CN111897290A - Smooth corner transition smoothing method for axial acceleration - Google Patents

Smooth corner transition smoothing method for axial acceleration Download PDF

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CN111897290A
CN111897290A CN202010787497.1A CN202010787497A CN111897290A CN 111897290 A CN111897290 A CN 111897290A CN 202010787497 A CN202010787497 A CN 202010787497A CN 111897290 A CN111897290 A CN 111897290A
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corner
speed
axis
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李�浩
王保升
闫注文
潘龙
吕东升
陆玄鸣
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Nanjing Institute of Technology
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/41—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention discloses a smooth corner transition smoothing method for axial acceleration, which comprises the following steps: designing a composite trigonometric function speed planning method; carrying out look-ahead initialization; constructing a corner transition curve, calculating the axial kinematic trajectories under the axial speed limit, the corner section length limit, the contour error limit, the maximum feeding speed limit and the maximum axial jerk limit on the coordinate axes respectively, and synthesizing the axial kinematic trajectories on the two coordinate axes to obtain the corner transition curve; and (4) carrying out reverse scanning, and carrying out composite trigonometric function speed planning on all interpolation line segments from the last small line segment in sequence. The invention utilizes the composite trigonometric function speed planning method to simultaneously complete the construction of the corner transition curve and the single-axis speed planning in one step, obviously reduces the processing time consumed by motion track control, realizes the control of smooth axis speed, axis acceleration and axis acceleration, and improves the processing efficiency and the processing quality of a numerical control machine.

Description

Smooth corner transition smoothing method for axial acceleration
Technical Field
The invention belongs to the technical field of numerical control machining, and particularly relates to a smooth corner transition smoothing method for axial acceleration.
Background
The local track smoothing technology is mainly characterized in that a transition curve, such as a broken line, an arc, a parameter curve and the like, is inserted into the joint of adjacent micro straight line segments to realize the smoothness of a numerical control machining track and improve the speed of a moving part of a numerical control machine tool passing through a corner, so that the machining efficiency and the machining quality are improved.
For example, some scholars calculate the maximum speed allowed at the corner according to the constraint conditions such as the acceleration/deceleration performance of the machine tool and the corner profile error, and realize the continuous processing of the numerical control program, but the processing path can only reach G0 continuity. Some scholars construct an arc, a cubic polynomial or a quadratic spline curve tangent to adjacent small line segments at the corners, so that the G1 continuity can be achieved, but the machine tool vibration can be caused due to abrupt change of the acceleration. Therefore, researchers use quintic polynomials, cubic Beziers, or quintic B-spline curves for corner transitions, generating a processing trajectory with G2 continuity. In order to further improve the smoothness of the machining path, some scholars achieve G3 continuity by constructing two symmetrical quadric bezier curves at the corners, while satisfying profile errors and real-time performance. Although the algorithm can generate a smooth machining track and improve the switching speed at the corner, the kinematic limit in the tangential direction is only considered, so that sudden changes of the speed in the uniaxial direction, the acceleration and the jerk are caused at the corner of a machining path, the vibration of a servo drive shaft is caused, and the machining quality is reduced.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention discloses a smooth corner transition smoothing method for the acceleration of an axis, which utilizes a composite trigonometric function speed planning method to simultaneously complete the construction of a corner transition curve and the speed planning of a single axis in one step, thereby obviously reducing the processing time consumed by motion trajectory control, realizing the control of smooth axis speed, axis acceleration and the acceleration of the axis, further improving the processing efficiency and precision of a complex curve curved surface and improving the processing quality of a numerical control machine tool.
The technical scheme is as follows: the invention adopts the following technical scheme: a smooth corner transition smoothing method for axial jerk is characterized by comprising the following steps:
s1, designing a composite trigonometric function speed planning method: assuming the displacement of the starting point, the speed and the acceleration of the starting point and the end point and the jerk, and constructing a smooth kinematic trajectory of the jerk;
s2, look-ahead initialization: initializing a maximum profile error, a maximum feeding speed, a maximum axial acceleration and a maximum axial jerk, and reading parameters of small line segments before and after at least one corner in a look-ahead buffer area, wherein the parameters comprise the length and the angle of each small line segment;
s3, constructing a corner transition curve: establishing a plane rectangular coordinate system, respectively calculating maximum corner speeds under the limitation of shaft speed, the limitation of corner section length, the limitation of contour error and the limitation of maximum feeding speed on two coordinate axes based on a composite trigonometric function speed planning method, obtaining maximum shaft acceleration, corner section length and a shaft kinematic trajectory by combining the maximum corner speed with the limitation of shaft acceleration, adjusting one shaft kinematic trajectory according to the motion time of the shaft kinematic trajectory on the two coordinate axes, synthesizing the shaft kinematic trajectories on the two coordinate axes after adjustment to obtain a corner transition curve, and storing the generated corner transition curve into a look-ahead buffer area;
s4, setting the starting speed of the first small line segment and the final speed of the last small line segment in the look-ahead buffer area to 0;
s5, reverse scanning: performing composite trigonometric function speed planning on all interpolation line segments from the last small line segment in the forward-looking buffer area in sequence, and entering the next interpolation line segment if the speed planning on the current interpolation line segment is successful; if the speed planning on the current interpolation line segment is unsuccessful, reconstructing a corner transition curve adjacent to the interpolation line segment until the speed planning on all the interpolation line segments in the look-ahead buffer zone is successful and then finishing reverse scanning;
s6, real-time interpolation: taking out a first small line segment from the look-ahead buffer area for processing, deleting the first small line segment from the look-ahead buffer area after the processing is finished, adding a small line segment at the tail of the look-ahead buffer area, constructing a corner transition curve at the corner of the small line segment at the tail of the look-ahead buffer area, setting the tail speed of the small line segment to be 0, and starting reverse scanning: repeatedly executing the steps S5 and S6, ending the reverse scanning when the speed planning on the interpolation line segment is successful in the execution process, and executing the step S6; when no small line segment is added at the tail of the look-ahead buffer area, sequentially taking out a first small line segment from the look-ahead buffer area for processing until all small line segments in the look-ahead buffer area are processed.
Preferably, in step S5, the step of performing composite trigonometric function speed planning on all interpolation line segments sequentially from the last small line segment in the look-ahead buffer is as follows:
s51, if the speed planning on the current interpolation line section meets the maximum axis acceleration limit and the maximum axis acceleration limit, the speed planning on the current interpolation line section is successful, and the next interpolation line section is entered to continue to carry out the composite trigonometric function speed planning; if the speed planning on the current interpolation line segment is not successful, executing step S52;
s52, if the starting speed of the current interpolation line segment is smaller than the final speed, the maximum speed which is decelerated to the starting speed in the interpolation line segment is made to be the new final speed, a corner transition curve corresponding to the final speed is reconstructed, the last interpolation line segment is returned, and the step S51 is executed;
otherwise, the maximum speed accelerated by the last speed in the interpolation line segment is set as a new starting speed, a corner transition curve corresponding to the starting speed is reconstructed, the next interpolation line segment is entered, and the step S51 is executed;
and S53, finishing the reverse scanning after the speed planning of the interpolation line segment of the first small line segment in the look-ahead buffer area is finished.
Preferably, in step S1, the kinematic trajectory is:
s(t)＝a+bt+ct2+d cos(et)
v(t)＝b+2ct-de sin(et)
a(t)＝2c-de2cos(et)
j(t)＝de3sin(et)
wherein s (t) is a displacement track, v (t) is a velocity track, a (t) is an acceleration track, j (t) is a jerk track, and a, b, c, d, and e are constant coefficients.
Preferably, in step S1, it is assumed that after a period of time T, the velocity v from the start pointsV to become endpointeAnd the displacement of the starting point, the acceleration of the starting point and the terminal point and the jerk are all zero, the kinematic trajectory is:
Figure BDA0002622472980000031
wherein, A is the maximum acceleration when T is T/2, and J is the maximum jerk when T is T/4.
Preferably, in step S3, taking the x-axis as an example, the first maximum corner speed under the axis speed limit is:
Figure BDA0002622472980000032
wherein A isxAnd JxMaximum axial acceleration and maximum axial jerk of the x-axis, respectively; theta1Is the angle between the small line segment before the corner and the positive direction of the x-axis, theta2Is the included angle between the small line sections before and after the corner.
Preferably, in step S3, taking the x-axis as an example, the second maximum corner speed under the limitation of the transition length is:
Figure BDA0002622472980000033
Lc，i＝min(li-Lc，i-1，li+1/2)
wherein A isxAnd JxMaximum axial acceleration and maximum axial jerk of the x-axis, respectively; theta1Is the angle between the small line segment before the corner and the positive direction of the x-axis, theta2The included angle between the small line sections before and after the corner is formed; l isc，i-1And Lc，iOf the (i-1) th and (i) th corners, respectivelyLength of corner section, /)iAnd li+1The lengths of the small line segments before and after the ith corner respectively.
Preferably, in step S3, taking the x-axis as an example, the third maximum corner speed under the contour error limit is:
Figure BDA0002622472980000041
Figure BDA0002622472980000042
Figure BDA0002622472980000043
r3＝cosθ1+cos(θ1+θ2)
wherein A isxAnd JxMaximum axial acceleration and maximum axial jerk of the x-axis, respectively; theta1Is the angle between the small line segment before the corner and the positive direction of the x-axis, theta2The included angle between the small line sections before and after the corner is formed; is the maximum profile error.
Preferably, in step S3, taking x-axis as an example, the maximum corner speed
Figure BDA0002622472980000044
Comprises the following steps:
Figure BDA0002622472980000045
wherein F is the maximum feed speed; v. of1Is a first maximum corner speed under shaft speed limit; v. of2Is a second maximum corner speed under the transition length limit; v. of3Is the third maximum corner velocity under contour error constraints.
Preferably, in step S3, TxTime of movement, T, of the x-axis kinematic trajectoryyThe movement time of the y-axis kinematic trajectory if Ty＞TxMaximum turn according to the kinematic trajectory of the y-axisCalculating the axial acceleration and the axial jerk of an x axis by the angular velocity and the motion time, and adjusting the kinematic trajectory of the x axis; if Ty＜TxCalculating the axis acceleration and the axis jerk of the y axis according to the maximum corner speed and the motion time of the x axis kinematic trajectory, and adjusting the y axis kinematic trajectory; if Ty＝TxThe x-axis kinematic trajectory and the y-axis kinematic trajectory are not adjusted.
Has the advantages that: the invention has the following beneficial effects:
1. the invention can complete the construction of the corner transition curve and the shaft kinematics planning in one step, and obviously reduce the processing time required by the motion trajectory control; meanwhile, the overlapping between the transition curves of adjacent corners can be effectively avoided;
2. the invention adopts a trigonometric function speed planning algorithm, can effectively reduce the calculated amount of a kinematic equation, realizes smooth control of the speed, the acceleration and the jerk of the shaft, and improves the processing quality;
3. the invention can realize global feeding speed planning and ensure the accessibility of adjacent corner speed by using the look-ahead processing algorithm, and the look-ahead processing algorithm adopts the termination judgment condition, so the look-ahead processing does not need to scan all small line segments in the buffer area, and the look-ahead processing efficiency can be effectively improved.
Drawings
FIG. 1 is a simplified process flow diagram of the present invention;
FIG. 2 is a flow chart of a method of the present invention;
FIG. 3 is a schematic illustration of a shaft displacement profile in a smooth shaft motion profile;
FIG. 4 is a schematic illustration of a shaft velocity profile in a smooth shaft motion profile;
FIG. 5 is a schematic illustration of a shaft acceleration profile in a smooth shaft motion profile;
FIG. 6 is a schematic illustration of a shaft jerk profile in a smooth shaft motion profile;
FIG. 7 is a schematic diagram of a corner transition curve;
FIG. 8 is a diagram of a real-time look-ahead buffer;
fig. 9 is a schematic diagram of a processing trajectory generated by the corner transition algorithm.
Detailed Description
The present invention will be further described with reference to the accompanying drawings.
The invention discloses a smooth corner transition smoothing method for the acceleration of an axis, which utilizes a composite trigonometric function speed planning method to simultaneously complete the construction of a corner transition curve and the speed planning of a single axis in one step, obviously reduces the processing time consumed by motion trail control, realizes the control of smooth axis speed, axis acceleration and improves the processing quality of a numerical control machine tool.
The invention provides a smooth corner transition smoothing method for axial acceleration, which solves the problems of processing efficiency and precision of a complex curve surface, and consists of 4 parts, namely prospective initialization, composite trigonometric function speed planning method design, symmetrical transition structure construction of a corner transition curve and reverse scanning, so that the processing time consumed by motion trajectory control is reduced, and the processing quality and efficiency are improved. As shown in fig. 1 and fig. 2, the method comprises the following specific steps:
s1, designing a composite trigonometric function speed planning method: and constructing an axis kinematic trajectory in a mode of compounding a polynomial function and a trigonometric function to obtain smooth axis displacement, axis speed, axis acceleration and axis jerk profiles.
The method for designing the composite trigonometric function speed planning comprises the following steps, taking an acceleration stage as an example:
s11, assuming that the displacement of the starting point, the acceleration of the starting point and the ending point and the jerk are all zero, after a period of time T, the speed is from vsAccelerate to veThe displacement formula for the acceleration phase can be expressed as:
s(t)＝a+bt+ct2+d cos(et) (1)
wherein s (t) is the displacement; t is time, T belongs to [0, T ], and T is movement time; a. b, c, d and e are constant coefficients.
S12, first, second and third order derivatives of equation (1) are taken with respect to time t to obtain velocity, acceleration and jerk equations for the acceleration phase:
v(t)＝b+2ct-de sin(et) (2)
a(t)＝2c-de2cos(et) (3)
j(t)＝de3sin(et) (4)
wherein v (t) is velocity; a (t) is acceleration; j (t) is jerk.
S13 and fig. 3 to 6 are smooth axial kinematic trajectories, and when T is 0 and T is T, the following relationships can be obtained according to the boundary conditions at the start point and the end point:
s(0)＝a+d＝0 (5)
v(0)＝b＝vs(6)
a(0)＝2c-de2＝0 (7)
a(T)＝2c-de2cos(eT)＝0 (8)
j(0)＝0＝0 (9)
j(T)＝de3sin(eT)＝0 (10)
s14, let J and-J be the maximum jerk and the minimum jerk, respectively, and a be the maximum jerk, as can be seen from fig. 5, when T is T/2, the acceleration curve reaches the maximum value, and therefore, the following relation can be obtained from equation (3):
a(T/2)＝2c-de2cos(eT/2)＝A (11)
meanwhile, when T is T/4 and T is 3T/4, as can be seen from fig. 6, the jerk curve reaches the maximum value and the minimum value, respectively, and the following relation can be obtained from equation (4),
j(T/4)＝de3sin(eT/4)＝J (12)
j(3T/4)＝de3sin(3eT/4)＝-J (13)
to simplify the calculation of the parameters, let:
eT＝2π (14)
s15, from equations (5) - (14), we can obtain the parameters of the kinematic equation:
Figure BDA0002622472980000071
s16, finally, substituting the parameters in the formula (15) into the formulas (1) to (4) to obtain a smooth shaft kinematic trajectory:
Figure BDA0002622472980000072
s2, look-ahead initialization: setting initial values of various variables to be used, preprocessing small line segments of corners to be processed, constructing processing tracks without overlapping between adjacent corner transition curves, and generating a smooth axis kinematic profile.
As shown in fig. 8, a look-ahead buffer of size N is used to store the kinematic information of the small line segments and corner transition curves. Before numerical control machining, firstly, reading N small line segments into a forward-looking buffer area, and constructing a corner transition curve at each adjacent corner, so as to obtain a machining track formed by the small line segments and the corner transition curves, as shown in fig. 9. As can be seen from FIG. 9, LiAnd Li+1Is the inflection point PiAnd Pi+1Length of corner segment, vc，iAnd vc，i+1Is its corresponding corner velocity. li+1Is the segment length of the i +1 th segment, di+1Is the interpolation segment length of the i +1 th segment.
In this step, the parameters to be initialized include: the segment length and angle of the small line segment before and after each corner, the maximum profile error of the constructed corner transition curve, the maximum feeding speed, the maximum axial acceleration and the maximum axial jerk, and storing the kinematic information of the small line segment into a look-ahead buffer area.
S3, constructing a symmetrical transition structure of the corner transition curve: and (3) by utilizing a composite trigonometric function speed planning method, simultaneously completing corner transition curve construction and single-axis speed planning in one step, and generating smooth axis displacement, axis speed, axis acceleration and axis jerk profiles.
Fig. 7 depicts the geometry of the corner transition curves. In FIG. 7, P iss，iThe point is set as the origin and is set up by the originA vertical x-y rectangular coordinate system, wherein the corner is formed by small line segments Pi-1PiAnd PiPi+1Is composed of segments of length liAnd li+1Point Ps，iOn a small line segment Pi-1PiUpper, point Pe，iOn a small line segment PiPi+1Upper, point Ps，iAnd point Pe，iThe dotted line between them is the resulting corner transition curve. To reduce the complexity of the corner transition curve construction, let us say the corner line segment Ps，iPiAnd PiPe，iAre all Lc，i，Lc，iI.e. the corner segment is long and it is assumed that there is the same velocity v at the start and end of the corner transition curvec，iThe same acceleration ac，i0 and the same jerk j c，i0. The purpose of the step is to calculate the maximum corner velocity v of the corner transition curve by an axis composite trigonometric function velocity planning method under the limitation of maximum profile errorc，iAnd corner segment length Lc，i。
To calculate the maximum corner velocity vc，iAt least one axis of axial acceleration or axial jerk should be maximized, so that vc，iIt should be determined by the axis of greater speed change, i.e., the constraint axis. Assuming the x-axis as the limiting axis, AxmaxAnd JxmaxThe limiting values of the shaft acceleration and the shaft jerk of the x shaft are respectively, F is the maximum feeding speed,iis the maximum profile error.
The symmetrical transition structure for constructing the corner transition curve comprises the following steps:
and S31, obtaining the maximum corner speed under the shaft speed limiting condition.
As can be seen from fig. 7, the starting point speed and the ending point speed of the corner transition curve on the x-axis are:
Figure BDA0002622472980000081
Figure BDA0002622472980000082
wherein, theta1Is a vector Pi-1PiAnd the positive half-axis of the x-axis by an angle theta2Is a vector Pi-1PiSum vector PiPi+1Angle between v and vc，iIs the corner velocity.
As can be seen from equation (16), when T is equal to T, the x-axis end point speed is:
Figure BDA0002622472980000083
wherein A isxAnd JxMaximum axial acceleration and maximum axial jerk, v, of the x-axis respectivelyx(T) is the speed on the x-axis at time T.
Substituting equations (17) and (18) into equation (19) can yield:
Figure BDA0002622472980000084
after simplifying equation (20), the first maximum corner velocity v can be obtained1：
Figure BDA0002622472980000091
And S32, obtaining the maximum corner speed under the condition of limiting the length of the corner section.
Because it is desirable to avoid overlap between adjacent corner transition curves, the corner segment lengths are set to:
Lc，i＝min(li-Lc，i-1，li+1/2) (22)
wherein L isc，iIs angle Pi-·PiPi+1The corner section length of the corner transition curve of (1), Lc，i-1Is the previous corner & lt Pi-2Pi-1PiThe corner section length of the corner transition curve of liAnd li+1Respectively a small line segment Pi-1PiAnd PiPi+1Length of (d).
According to FIG. 7, the displacement s on the x-axiscx，iCan be expressed as:
scx，i＝Lc，icosθ1+Lc，icos(θ1+θ2) (23)
from equation (16), when T is T, the displacement s on the x-axiscx，iCan be expressed as:
Figure BDA0002622472980000092
from the formula (17) and the formulas (22) to (24), the second maximum corner velocity v can be obtained2：
Figure BDA0002622472980000093
And S33, obtaining the maximum corner speed under the contour error limiting condition.
As can be seen from FIG. 7, point Pm，iIs the middle point of the corner transition curve. Since the starting point and the ending point of the corner transition curve have the same tangential velocity, acceleration and jerk, the corner transition curve is about & lt Pi-1PiPi+1Is symmetrical, so that point PiAnd point Pm，iThe distance between the two is the maximum profile error of the corner transition curvei。
According to FIG. 7, point PiThe x-axis component of (a) is:
xi＝Lc，icosθ1(26)
the x-axis component of the maximum profile error of the corner transition curve is:
Figure BDA0002622472980000094
wherein the content of the first and second substances,iis the maximum profile error of the corner transition curve,x，ias maximum profile erroriProjection on the x-axis.
According to equation (16), when T is T/2, the x-axis component of the midpoint of the corner transition curve is:
Figure BDA0002622472980000101
let xm，i-xi＝x，i，iIs as follows. According to the formula (17) and the formulas (26) to (28), the third maximum corner velocity v can be obtained3：
Figure BDA0002622472980000102
Wherein the content of the first and second substances,
Figure BDA0002622472980000103
Figure BDA0002622472980000104
r3＝cosθ1+cos(θ1+θ2)
and S34, calculating a track parameter according to the shaft speed, the corner section length, the contour error limit and the maximum corner speed under the condition of the maximum feeding speed, and obtaining a smooth shaft kinematic contour.
Maximum corner velocity
Figure BDA0002622472980000105
Is determined by the following formula:
Figure BDA0002622472980000106
where F is the maximum feed speed.
Will be provided with
Figure BDA0002622472980000107
Substituting the formula (17) and the formula (18) to obtain the speed of the starting point and the ending point of the corner transition curve on the x axis;
will be provided with
Figure BDA0002622472980000108
And Jx＝JxmaxBy substituting the formula (21), the acceleration A of the x-axis can be obtainedxWherein JxmaxA limit value for the initialized axis jerk for the x-axis;
will be provided with
Figure BDA0002622472980000109
AxAnd JxSubstituting into equation (25) can obtain the length L of the corner sectionc，i；
Will be provided with
Figure BDA00026224729800001010
AxAnd JxSubstituting the formula (16) into the formula (16), and obtaining the smooth axial kinematic trajectory of the axial acceleration of the x axis;
then, the y axis is used as a limiting axis, and an axis jerk smooth axis kinematic trajectory of the y axis is obtained according to the method.
Let TxAnd TyThe movement times in the x-axis and y-axis, respectively, if Ty＞TxThen the y-axis is the actual limiting axis, and in order to synchronize the corner motion of the x-y axis, let
Figure BDA00026224729800001011
Ty＝Tx', according to the formula (16), the formula (19),
Figure BDA00026224729800001012
And Tx', maximum axial acceleration A to the x-axisxAnd maximum axial jerk JxAnd adjusting, and obtaining the smooth axial kinematic trajectory of the axial acceleration of the x axis according to the new parameters. In the same way, if Ty＜TxWhen the x-axis is the actual limiting axis, the method is followed
Figure BDA00026224729800001013
Tx＝Ty', according to the formula (16), the formula (19),
Figure BDA00026224729800001014
And Ty', maximum axial acceleration A to the y-axisyAnd maximum axial jerk JyAdjusting, and obtaining a smooth axial kinematic trajectory of the axial jerk of the y axis according to the new parameters; if Ty＝TxThe x-axis kinematic trajectory and the y-axis kinematic trajectory are not adjusted. And finally, synthesizing the axis kinematic trajectories on the x axis and the y axis to obtain a corner transition curve, and storing the kinematic information of the corner transition curve into a look-ahead buffer area.
S4, reverse scanning: the corner maximum speed and the projected global feed speed are determined.
To ensure the length d of the interpolation segmenti+1Internal velocity can be from vc，iAcceleration/deceleration to vc，i+1And the accessibility of the global feed speed is ensured, the following five steps need to be performed.
S41: starting speed v of the first small line segment in the look-ahead bufferc，0And the last velocity v of the Nth small line segmentc，NSet to zero and let j-N-1 and p-0.
S42: the velocity profile is then plotted over the interpolated line segment using the method described in step S1, such that the interpolated segment length dj+1Internal velocity from vc，jAcceleration/deceleration to vc，j+1。
If the segment length d is interpolatedj+1The internal speed planning is successful, that is, the speed planning on the interpolation line section meets the maximum axis acceleration limit and the maximum axis jerk limit, that is, the termination condition is met, j is made to be j-1, and the process goes to step S42; otherwise, the following steps are performed, reducing the speed vc，jOr vc，j+1。
If v isc，j＜vc，j+1Calculating the length of the segment dj+1Can decelerate to vc，jOf maximum speed v'c，j+1Let v stand forc，j+1＝v′c，j+1J +1, and reconstructing a corner transition curve, and then, proceeding to step S42; otherwise, the length d of the segment is calculatedj+1Can be selected from vc，j+1Maximum speed v 'accelerated to'c，j。
S43: the reverse scan processing is ended only when one of the following two conditions is satisfied.
(1)j≤0。
(2) p is 1 and satisfies the termination condition.
Otherwise, let vc，j＝v′c，jAnd reconstructing the corner transition curve. Then, let j equal j-1, the process proceeds to step S42.
S44: and (4) performing real-time interpolation, namely taking out the first section of small line segment from the look-ahead buffer area for processing. And after the first section of small line segment is processed, deleting the first section of small line segment from the look-ahead buffer area. If p is 0, let p be 1.
S45: and adding a small line segment at the tail of the look-ahead buffer, setting the tail speed of the small line segment to be zero, and constructing a corner transition curve. Then, the process proceeds to step S42, where j is set to N-1, and the reverse scan is continued.
And S46, when no small line segment is added at the tail of the look-ahead buffer area, sequentially taking out a first small line segment from the look-ahead buffer area for processing until all small line segments in the look-ahead buffer area are processed.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (9)

1. A smooth corner transition smoothing method for axial jerk is characterized by comprising the following steps:
s1, designing a composite trigonometric function speed planning method: assuming the displacement of the starting point, the speed and the acceleration of the starting point and the end point and the jerk, and constructing a smooth kinematic trajectory of the jerk;
s2, look-ahead initialization: initializing a maximum profile error, a maximum feeding speed, a maximum axial acceleration and a maximum axial jerk, and reading parameters of small line segments before and after at least one corner in a look-ahead buffer area, wherein the parameters comprise the length and the angle of each small line segment;
s3, constructing a corner transition curve: establishing a plane rectangular coordinate system, respectively calculating maximum corner speeds under the limitation of shaft speed, the limitation of corner section length, the limitation of contour error and the limitation of maximum feeding speed on two coordinate axes based on a composite trigonometric function speed planning method, obtaining maximum shaft acceleration, corner section length and a shaft kinematic trajectory by combining the maximum corner speed with the limitation of shaft acceleration, adjusting one shaft kinematic trajectory according to the motion time of the shaft kinematic trajectory on the two coordinate axes, synthesizing the shaft kinematic trajectories on the two coordinate axes after adjustment to obtain a corner transition curve, and storing the generated corner transition curve into a look-ahead buffer area;
s4, setting the starting speed of the first small line segment and the final speed of the last small line segment in the look-ahead buffer area to 0;
s5, reverse scanning: performing composite trigonometric function speed planning on all interpolation line segments from the last small line segment in the forward-looking buffer area in sequence, and entering the next interpolation line segment if the speed planning on the current interpolation line segment is successful; if the speed planning on the current interpolation line segment is unsuccessful, reconstructing a corner transition curve adjacent to the interpolation line segment until the speed planning on all the interpolation line segments in the look-ahead buffer zone is successful and then finishing reverse scanning;
s6, real-time interpolation: taking out a first small line segment from the look-ahead buffer area for processing, deleting the first small line segment from the look-ahead buffer area after the processing is finished, adding a small line segment at the tail of the look-ahead buffer area, constructing a corner transition curve at the corner of the small line segment at the tail of the look-ahead buffer area, setting the tail speed of the small line segment to be 0, and starting reverse scanning: repeatedly executing the steps S5 and S6, ending the reverse scanning when the speed planning on the interpolation line segment is successful in the execution process, and executing the step S6; when no small line segment is added at the tail of the look-ahead buffer area, sequentially taking out a first small line segment from the look-ahead buffer area for processing until all small line segments in the look-ahead buffer area are processed.
2. The method for smoothing the corner transition of the axial jerk according to claim 1, wherein in step S5, the step of performing the composite trigonometric function speed planning on all the interpolated line segments sequentially from the last small line segment in the look-ahead buffer area is as follows:
s51, if the speed planning on the current interpolation line section meets the maximum axis acceleration limit and the maximum axis acceleration limit, the speed planning on the current interpolation line section is successful, and the next interpolation line section is entered to continue to carry out the composite trigonometric function speed planning; if the speed planning on the current interpolation line segment is not successful, executing step S52;
s52, if the starting speed of the current interpolation line segment is smaller than the final speed, the maximum speed which is decelerated to the starting speed in the interpolation line segment is made to be the new final speed, a corner transition curve corresponding to the final speed is reconstructed, the last interpolation line segment is returned, and the step S51 is executed;
otherwise, the maximum speed accelerated by the last speed in the interpolation line segment is set as a new starting speed, a corner transition curve corresponding to the starting speed is reconstructed, the next interpolation line segment is entered, and the step S51 is executed;
and S53, finishing the reverse scanning after the speed planning of the interpolation line segment of the first small line segment in the look-ahead buffer area is finished.
3. The method of claim 1, wherein in step S1, the kinematic trajectory is:
s(t)＝a+bt+ct2+dcos(et)
v(t)＝b+2ct-desin(et)
a(t)＝2c-de2cos(et)
j(t)＝de3sin(et)
wherein s (t) is a displacement track, v (t) is a velocity track, a (t) is an acceleration track, j (t) is a jerk track, and a, b, c, d, and e are constant coefficients.
4. The method of claim 3, wherein in step S1, the velocity is assumed to be v from the starting point after a period of time TsV to become endpointeAnd starting pointThe displacement, the acceleration of the starting point and the ending point, and the jerk of the two are all zero, then the kinematic trajectory is:
Figure FDA0002622472970000021
wherein, A is the maximum acceleration when T is T/2, and J is the maximum jerk when T is T/4.
5. The method of claim 4, wherein in step S3, taking the x-axis as an example, the first maximum corner velocity under the axle velocity limit is:
Figure FDA0002622472970000022
wherein A isxAnd JxMaximum axial acceleration and maximum axial jerk of the x-axis, respectively; theta1Is the angle between the small line segment before the corner and the positive direction of the x-axis, theta2Is the included angle between the small line sections before and after the corner.
6. The method of claim 4, wherein in step S3, taking the x-axis as an example, the second maximum corner velocity under the limitation of the transition length is:
Figure FDA0002622472970000031
Lc，i＝min(li-Lc，i-1，li+1/2)
wherein A isxAnd JxMaximum axial acceleration and maximum axial jerk of the x-axis, respectively; theta1Is the angle between the small line segment before the corner and the positive direction of the x-axis, theta2The included angle between the small line sections before and after the corner is formed; l isc，i-1And Lc，iThe length of the corner segments, l, of the ith-1 and ith corners, respectivelyiAnd li+1The lengths of the small line segments before and after the ith corner respectively.
7. The method of claim 4, wherein in step S3, taking the x-axis as an example, the third maximum corner velocity under the contour error limit is:
Figure FDA0002622472970000032
Figure FDA0002622472970000033
Figure FDA0002622472970000034
r3＝cosθ1+cos(θ1+θ2)
wherein A isxAnd JxMaximum axial acceleration and maximum axial jerk of the x-axis, respectively; theta1Is the angle between the small line segment before the corner and the positive direction of the x-axis, theta2The included angle between the small line sections before and after the corner is formed; is the maximum profile error.
8. The method of claims 5-7, wherein in step S3, taking x-axis as an example, the maximum corner velocity is set
Figure FDA0002622472970000035
Comprises the following steps:
Figure FDA0002622472970000036
wherein F is the maximum feed speed; v. of1Is a first maximum corner speed under shaft speed limit; v. of2Is a second maximum corner speed under the transition length limit; v. of3Is the third maximum corner velocity under contour error constraints.
9. The method of claim 4, wherein in step S3, T isxTime of movement, T, of the x-axis kinematic trajectoryyThe movement time of the y-axis kinematic trajectory if Ty＞TxCalculating the axis acceleration and the axis jerk of the x axis according to the maximum corner speed and the motion time of the y axis kinematic trajectory, and adjusting the x axis kinematic trajectory; if Ty＜TxCalculating the axis acceleration and the axis jerk of the y axis according to the maximum corner speed and the motion time of the x axis kinematic trajectory, and adjusting the y axis kinematic trajectory; if Ty＝TxThe x-axis kinematic trajectory and the y-axis kinematic trajectory are not adjusted.
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