CN118466401A - Multistage S-shaped rising-based large-section speed look-ahead method for multi-axis machine - Google Patents
Multistage S-shaped rising-based large-section speed look-ahead method for multi-axis machine Download PDFInfo
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Abstract
The invention discloses a large-section speed prospective method of a multi-shaft machine based on multistage S-shaped ascending, which comprises the steps of dividing a track into a plurality of micro sections, and dividing a plurality of continuous micro sections into a large section; and then dividing the large-section speed lifting into n-level S-shaped speed lifting, wherein the speed upper limit and the speed lower limit of each level are different in acceleration and jerk. The invention adopts a grading S-shaped acceleration method, which allows the physical axis acceleration, and the jerk can exceed a set value in a certain range in some places. The invention is applicable to multi-axis linkage control processing, so that the motion is smoother and more flexible, the calculated amount is greatly reduced, and the operation efficiency is improved; the method also provides a high-efficiency and stable S-shaped speed look-ahead general scheme, and has good practicability.
Description
Technical Field
The invention belongs to the technical field of multi-axis linkage robot control, and particularly relates to a large-section speed look-ahead method of a multi-axis machine based on multistage S-shaped ascending.
Background
The manufacturing industry is the basis of national production capacity and economic and social development, is a carrier for industrialization of high and new technology, and represents the development level of social productivity. In order to meet the development needs of the equipment manufacturing industry, a series of advanced processing technologies such as bamboo shoots in spring after rain are produced and developed, and the most representative is the machine tool processing technology. The advent and rapid upgrades of advanced digital technology have marked the machine tool field as having entered the era of intelligent manufacturing with digital automation as the core. In particular, in recent decades, with the rapid development of computer network technology, machine tool manufacturing has also entered the era of numerical control mainly characterized by high speed, high precision and high efficiency.
With the continuous development of economy and society, the demands of people for personalized products are increasing, and the supply and demand relationship promotes the speed and precision of processing of product manufacturing enterprises to be improved. This is because the processing speed determines the production efficiency of the product, and the processing accuracy is an important guarantee of the product quality. Meanwhile, the high-speed and high-precision processing demands are urgent to further improve the computing and control capabilities of the numerical control system. This is mainly manifested in two aspects:
Firstly, the numerical control system has high operation speed, and particularly comprises the conciseness and effectiveness of a core algorithm and the reaction rapidity of each moving part, so that the time for processing preparation is shortened;
Secondly, the actuating mechanisms are required to not generate the phenomena of impact, oscillation, step-out and the like in the motion process, so that the requirements of high-speed and high-precision processing are met.
The acceleration and deceleration control algorithm commonly used in the numerical control system comprises a linear acceleration and deceleration algorithm, an exponential acceleration and deceleration algorithm, an S-shaped acceleration and deceleration algorithm, a polynomial acceleration and deceleration algorithm and the like, and the S-shaped acceleration and deceleration is focused by students most because of the practicability. The main research hot spot of S-shaped acceleration and deceleration at present is an efficient and general solving model. The ideal S-shaped acceleration and deceleration solving model has smaller computational complexity and higher-precision analytic solution, and a perfect solution is not available in the aspect of acceleration and deceleration model solving temporarily. In order to ensure the processing stability, a high-grade numerical control system generally adopts flexible acceleration and deceleration, and S-shaped acceleration and deceleration is most used in the numerical control system due to the practicality. The main problem existing in the S-shaped acceleration and deceleration at present is that an efficient general solving method is not available.
In the aspect of multi-axis linkage control, a five-axis linkage numerical control system is most commonly used at present. Two rotating shafts are added on the basis of three translational shafts, so that the complex curved surface can be processed more flexibly. However, most of the existing S-shaped speed look-ahead is only aimed at three-axis linkage processing equipment, physical quantities such as acceleration, jerk and the like at a certain position are calculated according to a space track geometry, one or more split micro-segments can be subjected to one-time S-shaped speed curve calculation, the speed frequently oscillates, the speed is slowly increased, and the complex motion situation is difficult to adapt.
Secondly, for the velocity planning of a spatial circular trajectory, there is a normal acceleration due to the presence of curvature, and for a particular physical axis there is a jerk due to the direction of the normal acceleration being changing. The faster the apparent speed, the faster the acceleration change, and the greater the jerk. For micro-segment line [ i ], its jerk is proportional to the third power of speed.
When the actual speed approaches the maximum speed MaxVByJerk limited by jerk, there is a physical axis jerk approaching the maximum value, and since the speed is S-shaped, the virtual axis speed itself has a larger jerk (the acceleration becomes smaller) when approaching MaxVByJerk, and at this time, the jerk due to the shape of the motion trajectory of the physical axis is superimposed on the jerk due to the change in the speed of the virtual axis, and may far exceed the set jerk (2 times the set jerk at the maximum).
If the jerk of the virtual axis is set to a small value, the speed increasing efficiency is low at a low speed, and the sum of jerks always exceeds the set value as long as the speed is close to MaxVByJerk, and the superposition of jerks of the physical axis inevitably exceeds the set value due to the unavoidable existence of jerks of the virtual axis. If the speed is made to be MaxVByJerk less, the jerk is ensured to meet the requirement, but the speed is always less than MaxVByJerk, the speed is sacrificed, and the method is not friendly for a longer track. This problem occurs not only in jerk but also in acceleration.
Disclosure of Invention
The invention aims to provide a method for looking ahead at the large-section speed of a multi-shaft machine based on multistage S-shaped rising, and aims to solve the problems.
The invention is realized mainly by the following technical scheme:
A method for looking ahead at the large-section speed of a multi-shaft machine based on multistage S-shaped rising divides a track into a plurality of micro-sections, and a plurality of continuous micro-sections are divided into one large section; then dividing the large-section speed lifting into n-level S-shaped speed lifting, wherein the upper and lower limits of the speeds, the acceleration and the jerk of each level are different; the method comprises the following steps:
Step A1: initializing the upper speed limits { VRefer, VRefer, VRefer, …, VRefern } of each stage of the large segment, the minimum acceleration { minA1, minA2, minA3, …, minAn } of each stage, the minimum jerk { minJ1, minJ2, minJ3, …, minJn } of each stage; wherein, the minimum acceleration minAn of each stage of the large segment is equal to the minimum acceleration minA of all micro segments of the large segment; each stage minimum jerk minJn is equal to the maximum jerk wholeJerkmax of the entire continuous track;
VRefern=min（MinVByAcc，MinVByJerk）×VreferScalen，
wherein: minVByAcc is the upper speed limit minimum of the acceleration limits for all micro-segments of the large segment;
MinVByJerk is the minimum upper speed limit of the jerk limit for all micro-segments of the large segment;
VREFERSCALEN is the maximum speed ratio of the acceleration and jerk limit occupied by the nth stage maximum speed;
Step A2: calculating to obtain the current length of the large section:
Line.L=Line.L0+line.l，
wherein: line.L0 is the length of the large segment before the current micro segment;
line.L is the length of the current large segment;
line.l is the length of the current micro-segment;
step A3: calculating the current minimum acceleration { minA, minA, minA3, …, minAn };
minAn=min（minAn，Acc），
Acc=wholeAxisVmax[k]×ratioA÷ratioL，
ratioA=1-ratioAn+AoverflowScale，
ratioAn=ratioVn2，
ratioVn=VRefern÷VLimitByAcc，
Wherein: acc is the acceleration of the virtual axis limited by the current physical axis k;
wholeAxisVmax [ k ] is the maximum speed of the physical axis k;
ratioA is the ratio of the acceleration of the current physical axis k to the set acceleration;
ratioAn is the ratio of the acceleration of the physical axis k of the track curvature uniform motion to the set acceleration when the nth stage reaches the upper speed limit;
ratioVn is the ratio of the nth stage speed VRefern to the upper speed limit of the acceleration limit of the current micro segment;
ratioL is the ratio of the physical axis k displacement to the virtual axis displacement;
AOverflowScale is the ratio of the value that the acceleration can exceed the set acceleration to the set acceleration;
VLimitByAcc is the upper speed limit of the acceleration limit for the current micro-segment;
Step A4: calculating the current minimum jerk { minJ, minJ, minJ, …, minJn } of each stage;
minJn=min（minJn，Jerk），
Jerk=wholeAxisJerkmax[k]×ratioJ÷ratioL，
ratioJ=1-ratioJn+JOverflowScale，
ratioJn=ratioVn3，
ratioVn=VRefern÷VLimitByJerk，
Wherein: jerk is the Jerk of the current S-type velocity profile;
wholeAxisJerkmax [ k ] is the maximum jerk of the physical axis k;
ratioJ is the ratio of the acceleration of the current physical axis k to the set jerk;
ratioJn is the ratio of the jerk of the physical axis k of the track curvature uniform motion to the set jerk when the nth stage reaches the upper speed limit;
ratioVn is the ratio of the nth stage speed VRefern to the upper speed limit of the jerk limit of the current micro-segment;
VLimitByJerk the upper speed limit of the jerk limit of the current micro-segment;
JOverflowScale is the ratio of the value that the jerk can exceed the set jerk to the set jerk;
Step A5: if the current micro-segment is the last micro-segment of the large segment, the step A6 is entered, otherwise, the step A2 is entered;
Step A6: updating the large-segment all-level accelerations { A1, A2, A3, …, an } to the all-level minimum accelerations { minA1, minA2, minA3, …, minAn } calculated in the step A3; the large stage jerk { J1, J2, J3, …, jn } is updated to the stage minimum jerk { minJ, minJ2, minJ, …, minJn } calculated in step A4.
In order to better implement the present invention, further, in the step A3, VLimitByAcc has the following formula:
VLimitByAcc=min（AxisStartVLimitByAcc[k]，AxisEndVLimitByAcc[k]），
wherein: axisStartVLimitByAcc k is the speed limit of the gudgeon junction of the physical axis k caused by acceleration,
AxisEndVLimitByAcc [ k ] is the speed limit of the shaft tail point of the physical shaft k caused by acceleration.
In order to better implement the present invention, further, in the step A4, the calculation formula of VLimitByJerk is as follows:
VLimitByJerk=min（AxisStartVLimitByJerk[k]，AxisEndVLimitByJerk[k]），
Wherein: axisStartVLimitByJerk k is the speed limit of the gudgeon node of physical axis k caused by jerk,
AxisEndVLimitByJerk [ k ] is the speed limit of the shaft tail point of the physical shaft k caused by jerk.
To better implement the present invention, further, calculating the end maximum speed Vemax of the micro-segment for each stage for the S-shaped curve for each stage includes the steps of:
Step B1: comparing the initial speed Vs with VRefern to obtain an S-type speed rising level m corresponding to the initial speed Vs, wherein m is smaller than or equal to n; further determining an m-level upper speed limit VReferm, an acceleration Am and a jerk Jm corresponding to the initial speed Vs;
step B2: if m is greater than 1, vs= VRefer (m-1), l=l- (m-1) × Lsvme; wherein Lsvme is the distance required for the initial velocity Vs to accelerate to VReferm;
if l is less than or equal to Lsvme or Vmax is less than or equal to VReferm, calculating an upper m-stage speed limit Vram:
Vsam=Vs+（Am）2÷Jm，
Vm=min（Vmax，VReferm），
if the calculated Vcam is greater than Vm, the step B3 is entered, otherwise, the step B4 is entered;
step B3: solving dV:
，
Vemax=Vs+dV；
step B4: calculating a distance Lsam required for accelerating the initial speed Vs to Vram, and if the movement distance l is smaller than Lsam, entering a step B3; otherwise calculate Vemax:
，
wherein: l is the movement distance;
dV is the speed at which it can rise;
Vm is the maximum speed that can be actually achieved during the movement;
Vmax is the maximum feed speed that can be achieved during movement.
In order to better implement the present invention, further, in the step B2, the calculation formula of Lsvme is as follows:
Lsvme=L1+L2，
wherein: l1 is the minimum distance required for the initial velocity Vs to rise to Vmax;
L2 is the minimum distance required for the end velocity Ve to rise to Vmax;
If L is larger than or equal to Lsvme, calculating L1 and L2 respectively:
Let dv=vmax-Vs, if dV is less than a 2/J, then the calculation formula for L1 is:
，
Wherein: a is the acceleration at which the initial velocity Vs accelerates to VReferm;
J is the jerk at which the initial velocity Vs accelerates to VReferm;
if dV is greater than or equal to A 2 J, then the calculation formula for L1 is:
，
let dv=max (Vmax-Ve, 0), if dV is less than a 2 ++j, then the calculation formula for L2 is:
，
If dV is greater than or equal to A 2 J, then the calculation formula for L2 is:
，
if L < Lsvme, vsam and Veam are calculated separately:
，
，
If Vsam is less than Ve, then Lsam =l1'; otherwise Lsam = L1'+l2';
Wherein: l1' is the minimum distance required for the initial velocity Vs to rise to the Vram velocity;
L2' is the minimum distance required for the end velocity Ve to rise to the Vram velocity;
l is the minimum distance required to rise from the start speed Vs to the vs+dv speed.
In order to better implement the present invention, further, the calculation formula of L is as follows:
if dV is less than A 2/J, then there are:
，
If dV is greater than or equal to A 2/J, then there are:
。
To better implement the invention, further, a continuous plurality of micro-segments therein are divided into one large segment if the following conditions are simultaneously satisfied:
the difference between the temporary upper speed limit maximum tempMaxV of the micro-segment and the temporary upper speed limit minimum tempMinV of the micro-segment is less than or equal to the range VRang of the difference between the upper speed limit maximum and the minimum of all the micro-segments;
the difference between the temporary upper speed limit maximum tempMaxVByAcc of the acceleration limit of the micro-segment and the temporary upper speed limit minimum tempMinVByAcc of the acceleration limit of the micro-segment is less than or equal to the range ACCVRANGE of the difference between the upper speed limit maximum and the minimum of the acceleration limits of all the micro-segments;
The difference between the micro-segment jerk limited temporary upper speed limit maximum tempMaxVByJerk and the micro-segment jerk limited temporary upper speed limit minimum tempMinVByJerk is less than or equal to the range JerkVRange of the difference between the upper speed limit maximum and the minimum of all micro-segment jerk limits;
The difference between the temporary acceleration maximum tempMaxA and the temporary acceleration minimum tempMinA of the micro-segment is less than or equal to the range AccRange of the difference between the maximum and minimum of the virtual axis accelerations of all micro-segments;
Wherein:
，
，
，
，
，
，
，
，
Wherein: maxV is the upper maximum of the speeds of all micro-segments;
MinV is the upper speed limit minimum for all micro-segments;
line1.StartVLimit is the limit of the head node speed of the next micro-segment line1 of the current micro-segment;
line1.EndVLimit is the tail node speed limit value of the next micro-segment line1 of the current micro-segment;
MinVByAcc is the upper speed limit minimum of the acceleration limits for all micro-segments;
MaxVByAcc is the maximum upper speed limit of the acceleration limits for all micro-segments;
line1.StartVLimitByAcc is the speed limit value of the acceleration limit of the head node of the next micro-segment line1 of the current micro-segment;
line1.EndVLimitByAcc is the speed limit value of the acceleration limit of the tail point of the next micro-segment line1 of the current micro-segment;
MinVByJerk is the minimum upper speed limit of the jerk limit for all micro-segments;
MaxVByJerk is the upper limit maximum of jerk limit for all micro-segments;
line1.StartVLimitByJerk is the jerk limit speed limit value for the next micro-segment line1 of the current micro-segment;
line1.EndVLimitByJerk is the jerk limit speed limit value of the tail point of the next micro-segment line1 of the current micro-segment;
MaxA is the acceleration maximum for all micro-segments;
MinA is the minimum acceleration for all micro-segments;
line1.Acc is the acceleration of the next micro-segment line1 of the preceding micro-segment.
The beneficial effects of the invention are as follows:
the invention adopts a grading S-shaped acceleration method, which allows the physical axis acceleration, and the jerk can exceed the set value in a certain range or in some places. The invention is applicable to multi-axis linkage control processing, so that the motion is smoother and more flexible, the calculated amount is greatly reduced, and the operation efficiency is improved; the method also provides a high-efficiency and stable S-shaped speed look-ahead general scheme, and has good practicability.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of the three stage S-shaped velocity ramp in example 1;
FIG. 3 is a three-stage S-shaped velocity profile of example 2;
Fig. 4 is an enlarged partial schematic view of fig. 3.
Detailed Description
Example 1:
A method for looking ahead at the speed of a large section of multi-shaft machine based on multi-stage S-shaped rising divides the speed rising of the large section into multi-stage S-shaped speed rising, the upper and lower limits of the speeds of each stage, the accelerations and the jerks are different, and the S-shaped speed curve allows the accelerations and the jerks to be smaller. The invention adopts a grading type speed-up method, which allows the physical axis acceleration, and the jerk can exceed the set value in a certain range or in some places.
Specifically, as shown in fig. 2, taking a three-stage step-up as an example, different jerks and accelerations are set for different speeds. In order to be able to reach maximum speed (jerk or acceleration reaches a maximum value at constant speed of the virtual axis), it is unavoidable that the acceleration and jerk will exceed the set value near this speed, and it can be set how much, e.g. 10%, at most.
As shown in fig. 1 and 2, the large segment rises at a three-stage S-shaped speed, and the establishment of the acceleration and jerk of the large segment includes the following steps:
2.1 initialisation VRefer, VRefer, 2, VRefer3. Initialization minA, minA, 2, minA3. Initialization minJ, minJ, 2, minJ3. The specific formula is as follows:
，
，
，
，
，
wherein: minVByAcc is the upper speed limit minimum of all micro-segment acceleration limits;
MinVByJerk is the upper speed limit minimum of all micro-segment acceleration limits;
MinA is the minimum of all micro-segment accelerations.
2.2 The current length divided into large segments is obtained:
Line.L=Line.L+line.l，
Wherein: the current large segment is Line, and the current micro segment is Line.
2.3 Calculate new minA, minA, minA3 from the physical axis information and acceleration of the current micro-segment.
For a specific physical axis k of the micro-segment, the ratio of the displacement of the physical axis k to the displacement of the virtual axis is set as follows:
，
(1) The three-level acceleration minA-minA 3 is updated by the physical axis k:
Let the upper speed limit of the micro-segment acceleration limit be:
，
The ratio of first stage speeds VRefer to VLimitByAcc is:
，
Calculating the ratio of the acceleration of a physical axis k of track curvature uniform motion to the set acceleration of the physical axis when the first stage reaches the upper limit of the speed:
，
when the virtual axis moves at a constant speed of V, the acceleration of a specific physical axis is proportional to the square of the speed due to the curvature of the space curve.
The physical axis may also have an acceleration at this time that is the ratio of the set acceleration of the physical axis:
，
Turning the acceleration of the physical axis k onto the virtual axis, the acceleration of the virtual axis limited by the physical axis k at this time:
，
update minA value:
。
Similarly, the ratio of second stage speeds VRefer to VLimitByAcc is:
，
And when the second stage reaches the upper speed limit, the physical axis k acceleration of uniform motion due to track curvature accounts for the ratio of the set acceleration of the physical axis:
，
the physical axis may also have an acceleration at this time that is the ratio of the set acceleration of the physical axis
，
Turning the acceleration of the physical axis k onto the virtual axis, the acceleration of the virtual axis limited by the physical axis k at this time:
，
Update minA value:
，
Likewise, the ratio of third stage speeds VRefer to VLimitByAcc is:
，
The third stage reaches the upper limit of the speed, and the physical axis k acceleration of the constant motion due to the track curvature accounts for the ratio of the set acceleration of the physical axis:
，
The physical axis may also have an acceleration at this time that is the ratio of the set acceleration of the physical axis:
，
Turning the acceleration of the physical axis k onto the virtual axis, the acceleration of the virtual axis limited by the physical axis k at this time:
，
updating minA the value of:
，
2.4 calculate new minJ, minJ2, minJ3 from the physical axis information and jerk of the current micro-segment:
(1) Three-level jerk minJ, minJ2, minJ3 are updated by the physical axis k:
The upper speed limit of the micro-segment jerk limit is set as follows:
，
the ratio of first stage speeds VRefer to VLimitByJerk is:
，
The first stage reaches the upper limit of the speed, and the physical axis k acceleration of the uniform motion due to the track curvature accounts for the ratio of the set acceleration of the physical axis:
，
when the virtual axis moves at a constant speed of V, the jerk of a specific physical axis is proportional to the cube of the speed due to the shape of the space curve.
The physical axis may also have a jerk to set jerk ratio of:
，
Turning the jerk of physical axis k onto the virtual axis, then the jerk of the virtual axis, which is now limited by physical axis k:
，
Update minJ value:
。
Likewise, the ratio of second stage speeds VRefer to VLimitByJerk is:
，
And when the second stage reaches the upper speed limit, the physical axis k acceleration of uniform motion due to track curvature accounts for the ratio of the set acceleration of the physical axis:
，
the physical axis may also have a jerk to set jerk ratio of:
，
Turning the jerk of physical axis k onto the virtual axis, then the jerk of the virtual axis, which is now limited by physical axis k:
，
Update minJ value:
。
likewise, the ratio of third stage speeds VRefer to VLimitByJerk is:
。
The third stage reaches the upper limit of the speed, and the physical axis k acceleration of the constant motion due to the track curvature accounts for the ratio of the set acceleration of the physical axis:
，
the physical axis may also have a jerk to set the jerk ratio of the physical axis to
，
Turning the jerk of the physical axis k onto the virtual axis, the jerk of the virtual axis limited by the physical axis k at this time
，
Updating minJ the value of:
。
2.5 judging whether the current micro-segment is the last micro-segment divided into a large segment, if so, turning to the step 2.6. If not, go to step 2.7.
2.6 The large sections A1, A2, A3 were set to minA1, minA2, minA 3. J1, J2, J3 are set to minJ1, minJ2, minJ3. The whole process ends.
2.7 The current micro-segment is set to be the next micro-segment to the current micro-segment. Turning to step 2.2.
At this time, all the micro-segments have been divided into large segments, which all rise in multiple stages. Of course, for some special curves, such as long segments, it is true that the first step rises because its VRefer, VRefer, VRefer3 is determined by acceleration and jerk limited maximum speed, which can be infinite for long segment VRefer1, greater than maximum speed MaxV that can be achieved.
Wherein:
AOverflowScale: the acceleration may exceed a ratio of a value of the set acceleration to the set acceleration;
JOverflowScale: the jerk may exceed a ratio of a value of the set jerk to the set jerk;
VREFERSCALE1: the first stage maximum speed occupies the maximum speed proportion of acceleration and jerk limitation;
VREFERSCALE2: the second stage maximum speed occupies a maximum speed ratio of acceleration and jerk limitation;
VREFERSCALE3: the third stage maximum speed occupies the maximum speed proportion of acceleration and jerk limitation;
Each large segment is newly added with the maximum speed VRefer, VRefer, VRefer3 of the three stages of physical quantity;
the original acceleration Acc is replaced by three-level acceleration A1, A2 and A3;
The original Jerk is replaced by three-level Jerk J1, J2, J3;
VRefer1, VRefer, 2, VRefer3: the first, second and third speed upper limits of the large section;
minA1, minA, 2, minA3: the first, second and third acceleration minimum values of the large section limited by each current micro section;
minJ1, minJ, 2, minJ3: the first, second and third stages of the large section limited by each current micro section are minimum jerk values;
example 2:
in this embodiment, further optimization is performed based on embodiment 1, and in the forward planning and backtracking process of the speed look-ahead, the most important step is how to obtain the maximum speed at the end of the micro-segment from the initial speed, the micro-segment length, the maximum speed, the acceleration and the jerk information.
The three-stage S-shaped speed curve is provided with the following variables:
L: a length;
StartV: an initial speed;
EndV: end speed;
t: micro-segment movement time;
MaxV: maximum speed allowed by the micro-segment;
VRefer1, VRefer, 2, VRefer3: maximum speed of three-stage S-shaped curve;
A1, A2, A3: maximum acceleration of the three-stage S-shaped curve;
j1, J2, J3: jerk of the three-stage S-shaped curve;
ts0, ts1, ts18: the movement time of each part;
totalTs0, totalTs1, totalTs: total movement time to each node;
vss0, vss1,..vss 17: speed when moving to each node;
ss0, ss1,..ss 17: total movement distance when moving to each node;
vm: maximum speed that can be actually achieved during the movement.
4.1 From the initial velocity Vs, the distance of movement l, the maximum acceleration, the maximum velocity, the jerk, a specific calculation of the last maximum velocity Vemax is obtained. The method specifically comprises the following steps:
(1) Judging the relation between Vs and VRefer, VRefer, VRefer3,
If Vs < VRefer, go to step (2);
If Vs is larger than or equal to VRefer and Vs is smaller than VRefer2, turning to step (3);
If Vs is not less than VRefer, go to step (4).
(2) If Vs < VRefer < 1,
Let the acceleration be A1 and the jerk be J1, calculate the distance Lsvme required for Vs to accelerate to VRefer. If l is less than or equal to Lsvme or Vmax is less than or equal to VRefer1, the process goes to the step (2-1), otherwise, the process goes to the step (2-2).
(2-1) Calculating a first stage upper speed limit. Let vsam=vs+ (A1) 2 ++j1, vm=min (Vmax, vRefer 1)
If Vram > Vm, the maximum acceleration cannot be reached, and the process goes to step (2-1-1). Otherwise, go to (2-1-2).
(2-1-1) Solving the third equation for dV:
，
Vemax=Vs+dV，
(2-1-2) let the acceleration be A1, the jerk be J1, the distance Lsam required for Vs to accelerate to Vcam is calculated. If l < Lsam, indicating that the maximum acceleration cannot be reached, and turning to the step (2-1-1); otherwise, the maximum acceleration can be reached, and Vemax is calculated:
，
(2-2) the second stage speed can be reached. Let l (current) =l (original) -Lsvme, vs= vRefer1. Turning to step (3).
(3) Let acceleration be A2 and jerk be J2, calculate (4.5) the distance Lsvme needed for Vs to accelerate to vRefer < 2 >. If l is less than or equal to Lsvme or Vmax is less than or equal to VRefer2, then the process goes to the step (3-1); otherwise, go to step (3-2).
(3-1) Calculating a second stage speed upper limit Vsam:
Vsam=Vs+（A2）2÷J2，
let vm=min (Vmax, VRefer 2),
If Vram is greater than Vm, indicating that maximum acceleration cannot be achieved, moving to step (3-1-1); otherwise, go to step (3-1-2).
(3-1-1) Solving the third equation for dV:
，
Vemax=Vs+dV，
(3-1-2) let the acceleration be A2, the jerk be J2, the distance Lsam required for Vs to accelerate to Vcam is calculated.
If l < Lsam, the maximum acceleration cannot be reached, and the process goes to step (3-1-1); otherwise, the maximum acceleration can be reached, calculate Vemax:
，
the speed (3-2) can reach the third stage, at which time let l (current) =l (original) -Lsvme, vs= vRefer2, go to step (4).
(4) Let the acceleration be A3 and the jerk be J3, calculate the distance Lsvme required for Vs to accelerate to Vmax.
If l is less than or equal to Lsvme, turning to the step 4-1; otherwise Vemax =vmax.
(4-1) Calculating Vram:
Vsam=Vs+（A3）2÷J3，
if Vram > Vmax, then maximum acceleration cannot be reached, go to step (4-1-1); otherwise, go to step (4-1-2).
(4-1-1) Solving the third equation for dV:
，
Vemax=Vs+dV，
(4-1-2) let the acceleration be A3, the jerk be J3, the distance Lsam required for Vs to accelerate to Vcam is calculated.
If l < Lsam, indicating that the maximum acceleration cannot be reached, turning to step (4-1-1); otherwise, the maximum acceleration can be reached, calculate Vemax:
，
4.5 from the starting speed Vs, the speed dV that can rise, the minimum distance L required to rise to the speed vs+dv is calculated in particular.
The minimum distance L required to rise to the velocity vs+dv is calculated from the velocity dV at which the velocity can rise, assuming that the acceleration a and the jerk are J, and the initial velocity Vs.
If it is，
If it is。
4.6 The parameters of the conventional 7-segment S-shaped speed curve are calculated specifically.
And calculating parameters of a conventional 7-segment S-shaped speed curve, solving the parameters by adopting Newton method from a start speed Vs, an end speed Ve, an acceleration A, a jerk J and a maximum speed Vmax, and calculating Ts0, the number of the segments, ts6, totalTs0, the number of the segments, totalTs1, vss0, the number of the segments, vss5, ss0, the number of the segments, and the number of the segments, ss5 and Vm.
(1) If J is less than or equal to 0 or Amax is less than or equal to 0, special case processing is carried out, and the process goes to the step (2), otherwise, the process goes to the step (3).
(2) T0...t6 are each assigned 0, where t3=l/Vs, totalTs0, totalTs1, totalTs2 are each assigned 0, total ts3.. totalTs6 are each assigned t3.
(3) The minimum distance L1 required for Vs to rise to Vmax speed is calculated from step 4.5. The minimum distance L2 required for Ve to rise to Vmax speed is calculated from step 4.5.
Let Lsvme = l1+l2, if L is not less than Lsvme, go to step (4); otherwise go to step (5).
(4) The maximum feed speed Vmax can be reached. Let dv=vmax-Vs, if dV < a 2/J, then maximum acceleration cannot be reached, go to step (4-1); otherwise, the maximum acceleration can be reached, and the process goes to the step (4-2).
(4-1)Turning to step (4-3).
(4-2) ，
，
Turning to step (4-3).
(4-3) Dv=max (Vmax-Ve, 0), if dV < a 2/J, the maximum acceleration cannot be reached, go to step (4-4); otherwise, the maximum acceleration can be reached, and the process goes to the step (4-5).
(4-4)，
Then, the process goes to step (4-6).
(4-5)，
。
Then, the process goes to step (4-6).
(4-6)。
(5) The maximum feed speed Vmax is not reached.
In the step planning, vs is equal to or less than Ve, and the variable isExchangeV is made to mark whether Vs and Ve are exchanged or not. If Vs > Ve then the exchange Vs is set to 1 with Ve isExchangeV, otherwise isExchangeV is set to 0.
Order the，
，
If Vsam < Ve, then the minimum distance L1 required for Vs to rise to Vsam speed is calculated from step 4.5 and Lsam =l1 otherwise, the minimum distance L1 required for Vs to rise to Vsam speed and the minimum distance L2 required for Ve to rise to Vsam speed are calculated from step 4.5 and Lsam =l1+l2.
As shown in FIGS. 3 and 4, the whole speed curve is composed of a three-stage S-shaped speed curve, the upper speed limit is 300mm/S, the acceleration is 4000mm/S 2, and the jerk is 200000mm/S 3. The higher the progression, the less the acceleration of the S-shape and the smoother the virtual axis speed curve appears. The speeds of all physical axes, including the virtual axis, are also relatively smooth and compliant.
The foregoing description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and any simple modification, equivalent variation, etc. of the above embodiment according to the technical matter of the present invention fall within the scope of the present invention.
Claims (7)
1. A large-section speed look-ahead method based on a multi-stage S-shaped ascending multi-axis machine is characterized in that a track is divided into a plurality of micro sections, and a plurality of continuous micro sections are divided into a large section; then dividing the large-section speed lifting into n-level S-shaped speed lifting, wherein the upper and lower limits of the speeds, the acceleration and the jerk of each level are different; the method comprises the following steps:
Step A1: initializing the upper speed limits { VRefer, VRefer, VRefer, …, VRefern } of each stage of the large segment, the minimum acceleration { minA1, minA2, minA3, …, minAn } of each stage, the minimum jerk { minJ1, minJ2, minJ3, …, minJn } of each stage; wherein, the minimum acceleration minAn of each stage of the large segment is equal to the minimum acceleration minA of all micro segments of the large segment; each stage minimum jerk minJn is equal to the maximum jerk wholeJerkmax of the entire continuous track;
VRefern=min（MinVByAcc，MinVByJerk）×VreferScalen，
wherein: minVByAcc is the upper speed limit minimum of the acceleration limits for all micro-segments of the large segment;
MinVByJerk is the minimum upper speed limit of the jerk limit for all micro-segments of the large segment;
VREFERSCALEN is the maximum speed ratio of the acceleration and jerk limit occupied by the nth stage maximum speed;
Step A2: calculating to obtain the current length of the large section:
Line.L=Line.L0+line.l，
wherein: line.L0 is the length of the large segment before the current micro segment;
line.L is the length of the current large segment;
line.l is the length of the current micro-segment;
step A3: calculating the current minimum acceleration { minA, minA, minA3, …, minAn };
minAn=min（minAn，Acc），
Acc=wholeAxisVmax[k]×ratioA÷ratioL，
ratioA=1-ratioAn+AOverflowScale，
ratioAn=ratioVn2，
ratioVn=VRefern÷VLimitByAcc，
Wherein: acc is the acceleration of the virtual axis limited by the current physical axis k;
wholeAxisVmax [ k ] is the maximum speed of the physical axis k;
ratioA is the ratio of the acceleration of the current physical axis k to the set acceleration;
ratioAn is the ratio of the acceleration of the physical axis k of the track curvature uniform motion to the set acceleration when the nth stage reaches the upper speed limit;
ratioVn is the ratio of the nth stage speed VRefern to the upper speed limit of the acceleration limit of the current micro segment;
ratioL is the ratio of the physical axis k displacement to the virtual axis displacement;
AOverflowScale is the ratio of the value that the acceleration can exceed the set acceleration to the set acceleration;
VLimitByAcc is the upper speed limit of the acceleration limit for the current micro-segment;
Step A4: calculating the current minimum jerk { minJ, minJ, minJ, …, minJn } of each stage;
minJn=min（minJn，Jerk），
Jerk=wholeAxisJerkmax[k]×ratioJ÷ratioL，
ratioJ=1-ratioJn+JOverflowScale，
ratioJn=ratioVn3，
ratioVn=VRefern÷VLimitByJerk，
Wherein: jerk is the Jerk of the current S-type velocity profile;
wholeAxisJerkmax [ k ] is the maximum jerk of the physical axis k;
ratioJ is the ratio of the acceleration of the current physical axis k to the set jerk;
ratioJn is the ratio of the jerk of the physical axis k of the track curvature uniform motion to the set jerk when the nth stage reaches the upper speed limit;
ratioVn is the ratio of the nth stage speed VRefern to the upper speed limit of the jerk limit of the current micro-segment;
VLimitByJerk the upper speed limit of the jerk limit of the current micro-segment;
JOverflowScale is the ratio of the value that the jerk can exceed the set jerk to the set jerk;
Step A5: if the current micro-segment is the last micro-segment of the large segment, the step A6 is entered, otherwise, the step A2 is entered;
Step A6: updating the large-segment all-level accelerations { A1, A2, A3, …, an } to the all-level minimum accelerations { minA1, minA2, minA3, …, minAn } calculated in the step A3; the large stage jerk { J1, J2, J3, …, jn } is updated to the stage minimum jerk { minJ, minJ2, minJ, …, minJn } calculated in step A4.
2. A method for large-segment speed look-ahead for multi-stage S-shaped rising multi-axis machines according to claim 1, wherein the formula for VLimitByAcc in step A3 is as follows:
VLimitByAcc=min（AxisStartVLimitByAcc[k]，AxisEndVLimitByAcc[k]），
wherein: axisStartVLimitByAcc k is the speed limit of the gudgeon junction of the physical axis k caused by acceleration,
AxisEndVLimitByAcc [ k ] is the speed limit of the shaft tail point of the physical shaft k caused by acceleration.
3. A method for large-segment speed look-ahead of multi-stage S-shaped rising multi-axis machine according to claim 1, wherein the calculation formula of VLimitByJerk in step A4 is as follows:
VLimitByJerk=min（AxisStartVLimitByJerk[k]，AxisEndVLimitByJerk[k]），
Wherein: axisStartVLimitByJerk k is the speed limit of the gudgeon node of physical axis k caused by jerk,
AxisEndVLimitByJerk [ k ] is the speed limit of the shaft tail point of the physical shaft k caused by jerk.
4. A method of large segment speed look-ahead for a multi-stage S-rise based multi-axis machine according to any of claims 1-3, characterized in that calculating the end maximum speed Vemax of the micro-segments of each stage for the S-curve of each stage comprises the steps of:
Step B1: comparing the initial speed Vs with VRefern to obtain an S-type speed rising level m corresponding to the initial speed Vs, wherein m is smaller than or equal to n; further determining an m-level upper speed limit VReferm, an acceleration Am and a jerk Jm corresponding to the initial speed Vs;
step B2: if m is greater than 1, vs= VRefer (m-1), l=l- (m-1) × Lsvme; wherein Lsvme is the distance required for the initial velocity Vs to accelerate to VReferm;
if l is less than or equal to Lsvme or Vmax is less than or equal to VReferm, calculating an upper m-stage speed limit Vram:
Vsam=Vs+（Am）2÷Jm，
Vm=min（Vmax，VReferm），
Wherein: vm is the maximum speed that can be actually achieved during the movement;
vmax is the maximum feed speed that can be achieved during movement;
if the calculated Vcam is greater than Vm, the step B3 is entered, otherwise, the step B4 is entered;
step B3: solving dV:
，
Vemax=Vs+dV；
wherein: dV is the speed at which it can rise;
step B4: calculating a distance Lsam required for accelerating the initial speed Vs to Vram, and if the movement distance l is smaller than Lsam, entering a step B3; otherwise calculate Vemax:
，
Wherein: l is the movement distance.
5. The method of large-segment speed look-ahead for multi-stage S-shaped rising multi-axis machine according to claim 4, wherein the calculation formula of Lsvme in step B2 is as follows:
Lsvme=L1+L2，
wherein: l1 is the minimum distance required for the initial velocity Vs to rise to Vmax;
L2 is the minimum distance required for the end velocity Ve to rise to Vmax;
If L is larger than or equal to Lsvme, calculating L1 and L2 respectively:
Let dv=vmax-Vs, if dV is less than a 2/J, then the calculation formula for L1 is:
，
Wherein: a is the acceleration at which the initial velocity Vs accelerates to VReferm;
J is the jerk at which the initial velocity Vs accelerates to VReferm;
if dV is greater than or equal to A 2 J, then the calculation formula for L1 is:
，
let dv=max (Vmax-Ve, 0), if dV is less than a 2 ++j, then the calculation formula for L2 is:
，
If dV is greater than or equal to A 2 J, then the calculation formula for L2 is:
，
if L < Lsvme, vsam and Veam are calculated separately:
，
，
If Vsam is less than Ve, then Lsam =l1'; otherwise Lsam = L1'+l2';
Wherein: l1' is the minimum distance required for the initial velocity Vs to rise to the Vram velocity;
L2' is the minimum distance required for the end velocity Ve to rise to the Vram velocity;
l is the minimum distance required to rise from the start speed Vs to the vs+dv speed.
6. The method of large-segment speed look-ahead for multi-stage S-shaped rising multi-axis machine according to claim 5, wherein the calculation formula of L is as follows:
if dV is less than A 2/J, then there are:
，
If dV is greater than or equal to A 2/J, then there are:
。
7. A method of large segment speed look-ahead for a multi-stage S-shaped rising multi-axis machine according to claim 1, characterized in that consecutive micro-segments are divided into one large segment if the following conditions are met at the same time:
the difference between the temporary upper speed limit maximum tempMaxV of the micro-segment and the temporary upper speed limit minimum tempMinV of the micro-segment is less than or equal to the range VRang of the difference between the upper speed limit maximum and the minimum of all the micro-segments;
the difference between the temporary upper speed limit maximum tempMaxVByAcc of the acceleration limit of the micro-segment and the temporary upper speed limit minimum tempMinVByAcc of the acceleration limit of the micro-segment is less than or equal to the range ACCVRANGE of the difference between the upper speed limit maximum and the minimum of the acceleration limits of all the micro-segments;
The difference between the micro-segment jerk limited temporary upper speed limit maximum tempMaxVByJerk and the micro-segment jerk limited temporary upper speed limit minimum tempMinVByJerk is less than or equal to the range JerkVRange of the difference between the upper speed limit maximum and the minimum of all micro-segment jerk limits;
The difference between the temporary acceleration maximum tempMaxA and the temporary acceleration minimum tempMinA of the micro-segment is less than or equal to the range AccRange of the difference between the maximum and minimum of the virtual axis accelerations of all micro-segments;
Wherein:
，
，
，
，
，
，
，
，
Wherein: maxV is the upper maximum of the speeds of all micro-segments;
MinV is the upper speed limit minimum for all micro-segments;
line1.StartVLimit is the limit of the head node speed of the next micro-segment line1 of the current micro-segment;
line1.EndVLimit is the tail node speed limit value of the next micro-segment line1 of the current micro-segment;
MinVByAcc is the upper speed limit minimum of the acceleration limits for all micro-segments;
MaxVByAcc is the maximum upper speed limit of the acceleration limits for all micro-segments;
line1.StartVLimitByAcc is the speed limit value of the acceleration limit of the head node of the next micro-segment line1 of the current micro-segment;
line1.EndVLimitByAcc is the speed limit value of the acceleration limit of the tail point of the next micro-segment line1 of the current micro-segment;
MinVByJerk is the minimum upper speed limit of the jerk limit for all micro-segments;
MaxVByJerk is the upper limit maximum of jerk limit for all micro-segments;
line1.StartVLimitByJerk is the jerk limit speed limit value for the next micro-segment line1 of the current micro-segment;
line1.EndVLimitByJerk is the jerk limit speed limit value of the tail point of the next micro-segment line1 of the current micro-segment;
MaxA is the acceleration maximum for all micro-segments;
MinA is the minimum acceleration for all micro-segments;
line1.Acc is the acceleration of the next micro-segment line1 of the preceding micro-segment.
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