NURBS curve asymmetric velocity planning method under geometric and kinematic constraints

Abstract

The present application relates to the technical field of numerical control machining, and specifically provides a NURBS curve asymmetric speed planning method under geometric and kinematic constraints, comprising: establishing an asymmetric S-shaped acceleration and deceleration model with independent maximum acceleration and acceleration change rate parameters in the acceleration and deceleration process; segmenting according to the local maximum points of the NURBS curve curvature and calculating the arc length; and determining the maximum allowable feed speed of each segment point in combination with geometric and kinematic constraints. Further, a first scanning operation is performed on each planning segment along the machining direction: presetting the acceleration and deceleration interval, determining the motion parameters based on the machine tool axis limit and the speed upper limit, verifying and adjusting the segment point speed by using the speed planning model, and iteratively correcting the interval boundary. Then, a second scanning operation is performed along the reverse machining direction for optimization. Finally, the asymmetric S-shaped speed planning curve satisfying all constraints is output. Through the parameter-independent asymmetric model, the present application realizes precise adaptation to the unequal motion capabilities of each axis of the machine tool and improves the machining efficiency.

Description

Technical Field

[0001] This invention belongs to the field of CNC machining technology, specifically relating to an asymmetric velocity planning method for NURBS curves under geometric and kinematic constraints. Background Technology

[0002] With the increasing demands for precision and efficiency in machining complex curved surface parts in the manufacturing industry, using NURBS curves to represent tool trajectories has become a key technology for achieving high-speed and high-precision machining. Speed ​​planning, as the core of a CNC system, directly determines machining quality, efficiency, and equipment lifespan. Existing speed planning methods are mainly divided into two categories: methods based on fixed acceleration / deceleration models typically only consider tangential constraints, which may violate the actual motion limits of each axis; while methods based on optimization introduce axial constraints, but mostly assume that the limits of each axis are symmetrical and equal. In actual machining, due to differences in the mechanical structure, drive performance, and load of each axis, its acceleration and jerk limits are often asymmetrical, and changes in curve geometry exacerbate the asymmetry of the motion process. Existing methods fail to fully consider this asymmetry, making it difficult to dynamically adapt to the unequal upper limits of each axis, resulting in the machine tool's motion potential not being fully realized, thus restricting further improvements in machining efficiency. Therefore, there is an urgent need for an intelligent speed planning method that can simultaneously consider geometric constraints and asymmetric kinematic constraints. Summary of the Invention

[0003] To address the aforementioned shortcomings of existing technologies, this invention provides an asymmetric velocity planning method for NURBS curves under geometric and kinematic constraints, thereby resolving the aforementioned technical problems.

[0004] In a first aspect, the present invention provides a method for managing doctor-patient interaction, comprising: An asymmetric S-shaped acceleration / deceleration model is established, in which the acceleration and deceleration processes have independent maximum acceleration and rate of change of acceleration parameters. Based on the curvature of each point on the NURBS curve, the local maximum point of curvature is selected as the segmentation point, the curve is divided into multiple planning segments, and the arc length of each segment is calculated. Based on the preset geometric and kinematic constraint parameters and the radius of curvature of each segment point, determine the maximum allowable feed rate of each segment point; The first scan operation is performed sequentially on each planned segment along the machining direction. The first scan operation includes: presetting the acceleration and deceleration interval for the current segment; determining the acceleration and acceleration change rate parameters of the current segment based on the machine tool axis limits and the maximum allowable feed speed at the segment point; verifying and adjusting the segment point speed to a feasible value according to the current segment arc length and speed planning model; and iteratively correcting the interval boundary based on the actual required acceleration and deceleration distance. The second scanning operation is performed sequentially on each planned segment along the reverse machining direction. The second scanning operation includes: determining the acceleration and acceleration change rate parameters of the current segment based on the machine tool axis limits and the maximum allowable feed speed of the segment point; verifying and adjusting the segment point speed to a feasible value according to the current segment arc length and speed planning model; and iteratively correcting the interval boundary according to the actual required acceleration and deceleration distance. Output the asymmetric S-shaped velocity planning curve that satisfies all constraints, obtained after the first and second scan operations.

[0005] In an optional implementation, the asymmetric S-shaped acceleration / deceleration model includes seven sequentially connected stages: an acceleration phase, a uniform acceleration phase, a deceleration phase, a uniform speed phase, an acceleration / deceleration phase, a uniform deceleration phase, and a deceleration / deceleration phase; wherein the acceleration phase, uniform acceleration phase, and deceleration phase constitute an acceleration process, and the acceleration / deceleration phase, uniform deceleration phase, and deceleration / deceleration phase constitute a deceleration process, and the acceleration process and the deceleration process each have their own independently set maximum acceleration value and maximum rate of change of acceleration value.

[0006] In an optional implementation, an asymmetric S-shaped acceleration / deceleration model is established, including: Obtain kinematic constraint parameters, including: the maximum acceleration and maximum rate of change of acceleration of each axis of the machine tool, the system command speed, the maximum bow height error and the maximum rate of change of normal acceleration determined by the machining process, and the starting speed and ending speed of the current planning segment; The acceleration and deceleration intervals of the current planning segment are discretized. For each discrete micro-segment, based on its motion direction and the acceleration and acceleration rate of change limits of each axis of the machine tool, the maximum tangential acceleration and tangential acceleration rate of change, as well as the maximum tangential acceleration and tangential acceleration rate of change during the deceleration process, which satisfy all axis constraints are calculated and determined respectively. Based on the maximum bow height error and the maximum rate of change of normal acceleration, the upper limit of instantaneous velocity of each point in the current planning segment is determined; Based on the initial velocity, the final velocity, the system command velocity, the determined tangential acceleration and rate of change of acceleration parameters, and the arc length of the planned segment, by comparing the arc length with the minimum displacement required to accelerate to the system command velocity, it is determined which of the following situations the velocity planning scenario belongs to: insufficient displacement to reach the system command velocity, able to reach the system command velocity but without a uniform velocity segment, or able to reach the system command velocity and with a uniform velocity segment. Based on the determined situation, and with the constraint of not exceeding the upper limit of instantaneous velocity, the duration of each stage in the asymmetric S-shaped acceleration / deceleration model is determined by solving the equations that satisfy the relationship between displacement and velocity under this situation.

[0007] In an optional implementation, based on the curvature of each point on the NURBS curve, local maxima of curvature are selected as segmentation points, dividing the curve into multiple planning segments, including: Discrete sampling is performed within the parameter range of the NURBS curve, and the curvature of each sampling point is calculated. Determine the curvature threshold based on the processing requirements; Sampling points with curvature greater than the curvature threshold and which are local maxima are selected as segmentation critical points; Arrange the starting point, ending point, and all segment critical points of the curve in parameter order, and define the curve segment between two adjacent points as a planning segment.

[0008] In one optional implementation, the calculation of the arc length includes: For parameter intervals The planning segment, its curve arc length s is expressed in integral form. ,in Let be the first derivative of the NURBS curve at parameter u; The integral value is approximated by iteratively bisecting the parameter interval and applying Simpson's formula: First, the approximate value of the Simpson integral S over the entire interval is calculated. total Then calculate the sum of the Simpson integral approximations on the two subintervals after bisecting the interval, S. sum ; Determine S total With S sum Is the difference less than the preset precision threshold? If so, then S sum If the result is not found, the same binary search and accuracy judgment process is recursively performed on each subinterval until the accuracy requirement is met, and the sum of the approximate integral values ​​of all subintervals that meet the accuracy requirement is taken as the arc length of the planning segment.

[0009] In an optional implementation, the maximum allowable feed rate for each segment point is determined based on preset geometric and kinematic constraint parameters and the radius of curvature of each segment point, including: Obtain preset constraint parameters, including: maximum permissible bow height error. Maximum permissible normal acceleration Maximum permissible rate of change of normal acceleration System command speed V m and the interpolation period T s ; For each of the aforementioned segment points, based on its radius of curvature Calculate the upper speed limit constrained by the bow height error, respectively. The upper limit of velocity is defined by the normal acceleration constraint. The upper limit of velocity is limited by the normal acceleration rate constraint. ; The system command speed V m With the calculated , , The minimum value in the range is determined as the maximum allowable feed rate for that segment point.

[0010] In an optional implementation, a first scanning operation is performed sequentially on each planned segment along the processing direction, including: Predetermine the initial parameter boundaries for the acceleration and deceleration intervals of the current planning segment; Based on the motion limits of each axis of the machine tool and the maximum allowable feed speed at the current segment point, the acceleration and deceleration intervals are discretized separately, and the components of the constraints of each axis of the computer tool in the corresponding direction are calculated according to the motion direction of each discrete micro-segment. Thus, the maximum allowable tangential acceleration and tangential acceleration change rate during the acceleration process, as well as the maximum allowable tangential acceleration and maximum tangential acceleration change rate during the deceleration process, are determined independently for the current planning segment. Based on the arc length, starting speed, and determined motion parameters of the current planning segment, the speed planning model constructed based on the asymmetric S-shaped acceleration and deceleration model is used to verify and adjust the speed continuity of adjacent segments at the segmentation point. If the speed planning model indicates that it is impossible to accelerate from the current starting speed to the expected speed at the current segmentation point, the expected speed is lowered to the highest speed that the speed planning model can achieve under the constraints of the arc length and parameters, and this speed is updated as the starting speed of the next planning segment. Based on the determined final motion parameters, initial velocity, and adjusted segment point velocity, the velocity planning model is run to obtain the actual acceleration and deceleration distances required for the current planning segment. The parameter range of the planning segment is used as the search range, and the parameter boundaries of the acceleration and deceleration range are iteratively corrected using a bisection method combined with arc length integral until the boundary error between the preset boundary and the actual motion process is less than a set threshold.

[0011] In an optional implementation, the method for constructing a velocity planning model based on the asymmetric S-shaped acceleration / deceleration model includes: The arc length, starting speed, ending speed, commanded speed, and the maximum tangential acceleration and rate of change of tangential acceleration during the acceleration and deceleration process of the planned segment are obtained as input parameters. Based on the input parameters, calculate the minimum displacement required to accelerate from the starting speed to the commanded speed, and the minimum displacement required to decelerate from the commanded speed to the ending speed; By comparing the arc length of the planned segment with the sum of the two minimum displacements, it is determined that the displacement capability of the planned segment belongs to one of the following three scenarios: insufficient displacement to reach the command speed, able to reach the command speed but without a uniform speed segment, or able to reach the command speed and has a uniform speed segment. Based on the determined scenario, and using the mathematical relationships between displacement, velocity, acceleration, and rate of change of acceleration defined by the asymmetric S-shaped acceleration / deceleration model, the duration of each of the seven motion stages is solved and determined.

[0012] In an optional implementation, a second scanning operation is performed sequentially on each planned segment along the reverse processing direction, including: Predetermine the initial parameter boundaries for the acceleration and deceleration intervals of the current planning segment; Based on the motion limits of each axis of the machine tool and the maximum allowable feed speed at the current segment point, determine the maximum allowable tangential acceleration and tangential acceleration change rate parameters for the current planned segment during reverse scanning; Based on the arc length, ending speed, and determined motion parameters of the current planning segment, the asymmetric S-shaped velocity planning model is used for reverse verification. If the model indicates that it is impossible to decelerate from the segment point to the ending speed of the current planning segment after forward scanning, then in order to fully improve processing efficiency, the speed of the segment point is increased to the highest speed that the model can achieve under the constraints of the arc length and parameters, and this speed is updated to the ending speed of the previous planning segment. Based on the final determined motion parameters and speed, the speed planning model is run to obtain the actual required acceleration and deceleration distance. The parameter boundaries of the acceleration and deceleration interval are then iteratively corrected using a bisection method until the set accuracy is met.

[0013] In an optional implementation, the output includes an asymmetric S-shaped velocity planning curve that satisfies all constraints, obtained after the first and second scan operations, comprising: Output a complete sequence of motion parameters. For each planning segment, the sequence includes the duration of the asymmetric S-shaped velocity curve determined by bidirectional scanning optimization in each motion stage, as well as the displacement, velocity and acceleration values ​​corresponding to the critical point of the stage, thus forming a continuous, smooth and time-optimal velocity planning curve that satisfies all geometric constraints and machine tool axial kinematic constraints. The motion phases include acceleration phase, uniform acceleration phase, deceleration phase, uniform speed phase, acceleration / deceleration phase, uniform deceleration phase, and deceleration / deceleration phase.

[0014] The beneficial effects of this invention lie in the fact that the asymmetric velocity planning method for NURBS curves under geometric and kinematic constraints provided by this invention, through the introduction of an asymmetric S-shaped acceleration / deceleration model with independent acceleration and deceleration process parameters, achieves precise adaptation to the unequal motion capabilities of each axis of the machine tool. Combined with curvature-based segmented processing and a bidirectional scanning iteration mechanism, it can dynamically optimize the velocity curve of each planning segment under the premise of strictly satisfying bow height error, normal kinematic constraints, and the physical limits of each axis. This method significantly improves the overall feed efficiency of machining complex NURBS curves, effectively avoids the problem of limited machining capabilities caused by asymmetric axial constraints, and ensures continuous acceleration and smooth motion, which helps to improve the surface quality of the machined material and extend the service life of the machine tool and cutting tools. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic flowchart of a method according to an embodiment of the present invention. Detailed Implementation

[0017] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention.

[0018] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0019] The NURBS curve asymmetric velocity planning method under geometric and kinematic constraints provided in this embodiment of the invention is executed by a computer device, and correspondingly, the NURBS curve asymmetric velocity planning system under geometric and kinematic constraints runs in the computer device.

[0020] Figure 1 This is a schematic flowchart illustrating a method according to an embodiment of the present invention. Wherein, Figure 1The executing entity can be a NURBS curve asymmetric velocity programming system under geometric and kinematic constraints. Depending on different requirements, the order of steps in this flowchart can be changed, and some steps can be omitted.

[0021] like Figure 1 As shown, the method includes: S1. Establish an asymmetric S-shaped acceleration / deceleration model, in which the acceleration and deceleration processes have independent maximum acceleration and rate of change of acceleration parameters; S2. Based on the curvature of each point on the NURBS curve, select the local maximum point of curvature as the segmentation point, divide the curve into multiple planning segments, and calculate the arc length of each segment; S3. Determine the maximum allowable feed rate for each segment point based on the preset geometric and kinematic constraint parameters and the radius of curvature of each segment point; S4. Perform the first scan operation on each planned segment sequentially along the machining direction. The first scan operation includes: presetting the acceleration and deceleration interval for the current segment; determining the acceleration and acceleration change rate parameters of the current segment based on the machine tool axis limits and the maximum allowable feed speed at the segment point; verifying and adjusting the segment point speed to a feasible value according to the current segment arc length and speed planning model; and iteratively correcting the interval boundary based on the actual required acceleration and deceleration distance. S5. Perform the second scan operation on each planned segment sequentially along the reverse machining direction. The second scan operation includes: determining the acceleration and acceleration change rate parameters of the current segment based on the machine tool axis limits and the maximum allowable feed speed of the segment point; verifying and adjusting the segment point speed to a feasible value according to the current segment arc length and speed planning model; and iteratively correcting the interval boundary according to the actual required acceleration and deceleration distance. S6. Output the asymmetric S-shaped velocity planning curve that satisfies all constraints after the first and second scan operations.

[0022] In one embodiment of the present invention, based on step S1, the following will provide a possible embodiment and describe its specific implementation in a non-limiting manner.

[0023] First, obtain the required kinematic constraint parameters. These parameters include: 1) Machine tool physical performance parameters, such as the maximum acceleration (A) along the X and Y axes. x A y ) and maximum rate of change of acceleration (J x J y ), and system command speed V m 2) Processing parameters, such as the maximum permissible bow height error δ m and the maximum permissible rate of change of normal acceleration J nm 3) Specific parameters from the current planning segment, i.e., the initial velocity V of this segment. s With the final velocity V eand the arc length already calculated through the aforementioned steps. .

[0024] Next, the kinematic constraints are dynamically mapped from the machine tool axis to the curve tangent. For the pre-defined acceleration and deceleration intervals of the current planning segment, discretization sampling is performed with small parameter increments Δu, resulting in a series of discrete points. For any discrete point within the acceleration interval, its corresponding curve tangent direction (i.e., the first derivative vector at that point) is calculated. The angle θ between the direction of the X-axis and the machine tool's X-axis. To ensure that neither the X-axis nor the Y-axis of the machine tool exceeds their limits at this point, the maximum permissible tangential acceleration at this point. The following conditions must be met simultaneously: and Therefore, the upper limit of the permissible tangential acceleration at this point is... Iterate through all discrete points within the acceleration interval, and take the minimum value calculated by the formula for all points as the maximum tangential acceleration A allowed for the acceleration process of this planned segment. m1 Similarly, using the maximum rate of change of acceleration J along each axis... x J y The maximum permissible rate of change of tangential acceleration J during the acceleration process can be calculated and determined. m1 By repeating the above process over the deceleration interval, the maximum permissible tangential acceleration A during the deceleration process can be determined independently. m2 and the maximum rate of change of tangential acceleration J m2 .

[0025] Subsequently, the upper limit constraint of instantaneous speed within the planning segment was determined. This was based on the maximum bow height error δ. m According to the formula (in (where ρ is the interpolation period and ρ is the radius of curvature) to calculate the upper limit of velocity at each point, limited by geometric accuracy; based on the maximum normal acceleration change rate J nm According to the formula Calculate the upper limit of velocity at each point, determined by motion stability. Take these two values ​​and the system command velocity V. m The minimum value in the range is taken as the upper limit of the instantaneous velocity v at that point. lim This constraint will be strictly adhered to in subsequent planning.

[0026] Then, a scenario judgment based on displacement constraints is performed for velocity planning. The starting velocity V is calculated. s Accelerate to system command speed V m Minimum displacement required and from V m Decelerate to final speed V e Minimum displacement required The current planned arc length s is compared with... , Compare: If s < If so, it falls under the category of insufficient displacement to reach the commanded speed; if If s ≥ , then it belongs to the case where the commanded speed can be reached but there is no uniform speed segment; if s ≥ If so, it falls under the category of being able to reach the commanded speed and having a constant speed segment.

[0027] Finally, based on the determined scenario, while adhering to the instantaneous velocity limit v lim Under constraints, solve for the time of each stage of an asymmetric S-shaped acceleration / deceleration model. For example, in the case of "insufficient displacement," we need to solve for a practically achievable maximum velocity V. max (V max <V m ), making V s Accelerate to V max Decelerate to V again e The total displacement is exactly equal to the arc length s, which can be solved using an iterative algorithm (such as the bisection method). In the case of "no uniform velocity segment," let the time of the uniform velocity segment T4 = 0, and solve for the intermediate velocity (which is equal to Vm) and the time of each stage by simultaneously solving the displacement equations for the acceleration and deceleration processes. In the case of "with a uniform velocity segment," the time of the uniform velocity segment T4 = (s- - ) / V m The acceleration and deceleration phase times are calculated and determined independently. By solving the equations for the corresponding scenario, the durations of the seven phases [T1,T2,...,T7] are finally determined, thus completing the construction of the asymmetric S-shaped velocity curve for this planning segment.

[0028] The complete asymmetric S-shaped acceleration and deceleration model consists of seven stages: acceleration stage, uniform acceleration stage, deceleration stage, uniform speed stage, acceleration and deceleration stage, uniform deceleration stage, and deceleration and deceleration stage. t For processing time, v For (tangential) velocity, a For (tangential) acceleration, j For (tangential) acceleration, V s Let the initial velocity be , V e The final velocity, V m For maximum speed, A m1 and A m2 These are the maximum accelerations during the acceleration and deceleration processes, respectively. J m1 and J m2 These are the maximum jerk during the acceleration and deceleration processes, respectively. Tk ( k = 1,2,…,7) represents the duration of each stage. t 0 = 0, These are the critical moments for each stage. The first three stages are defined as the acceleration process, and the last three stages are defined as the deceleration process.

[0029] The jerk of the algorithm j ( t This can be represented as the following function:

[0030] The algorithm's acceleration a ( t This can be represented as the following function:

[0031] The speed of the algorithm v ( t This can be represented as the following function:

[0032] The displacement of the algorithm s ( t This can be represented as the following function:

[0033] in, t k = t – t k-1 ( k = 1,2,…,7) represents the running time relative to the initial time of each stage. V k ( k = 1,2,…,6) represents the final velocity of each stage. S k ( k = 1,2,…,6) represent the final displacements at each stage. For the asymmetric S-shaped velocity programming model, after determining the kinematic parameters, the critical displacements for reaching the final velocity, maximum velocity, and maximum acceleration can be calculated based on the existing velocity programming model. S c1 , S c2 / S c3 , S c4 / S c5 The system identifies possible speed planning types and further calculates and determines the specific planning type of the target planning path, thereby completing the time allocation of the asymmetric S-shaped speed planning curve at each stage.

[0034] In one embodiment of the present invention, based on step S2, the following will provide a possible embodiment and describe its specific implementation in a non-limiting manner.

[0035] S201. Based on the curvature of each point on the NURBS curve, select the local maxima of curvature as segmentation points to divide the curve into multiple planning segments, including: For a k The mathematical expression for the NURBS curve is:

[0036] in u For parameter variables, C ( u ) represents the corresponding parameter on the curve u point, P i ( i = 0,1,…, n () represents the coordinates of the control point. oh i ( i = 0,1,…, n ) is the control point P i The corresponding weights N i,k ( u ) is defined in the node vector U basis functions on, U ={ u 0, u 1, …, u n+k+1} is a monotonically non-decreasing sequence of real numbers. u i These are the node values ​​in the node vector. For the basis functions... N i,k ( u The parameters can be calculated using the Cox-de-Boor recursive formula, as shown below, where "0 / 0 = 0" is specified. Furthermore, the parameters can be determined by combining the control points and weights. u Coordinates of the corresponding point on the curve C ( u ).

[0037]

[0038] Segmentation of the curve: The curve is preprocessed by segmentation based on curvature. The parameter range of the curve is then determined. u ∈[0,1] according to the scale value Δ u Uniform subdivision yields parameters at discrete points.u j Calculate the parameters on the curve u j Corresponding curvature k j :

[0039] Where C′( u j ) and C″( u j The first and second derivatives of the NURBS curve are given by the following formula:

[0040]

[0041] In the formula, the basis functions N i,k ( u j The first derivative of ) N i,k ′( u j and second derivative N i,k "( u j )for:

[0042]

[0043] Based on the maximum bow height error d m Maximum normal acceleration A nm Maximum normal jerk J nm With command speed V m Determine the threshold of curvature k cr :

[0044] The interpolation period is . T s If curvature k j satisfy:

[0045] If this point exceeds the curvature threshold and is a local maximum, then this point is selected as the segmentation critical point, and the beginning and end endpoints of the curve ( u = 0、 u= 1) Also used as a segmentation point, recording the segmentation point parameter value.

[0046] S202. Calculate the length of each arc segment, including: The arc length between adjacent segment points is calculated using the adaptive Simpson method. (NURBS curve) C ( u In parameters u ∈[ x , y Arc length within the interval s ( x , y It can be calculated as:

[0047] Simpson's formula can be expressed as follows:

[0048] For the application scenarios of this invention, the formula can be set as follows: f ( u ) = || C ' ( u )||. The interval [ x , y Divided into [ ] x , ( x + y ) / 2] and [( x + y ) / 2, y Calculate the sum of the lengths of the line segments in the two intervals: s ( x , ( x + y ) / 2) + s (( x + y ) / 2, y ), given precision g Perform a check; if the following conditions are met:

[0049] but s ( x , ( x + y ) / 2) + s (( x + y ) / 2, y The parameter range is denoted as ) u ∈[ x , y The arc length within the interval is determined by the given information; otherwise, the interval is further divided into two parts, and the above process is iterated until the accuracy requirement is met. At this point, the sum of the lengths of all interval segments is the parameter interval. u ∈[ x , y The arc length within ]

[0050] In one embodiment of the present invention, based on step S3, the following will provide a possible embodiment and describe its specific implementation in a non-limiting manner.

[0051] The first scan operation processes each planned segment sequentially along the processing path. First, the initial parameter boundaries of the acceleration and deceleration intervals are preset for the currently processed planned segment. Typically, the acceleration end point (i.e., the deceleration start point) can be initially set as the midpoint of the parameters of this segment.

[0052] Subsequently, the crucial kinematic parameters are dynamically determined. The preset acceleration and deceleration intervals are discretized with small parameter step sizes, resulting in a series of discrete points. For each discrete point, based on the angle between the curve tangential at that point and each coordinate axis of the machine tool (e.g., X-axis, Y-axis), the allowable tangential components of the maximum acceleration and maximum rate of change of acceleration for each axis in that motion direction are calculated. By minimizing the calculation results for all discrete points within each interval, the maximum tangential acceleration and maximum rate of change of tangential acceleration that can be safely used during acceleration, as well as the maximum tangential acceleration and maximum rate of change of tangential acceleration that can be safely used during deceleration, can be independently determined for the current planned segment. This process maps the unequal physical limits of each axis of the machine tool into tangential constraints along the curve in real time and with precision.

[0053] Next, a velocity continuity verification and adjustment are performed using a velocity planning model based on an asymmetric S-shaped acceleration / deceleration model. The arc length of the current segment, the initial velocity, and the motion parameters determined in the previous step are input into the model. The model will determine whether, under the current constraints, it is possible to accelerate from the initial velocity of the current segment to the expected velocity at the segment point. If the model calculation indicates that this is not possible, the expected velocity at the segment point is lowered to the highest achievable velocity value calculated by the model, and this lowered velocity value is updated as the starting velocity of the next planned segment, thereby ensuring the feasibility of velocity connection between adjacent segments.

[0054] Then, based on the final determined motion parameters and speeds (including the initial speed and the adjusted segment speeds), the speed planning model is run again to accurately calculate the actual acceleration and deceleration distances required to complete the motion segment. To ensure that the preset acceleration and deceleration intervals match the actual motion requirements, a bisection method is used to iteratively search within the parameter interval of the planned segment: by calculating the arc lengths corresponding to different parameter points (using numerical integration methods) and comparing them with the actual acceleration and deceleration distances output by the model, the parameter positions of the acceleration end point and deceleration start point are continuously corrected until the error between the preset interval boundary and the boundary required by the actual motion is less than the set accuracy threshold.

[0055] The core logic of the velocity planning model is to solve it in reverse based on the mathematical relationships of the asymmetric S-shaped acceleration / deceleration model. Its input parameters include: the arc length of the planning segment, the initial velocity, the ending velocity, the system command velocity, and the independently determined maximum tangential acceleration and rate of change of tangential acceleration during the acceleration / deceleration process.

[0056] The model first calculates two key thresholds: the minimum displacement required to accelerate from the initial velocity to the system command velocity, and the minimum displacement required to decelerate from the system command velocity to the final velocity. Then, by comparing the actual arc length of the current planned segment with the sum of these two minimum displacements, it accurately determines which of the three basic scenarios the motion of that segment belongs to: 1) Insufficient displacement, unable to accelerate to the system command velocity; 2) Displacement just enough to accelerate to the command velocity and decelerate, but without a constant speed phase; 3) Sufficient displacement, including a constant speed phase between the acceleration and deceleration phases.

[0057] Based on the specific scenario, the model establishes a set of equations according to the inherent mathematical relationship between displacement, velocity, acceleration, and rate of change of acceleration defined by the asymmetric S-shaped acceleration / deceleration curve. By solving this set of equations, the precise duration required for each of the seven motion stages—acceleration, uniform acceleration, deceleration, uniform speed, acceleration / deceleration, uniform deceleration, and deceleration / deceleration—is finally determined, thereby generating the complete velocity planning curve for this planning segment.

[0058] In a specific example, because discretized interpolation causes the actual trajectory to deviate from the theoretical curve profile, it is necessary to control geometric errors, i.e., bow height errors. Given an interpolation period... T s ,parameter u j Corresponding interpolation point C ( u j ), feed rate v j radius of curvature r j The target NURBS curve is approximated by... O j With the center of the circle, r j The arc has a radius of [radius value]. The bow height error generated within this period. d j It can be represented as:

[0059] in r j It can be calculated as:

[0060] The maximum allowable bow height error is set as follows: d m Then the interpolation point C ( u j The maximum speed allowed v j,δ for:

[0061] The machine tool generates normal acceleration and normal jerk. The maximum value of the normal acceleration is set. A nm Maximum normal acceleration J nm interpolation point C ( u j The maximum speed allowed v j,An , v j,Jn for:

[0062]

[0063] Under the aforementioned geometric and normal kinematic constraints, given the commanded velocity V m Determine the maximum allowable feed rate at the segment point. v j,max :

[0064] Immediately after, the system command speed V m With the calculated , , The minimum value in the range is determined as the maximum allowable feed rate for that segment point.

[0065] In one embodiment of the present invention, based on step S4, the following will provide a possible embodiment and describe its specific implementation in a non-limiting manner.

[0066] The key steps and logical relationships in the forward scanning process include: after the aforementioned steps, obtaining the initial parameters for each segment. u sk End parameters u ek Starting speed v sk End speed v ek Maximum speed v tk Arc length s kEach segment is treated as a unit for velocity planning and defined as a planning element. k ∈[1, n ]. n The number of planning elements. First, determine if there are any unscanned planning elements: if... k > n If the result is positive, then step 4 ends and proceed to step 5; otherwise, proceed to step 4-1.

[0067] Step 4-1: Begin forward scanning.

[0068] Within the parameter interval corresponding to each planning element, an acceleration interval and a deceleration interval are divided. Assume that the corresponding paths of these intervals represent the acceleration and deceleration processes of the planning element, respectively. Let the parameter at the acceleration endpoint be... u ack The parameters for the deceleration start point are: u dck ,make u ack = u dck =0.5( u sk + u ek ), that is, the acceleration range is: [ u sk , u mk The deceleration range is: [ u mk , u ek ]. Step 4-2: Axial kinematic constraints based on parameter discretization.

[0069] Given parameter scale value Δ u By uniformly subdividing the acceleration and deceleration intervals according to the scale value, a series of discrete points on the curve can be obtained as micro-line segments. Calculation parameters u j Corresponding position C ( u j ), and adjacent discrete points C ( u j The angle between the line segment formed and the X-axis of the machine tool. i j Set the maximum acceleration limit of the machine tool's X-axis to... A x The maximum jerk limit is J x The maximum acceleration limit along the Y-axis is A y The maximum jerk limit is Jy To ensure the axial kinematic constraints of the machine tool, the first... k The maximum acceleration of each planning element during the acceleration process A 1k With maximum jerk J 1k They are respectively:

[0070] No. k The maximum acceleration of a planning element during deceleration. A 2k With maximum jerk J 2k for:

[0071] Step 4-3: Velocity constraints based on the velocity planning model.

[0072] The time constant of the current planning element in the acceleration process T j1k = A 1k / J 1k Accelerate the duration of each stage for T ik ( i = 1,2,3). The velocity starts from the initial velocity and accelerates; calculate the critical displacement where there is just no uniform acceleration phase. s ck :

[0073] If the planning element arc length s k ≥ s ck Then there exists a uniformly accelerated segment, that is T 1k = T 3k = T j1k , T 2k >0; Uniform acceleration time T 2k It can be calculated using the following formula:

[0074] in accordance with v ( t The curve can be used to calculate the final speed under the current speed planning. v ek ' .like vek ' < v ek If the actual ending speed cannot reach the expected ending speed, then update the ending speed of the planning element and the starting speed of the next planning element, that is, let v ek = v ek ' , v s(k+1) = v ek ' ( k < n Otherwise, maintain the original speed.

[0075] Step 4-4: Asymmetric S-shaped velocity planning.

[0076] The length of the planning element (arc length) s k initial speed v sk End speed v ek Maximum speed v tk Maximum acceleration A 1k , A 2k Maximum jerk J 1k , J 2k Input the existing velocity planning model and perform an asymmetric S-shaped velocity planning process to obtain the time allocation of the planning element velocity planning.

[0077] Steps 4-5: Correction of acceleration / deceleration intervals based on arc length parameterization.

[0078] Based on the asymmetric S-shaped acceleration / deceleration model s ( t The curve can be used to calculate the displacement of the critical point, from which the actual acceleration distance can be determined. s ak Compared to actual deceleration distance s dk The parameter values ​​corresponding to the acceleration / deceleration critical points are solved using the bisection method. u ak and u dk The bisection interval is [ u sk , u ekWithin the interval, the arc length corresponding to the parameter interval is calculated using Simpson's integral method. This arc length is then compared with the actual acceleration (deceleration) distance. If the error is less than a threshold, the iterative calculation stops, and the result is obtained. u ak and u dk .

[0079] Given calculation precision x If | u ack – u ak |< x And| u dck – u dk |< x If the actual acceleration (deceleration) process matches the expected acceleration / deceleration range, then the current planning segment ends, and the process moves to the next planning element. k = k + 1, jump to step 4-1; like u ack > u ak ,but u ack = u ack - 0.01; if u ack < u ak ,but u ack = u ack + 0.01; if u dek > u dk ,but u dek = u dek - 0.01; if u dek < u dk ,but u dek = u dek + 0.01. Jump to step 4-2.

[0080] In one embodiment of the present invention, based on step S5, a possible embodiment will be given below, and its specific implementation will be described in a non-limiting manner.

[0081] Similar to step 4, starting from the last planning element ( k =n The reverse scan begins, performing axial kinematic constraints based on parameter discretization and velocity constraints based on the velocity planning model (distinct from the forward scan, step 4-3...). v sk ; v ek ; A 1k ; J 1k ; T 1k ; T 2k ; T 3k ; v s(k+1) Replace with [ v ek ; v sk ; A 2k ; J 2k ; T 5k ; T 6k ; T 7k ; v e(k-1) Asymmetric S-shaped velocity planning is performed on the planning element, and the acceleration and deceleration intervals are corrected based on arc length parameterization. This continues until the first planning element is completed. k = 1) scan, at which point all kinematic parameters can be determined, and velocity planning results that satisfy geometric and kinematic constraints can be obtained.

[0082] The second scan operation is performed after the forward scan is completed. Its input consists of the speed and initial parameter values ​​of each planned segment after the forward scan. Its core purpose is to optimize the speed of each segment in reverse while ensuring all constraints are met, thereby further improving processing efficiency.

[0083] Step 1: Initialization and Parameter Determination First, preset the initial parameter boundaries for the acceleration and deceleration intervals of the planning segment currently undergoing reverse scanning. Typically, the acceleration end point (i.e., the deceleration start point) can be initialized as the midpoint of the segment's parameters.

[0084] Next, based on the motion limits (maximum acceleration A) of each axis of the machine tool (such as the X and Y axes) x A y With the maximum rate of change of acceleration J x J y And the maximum permissible feed rate v at the current segment point. limThe kinematic parameters allowed for the current segment in the reverse scan are determined. Specifically, the preset acceleration and deceleration intervals are discretized, and for each discrete micro-segment, the upper limit of the tangential acceleration satisfying all axial constraints at that point is calculated based on its motion direction angle θ. By traversing all discrete points within their respective intervals and taking the minimum value, the maximum tangential acceleration for the current reverse scan calculation is obtained. With the rate of change of acceleration and the maximum tangential acceleration during deceleration. With the rate of change of acceleration These parameters may differ from the values ​​used in the forward scan because this calculation is performed again based on the currently preset interval.

[0085] Step 2: Reverse speed verification and adjustment Based on the arc length s and the ending velocity V of the current planning segment e (That is, the speed at the end of this segment, which is usually zero at the end of the path, and the starting speed of the adjacent segment between segments) and the motion parameters determined in the previous step, the inverse feasibility is verified using an asymmetric S-shaped velocity programming model. The model will use the speed V at the end of this segment as the starting speed. e The target final velocity is the velocity V determined after forward scanning at this segment point. forward Using the initial velocity as the basis, perform reverse "deceleration" planning calculations (i.e., from a higher V). forward Decelerate to a lower V e ).

[0086] If the model calculations show that, given the arc length s and motion parameters... Under constraints, it is impossible to obtain from V forward Decelerate to V e This indicates that the speed margin retained during the forward scan is conservative. To fully exploit the processing potential, the segmentation point speed V... forward Adjust upwards. The goal of adjusting upwards is to find a higher speed value V. new This makes V new Decelerate to V e It is feasible under the same constraints. This can be achieved by considering the interval... Implemented internally using iterative search (such as binary search), where... This is the maximum permissible feed rate limit at this segment point. Once V is found... new That is, use it to update the velocity of the current segment point, and set this V new As the new ending speed of the previous planning segment (which is located before the current segment in the processing sequence), the optimization effect is passed on in reverse.

[0087] Step 3: Model Running and Interval Boundary Iterative Correction After completing the speed adjustment and update, based on the final determined starting speed (i.e., the updated segment point speed) and ending speed V of the current planning segment. e Motion parameters Given the arc length s, run an asymmetric S-shaped velocity programming model to obtain the actual acceleration distance S required for this segment. a and deceleration distance S d .

[0088] Subsequently, a bisection method is used to iteratively correct the preset acceleration / deceleration interval parameter boundaries. This is to correct the parameter u at the end point of the acceleration interval. ac For example: taking the parameter range of the current planning segment To define the search range, calculate the parameter interval. The corresponding arc length, and its relationship with the actual acceleration distance S calculated by the model. a Compare the results. Adjust based on the comparison. The value of S is taken, and this process is repeated until the preset interval length is equal to S. a The error is less than the set accuracy. For the parameters at the start point of the deceleration interval... Perform a similar operation to make its corresponding arc length approximate S. d This iterative process ensures that the preset motion range precisely matches the actual physical motion process.

[0089] In one embodiment of the present invention, based on step S6, a possible embodiment will be given below, and its specific implementation will be described in a non-limiting manner.

[0090] Step 1: Generation and organization of motion parameter sequences For each planning segment, the algorithm encapsulates a separate data structure containing all motion parameters determined after bidirectional scan optimization for that segment. These parameters are divided into two categories: Stage Time Parameters: The durations of the seven motion stages within this segment of the asymmetric S-shaped velocity curve are explicitly given, in the following order: acceleration stage T1, uniform acceleration stage T2, deceleration stage T3, uniform velocity stage T4, acceleration / deceleration stage T5, uniform deceleration stage T6, and deceleration / deceleration stage T7. These time parameters are precise results obtained by the velocity planning model based on the arc length, start and end velocities, and dynamically determined acceleration / deceleration capacity constraints.

[0091] Critical point motion state parameters: In addition to time, the precise motion state corresponding to each stage's critical point (i.e., stage transition moment) is also provided. For the k-th stage endpoint (k=1,2,...,7), this includes: Displacement S k : The cumulative arc length from the starting point of this segment to the critical point.

[0092] Speed ​​V kThe instantaneous feed rate (tangential rate) at the critical point.

[0093] Acceleration A k : The instantaneous tangential acceleration at the critical point.

[0094] V7 and A7 are the ending velocity and ending acceleration of this segment.

[0095] The parameters of all planned segments are arranged in the processing order to form a complete sequence of motion commands that runs through the entire NURBS curve processing path.

[0096] Step Two: Formation and Application of Continuous Velocity Planning Curves The above sequence of motion parameters defines the precise velocity and acceleration variations with time as the independent variable and displacement as the intermediate variable. The CNC system's interpolator will use this sequence to calculate the velocity and acceleration within each interpolation cycle Ts: Based on the current cumulative time, determine the current planning segment and movement stage.

[0097] Using the displacement, velocity, and acceleration functions of the corresponding stages (uniquely determined by T1~T7 and the critical point state), calculate the target position (displacement) and feed rate at the end of the current cycle.

[0098] Generate corresponding position commands for each axis to drive the servo system.

[0099] In this way, the sequence is transformed into a continuous and smooth actual velocity planning curve. Its continuity is reflected in the continuity of the acceleration curve (the jerk is bounded), and its smoothness is reflected in the absence of abrupt changes in both velocity and acceleration.

[0100] The final output speed planning curve is the result of bidirectional scanning iterative optimization, under the premise of strictly satisfying geometric constraints (the upper limit of the speed at each point is limited by the maximum bow height error and normal acceleration / jerk), machine tool axial kinematic constraints (the acceleration and jerk limits of each axis are observed through dynamic mapping), and displacement constraints (the length of each arc segment). It makes full use of the asymmetric performance of the machine tool in each direction of motion, achieving time-optimal or near-optimal results under given constraints, thereby maximizing machining efficiency while ensuring machining accuracy and equipment safety.

[0101] The same or similar parts between the various embodiments in this specification can be referred to mutually. In particular, the device embodiments are basically similar to the method embodiments, so the description is relatively simple, and the relevant parts can be referred to the description in the method embodiments.

[0102] In the embodiments provided by this invention, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the system embodiments described above are merely illustrative. For instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between systems or modules may be electrical, mechanical, or other forms.

[0103] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical modules; that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0104] In addition, the functional modules in the various embodiments of the present invention can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0105] Although the present invention has been described in detail with reference to the accompanying drawings and preferred embodiments, the present invention is not limited thereto. Various equivalent modifications or substitutions can be made to the embodiments of the present invention by those skilled in the art without departing from the spirit and essence of the invention, and such modifications or substitutions should all be within the scope of the present invention. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should also be covered within the protection scope of the present invention.

Claims

1. A method for asymmetric velocity programming of NURBS curves under geometric and kinematic constraints, characterized in that, include: An asymmetric S-shaped acceleration / deceleration model is established, in which the acceleration and deceleration processes have independent maximum acceleration and rate of change of acceleration parameters. Based on the curvature of each point on the NURBS curve, the local maximum point of curvature is selected as the segmentation point, the curve is divided into multiple planning segments, and the arc length of each segment is calculated. Based on the preset geometric and kinematic constraint parameters and the radius of curvature of each segment point, determine the maximum allowable feed rate of each segment point; The first scan operation is performed sequentially on each planned segment along the machining direction. The first scan operation includes: presetting the acceleration and deceleration interval for the current segment; determining the acceleration and acceleration change rate parameters of the current segment based on the machine tool axis limits and the maximum allowable feed speed at the segment point; verifying and adjusting the segment point speed to a feasible value according to the current segment arc length and speed planning model; and iteratively correcting the interval boundary based on the actual required acceleration and deceleration distance. The second scanning operation is performed sequentially on each planned segment along the reverse machining direction. The second scanning operation includes: determining the acceleration and acceleration change rate parameters of the current segment based on the machine tool axis limits and the maximum allowable feed speed of the segment point; verifying and adjusting the segment point speed to a feasible value according to the current segment arc length and speed planning model; and iteratively correcting the interval boundary according to the actual required acceleration and deceleration distance. Output the asymmetric S-shaped velocity planning curve that satisfies all constraints, obtained after the first and second scan operations.

2. The method according to claim 1, characterized in that, The asymmetric S-shaped acceleration / deceleration model comprises seven sequentially connected stages: acceleration phase, uniform acceleration phase, deceleration phase, uniform speed phase, acceleration / deceleration phase, uniform deceleration phase, and deceleration / deceleration phase. The acceleration phase, uniform acceleration phase, and deceleration phase constitute an acceleration process, and the acceleration / deceleration phase, uniform deceleration phase, and deceleration / deceleration phase constitute a deceleration process. The acceleration process and the deceleration process each have their own independently set maximum acceleration value and maximum rate of change of acceleration value.

3. The method according to claim 2, characterized in that, Establish an asymmetric S-shaped acceleration / deceleration model, including: Obtain kinematic constraint parameters, including: the maximum acceleration and maximum rate of change of acceleration of each axis of the machine tool, the system command speed, the maximum bow height error and the maximum rate of change of normal acceleration determined by the machining process, and the starting speed and ending speed of the current planning segment; The acceleration and deceleration intervals of the current planning segment are discretized. For each discrete micro-segment, based on its motion direction and the acceleration and acceleration rate of change limits of each axis of the machine tool, the maximum tangential acceleration and tangential acceleration rate of change, as well as the maximum tangential acceleration and tangential acceleration rate of change during the deceleration process, which satisfy all axis constraints are calculated and determined respectively. Based on the maximum bow height error and the maximum rate of change of normal acceleration, the upper limit of instantaneous velocity of each point in the current planning segment is determined; Based on the initial velocity, the final velocity, the system command velocity, the determined tangential acceleration and rate of change of acceleration parameters, and the arc length of the planned segment, by comparing the arc length with the minimum displacement required to accelerate to the system command velocity, it is determined which of the following situations the velocity planning scenario belongs to: insufficient displacement to reach the system command velocity, able to reach the system command velocity but without a uniform velocity segment, or able to reach the system command velocity and with a uniform velocity segment. Based on the determined situation, and with the constraint of not exceeding the upper limit of instantaneous velocity, the duration of each stage in the asymmetric S-shaped acceleration / deceleration model is determined by solving the equations that satisfy the relationship between displacement and velocity under this situation.

4. The method according to claim 1, characterized in that, Based on the curvature of each point on the NURBS curve, local maxima of curvature are selected as segmentation points, dividing the curve into multiple planned segments, including: Discrete sampling is performed within the parameter range of the NURBS curve, and the curvature of each sampling point is calculated. Determine the curvature threshold based on the processing requirements; Sampling points with curvature greater than the curvature threshold and which are local maxima are selected as segmentation critical points; Arrange the starting point, ending point, and all segment critical points of the curve in parameter order, and define the curve segment between two adjacent points as a planning segment.

5. The method according to claim 4, characterized in that, Calculate the length of each arc segment, including: For parameter intervals The planning segment, its curve arc length s is expressed in integral form. ,in Let be the first derivative of the NURBS curve at parameter u; The integral value is approximated by iteratively bisecting the parameter interval and applying Simpson's formula: First, the approximate value of the Simpson integral S over the entire interval is calculated. total Then calculate the sum of the Simpson integral approximations on the two subintervals after bisecting the interval, S. sum ; Determine S total With S sum Is the difference less than the preset precision threshold? If so, then S sum If the result is not found, the same binary search and accuracy judgment process is recursively performed on each subinterval until the accuracy requirement is met, and the sum of the approximate integral values ​​of all subintervals that meet the accuracy requirement is taken as the arc length of the planning segment.

6. The method according to claim 1, characterized in that, Based on preset geometric and kinematic constraint parameters and the radius of curvature of each segment point, determine the maximum allowable feed rate for each segment point, including: Obtain preset constraint parameters, including: maximum permissible bow height error. Maximum permissible normal acceleration Maximum permissible rate of change of normal acceleration System command speed V m and the interpolation period T s ; For each of the aforementioned segment points, based on its radius of curvature Calculate the upper speed limit constrained by the bow height error, respectively. The upper limit of velocity is defined by the normal acceleration constraint. The upper limit of velocity is limited by the normal acceleration rate constraint. ; The system command speed V m With the calculated , , The minimum value in the range is determined as the maximum allowable feed rate for that segment point.

7. The method according to claim 1, characterized in that, Perform the first scan operation on each planned segment sequentially along the processing direction, including: Predetermine the initial parameter boundaries for the acceleration and deceleration intervals of the current planning segment; Based on the motion limits of each axis of the machine tool and the maximum allowable feed speed at the current segment point, the acceleration and deceleration intervals are discretized separately, and the components of the constraints of each axis of the computer tool in the corresponding direction are calculated according to the motion direction of each discrete micro-segment. Thus, the maximum allowable tangential acceleration and tangential acceleration change rate during the acceleration process, as well as the maximum allowable tangential acceleration and maximum tangential acceleration change rate during the deceleration process, are determined independently for the current planning segment. Based on the arc length, starting speed, and determined motion parameters of the current planning segment, the speed planning model constructed based on the asymmetric S-shaped acceleration and deceleration model is used to verify and adjust the speed continuity of adjacent segments at the segmentation point. If the speed planning model indicates that it is impossible to accelerate from the current starting speed to the expected speed at the current segmentation point, the expected speed is lowered to the highest speed that the speed planning model can achieve under the constraints of the arc length and parameters, and this speed is updated as the starting speed of the next planning segment. Based on the determined final motion parameters, initial velocity, and adjusted segment point velocity, the velocity planning model is run to obtain the actual acceleration and deceleration distances required for the current planning segment. The parameter range of the planning segment is used as the search range, and the parameter boundaries of the acceleration and deceleration range are iteratively corrected using a bisection method combined with arc length integral until the boundary error between the preset boundary and the actual motion process is less than a set threshold.

8. The method according to claim 1, characterized in that, The method for constructing a velocity planning model based on the aforementioned asymmetric S-shaped acceleration / deceleration model includes: The arc length, starting speed, ending speed, commanded speed, and the maximum tangential acceleration and rate of change of tangential acceleration during the acceleration and deceleration process of the planned segment are obtained as input parameters. Based on the input parameters, calculate the minimum displacement required to accelerate from the starting speed to the commanded speed, and the minimum displacement required to decelerate from the commanded speed to the ending speed; By comparing the arc length of the planned segment with the sum of the two minimum displacements, it is determined that the displacement capability of the planned segment belongs to one of the following three scenarios: insufficient displacement to reach the command speed, able to reach the command speed but without a uniform speed segment, or able to reach the command speed and has a uniform speed segment. Based on the determined scenario, and using the mathematical relationships between displacement, velocity, acceleration, and rate of change of acceleration defined by the asymmetric S-shaped acceleration / deceleration model, the duration of each of the seven motion stages is solved and determined.

9. The method according to claim 8, characterized in that, Perform the second scanning operation on each planned segment sequentially along the reverse processing direction, including: Predetermine the initial parameter boundaries for the acceleration and deceleration intervals of the current planning segment; Based on the motion limits of each axis of the machine tool and the maximum allowable feed speed at the current segment point, determine the maximum allowable tangential acceleration and tangential acceleration change rate parameters for the current planned segment during reverse scanning; Based on the arc length, ending speed, and determined motion parameters of the current planning segment, the asymmetric S-shaped velocity planning model is used for reverse verification. If the model indicates that it is impossible to decelerate from the segment point to the ending speed of the current planning segment after forward scanning, then in order to fully improve processing efficiency, the speed of the segment point is increased to the highest speed that the model can achieve under the constraints of the arc length and parameters, and this speed is updated to the ending speed of the previous planning segment. Based on the final determined motion parameters and speed, the speed planning model is run to obtain the actual required acceleration and deceleration distance. The parameter boundaries of the acceleration and deceleration interval are then iteratively corrected using a bisection method until the set accuracy is met.

10. The method according to claim 1, characterized in that, The output is the asymmetric S-shaped velocity planning curve obtained after the first and second scan operations, which satisfies all constraints, including: Output a complete sequence of motion parameters. For each planning segment, the sequence includes the duration of the asymmetric S-shaped velocity curve determined by bidirectional scanning optimization in each motion stage, as well as the displacement, velocity and acceleration values ​​corresponding to the critical point of the stage, thus forming a continuous, smooth and time-optimal velocity planning curve that satisfies all geometric constraints and machine tool axial kinematic constraints. The motion phases include acceleration phase, uniform acceleration phase, deceleration phase, uniform speed phase, acceleration / deceleration phase, uniform deceleration phase, and deceleration / deceleration phase.

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