CN112698623B - Multi-axis contour control method for multi-axis contour application occasion - Google Patents
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Abstract
The invention discloses a multi-axis contour control method used in multi-axis contour application occasions, which describes the contour shape by using a high-order spline mode, is used for ensuring the geometric second-order continuity c2, and realizes the controllability of the geometric shape through a node reconstruction algorithm; performing speed planning in a time domain based on the planned geometric path to meet path kinematics constraint; fitting the planned data of the geometric domain and the time domain again to realize the combination of the geometric domain and the time domain and obtain interpolation data of each axis in the time domain which meets the geometric constraint of the overall contour; and finally, shaping the time domain interpolation data planned by each axis, improving the outward convex phenomenon of the outline of a corner, particularly a high-curvature part, and optimizing the acceleration of each axis so as to realize the active vibration suppression function.
Description
Technical Field
The invention relates to a multi-axis contour control method for multi-axis electronic manufacturing equipment such as an industrial robot, a CNC (computerized numerical control) machining center and the like.
Background
Contour control capability has been a key indicator of the performance of multi-axis electronic manufacturing equipment such as industrial robots, CNC machining centers, and the like. Therefore, in pursuit of a geometric description form with high flexibility and high-order continuity, designing a speed planning algorithm satisfying various kinematic constraints is also a research focus in the field of contour control, and great efforts have been made. Among them, document 1 discloses a method of real-time contour control by looking ahead through a small segment and smoothly transitioning adjacent segments with B-splines, but the method has a limited overall geometric description capability and can only perform linear description of contours, in terms of a method Zhao, LiMin Zhu, Han ding. Document 2 Wang F-C, Yang DCH, New arm-length parametrized quantitative-spline interpolyment for precision machining, Computing Aided Desgin 1993, published in Computer-Aided Degsin; the article discloses a quintic spline interpolation method approximate to arc length parameterization, which improves geometric description capacity by describing a contour in a quintic spline form, but lacks certain flexibility and cannot realize further contour adjustment, and the article enables a derivative value at the center of each quintic spline section to be 1 in a normalization mode, readjusts chord length values of each section to compensate speed fluctuation caused by difference between the chord length and the arc length, but only realizes constant speed control and cannot meet other kinematic constraints; document 3, Kaan Erkorkmaz, Yusuf Altingas high speed CNC system design, part I, published in International Journal of Machine Tools & Machine failure: the Jerk limited project generation and cationic spline interpolation, this article discloses an acceleration constrained trajectory generation and quintic spline interpolation method for CNC machines, the method continues the mode of document 2, adopts 5-order splines to describe the contour, does not improve the defect of poor flexibility of contour adjustment, cannot avoid the contour convex phenomenon especially at high curvature, and only 0-order continuity (c0) is guaranteed at the head-tail node, but the constant speed constraint can be satisfied by combining the geometric domain and the time domain, other multiple kinematic constraints such as acceleration, jerk and the like can also be satisfied, however, once these parameters are fixed, the kinematics of each axis (joint end) cannot be re-optimized, particularly under planned geometric constraints.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a multi-axis contour control method for a multi-axis contour application occasion, which can realize geometric domain planning with controllable contour shape and simultaneously support multiple kinematic constraints on a time domain.
The method of the invention describes the contour shape by a high-order spline mode, is used for ensuring the continuity of geometric second order (c2), and realizes the controllability of the geometric shape through a node reconstruction algorithm; performing speed planning in a time domain based on the planned geometric path to meet path kinematics constraint; fitting the planned data of the geometric domain and the time domain again to realize the combination of the geometric domain and the time domain and obtain interpolation data of each axis in the time domain which meets the geometric constraint of the overall contour; and finally, shaping the time domain interpolation data planned by each axis, improving the outward convex phenomenon of the outline of a corner, particularly a high-curvature part, and optimizing the acceleration of each axis so as to realize the active vibration suppression function.
The basic idea of the invention is as follows: for the node information for describing the contour provided by a user, firstly, node reconstruction preprocessing is carried out to meet various contour requirements, calculation load is considered, exponential densification in the linear direction of adjacent nodes is often adopted, the more nodes are subjected to densification, the closer the forming is to the geometric shape described by a straight line, and on the contrary, the smoother the contour is. Based on the reconstructed contour nodes obtained after preprocessing, all sections among the nodes are described in a high-order polynomial spline form:
Pi(u)＝K1i+K2iu+K3iu2+...+K(j+1)iuj,i＝1,....,m
wherein, P is each planned axis position, i is the axis number (joint end), u is the geometric path parameter (geometric field), K is the polynomial strip coefficient, m is the total axis number, j is the polynomial order number, in order to satisfy c2, j should not be less than 3, along with the promotion of order, can obtain the continuity of higher order, also can satisfy more restraint, but also must provide sufficient reasonable constraint value, these constraint terms are often provided by low order or same order splines, higher order can be obtained by the form that the lower order solves layer by layer. Balancing the contradiction between the order and the calculation load, a quintic polynomial spline is often adopted to describe the geometric shape of the contour, and the second-order DD at the node required by coefficient solvingnThe derivative information is provided by a cubic interpolation spline:
wherein,
γn＝1-αn，
Lnas a neighboring node PnAnd Pn-1The segment chord length utilizes the boundary constraint conditions that:
α0＝1，
γ0＝1，
wherein D is0，DnRespectively are head and tail node derivative values, when the curve is a closed curve, the head node lacks information and is provided by the tail node, and vice versa; when the curve is an open curve, the prediction can be carried out in a point densification mode; and the information at other nodes is easy to obtain after the DD is solved. And further, the position boundary adjustment at the initial node and the final node of each segment can be combined, so that the spline expression of each segment is easy to obtain.
The method is characterized in that the chord length is directly used for replacing the arc length to easily cause larger deviation, for each obtained section of the quintic spline curve, the interpolation speed F is used as the step length to subdivide each section of the curve, the subdivided chord length integral mode is used for obtaining the further accurate total arc length TotL, and the speed planning is carried out in a time domain by combining the kinematic constraints of speed, acceleration and the like, and is usually realized in the form of an S curve or a polynomial.
And (3) respectively planning the interpolation Step length Step on the path in a geometric domain and a time domain simultaneously, namely acquiring the position information of each interpolation point taking the Step length as the Step length on the path in the geometric domain, calculating the time interval T required by the Step length running in the time domain, performing 5-time spline refitting by using the obtained information, and similarly, providing a first-order second-order derivative at each node required by calculating 5-time spline coefficients by using a low-order spline. Slight adjustments to the actual achievable kinematic parameters may exist due to quantization errors, etc.
And finally, shaping each axis in the following way to avoid the outward convex phenomenon of the outline at the extremely high curvature part of the corner, and simultaneously adjusting the parameter tau according to the resonant frequency of each axis and the allowable range of the outline precision, namely:
wherein N isiFs is the interpolated sampling frequency, p (k) is the shaped data, and p (k) is the axis shapingAnd D, interpolating data in real time before the shape, wherein P (k-1) is previous interpolation data, and the like. Tau has obvious physical significance, the larger the value is, the smoother the corner is, and simultaneously, the frequency response of the formula has a lobe-shaped characteristic, and the function of restraining the vibration of notch filtering is provided, for example, the resonance frequency of an axis 0 is assumed to be omega0Then can design
For omega0Filtering is carried out, the mode has superposition characteristic and can be designed aiming at multiple resonance frequencies
To ensure that the planned geometric profile shape is still met, the same value of τ is used for each axis.
Based on the technical idea, the invention provides a multi-axis contour control method for multi-axis contour application occasions for achieving the purpose of the invention, which comprises the following steps:
Step 2, based on the reconstructed nodes, aiming at two adjacent nodes, according to natural boundary conditions (the head and tail positions of each section are known) and continuity constraints on each node, namely, at least ensuring the continuity of c2, a first derivative and a second derivative at the termination of a front section in the front section and a rear section of each node are equal to a first derivative and a second derivative at the initial position of a rear section, and each initial section can be obtained by a recursion solving mode
And position P of terminationi0，Pi1And a first guide
And a second derivative value
If the spline number of the final contour fitting is too high (>5) Then, the level should be increased successivelyAnd repeating the process of the step 2 to obtain node derivative information required for fitting a spline of a higher order.
And 3, establishing an equation system for fitting spline coefficients by the contour by using the information obtained in the step 2, namely the initial and ending positions of each segment and the corresponding derivative information, namely,
Pi(0)＝K1i＝Pi0 Pi(Li)＝K1i+K2iLi+K3iLi 2+...+K(j+1)iLi j＝Pi1；
…
solving this system of equations can obtain the various coefficients needed for the fit.
And 4, subdividing each section of curve at the interpolation speed F, and integrating each subdivided chord length to obtain the approximate total arc length TotL.
And 5, planning the speed in the time domain by using the TotL and combining other kinematic parameters.
And 6, enabling the interpolation Step length to be F × Ts, and simultaneously interpolating in the geometric domain and the time domain according to the Step length to obtain interpolation position data in the geometric domain and the time length T required by the Step length running in the time domain.
And 7, re-fitting a spline curve of a specified order taking time as an independent variable in a time domain by using the information obtained in the step 6, and carrying out real-time interpolation according to an interpolation period.
And 8, shaping the interpolation data of each axis to obtain final interpolation data of each axis.
The multi-axis contour control method for the multi-axis contour application occasion can realize the geometric domain planning with controllable contour shape and simultaneously support multiple kinematic constraints on a time domain. Compared with the traditional straight line circular arc described contour, the flow and the method provided by the invention not only greatly improve the geometric smoothness of the described contour, but also can realize smooth transition of corners, particularly high curvature positions, through simple parameter adjustment, thereby avoiding the contour convex phenomenon which often occurs in the traditional spline fitting process; meanwhile, the method can meet various path kinematic constraints required by a user, such as speed, acceleration and the like, and allows the speed of each shaft (joint end) to be integrally re-planned under the planned geometric constraint, thereby providing an active vibration suppression function, ensuring high-efficiency processing efficiency and greatly improving product quality. The present invention can provide excellent profile control capability for multi-axis electronic manufacturing equipment such as industrial robots, CNC machining centers, and the like.
Drawings
FIG. 1 is a flow chart of a multi-axis contour control method of the present invention for use in multi-axis contour applications.
FIG. 2 is a schematic diagram of a node reconstruction algorithm in the embodiment.
FIG. 3 is a profile curve of the embodiment without node reconstruction.
FIG. 4 is a profile curve of the embodiment when the nodes are reconstructed.
FIG. 5 is a position curve of the planned S-trajectory according to the embodiment.
FIG. 6 is a velocity curve of the planned S-trajectory according to an embodiment.
FIG. 7 is a contour curve of each shaft after shaping in the embodiment.
Detailed Description
The process of the present invention will be described in further detail below with reference to examples and the accompanying drawings.
Example (b): taking a quintic spline as an example to describe the profile, in this example the user provides the raw data of the two-dimensional profile as follows, and constrains the linear velocity of the travel to 100mm/s and the acceleration to 200mm/s2Deceleration 200mm/s2Acceleration of 500mm/s3。
The original data is first subjected to a node reconstruction as shown in fig. 2. Wherein L is an adjacent node PiAnd Pi+1The chord length of the section to be reconstructed, Lv is an intermediate calculation parameter, Ke is an expansion coefficient expected by a user, Ke can adopt a fixed value, and can also be respectively designed by a reference smoothing distance according to the specific chord length of each section, the larger the value of Ke, the closer the contour is to the original data, the contour is described by a straight line, and the smaller the value of Ke, the smoother the contour is geometrically.
When Ke is odd:
when Ke is an even number:
p (n) is the reconstructed node data, wherein n is the element of [0, Ke ].
For comparison, the geometric profile designed according to the flow shown in fig. 1 is shown in fig. 3 when Ke is 0, and for convenience, the profile shape planned when the fixed value of Ke is 8 is shown in fig. 4.
According to the interpolation speed F being 200mm/s, the approximate total arc length totL being 277.818mm, the interpolation step length being 0.199mm and the kinematic parameter acceleration Acc being 200mm/s2Deceleration Dec is 200mm/s2And acceleration Jerk of 500mm/s3Go in the time domainStandard S-curve planning is performed, and the planned position curve and speed curve are shown in fig. 5 and fig. 6.
And synchronously interpolating in a geometric domain and a time domain respectively according to the calculated step length, and re-fitting by using interpolation data to obtain each axis interpolation data under each axis interpolation sampling frequency.
And finally, shaping the interpolation data of each axis, designing a shaping adjustment parameter tau, and ensuring that the contour corner, particularly the high curvature part is smoother when the value of tau is larger, and designing the resonance frequency of each axis. The profile shape after optimization when let τ be 0.05 is shown in fig. 7.
Claims (1)
1. A multi-axis contour control method for multi-axis contour application comprises the following steps:
step 1, reconstructing original contour nodes provided by a user according to requirements, and carrying out densification along the linear direction of each adjacent node in a normal distribution manner;
step 2, based on the reconstructed nodes, aiming at two adjacent nodes, according to natural boundary conditions and continuity constraints on each node, ensuring geometric second-order continuity, wherein first derivatives and second derivatives at front-section termination positions in front and rear sections of each node are equal to first derivatives and second derivatives at initial positions of rear sections, and the position P of each section of initial and termination positions can be obtained in a recursion solving modei0，Pi1And a first guide
And a second derivative value
Number of splines finally fitted to the contour>5, successively increasing the order and repeating the process of the step 2 to obtain node derivative information required by fitting a spline with a higher order;
and 3, establishing an equation set for fitting spline coefficients by the contour by using the initial and ending positions of each section and the corresponding derivative information obtained in the step 2:
Pi(0)＝K1i＝Pi0 Pi(Li)＝K1i+K2iLi+K3iLi 2+...+K(j+1)iLi j＝Pi1；
…
solving the equation set can obtain each coefficient required by fitting;
step 4, subdividing each section of curve at the interpolation speed F, and integrating each subdivided chord length to obtain an approximate total arc length TotL;
step 5, utilizing TotL to plan the speed in the time domain;
step 6, enabling the interpolation Step length Step to be F × Ts, and simultaneously interpolating in the geometric domain and the time domain according to the Step length respectively to obtain interpolation position data in the geometric domain and time length T required by the Step length running in the time domain;
step 7, re-fitting a spline curve of a specified order taking time as an independent variable in a time domain by using the information obtained in the step 6, and carrying out real-time interpolation according to an interpolation period;
and 8, shaping the interpolation data of each axis to obtain final interpolation data of each axis.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN104007705A (en) * | 2014-05-05 | 2014-08-27 | 上海交通大学 | Prospective interpolation system for compressing and smoothening small segment paths |
| CN105773620A (en) * | 2016-04-26 | 2016-07-20 | 南京工程学院 | Track planning and control method of free curve of industrial robot based on double quaternions |
| CN108227630A (en) * | 2018-01-18 | 2018-06-29 | 合肥工业大学 | A kind of NC Machining of Free-form Surfaces method using time parameter polynomial interpolator |
| CN110865610A (en) * | 2019-10-18 | 2020-03-06 | 中国工程物理研究院机械制造工艺研究所 | Tool path interpolation and speed planning method based on machine tool vibration suppression |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN104007705A (en) * | 2014-05-05 | 2014-08-27 | 上海交通大学 | Prospective interpolation system for compressing and smoothening small segment paths |
| CN105773620A (en) * | 2016-04-26 | 2016-07-20 | 南京工程学院 | Track planning and control method of free curve of industrial robot based on double quaternions |
| CN108227630A (en) * | 2018-01-18 | 2018-06-29 | 合肥工业大学 | A kind of NC Machining of Free-form Surfaces method using time parameter polynomial interpolator |
| CN110865610A (en) * | 2019-10-18 | 2020-03-06 | 中国工程物理研究院机械制造工艺研究所 | Tool path interpolation and speed planning method based on machine tool vibration suppression |
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