CN102063088A

CN102063088A - Method and system for planning auxiliary discrete movement of computer

Info

Publication number: CN102063088A
Application number: CN2010105367822A
Authority: CN
Inventors: 江俊逢
Original assignee: Individual
Current assignee: Digital Drive Technology Co ltd
Priority date: 2010-11-05
Filing date: 2010-11-05
Publication date: 2011-05-18
Anticipated expiration: 2030-11-05
Also published as: CN102063088B

Abstract

The invention discloses a method and system for planning the auxiliary discrete movement of a computer for an open type numerical control system, which plans the T partition delta ti (i=1,..., m) based on a driving shaft and adjusts the linkage list and follow-up list of the associated data streams based on the intrinsic L partition of a curve, thereby realizing the optimization of the movement stationarity of coordinates and the fineness of acceleration and deceleration control.

Description

A kind of area of computer aided discrete motion planing method and system

Technical field

The invention belongs to advanced control and advanced manufacturing field, be specifically related to a kind of area of computer aided discrete motion planing method and the system of digital control system in open type.

Technical background

Computerized numerical system (abbreviation digital control system) is a target with the determinacy kinematic relation between the control mechanical system and the logical relation of gauge tap device.PLC control is adopted in the logic control of switchgear, i.e. programmable logic control belongs to the routine techniques means.Determinacy kinematic relation between the control coordinate axis then is the main target of digital control system.

Formerly system is made the field, and speed of feed F is the technological parameter of user's appointment, refers to the speed of reference point when cutter path moves with respect to workpiece on the cutter.The desired workpiece profile of user program depends on that the track of center cutter is cutter track (Tool Path) curve.The cutter track curve then is achieved by the straight-line displacement or the compound of corner of relevant coordinate axis, thereby the speed of feed aggregate velocity of relevant coordinate axis just.Easy for what narrate, in this application, the cutter track curve generally abbreviates curve as.

Realizing displacement or synthesizing of angular displacement of the relevant coordinate axis of cutter track curve negotiating.This motion that just means relevant coordinate axis must be related on sequential, and just relevant coordinate axis must link.The determinacy of workpiece profile curve shows that the kinematic relation between the coordinate axis is deterministic.Digital control information in the determinacy kinematic relation between the coordinate axis can be divided into two parts: the related information between the discrete location information of coordinate axis feeding and these discrete location information.

Therefore, control the field, adopt what technology to produce the discrete location information of the desired coordinate axis feeding of user program and the related information between these discrete location information, become the core technology of digital control system the advanced person.

The target of digital control processing is to realize high-precision processing.Workpiece profile generally is made of some curves, has many flex points and wedge angle, coordinate axis thereby must constantly commutate.The startup of motor during commutation/stop to cause the unsmooth vibration that produces mechanical system with the acceleration sudden change of speed of feed, this just must influence machining precision.In addition, for the flex point on the workpiece profile, some wedge angles particularly, high speed feed also will produce bigger profile errors even cause the mistake of part to be cut.In these cases, all must carry out acceleration and deceleration control.

Consider continuous cutter track curve, for example circular arc.This curve by discrete be a line segment Δ L slightly ₁..., Δ L _nAt little line segment Δ L ₁..., Δ L _nBetween, the speed of feed of coordinate axis certainly leads to saltus step, and this is the inherent attribute of discrete motion.The hop value of coordinate axis speed of feed has reflected the robust motion of coordinate axis.

Implement acceleration and deceleration control for every little line segment, can reduce the hop value of the speed of feed between little line segment, obviously, thereby this will cause coordinate axis to be quickened continually and reduction crudy and the process velocity of slowing down.Therefore, make little line segment Δ L ₁..., Δ L _nBetween the hop value of speed of feed remain in the suitable scope and can increase substantially crudy and process velocity, become the important technical of high-speed, high precision processing.

So-called motion planning refers to, and for continuous cutter track curve, the speed of feed that reduces coordinate axis is at little line segment Δ L ₁..., Δ L _nBetween hop value, thereby improve the robust motion of coordinate axis, realize high-speed, high precision processing.

In existing digital control system in open type, speed prediction control (Look ahead) is similar with motion planning.So-called speed prediction control is exactly in interpolation operation, shifts to an earlier date pre-interpolation one segment distance, to reaching 1000～5000 little line segment Δ L _iHandle in real time, with the speed of feed that reduces coordinate axis at little line segment Δ L ₁..., Δ L _nBetween hop value.

Speed prediction control is one of gordian technique in the existing digital control system in open type.

Existing digital control system adopts interpolation iteration control method to carry out digital control to mechanical system.Interpolation precision and interpolation rate become the core technology index of existing digital control system.The basic technical scheme of interpolation iteration control method is, for the given cutter track curve and the speed of feed of cutter, under the control of real time operating system, as the timesharing cycle, adopt the interpolation iterative algorithm to calculate the whole digital control informations of relevant coordinate axis in real time at given time with interpolation cycle.Described digital control information comprises the discrete location information of coordinate axis feeding and the related information between these discrete location information.

As everyone knows, when finding the solution the coordinate figure increment of curve, interpolation is a kind of iterative algorithm in the numerical computation method.So-called interpolation algorithm in itself, is exactly from X _nThe middle X that obtains _N+1Operation rule.Since the continuity of a function, X _nIn must contain X _N+1Partial information, making full use of these information, to cause the high-order strength reduction be the low order simple operation, thereby improve the speed of interpolation algorithm greatly.For avoiding complicated high exponent arithmetic(al), some optimum interpolation iterative algorithms can't use.On the other hand, for some complex curves, from X _nThe middle X that obtains _N+1Operation rule be quite the difficulty.Therefore, the interpolation iterative control algorithm of high-speed, high precision becomes the core technology in the existing Numeric Control Technology.

The inventor finds that there are following four essential characteristic in interpolation iteration control method.

1, in order to improve speed of feed, existing open digital control system must adopt time-divided method (claiming the digital increments method again) to carry out the interpolation iteration control.

For straight line, according to speed of feed F and interpolation cycle T, time-divided method must disperse straight line and be some the little line segment Δ L that are referred to as the profile step-length _i: ∑ Δ L _i=L, Δ L _i=FT.

As everyone knows, be the straight line of L for long, as long as provide speed of feed F, just can finish processing tasks.Yet above-mentioned formula shows, because the real-time iteration that interpolation cycle causes, interpolation iteration control method is had to discrete some the little line segment Δ L of being of straight line _iLittle line segment Δ L _iLength must be the integral multiple of FT.

For curve, time-divided method is at first used some broken line Δ L _iApproach Δ L _i=FT, this is a rough interpolation.And then carry out smart interpolation, promptly to every broken line Δ L _iCarry out closeization of data point.

Formula

e _r＝(TF) ²/(8r)

Approximate error e has been described _rAnd the relation between speed of feed F and interpolation cycle T, the radius-of-curvature r.

This formula points out, for curve interpolating, and approximate error e _rWith square being directly proportional of speed of feed F and interpolation cycle T, r is inversely proportional to radius-of-curvature.The growth of speed of feed F and interpolation cycle T will cause approximate error e _rExponential increase, in other words, approximate error e _rExtremely sensitive to time and curvature.

Therefore, in interpolation iteration control method, approximate error e _rHigh susceptibility to the time causes the time to be locked by interpolation cycle, is not a controlled external variable, but a systematic parameter.

Time becomes first essential characteristic that systematic parameter is an interpolation iteration control method, is the basic defect of giving birth in the interpolation iteration control technology.

2, in interpolation iteration control method, in each interpolation cycle by digital control information that interpolation generated, send to kinetic control system (step-by-step control system/servo-control system) on the one hand immediately in real time and be used for the motion of Real Time Drive coordinate axis, carry out iteration in real time generating next digital control information as the input of next interpolation cycle again on the other hand, thereby constitute the real-time iteration of digital control information.Follow the beat of interpolation cycle, digital control information constantly generates, sends, carries out, from and go round and begin again in the mode of process iteration, constitute the real-time iteration of control procedure.Therefore, by the real-time iteration of digital control information and the real-time iteration of control procedure, interpolation iteration control method gives real time implementation with the whole manufacturing process of the generation of digital control information, transmission, execution.

The real-time iteration of digital control information and the real-time iteration of control procedure (the real-time iteration of abbreviation information and the real-time iteration of process, i.e. I﹠amp; The real-time iteration of P) being second essential characteristic of interpolation iteration control method, is the basic defect of giving birth in the interpolation iteration control technology.

3, in interpolation iteration control method, the I﹠amp under the interpolation cycle unified command of real time operating system; The real-time iteration of P is a kind of focus control mode.In this control model, real time operating system is commanded all, and " arrogate all authority to oneself, and Xiao Quan is not put " carried a task right down to the grass-roots level, and planning, design, construction be bag entirely, and is " limit planning, limit design, limit construction ".

The focus control mode of " limit planning, limit design, limit construction " is the 3rd essential characteristic of interpolation iteration control method, is the basic defect of giving birth in the interpolation iteration control technology.

4, in interpolation iteration control method, approximate error e _rR is inversely proportional to radius-of-curvature, with square being directly proportional of speed of feed F and interpolation cycle T.

Yet workpiece profile is a geometrical issues, thereby cutter track curve and approximate error e _rWith radius-of-curvature r also geometrical issues just.What speed of feed finishing processing tasks as for center cutter with, then is the dynamics problem of a process issues and mechanical system.

In interpolation iteration control method, approximate error e _r, radius-of-curvature r, the whole close-coupled of interpolation cycle T, speed of feed F together, relate to space, time, speed, acceleration (retarded velocity), acceleration even.In other words, interpolation iteration control method with the whole close-coupled of dynamic characteristic of the geometric properties of workpiece profile, technology characteristics, mechanical system together.Coupled relation between this space-time can abbreviate the coupling of space-time structure as.

The coupling of space-time structure is the 4th essential characteristic of interpolation iteration control method, is the basic defect of giving birth in the interpolation iteration control technology.

The inventor finds, owing to there is the basic defect of giving birth in above-mentioned four, interpolation iteration control technology is as the pervasive control method of existing digital control system in open type, has the problem aspect following on motion planning:

1, existing speed prediction control must be to reaching 1000～5000 little line segment Δ L _iHandle in real time, thereby interpolation iterative control algorithm and chip speed have been proposed very high requirement, make digital control method complicated greatly, expended the software and hardware computational resource of a large amount of costlinesses.

2, the basic task of digital control system is, the displacement of the relevant coordinate axis of control and by synthesizing of these displacements realizing the cutter track curve.Speed of feed F then is a technological parameter.

The geometric properties of cutter track curve is obvious and speed of feed F is irrelevant.In other words, there is not coupled relation between the geometric properties of cutter track curve and the speed of feed F in itself.

Yet in existing speed prediction control, the coupling of space-time structure with speed prediction control real time implementation and then high complexityization, thereby has been lost opening with the discrete geometric properties and the speed of feed close-coupled of cutter track curve.

3, for digital control, time control was the simplest originally.In existing speed prediction control, the time is locked into system clock by interpolation cycle, can't use the simplest time control, can not realize the optimization of coordinate axis robust motion and becoming more meticulous of acceleration and deceleration control.

4, the discrete geometrical property and the discrete motion characteristic of cutter track curve ignored in existing speed prediction control fully, for example, ignored the non-Europe error of cutter track curve fully, and the notion that does not have intrinsic L to cut apart does not have the notion of main drive shaft and universal driving shaft yet.Thereby existing speed prediction control certainly leads to bigger profile errors.

The application propose a kind of area of computer aided discrete motion planing method (ComputerAided DiscreteKinematics Planning, DKP).The DKP method is with the geometric properties of workpiece profile and the temporal characteristics decoupling zero of processing technology, with the time as an independently regulatable parameter, carrying out T based on main drive shaft cuts apart, the L that carries out the cutter track curve based on the geometric factor of universal driving shaft is cut apart, solve the problems referred to above of existing digital control system in open type fully, thereby realized the optimization of coordinate axis robust motion and becoming more meticulous of acceleration and deceleration.

Summary of the invention

The objective of the invention is to propose a kind of area of computer aided discrete motion planing method (ComputerAided Discrete Kinematics Planning, DKP), with the time as an independently regulatable parameter, cut apart from T and to cut apart two aspects with L and carry out motion planning and acceleration and deceleration control, thereby realize that continuous path adds the optimization of coordinate axis robust motion in man-hour and becoming more meticulous of acceleration and deceleration.

This area of computer aided discrete motion planing method that the present invention proposes comprises,

Cutter track curve planning step (1):, be k bar curve with the cutter track curve segmentation according to unique point; Every curve to after cutting apart is divided into main drive shaft and universal driving shaft with coordinate axis, generates the cutter track curve file;

L is cut apart planning step (2): to every curve in the described k bar curve, according to the optimization aim of setting, the intrinsic L that meets described optimization aim by guiding point pointwise structure is cut apart Δ L _i(i=1 ..., n);

T is cut apart planning step (3): described intrinsic L is cut apart Δ L _i(i=1 ..., n), generate T and cut apart Δ t _i(i=1 ..., m).

In the auxiliary discrete motion planing method of aforementioned calculation machine, described L is cut apart planning step (2) and is comprised the steps:

Step (201), from described k bar curve, take out a curve in turn, set optimization aim;

Step (202), be original guiding point, generate described original guiding neighborhood of a point with the starting point of described curve;

Step (203), according to the optimization aim of setting, in described original guiding neighborhood of a point, determine a guiding point, generate the coordinate figure increment of described guiding point and described original guiding point;

Step (204), between described guiding point and described original guiding point, generate the straight line section;

Step (205), on the cutter track orientation, generate the neighborhood of described straight-line segment,, judge whether the neighborhood of described straight-line segment is the subclass of the neighborhood of described segment of curve for the segment of curve of described curve between described guiding point and described original guiding point;

Step (206) is then returned step (203) if the neighborhood of described straight-line segment is the subclass of the neighborhood of described segment of curve, continues to generate next guiding point;

Step (207) is not if the neighborhood of described straight-line segment is the subclass of the neighborhood of described segment of curve, then a last guiding point of described guiding point is exactly the intrinsic reflection, described intrinsic reflection is the terminal point of described little line segment, and the coordinate figure increment of a described last guiding point and described original guiding point is exactly the coordinate figure increment of described little line segment;

Step (208), with the original guiding point of described intrinsic reflection as the little line segment of next bar, order repeating step (201) is to step (207), generate the little line segment of next bar of described curve, until the terminal point of described curve, the intrinsic L that meets described optimization aim that generates described curve is cut apart Δ L _i(i=1 ..., n).

In the auxiliary discrete motion planing method of aforementioned calculation machine, described T is cut apart planning step (3) and is also comprised the steps:

Step (301), for a curve in the described k bar curve, carry out described L and cut apart planning step (2), the intrinsic L that generates the optimization aim meet setting is cut apart Δ L _i(i=1 ..., n);

Step (302), the little line segment of n bar during the intrinsic L of described curve cut apart are from Δ L _iSlope and the speed of feed F speed of feed component F of calculating main drive shaft y _{I, y}Speed of feed component F with universal driving shaft x _{I, x}According to Δ t _i=Δ L _{I, y}/ F _{I, y}With Δ t _i〉=Δ t _Min, generate T and cut apart Δ t _i(i=1 ..., m); Step (303), Δ F is set _xWith Δ F _yReference value and deviation δ thereof _x, δ _y

The robust motion constraint condition a of step (304), check main drive shaft y

To the little line segment Δ of n bar L ₁..., Δ L _n, the robust motion constraint condition a of check main drive shaft y:

(ΔF _i，y-ΔF _y)≤δ _y(i＝1，...，m)；

If described constraint condition a does not satisfy, then adjust F to satisfy described constraint condition a; According to adjusted speed of feed F, plan that again T cuts apart Δ t _i(i=1 ..., m);

The robust motion constraint condition b of step (305), check universal driving shaft x

If Δ L _iBe little line segment of having planned; Calculate universal driving shaft x at point (x _I+1, y _I+1) the speed of feed hop value Δ F that locates _{I+1, x}=(F _{I+1, x}-F _{I, x}), the robust motion constraint condition b of check universal driving shaft x:

(ΔF _i，x-ΔF _x)≤δ _x；

Step (306) then increases Δ t if described constraint condition b does not satisfy _I+1To reduce F _{I+1, x}, described constraint condition b is satisfied; If increase Δ t _I+1Can not satisfy described constraint condition b, then reduce Δ L _{I+1, x}To reduce F _{I+1, x}, described constraint condition b is satisfied;

Step (307), calculating Δ L _{I+1, x}, Δ L _{I+1, y}, adjust Δ t _I+1With little line segment Δ L _I+1

Step (308), with described little line segment Δ L _I+1Terminal point be made as ground zero, to the curve between the terminal point of described ground zero and described curve, the order repeating step (301) to step (307), until the terminal point of described curve;

Step (309), to every curve in the k bar curve in the described cutter track curve, the order repeating step 301 to step 308.

In the auxiliary discrete motion planing method of aforementioned calculation machine, described coordinate axis is more than three.

The present invention also proposes a kind of area of computer aided discrete motion planning system, comprises hardware platform, software platform and application software system, and described hardware platform is the PC system, and software platform is a graphical interfaces operating system; Described application software system comprises:

Cutter track curve planning module: being used for according to unique point, is k bar curve with the cutter track curve segmentation; Every curve to after cutting apart is divided into main drive shaft and universal driving shaft with coordinate axis, generates the cutter track curve file;

L is cut apart planning module: be used for every curve to described k bar curve, according to the optimization aim of setting, the intrinsic L that meets described optimization aim by guiding point pointwise structure is cut apart Δ L _i(i=1 ..., n);

T is cut apart planning module: be used for described intrinsic L is cut apart Δ L _i(i=1 ..., n), generate T and cut apart Δ t _i(i=1 ..., m; M=n-1).

The aforementioned calculation machine is assisted the discrete motion planning system, and described application software system is based upon on the middleware, adopts application programming interface API between each module.

The aforementioned calculation machine is assisted the discrete motion planning system, and described software platform also comprises 3 d graphic library.

The present invention is compared with the prior art the beneficial effect that is had:

1, well-known, in existing digital control system in open type, the coupling of space-time structure is with the geometric properties and the speed of feed close-coupled of cutter track curve, and the time is locked as systematic parameter by interpolation cycle.Existing speed prediction control is with acceleration and deceleration control thereby become a kind of real-time control method, complexity, weak effect, shortage opening.

The present invention carries out motion planning with the geometric properties and the processing technology decoupling zero of cutter track curve under area of computer aided.Motion planning method of the present invention is not a real-time control method, but non real-time planing method, thereby have the unexistent non real-time of prior art, irrelevant with the interpolation algorithm (comprising discrete logarithm) of cutter track curve, with technical characterictics such as real time operating system is irrelevant, have the open fully remarkable result that waits of simple and flexible with outstanding progressive.

2. in existing digital control system in open type, speed prediction control separates with acceleration and deceleration control, become two independently functional module be real-time speed prediction control module and acceleration and deceleration control module in real time.The present invention controls unification for discrete motion planning with speed prediction control and acceleration and deceleration, is converted into the off-line planning problem under the area of computer aided, has saved a large amount of software and hardware computational resources, and existing relatively speed prediction is controlled, and effect is more remarkable.

3, in existing digital control system in open type, the time is locked as systematic parameter by interpolation cycle, can only adjust the broken line that approaches of cutter track curve in speed prediction control is controlled with acceleration and deceleration.The present invention is from Δ L _iWith Δ t _iThe movement velocity of axle is adjusted in two aspects, and both can adjust the servo-actuated table is that T is cut apart Δ t _i(i=1 ..., n), the L that can adjust linkage table again and be the cutter track curve is cut apart, thereby has realized that continuous curve adds the optimization of coordinate axis robust motion in man-hour and becoming more meticulous of acceleration and deceleration control, has outstanding substance progress.

Description of drawings

Fig. 1 is the quadrature discrete coordinate system synoptic diagram in the embodiment;

Fig. 2 is the synoptic diagram of area of computer aided discrete motion planning system;

Fig. 3 is the process flow diagram of area of computer aided discrete motion planing method.

Embodiment

The geometry of workpiece profile is predetermined, and therefore, the kinematic relation between the coordinate axis is deterministic.The core missions of digital control system are made digital control information exactly, the synthetic realization cutter track curve of the displacement (angular displacement) by relevant coordinate axis, and the coordinate axis that is used for the Control work machine is finished given determinacy mechanical motion.The resultant displacement that displacement produced of relevant coordinate axis must be realized by the interlock of relevant coordinate axis; The synthetic continuously time interval that then needs to control between the described resultant displacement of described resultant displacement.The interlock of relevant coordinate axis is a geometrical issues, and synthesizing continuously of described resultant displacement relates to speed of feed and acceleration and deceleration control, is a motion planning problem.

As everyone knows, in the newtonian motion of classics, the space is an Euclidean space, and direction of motion is arbitrarily, and its displacement then is continuous.

Direction of motion is tied and the discrete motion rule of displacement when discrete in the discrete motion research non euclidean space, disclose the structure of associated data stream and the inner link between the movement locus, for the area of computer aided discrete motion planing method that the application proposed has been established theoretical foundation and technical foundation.

Be without loss of generality, the present invention is an example with the two dimensional motion in the x-y coordinate setting table, sets up some key concepts of discrete motion.

(1), discrete coordinates system

Digitizing replaces continuous quantity with discrete magnitude, and this just certainly leads to error.In digital control system, must be with the certain precision discrete curve.The discretization error of this predefined permission is also referred to as discrete scale, is designated as e.

For coordinate axis, because the influence of the factors such as rigidity of gap between the mismachining tolerance of parts and rigging error, the kinematic pair and friction, unrelieved stress, mechanical system, minimum resolution of its mechanical shift existence generally is referred to as the feeding equivalent, with e _fShow it.For coordinate axis, less than e _fMechanical shift be skimble-skamble.

Generally speaking, discrete scale equals the feeding equivalent.In fine structure, discrete scale is less than the feeding equivalent.

The discrete scale of each coordinate axis can be different, and for example, the discrete scale of x axle is e _{X, y}The discrete scale of axle is e _y

With discrete scale that coordinate axis is discrete, distance each other is that the parallel lines of discretization error are with the coordinate plane gridding.The coordinate system of Jian Liing is referred to as discrete coordinates system thus.Discrete scale e _x..., e _yIt is the systematic parameter of discrete coordinates system.

As shown in Figure 1, the orthogonal discrete coordinates of the direction of motion of coordinate axis system is referred to as quadrature discrete coordinate system, for example rectangular coordinate system, polar coordinate system; The mutual off plumb discrete coordinates of the direction of motion of coordinate axis system is referred to as nonopiate discrete coordinates and is.

Non-perpendicularity between the coordinate axis, nonparallelism, and the backlass of coordinate axis, pitch error etc. are the inherent features of mechanical system, also are the systematic parameters of discrete coordinates system.

(2), lattice point

In the quadrature discrete coordinate system, distance is that the equal space line of discrete scale is with the coordinate plane gridding.The intersection point of equal space line parallel to each other is called lattice point, as intersection points such as a among Fig. 1, b, c.

The position that the discrete motion of having only lattice point to be only coordinate axis can reach.

(3), allow direction of motion, exclusion movement direction and preferential direction of motion

In digital control system, the direction of motion of coordinate axis is affined.For example, for the x/y coordinate setting table, direction of motion is ± the x direction, ± y direction and x axle and the formed+x/+y of y axle interlock ,+x/-y ,-x/+y ,-the x/-y four direction.These 8 direction of motion are referred to as the permission direction of motion of mechanical system.

In digital control system, processing is the motion process of the relative workpiece of cutter, and the extension of cutter track curve has directivity, exists counterclockwise and clockwise two kinds of bearing of trends.This directivity is referred to as the cutter track orientation.

For example, for the counterclockwise arc of the 1st quadrant, the cutter track orientation is a northwest position.

When the cutter track orientation is northwest position, have only-the x direction ,+the y direction is to allow direction of motion with-x/+y direction, other directions are the exclusion movement direction.

The tangent slope of putting on the circular arc has further retrained direction of motion.For example, for the point on the circular arc, if this some place tangent slope is greater than 1, the motion of-x direction must depart from circular arc, thereby-the x direction is the exclusion movement direction, in other words,-x direction is contained by-x/+y direction, allow direction of motion be+the y direction and-the x/+y direction; If this some place tangent slope is less than 1, the motion of+y direction must depart from circular arc, thereby+the y direction is the exclusion movement direction, in other words ,+y direction is contained by-x/+y direction, allow direction of motion be-the x direction and-the x/+y direction.

If the close x axle of the tangent line at this some place, then-the x direction is preferential direction of motion; If the close y axle of the tangent line at this some place, then+the y direction is preferential direction of motion; If the close 45 ° of lines of the tangent line at this some place, then-the x/+y direction is preferential direction of motion.

(4), the reflection collection of curve

Point on the curve is called preimage, as point of the m among Fig. 1 and n point.

A lattice point if be less than or equal to discretization error with the distance of certain preimage of curve, then is called the numeral reflection of this preimage, abbreviates reflection as, as a among Fig. 1, b, c, d, all points of e.

Whole reflections of curve constitute a set, are referred to as the reflection collection of this curve.For example, be the circle of r for radius, e is a discrete scale, radius for the circle of (r-e) and radius be on the annulus between the circle of (r+e) with annulus in whole lattice points be exactly the reflection collection of this circle.

In given discrete coordinates system, the geometry of this curve is depended in the reflection collection of curve and the distribution in discrete coordinates system thereof fully.

Obviously, there are a plurality of reflections in a preimage on the curve; Otherwise,, on this curve, then have a plurality of preimages for a reflection.

For a given reflection, be referred to as the neighborhood of this reflection at the whole reflections that allow on the direction of motion distance with the preimage of this curve to be less than or equal to discretization error.For example for the reflection b among Fig. 1, if the cutter track curve is counterclockwise, its neighborhood is a point; If the cutter track curve is clockwise, its neighborhood is d point and e point, and the c point is positioned at the exclusion movement direction, is not the neighborhood of reflection b.

For given curve, its whole neighborhoods constitute a set, are referred to as this neighborhood of a curve collection.The neighborhood of a curve collection is that its reflection collection is in a subclass that allows on the direction of motion.

(5), associated data stream

Digitizing is exactly a discretize.By discrete scale curve being dispersed is a sequence of its reflection.Coordinate figure increment between the reflection is a discrete scale, promptly equals " 1 " or " 0 ", and this reflection sequence is called the microcosmic numeral reflection of curve.For all coordinate axis, the microcosmic numeral reflection of curve to be arranged in order, the coordinate axis discrete location information of " 1 " " 0 " form that is produced is exactly the stepping type associated data stream of this curve.

The stepping type associated data stream description of curve the fine microstructures of this curve.

If the increment of each coordinate figure between the reflection is not a discrete scale but several discrete scales, this reflection sequence is called the incremental numeral and videos.For all coordinate axis, the incremental numeral reflection of curve to be arranged in order, the coordinate axis discrete location information of the coordinate figure incremental form that is produced is exactly the incremental associated data stream of this curve.

For a plurality of coordinate axis, described associated data stream constitutes the multidimensional associated data stream.

(6), main drive shaft and universal driving shaft

Obviously, be ± 1 straight line for slope, its stepping type associated data stream is " 1 " entirely.

For other oblique lines, in its stepping type associated data stream, the data stream of certain is inevitable to be " 1 " entirely, and in other words, " 1 " is continuous, and this axle is called main drive shaft; Another data stream is inevitable not to be complete " 1 ", and in other words, " 1 " is not continuous, but about a kind of distribution of main drive shaft data stream, this axle is referred to as universal driving shaft.This just means that the main drive shaft data stream can be considered discrete independent variable, and the universal driving shaft data stream then is the distribution of main drive shaft data stream.

For any curve, zeroaxial 45 ° of oblique lines and 135 ° of oblique lines are divided into 8 intervals with 4 quadrants.The intersection point of these two oblique lines and curve is called the unique point of curve.In unique point, curve enters another interval from an interval, and x axle and y axle will change active/interlock attribute.

(7), L is cut apart

For a curve in the cutter track curve, be less than or equal to some end to end small straight-line segment Δ L of discretization error with the maximum normal direction distance of this curve _iThe summation of (being called for short little line segment) is referred to as the broken line that approaches of this curve, or is called about the discrete of little line segment of this curve and cuts apart, abbreviate L as and cut apart, note be Δ L ₁..., Δ L _n

For coordinate axis, with the point on subscript differentiation coordinate axis and the axle.For example, use Δ L _{I, x}, Δ L _{I, y}Represent little line segment Δ L _iThe coordinate axis component.At Δ L _{I, x}In, first subscript " i " represents that the starting point of this little line segment is x _i, the little line segment Δ L of second subscript " x " expression _iX axle component.

To i arbitrarily, little line segment Δ L _iBe no more than discrete scale with the error of this curve.

It is the incremental associated data stream that the L of curve is cut apart pairing associated data stream, and in other words, it is exactly the incremental numeral reflection of curve that the L of curve is cut apart.

(8), geometric factor

If Δ L ₁..., Δ L _nBe the little line segment of the L of curve in cutting apart, and do not comprise unique point, Δ L _{I, x}, Δ L _{I, y}Be Δ L _iX axle, the component of y axle.

Establishing the x axle again is main drive shaft, obviously, and for all Δ L _{I, x}Axle is always main drive shaft.The data stream of universal driving shaft y is the distribution of the data stream of main drive shaft x, and therefore, the geometric properties of curve only depends on the component Δ L of universal driving shaft y _{I, y}

Curve is at point (x _i, y _i) curvature cause little line segment Δ L _iLength certainly exist a maximal value.This maximal value is referred to as curve at point (x _i, y _i) intrinsic length.As Δ L _iDuring for intrinsic length, the component Δ L of universal driving shaft y _{I, y}Be referred to as point (x _i, y _i) geometric factor, with G _{I, y}Show it, Δ L _iTerminal point then be called intrinsic reflection.G _{I, y}Integral multiple for discretization error e.

For all i, if little line segment Δ L _iLength be intrinsic length, i.e. the component Δ L of universal driving shaft y _{I, y}Be equal to little line segment Δ L _iStarting point (x _i, y _i) geometric factor G _{I, y}, this L is cut apart the intrinsic L that is curve and is cut apart, and is designated as Δ L _i(i=1 ..., n).

Obviously, for i arbitrarily, Δ L _{I, y}Length can only be less than or equal to G _{I, y}Therefore, for this curve, how much equivalent G of universal driving shaft y _{I, y}It is the inherent geometric attribute of this curve.

(9), T is cut apart

Time T is divided into is uneven in length and end to end some intervals: Δ t ₁..., Δ t _i..., Δ t _mThese Δs t _iSummation be referred to as to cut apart about the discrete of time T, abbreviate T as and cut apart, with Δ t _i(i=1 ..., m) show it, m=n-1 in the formula, n are the bar number of little line segment.

(10), the linkage of associated data stream and linkage table

The stepping type associated data stream is at each sequential point t _iThe coordinate figure increment of " 0 " or " 1 " form be referred to as the stepping type associated data stream at this sequential point t _iState; Similarly, the incremental associated data stream is at each time interval Δ t _iInterior coordinate figure increment is referred to as the incremental associated data stream at this time interval Δ t _iInterior state.

Obviously, associated data stream is a kind of state flow of discrete location information.In the state flow of associated data stream, both comprised discrete location information, comprise the related information between these discrete location information again.These related informations have been described the linkage between the discrete location information described in the associated data stream.

The linkage of described associated data stream refers to, at each time interval Δ t _iInterior (or each sequential point t _i) the coordinate figure increment of relevant coordinate axis feeding simultaneously, promptly L is cut apart.

The linkage of associated data stream has determined relevant coordinate axis at each time interval Δ t _iInterior (or each sequential point t _i) displacement and the resultant displacement of generation, reflected the geometric properties of curve, be numerically controlled essential attribute.

For given cutter track curve, discrete location information in the associated data stream and linkage thereof are the discrete geometry attributes of cutter track curve, and relevant coordinate axis with control realizes that the method for cutter track curve and process have nothing to do.

According to given data layout, set up linkage table at storage space and describe L and cut apart.By described linkage table, with each time interval Δ t _iInterior (or each sequential point t _i) needed displacement conversion was the spatial correlation of associated data stream at storage space when relevant coordinate axis linked.

(11), the servo-actuated of associated data stream and servo-actuated table

The related information of described associated data stream also comprises the servo-actuated between the adjacent states in the associated data stream.

The servo-actuated of so-called associated data stream, refer to the transmission speed of associated data stream, just the time interval of associated data stream between adjacent states is exactly that T is cut apart concerning the incremental associated data stream, is exactly each sequential point t concerning the stepping type associated data stream _iBetween the time interval (also can be called T cuts apart).

The servo-actuated of associated data stream has determined the speed of following between the described resultant displacement with the geometric properties of cutter track curve and the temporal characteristics decoupling zero of processing technology, and just the speed of feed of cutter is numerically controlled non-essential attribute.

According to given data layout, set up the servo-actuated table at storage space and describe T and cut apart.By described servo-actuated table, the speed of feed of cutter is converted to the spatial correlation of associated data stream at storage space.

(12), the time equivalent of kinetic control system

Control the field the advanced person, stepper motor and servomotor are two kinds of basic motive equipment realizing motion control.Control for stepping.When speed of feed surpassed the highest step frequency, stepper motor is step-out then, thereby the inverse of the highest step frequency of stepper motor can be referred to as the time equivalent of step motion control system, just went on foot the further needed time; For servocontrol, satisfying under dynamic (dynamical) requirement, the minimum sampling period when amount of feeding is the feeding equivalent then is similar to the highest step frequency of stepper motor, speed of feed surpasses minimum during the sampling period, servomotor is step-out then, thereby the described minimum sampling period also can be referred to as the time equivalent of servo motion control system.With E _tThe time equivalent of expression kinetic control system.

The inventor finds that the discrete motion learning aid has following seven essential characteristics.

1, first essential characteristic of discrete motion

In discrete motion, the direction of motion of coordinate axis is affined, and for example, x axle, y axle can only be made discrete rectilinear motion forward or backwards.Because direction of motion is restrained, isotropy has been lost in the space.Therefore, in discrete motion, the space no longer is an Euclidean space, and the cutter track curve no longer is the Euclidean curve.

The directivity in space is the non-europeanized of space.This is discrete geometric first essential characteristic.

2, second of discrete motion essential characteristic

In discrete coordinates system, the directivity in space causes x axle, y axle asymmetric, has initiatively the difference with interlock.

There is asymmetry in coordinate axis, has active/interlock attribute.This is second essential characteristic of discrete motion.

3, the 3rd of discrete motion the essential characteristic

By advance planning, the determinacy kinematic relation between the control coordinate axis is in the scope of ascertainment error, and this is numerically controlled essence.

The geometry of workpiece profile and cutter is predetermined, and therefore, the kinematic relation between the coordinate axis is deterministic.The core missions of digital control system are made digital control information exactly, and the coordinate axis that is used for the Control work machine is finished given determinacy mechanical motion, and pass through the synthetic realization cutter track curve of the displacement (angular displacement) of relevant coordinate axis.The synthetic one side of displacement requires relevant coordinate axis to link, and requires on the other hand to realize the synthetic of displacement continuously with optimum speed of feed.The synthetic continuous realization with resultant displacement of displacement is two problems of different in kind.The synthetic state that depends on associated data stream of displacement relates to the space structure of cutter track curve; The time interval of associated data stream between adjacent states depended in the continuous realization of resultant displacement, relates to the technological parameter that adds man-hour.Therefore, the space-time structure of associated data stream is not to be coupled in itself.

The non-coupling of the space-time structure of associated data stream, this is the 3rd essential characteristic of discrete motion.

4, the 4th of discrete motion the essential characteristic

In discrete motion, the time is an independently free variable, and this is the 4th essential characteristic of discrete motion.

5, the 5th of discrete motion the essential characteristic

Zeroaxial 45 ° of oblique lines and 135 ° of oblique lines are divided into 8 intervals with 4 quadrants.The intersection point of these two oblique lines and cutter track curve is called the unique point of curve.In unique point, curve enters another interval from an interval, and x axle and y axle will change active/interlock attribute.

The unique point that x axle and y axle are followed curve constantly alternately changes active/interlock attribute, and this is the 5th essential characteristic of discrete motion.

6, the 6th of discrete motion the essential characteristic

In newtonian motion, the displacement of curvilinear motion and speed can be decomposed into axial displacement component of corresponding coordinate and component velocity according to parallelogram law, and vice versa.

In discrete motion, curvilinear motion is the synthetic of corresponding coordinate axial translation.The displacement that changes the corresponding coordinate axle is the sufficient and necessary condition of resultant curve.The aggregate velocity that component velocity produced of each coordinate axis is also disobeyed parallelogram law.

The parallelogram of velocities rule lost efficacy, and this is the 6th essential characteristic of discrete motion.

7, the 7th of discrete motion the essential characteristic

During the processing continuous curve, the L of curve is divided into Δ L ₁..., Δ L _n, T is divided into Δ t _i(i=1 ..., m), m=n-1 here.

At Δ t _iDuring this time, x axle and the interlock of y axle, promptly x axle, y axle produce displacement L _{I, x}, Δ L _{I, y}Thereby, form resultant displacement Δ L _iFor each Δ t _i, resultant displacement Δ L _iSize and direction all change.This is the inherent attribute of cutter track curve.

Because of F _{I, x}=Δ L _{I, x}/ Δ t _i, F _{I, y}=Δ L _{I, y}/ Δ t _iThereby,, cut apart Δ t for T _i(i=1 ..., m), the movement velocity of coordinate axis certainly leads to saltus step, and in other words, the movement velocity of coordinate axis is discontinuous.

For continuous curve processing, the movement velocity of coordinate axis certainly leads to saltus step, causes the uncontinuity of coordinate axis movement velocity, and this is the 7th essential characteristic of discrete motion.

Above-mentioned seven essential characteristics of discrete motion provide new technological means for motion planning, have established the basis of area of computer aided speed planning.

Clearer for the purpose, technical characterictic and the implementation result that make present embodiment, the technical scheme to the application's discrete motion planing method is described in detail below in conjunction with the accompanying drawings and the specific embodiments.

If the cutter track curve is the function of 5 variablees such as X, y, Z, A, B.Table 1 has been described the structure of 5 interlock incremental associated data streams.

Table 1

As known from Table 1, time T is dispersed and is divided into n interval: Δ t _i, i=1 ..., n.Five of X, y, Z, A, B etc. are at Δ t _iInterior displacement is Δ X _i, Δ y _i, Δ Z _i, Δ A _i, Δ B _i

This shows that discrete control information comprises two parts.First is, at Δ t _iIn, needed displacement information when X, y, Z, A, B five-axle linkage, i.e. Δ X _i, Δ y _i, Δ Z _i, Δ A _i, Δ B _iTo produce desired resultant displacement; Second portion is, at Δ t _iIn, thereby finishing the speed of described displacement, X, y, Z, A, five of B determined that T cuts apart the time interval between the just described resultant displacement.

Obviously, X, y, Z, A, the desired resultant displacement of B five-axle linkage are a discrete geometric programming problem purely, and promptly L is cut apart planning problem.

The time interval between the described resultant displacement then is a discrete motion planning problem, and promptly T is cut apart planning problem.

The core missions of computerized numerical system are, with the digital control information decompress(ion) that is compressed in cutter track curve and the speed of feed, make the digital control information of cutter track curve, and the L that just makes the cutter track curve is cut apart with T and cut apart.

Described L is cut apart the displacement information linkage desired with it that comprises relevant coordinate axis, is used to control relevant coordinate axis interlock to produce desired resultant displacement.Described T is cut apart the velocity information servo-actuated desired with it that comprises when described resultant displacement is synthetic continuously, is used to control the time interval between the described resultant displacement.

Described L is cut apart the discrete geometry that relates to the cutter track curve, is a discrete geometric programming problem, and described T is cut apart and related to speed of feed, is a discrete motion planning problem.

A kind of area of computer aided discrete motion planning system (Computer AidedDiscrete Kinematics Planning as shown in Figure 2, CADKP), comprise hardware platform, software platform and application software system, its hardware platform is general PC system, and software platform is a graphical interfaces operating system.

Described software platform also comprises 3 d graphic library, for example OpenGL.OpenGL is the abbreviation of OpenGraphics Library, is the 3 d graphic library that a cover is independent of operating system and hardware environment, powerful graphing capability and good cross-platform transfer ability is arranged, the graphics standard on having come true.OpenGL is widely used in numerous areas such as Computer Simulation, visualization technique, solid modelling, CAD/CAM/CAE.

By means of powerful three-dimensional artificial ability and the good man computer interface of OpenGL in the PC system, the CADKP method with good, open man-machine interface with the servo-actuated table of incremental associated data stream, the method for making the servo-actuated table control with process and acceleration and deceleration, static time lag compensation all gives visual, CADGP method thereby be open is for the software implementation of digital control technology has been established solid foundation.

Described application software system comprises:

Cutter track curve planning module, described cutter track tracing analysis module is used for according to unique point, is k bar curve with the cutter track curve segmentation; Every curve to after cutting apart is divided into main drive shaft and universal driving shaft with coordinate axis, generates the cutter track curve file;

L is cut apart planning module, and described L is cut apart planning module and is used for every curve to described k bar curve, and according to the optimization aim of setting, the intrinsic L that meets described optimization aim by guiding point pointwise structure is cut apart Δ L _i(i=1 ..., n);

T is cut apart planning module, and described T is cut apart module and is used for described intrinsic L is cut apart, and generates T and cuts apart Δ t _i(i=1 ..., m).

Described application software system is based upon on the middleware, adopts application programming interface API between each module of described application software system.

If the cutter track curve is a continuous curve, circular arc for example then must be little line segment Δ L with this curve is discrete ₁..., Δ L _nAt little line segment Δ L ₁..., Δ L _nBetween, the speed of feed of coordinate axis certainly leads to saltus step, and this is the inherent attribute of discrete motion.The hop value of coordinate axis speed of feed has reflected the robust motion of coordinate axis.

For little line segment Δ L ₁..., Δ L _nIn every little line segment implement acceleration and deceleration control, can reduce the hop value of the speed of feed between little line segment, obviously, thereby this will cause coordinate axis to quicken continually to reduce crudy and process velocity with slowing down.Therefore, make little line segment Δ L ₁..., Δ L _nBetween the hop value of speed of feed remain in the suitable scope and can increase substantially crudy and process velocity, become the important technical of high-speed, high precision processing.

Therefore, the basic problem of discrete motion planning is that when the processing continuous curve, for given speed of feed F, planning L is cut apart and planned that relevant coordinate axis is at Δ t _iSpeed of feed during this time makes little line segment Δ L ₁..., Δ L _nBetween the hop value of speed of feed remain in the suitable scope, thereby determining that T is cut apart with L cuts apart.

Obviously, for the given speed of feed F of user, T is cut apart the discrete geometry that depends on curve and the dynamics of main drive shaft y, comprises peak acceleration a _{Max, y}, kinetic control system time equivalent E _tDeng.

For all little line segment Δ L _i, from Δ L _iSlope and the speed of feed F speed of feed component F of obtaining main drive shaft y _{I, y}, and according to Δ t _i=Δ L _{I, y}/ F _{I, y}Try to achieve Δ t _i, obtain T and cut apart Δ t _i(i=1 ..., m), m=n-1 here, n is the bar number of little line segment.

The saltus step of speed of feed is the inherent attribute of discrete motion.Thereby, for the saltus step that makes speed of feed remains in the suitable scope, must adjust L and cut apart with T and cut apart.

Circle is the fundamental curve in the cutter track curve, and non-circular curve can approach with some circular arcs.Be without loss of generality, to establish the cutter track curve be the counterclockwise arc in the 1st quadrant and do not comprise unique point.

If x is a universal driving shaft, y is a main drive shaft.Obviously, for all Δ L _{I, y}Axle is always main drive shaft.The geometric properties of curve only depends on the component Δ L of universal driving shaft x _{I, x}

If the cutter track curve is counterclockwise arc in the 1st quadrant, its radius is r, and starting point is on the x axle, and coordinate is (r, 0), and terminal point is a unique point, and coordinate is From the starting point to the unique point, for every broken line Δ L _i, the amount of feeding of universal driving shaft x increases gradually from 0, and its total feed amount is roughly 0.3r.The amount of feeding of main drive shaft y then reduces gradually from maximum, and its total feed amount is roughly 0.7r.During near unique point, the amount of feeding of the two equates.The total feed amount of main drive shaft y roughly is 2.3 times of total feed amount of universal driving shaft x.

From the starting point to the unique point, for every broken line Δ L _i, the speed of feed of universal driving shaft x is increased to 0.7F gradually from 0, and total change amount of its speed of feed is roughly 0.7F.The speed of feed of main drive shaft y then is reduced to 0.7F gradually from F, and total change amount of its speed of feed is roughly 0.3F.Therefore, total change amount of universal driving shaft x speed of feed roughly is 2.3 times of total change amount of main drive shaft y speed of feed.

The given speed of feed of user is F, and F is less than the maximum speed of feed F of x axle _{Max, x}Maximum speed of feed F with the y axle _{Max, y}: F≤F _{Max, x}, F≤F _{Max, y}

In time T, from the starting point to the unique point, main drive shaft y begins to do retarded motion from F, and universal driving shaft x begins to do accelerated motion from static, and when arriving unique point, the movement velocity of the two equates, for

The speed of feed of main drive shaft y from F, reaches through m saltus step

The mean value of speed of feed saltus step is

With Δ F _yShow it.

The speed of feed of universal driving shaft x from static, reaches through m saltus step The mean value of speed of feed saltus step is

With Δ F _xShow it.

If the cutter track curve is counterclockwise arc in the 1st quadrant.Little line segment Δ L _iStarting point be (x _i, y _i), terminal point is (x _I+1, y _I+1).At Δ t _iDuring this time, the speed of feed of y axle is F _{I, y}=Δ L _{I, y}/ Δ t _iAt Δ t _I+1During this time, the speed of feed of y axle is F _{I+1, y}=Δ L _{I+1, y}/ Δ t _I+1At point (x _I+1, y _I+1) locate, y axle speed of feed produces negative saltus step, and its hop value is (F _{I, y}-F _{I+1, y}), be designated as Δ F _{I+1, y}At point (x _I+1, y _I+1) locate, x axle speed of feed produces positive transition, and its hop value is Δ F _{I+1, x}=(F _{I+1, x}-F _{I, x}).

Cut apart Δ L for the L of this curve ₁..., Δ L _n, from origin-to-destination, main drive shaft y experiences m saltus step, m=n-1 here.With F _{S, y}With F _{E, y}Expression y axle in the ordinary course of things, can be used (F in the speed of feed of Origin And Destination _{S, y}-F _{E, y})/m estimates Δ F _yReference value.Equally, can use (F _{E, x}-F _{S, x})/m estimates Δ F _xReference value.

The robust motion of coordinate axis requires Δ F _I+1x, Δ F _{I+1, y}At its reference value Δ F _x, Δ F _yDeviation range in.

With δ _x, δ _yExpression Δ F _x, Δ F _yDeviation, then the stationarity constraint condition of coordinate axis motion can be expressed as:

(ΔF _i+1x-ΔF _x)≤δ _x

(ΔF _i+1，y-ΔF _y)≤δ _y。

Δ F _x, Δ F _yReference value and deviation thereof be empirical value, depend on that high-speed, high precision adds the technological requirement in man-hour.According to the technological requirement of crudy, according to practical experience, the user can be provided with Δ F voluntarily _x, Δ F _yReference value and deviation δ thereof _x, δ _y

For circular arc, Δ F _xBe approximately Δ F _y2.3 times, thereby Δ F _xReference value be approximately Δ F _y2.3 times of reference value.This is the constraint condition of giving birth in the circular arc.

The robust motion of coordinate axis is relevant with the driving force of servo motion control system.The driving force of servo motion control system then with the maximal rate F of coordinate axis _Max, peak acceleration a _Max, coordinate axis is relevant with the factors such as timeconstant of servo motion control system.Because F is retrained by the maximal rate of coordinate axis and peak acceleration, the robust motion of coordinate axis is main relevant with τ.Secondly, also different with finishing, roughing etc. the processing technology of the robust motion of coordinate axis is relevant.

In existing digital control system in open type, the motion planning technology is referred to as speed of feed prediction control (Look ahead).So-called speed of feed prediction control is exactly in interpolation operation, shifts to an earlier date pre-interpolation one segment distance, carries out motion planning in real time to reaching 1000～5000 little line segment Δ Li, with the speed of feed that reduces coordinate axis at little line segment Δ L ₁..., Δ L _nBetween hop value.Speed of feed prediction control is one of gordian technique in the existing digital control system in open type.

When motion planning, prior art has been ignored the discrete geometrical property and the discrete motion characteristic of cutter track curve fully, and the notion that does not have intrinsic L to cut apart does not have the notion of main drive shaft and universal driving shaft yet.

When motion planning, prior art has been ignored the non-Europe error of cutter track curve fully.

In existing digital control system, the time is dispersed by interpolation cycle T and is divided into the equal time interval: all Δ t _i(i=1 ..., m) be equal to interpolation cycle T.In i interpolation cycle, according to formula F=Δ L _I+1* T, interpolation algorithm calculate Δ L _I+1, again according to F and Δ L _I+1Slope, calculate the speed of feed F of x axle and y axle _{I+1, x}, F _{I+1, y}, calculate i+1 coordinate figure increment Delta L of x axle and y axle then _{I+1, x}, Δ L _{I+1, y}, export to x axle and y axle servo motion control system, as x axle in i+1 cycle and y shaft position ring set-point.

The non-coupling of the space-time structure of associated data stream is the essential characteristic of discrete motion.The prior art time that produced is forced to systematic parameter, I﹠amp by interpolation cycle; The basic defect of giving birth in four of the control model of the real-time iteration of P, " limit planning, limit design, limit construction ", the couplings of space-time structure etc., with approximate error, radius-of-curvature, interpolation cycle, the whole close-coupled of speed of feed together, must carry out speed of feed prediction control in real time, cause motion planning very complicated, expended a large amount of software and hardware computational resources.On the other hand, interpolation iteration control method is an interpolation cycle with time lock, can only adjust L merely and cut apart, and has lost adjustment Δ t _iTechnological means, be difficult to realize the optimization of coordinate axis robust motion.

The present invention is based on the discrete geometry and the discrete motion characteristic of cutter track curve, the optimization of planning for discrete motion proposes a kind of technical method.

The technical scheme of described discrete motion planning is as follows.

The discrete geometry of curve only depend on intrinsic L cut apart in the component Δ L of universal driving shaft x _{I, x}This this simultaneously because the non-coupling of space-time structure of associated data stream, the intrinsic L of curve is cut apart with speed of feed F irrelevant.

Intrinsic L for curve is cut apart, the component Δ L of universal driving shaft x _{I, x}Be point (x _i, y _i) geometric factor, that is to say, at point (x _i, y _i) locate the geometric factor G of universal driving shaft x _{X, i}Be little line segment Δ L _iDetermined the upper limit, Δ L _{I, x}Can only reduce and to increase.It is its upper limit of all approaching broken line that the intrinsic L of curve is cut apart.Thereby, for given Δ t _i, intrinsic L is cut apart the upper limit of the speed of feed that has determined universal driving shaft.

In this application, the technical characterictic of discrete motion planning is, when the processing continuous curve, for given speed of feed F and given cutter track curve, cut apart according to the intrinsic L of curve, adjust speed of feed F based on main drive shaft, planning T is cut apart, and checks the robust motion of main drive shaft; Then, check the robust motion of universal driving shaft based on the structure factor of universal driving shaft, the L that generates the cutter track curve is cut apart with T and is cut apart.

1), checks the given speed of feed F of user

The given speed of feed F of user must satisfy following constraint condition:

F≤F _max，x，F≤F _max，y，

E _t≤Δt _min

ΔF _x≤a _max，x×Δt _min、ΔF _y≤a _max，y×Δt _min，

F in the formula _{Max, x}, F _{Max, y}Maximum speed of feed for x axle, y axle; a _{Max, x}, a _{Max, y}Peak acceleration for x axle, y axle; E _tBe the maximal value in the time equivalent of x axle, y axle kinetic control system; Δ t _MinFor T is cut apart Δ t _i(i=1 ..., minimum value m).

Check constraint condition 1:

F≤F _max，x，F≤F _max，y；

If described constraint condition 1 does not satisfy, then reduce F to satisfy constraint condition 1.

Constraint condition 2:E is set _t≤ Δ t _Min

Check constraint condition 3:

ΔF _x≤a _max，x×Δt _min、ΔF _y≤a _max，y×Δt _min，

If described constraint condition 3 does not satisfy, then reduce F to satisfy constraint condition 3.

Above-mentioned constraint condition 1,2,3 is external constraint, finishes with interactive means by the dialog box in the man-machine interface.

2), check the robust motion of coordinate axis, the L that adjusts the cutter track curve is cut apart with T and is cut apart

A, robust motion constraint condition is set

Δ F is set _xWith Δ F _yReference value and deviation δ thereof _x, δ _y

The robust motion constraint condition of coordinate axis can be expressed as:

(ΔF _i+1，x-ΔF _x)≤δ _x

(ΔF _i+1，y-ΔF _y)≤δ _y。

The L of b, generation cutter track curve is cut apart with T and is cut apart

The little line segment Δ of n bar L during the intrinsic L of described curve cut apart ₁..., Δ L _n, from Δ L _iSlope and the speed of feed F speed of feed component F of calculating main drive shaft y _{I, y}Speed of feed component F with universal driving shaft x _{I, x}According to Δ t _i=Δ L _{I, y}/ F _{I, y}With Δ t _i〉=Δ t _Nin, generate T and cut apart Δ t _i(i=1 ..., m).

The robust motion constraint condition a of c, check main drive shaft y

(ΔF _i+1，y-ΔF _y)≤δ _y；

If described constraint condition a does not satisfy, then adjust F to satisfy described constraint condition a; According to adjusted speed of feed F, adjust T and cut apart Δ t _i(i=1 ..., m).

The robust motion constraint condition b of d, check universal driving shaft x

If Δ L _iBe little line segment of having planned.Thereby, to little line segment Δ L _I+1, discrete motion planning should be checked universal driving shaft x at point (x _I+1, y _I+1) the speed of feed hop value Δ F that locates _{I+1, x}=(F _{I+1, x}-F _{I, x}).

Universal driving shaft x is at point (x _I+1, y _I+1) the robust motion constraint condition b that locates is:

(ΔF _i+1，x-ΔF _x)≤δ _x。

For the little line segment Δ of next bar L _I+1If described constraint condition b does not satisfy, then increase Δ t earlier _I+1To reduce F _{I+1, x}, and then reduce Δ L _{I+1, x}To reduce F _{I+1, x}, increase Δ t _I+1With reduce Δ L _{I+1, x}Can carry out repeatedly, satisfy until described constraint condition b.

Calculate Δ L then _{I+1, x}, Δ L _{I+1, y}, adjust Δ t _I+1With little line segment Δ L _I+1With described little line segment Δ L _I+1Terminal point be made as ground zero, the curve between the terminal point of described ground zero and described curve is planned again that L is cut apart with T cuts apart, until the terminal point of described curve.

Every curve in the described k bar curve repeats above step, and the L that generates described cutter track curve is cut apart with T and cut apart, and realizes the optimization of axle robust motion.

In the present invention, the discrete logarithm that discrete motion planning process and L are cut apart is irrelevant, and is irrelevant with real time operating system.On the other hand, formula F _i=Δ L _i/ Δ t _iIllustrate that the present invention is under area of computer aided, from Δ L _iWith Δ t _iTwo aspects are adjusted the movement velocity of axle repeatedly, just can adjust L repeatedly and cut apart with T and cut apart, thereby realize the optimization of coordinate axis robust motion.

In the present invention, area of computer aided discrete motion planning process is open simply, flexibly and fully.

Fig. 3 is the process flow diagram of described area of computer aided discrete motion planing method.

For a continuous curve, described area of computer aided discrete motion planing method may further comprise the steps:

L is cut apart planning step (2): for every curve in the described k bar curve, according to the optimization aim of setting, the intrinsic L that meets described optimization aim by guiding point pointwise structure is cut apart Δ L _i(i=1 ..., n);

Disperse and cut apart planning step (3): cut apart for described intrinsic L, generate T and cut apart Δ t _i(i=1 ..., m).

For a continuous curve of k bar curve in the described cutter track curve, described L is cut apart planning step (2) and is comprised the steps:

Described step (205) is used to judge whether described straight-line segment is little line segment of described segment of curve.Prior art is considered as the Euclidean curve with described segment of curve, calculates the maximum normal direction distance between described straight-line segment and the described segment of curve and judges whether described maximum normal direction distance is less than or equal to discretization error, thereby produce non-Europe error.

The present invention is based on the discrete geometry of curve, judge by the neighborhood of more described straight-line segment and the neighborhood of described segment of curve whether described straight-line segment is little line segment of described segment of curve.Because all guiding neighborhoods of a point constitute the neighborhood of described segment of curve, so on the cutter track orientation, if the neighborhood of described straight-line segment is the subclass of the neighborhood of described segment of curve, described straight-line segment then is little line segment of described segment of curve.

For a continuous curve of k bar curve in the described cutter track curve, describedly discrete cut apart planning step (3) and may further comprise the steps:

Step (301), the given speed of feed F of check user

Step (301-1), check constraint condition 1:

F≤F _max，x，F≤F _max，y；

If described constraint condition 1 does not satisfy, then reduce F to satisfy described constraint condition 1.

Step (301-2), constraint condition 2:E is set _t≤ Δ t _Min

Step (301-3), the Δ F that sets according to the user _xWith Δ F _y, check Δ t _Min, make it to satisfy following constraint condition 3:

ΔF _x≤a _max，x×Δt _min，ΔF _y≤a _max，y×Δt _min；

Described constraint condition 1,2,3 is external constraint, finishes with interactive means by the dialog box in the man-machine interface.

Step (302), for a curve in the described k bar curve, carry out described L and cut apart planning step (2), the intrinsic L that generates the optimization aim meet setting is cut apart Δ L _i(i=1 ..., n);

Step (303), the little line segment Δ of the n bar L during the intrinsic L of described curve cut apart ₁..., Δ L _n, from Δ L _iSlope and the speed of feed F speed of feed component F of calculating main drive shaft y _{I, y}Speed of feed component F with universal driving shaft x _{I, x}According to Δ t _i=Δ L _{I, y}/ F _{I, y}With Δ t _i〉=Δ t _Min, generate T and cut apart Δ t _i(i=1 ..., m);

Step (304), Δ F is set _xWith Δ F _yReference value and deviation δ thereof _x, δ _y

The robust motion constraint condition of step (305), check main drive shaft y

(ΔF _i，y-ΔF _y)≤δ _y(i＝1，...，m)；

The robust motion constraint condition of step (306), check universal driving shaft x

(ΔF _i，x-ΔF _x)≤δ _x；

Step (307) illustrates F if described constraint condition b does not satisfy _{I+1, x}Too big, then at first increase Δ t _I+1To reduce F _{I+1, x}, described constraint condition b is satisfied; If increase Δ t _I+1Can not satisfy described constraint condition b, Δ L is described _I+1Oversize, then reduce Δ L _{I+1, x}To reduce F _{I+1, x}, described constraint condition b is satisfied;

Step (308), calculating Δ L _{I+1, x}, Δ L _{I+1, y}, adjust Δ t _I+1With little line segment Δ L _I+1

Step (309), with described little line segment Δ L _I+1Terminal point as ground zero, to the curve between the terminal point of described ground zero and described curve, repeating step (302) is to step (308), until the terminal point of described curve;

Step (3010), to every curve in the k bar curve in the described cutter track curve, the order repeating step (302) to step (309).

In described step (307), increase/Δ ti+1 with reduce Δ Li+1, x can carry out repeatedly repeatedly.

In existing digital control system, acceleration and deceleration control is a gordian technique, and the acceleration and deceleration control module becomes the important component part of interpolation module.

In fact, so-called acceleration and deceleration control is the speed of feed at certain coordinate axis, just at the rectilinear motion of this coordinate axis.Speed of feed according to the speed of feed before quickening, at the uniform velocity the time with slow down after input parameters such as speed of feed, straight line is divided into accelerating sections, at the uniform velocity section and braking section, determine to quicken terminal point and deceleration starting point.The section of will speed up and braking section are discrete to be a line segment slightly, to this slightly line segment to carry out motion planning be exactly so-called acceleration and deceleration control.

Different with the processing continuous curve, the processing for straight line, there is not saltus step in the movement velocity of coordinate axis.Thereby, in acceleration and deceleration control, can promptly select suitable acceleration and deceleration curves, as the parabolic type S curve of routine and trigonometric function type S curve etc. according to the Changing Pattern of different technological requirement planning speed of feed.

Existing acceleration and deceleration control is real-time, must carry out under the control of real time operating system, and can only adjust little line segment, thereby acceleration and deceleration control is difficult to become more meticulous.

In the present invention, the special case of only planning for discrete motion is controlled in acceleration and deceleration.For the straight line that needs to carry out acceleration and deceleration control on the cutter track curve, determine input parameter; According to described parameter, described straight line is divided at the uniform velocity section, accelerating sections and braking section, determine to quicken terminal point and deceleration starting point; According to given optimization aim, select suitable acceleration and deceleration curves; Accelerating sections and braking section to described straight line carry out discrete motion planning, generate the linkage table and the servo-actuated table of described accelerating sections and braking section at storage space, thereby finish acceleration and deceleration control.

This shows that the present invention controls acceleration and deceleration the routine techniques means that are converted in the discrete motion planning.On the other hand, the present invention can be cut apart the Changing Pattern of cutting apart two aspect unified plan speed of feed with T from L, thereby has realized becoming more meticulous of acceleration and deceleration control.

Above content is to further describing that area of computer aided discrete motion planing method is done in conjunction with concrete preferred implementation.The present invention is an example with two motions, and the technical scheme of implementing area of computer aided discrete motion planing method and system has been described, can not assert that concrete enforcement of the present invention is confined to these explanations.For the general technical staff of the technical field of the invention; without departing from the inventive concept of the premise; can also make the area of computer aided discrete motion planing method that some simple deduction or replace are used to make up three and even multiaxial motion, all should be considered as belonging to protection scope of the present invention.

Claims

1. an area of computer aided discrete motion planing method is characterized in that, comprise,

2. area of computer aided discrete motion planing method as claimed in claim 1 is characterized in that, described L is cut apart planning step (2) and comprised the steps:

3. area of computer aided discrete motion planing method as claimed in claim 2 is characterized in that, described T is cut apart planning step (3) and comprised the steps:

|ΔF _i，y-ΔF _y?|≤δ _y(i＝1，...，m)；

If Δ L _iBe little line segment of having planned; Calculate universal driving shaft x at point (x _I+1, y _I+1) the speed of feed hop value Δ F that locates _I+1, _x=(F _{I+1, x}-F _{I, x}), the robust motion constraint condition b of check universal driving shaft x:

|ΔF _i，x-ΔF _x?|≤δ _x；

4. as any described area of computer aided discrete motion planing method in the claim 1 to 3, it also is characterised in that: described coordinate axis is more than three.

5. an area of computer aided discrete motion planning system comprises hardware platform, software platform and application software system, and described hardware platform is the PC system, and software platform is a graphical interfaces operating system; It is characterized in that described application software system comprises:

6. area of computer aided discrete motion planning system as claimed in claim 5 is characterized in that described application software system is based upon on the middleware, adopts application programming interface API between each module.

7. area of computer aided discrete motion planning system as claimed in claim 6 is characterized in that described software platform also comprises 3 d graphic library.