sampling. Let tk = min(kT, T), calculate s(tk) - s(tk-1) as the path direction displacement increment for the k-th interpolation cycle, and map it to the position increment of each axis or pulse command. The last sampling time is set to T to ensure that the position boundary, velocity boundary, and acceleration boundary are consistent with the desired generalized cycloidal curve. If the discrete sampling error exceeds the threshold, the system can perform multi-period error amortization, reselect T, or degenerate to zero-acceleration boundary planning.

[0115] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A velocity planning and fixed-period interpolation method based on a normalized cycloidal function, characterized in that: The method includes: Step 101: The system collects CNC motion segment parameters and determines the normalized cycloidal velocity function; Step 102: Calculate the shape constraint coefficients based on the derivative of the normalized cycloid function, and convert the normalized cycloid function into engineering constraint parameters that can be directly corresponding to the machine tool, thus forming a normalized cycloid function constraint conversion framework. Step 103: Determine the working condition type. Based on the same normalized cycloidal function constraint conversion framework, execute different cycloidal planning time constraint equations for different working condition types. After solving, different cycloidal planning time constraints are formed. The working condition types include long-stroke working conditions and short-stroke working conditions. Step 104: Based on the time constraint of cycloidal planning, directly solve the cumulative displacement in the path direction from the cycloidal integral result, sample the cumulative displacement according to the fixed interpolation period, and calculate the displacement increment in the path direction for each interpolation period; Step 105: Map the path direction displacement increment to each axis increment, wherein each axis increment includes the target position of each axis, the position increment of each axis, and the speed command or pulse command; Step 106: Output the CNC executable interpolation sequence, which includes the path direction displacement increment and the increment of each axis per cycle.

2. The velocity planning and fixed-period interpolation method based on the normalized cycloidal function according to claim 1, characterized in that: The CNC motion segment parameters include: the path length of the motion to be planned, the starting speed, the ending speed, the maximum allowable speed, the maximum allowable acceleration, the maximum allowable jerk, the interpolation period, and the path geometry information; The path length includes the length of a straight line, the arc length of a circular arc, the arc length of a spline curve, or the equivalent path length obtained through preprocessing.

3. The velocity planning and fixed-period interpolation method based on the normalized cycloidal function according to claim 1, characterized in that: The normalized cycloidal velocity function should meet the requirements of continuous boundary velocity and smooth transition, and the normalized cycloidal velocity function should be integrated once to form an integral function.

4. The velocity planning and fixed-period interpolation method based on the normalized cycloidal function according to claim 1, characterized in that: The shape constraint coefficients include normalized maximum acceleration coefficients and normalized maximum jerk coefficients. The normalized maximum acceleration coefficients are the maximum absolute value of the first derivative of the normalized cycloidal velocity function, and the normalized maximum jerk coefficients are the maximum absolute value of the second derivative of the normalized cycloidal velocity function.

5. The velocity planning and fixed-period interpolation method based on the normalized cycloidal function according to claim 1, characterized in that: The process of converting the normalized cycloidal function into engineering constraint parameters that can be directly corresponding to the machine tool, forming a normalized cycloidal function constraint conversion framework, includes: For a candidate peak velocity Vp, the system calculates the velocity change as follows: ΔVa = Vp - Vs, ΔVd = Vp - Ve; where ΔVa refers to the velocity change during the acceleration phase, ΔVd is the velocity change during the deceleration phase, Vs refers to the starting velocity, and Ve refers to the ending velocity. Calculate the acceleration period time Ta and the deceleration period time Td: Ta = max(ΔVa·Ca / Amax, sqrt(ΔVa·Cj / Jmax)), Td = max(ΔVd·Ca / Amax, sqrt(ΔVd·Cj / Jmax)); Where Ca and Cj refer to the normalized maximum acceleration coefficient and the normalized maximum jerk coefficient, respectively; Amax refers to the maximum allowable acceleration; and Jmax refers to the maximum allowable jerk.

6. The velocity planning and fixed-period interpolation method based on the normalized cycloidal function according to claim 5, characterized in that: The determined operating condition types include: The system takes the maximum allowable speed as the candidate peak speed, and calculates the acceleration section displacement La, deceleration section displacement Ld and remaining constant-speed section displacement Lc: La=Ta·(Vs+Vp) / 2; Ld=Td·(Vp+Ve) / 2; Lc=L-La-Ld; Wherein, if Lc≥0, it is determined as a long-stroke working condition, the system takes Vp=Vmax, the constant-speed section time Tc=Lc / Vp, and the total planning time is: Ta+Tc+Td; wherein Vmax refers to the maximum allowable speed; If Lc<0, it is determined as a short-stroke working condition, the system searches for the candidate peak speed Vp1 in the interval [max(Vs,Ve), Vmax] to make La(Vp1)+Ld(Vp1) match the path length, wherein La(Vp1) and Ld(Vp1) respectively refer to the acceleration section displacement and deceleration section displacement at the candidate peak speed Vp1. After the search is completed, the system sets Tc to zero, so as to obtain a cycloid planning result without a constant-speed section.

7. The velocity planning and fixed-period interpolation method based on the normalized cycloidal function according to claim 6, characterized in that: The directly solving the cumulative displacement in the path direction from the cycloid integration result based on the cycloid planning time constraint, and sampling the cumulative displacement according to a fixed interpolation period includes: Constructing the cumulative displacement functions of the acceleration section, the constant-speed section and the deceleration section: For the acceleration section 0≤t≤Ta, let x=t / Ta, then: v(t)=Vs+(Vp-Vs)·g(x); s(t)=Vs·t+(Vp-Vs)·Ta·G(x); For the constant-speed section Ta<t≤Ta+Tc, then: v(t)=Vp; s(t)=La+Vp·(t-Ta); For the deceleration section Ta+Tc<t≤Ta+Tc+Td, let x=(t-Ta-Tc) / Td, then: v(t)=Vp-(Vp-Ve)·g(x); s(t)=La+Lc+Vp·(t-Ta-Tc)-(Vp-Ve)·Td·G(x); Wherein, t is the time variable counted from the start point of the current planning section; v(t) is the instantaneous speed or feed speed in the path direction corresponding to time t; s(t) is the cumulative displacement in the path direction corresponding to time t; Vs is the start point speed of the planning section; Vp is the peak speed; Ta is the acceleration section time; x=t / Ta is the normalized time of the acceleration section; g(x) is the normalized cycloid speed transition function; G(x) is the first integral function of g(x).

8. The velocity planning and fixed-period interpolation method based on the normalized cycloidal function according to claim 1, characterized in that: The calculating the displacement increment in the path direction for each interpolation period includes: Sampling the cumulative displacement according to the fixed interpolation period, the system sets the k-th sampling moment as: tk=min(kT, Ta+Tc+Td); Calculate the displacement increment Δsk in the path direction of the k-th interpolation period: Δsk=s(tk)-s(tk-1).

9. The velocity planning and fixed-period interpolation method based on the normalized cycloidal function according to claim 1, characterized in that: The mapping the displacement increment in the path direction to the increments of each axis further includes: For linear motion, the system distributes the displacement increment in the path direction according to the proportion of each axis direction; for circular arc, spline or other curve motion, the system converts the displacement increment in the path direction into the target position of each axis, the position increment of each axis, the speed command or the pulse command according to the corresponding relationship between the path geometric parameters and the arc length.

10. The velocity planning and fixed-period interpolation method based on the normalized cycloidal function according to claim 1, characterized in that: Further comprising: If the interpolation period cannot be divided by the total planning time, then the last sampling time is taken as the total planning time, and the last displacement increment is taken as the difference between the target total length and the output cumulative length, so that the cumulative output length is equal to the target path length and the endpoint speed is consistent with the target endpoint speed.

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