CN103480534A - Robot spray workpiece surface modeling method - Google Patents

Abstract

The invention discloses a robot spray workpiece surface modeling method. The method includes the steps of performing triangular grid partitioning on a workpiece surface, setting a maximum normal vector threshold, connecting triangular faces into small flat patches according to a triangular face connecting method, creating a flat patch adjacency graph, and merging all the small flat patches to a plurality of new large flat patches according to a flat patch adjacency graph merging algorithm. The method is applicable to surface modeling of various complicated sprayed workpieces, particularly applicable to surface modeling of workpieces large in curvature change and fast in calculation, so that preparations are made for follow-up spraying robot route planning and trajectory optimization so as to meet requirements on working of a spraying robot, and working efficiency of the spraying robot and quality of products can be improved.

Description

Control During Paint Spraying by Robot curve surface of workpiece formative method

Technical field

The present invention relates to a kind of Control During Paint Spraying by Robot curve surface of workpiece formative method, relate in particular to the spraying curve surface of workpiece formative method used in a kind of spray robot off-line programing system.

Background technology

The structure of spray robot off-line programing system mainly comprises following six large modules: workpiece moulding module, parameter arrange module, spray robot track generation module, robot motion's track generation module, analyze emulation module and robot program's generation module.In workpiece moulding module, for plane or ruled surface, can directly write out its expression formula; And, for free form surface or complex-curved, need, with specific process, curved surface is carried out to moulding, after moulding, just deposited the cad data of object in the system CAD database, for spray robot track generation module provides workpiece data information.

The moulding of spraying curve surface of workpiece is the first step of carrying out the spray robot track optimizing, is also design spray robot spraying path and the key of optimizing spraying profile.Use a kind of suitable Applications of Surface Modeling Methods, particularly important to follow-up spray robot spraying path planning and track optimizing work.In prior art, for the spraying curve surface of workpiece formative method that can use in the spray robot off-line programing system, mainly contain following three kinds: (1) formative method based on parametric surface.(2) Applications of Surface Modeling Methods based on cad model.(3) Applications of Surface Modeling Methods based on workpiece scanning system.These three class methods have limitation: both be not suitable for curvature and changed surface modeling greatly, also not being suitable for the surface that need to carry out the burst processing is complex-curved workpiece moulding.Therefore, due to diversity and the complexity of spraying workpiece, finding a set of complete, practical and Applications of Surface Modeling Methods that can be applicable on spraying workpiece that surface curvature change is larger is not an easy thing.Disclose the spray gun track planing method of a kind of free curved surface spraying robot in the patent documentation that application number is CN201210050434, proposed in the method will directly be divided into by sprayed surface the zone of several regular shape in 3D sculpting software.This method is fairly simple to the processing of surface modeling, can only be applicable to curvature and change in less free form surface, can not be for the spraying operation on complex curved surface part surface with multiply-connected logical zone.A kind of optimizing method of spray coating robot spray gun track on complex-curved has been proposed in the patent documentation that the patent No. is ZL200810020500.6, in the method, propose burst after complex-curved triangulation is processed, but this processing mode precision is lower, can only change less curved surface for curvature, and can not be applicable on 3D solid that the normal vector angle of each spray-coating surface is larger.

In sum, due to diversity and the complexity of spraying workpiece, in prior art, still do not have a whole set of complete surface that is applicable to change the Applications of Surface Modeling Methods of spraying workpiece greatly for complex-curved and curvature.

Summary of the invention

The object of the present invention is to provide a kind of Control During Paint Spraying by Robot curve surface of workpiece formative method, be applicable to surface for surface modeling complex-curved and curvature variation spraying workpiece greatly.

Purpose of the present invention is achieved by the following technical programs:

A kind of Control During Paint Spraying by Robot curve surface of workpiece formative method comprises the following steps:

1) curve surface of workpiece triangulation; Curved surface carries out with mathematic(al) representation, being expressed as after triangulation:

M=｛T _i:i=1,…,P｝

T wherein _ibe i triangular facet in triangle gridding, P is total number of triangle gridding intermediate cam face;

2) set maximum normal vector threshold value θ _th;

3) according to the triangular facet connection method, triangular facet is connected into to less planar chip; Described triangular facet connection method comprises the following steps:

(1) specifying any one triangular facet is initial triangular facet;

(2) find the triangular facet contiguous with initial triangular facet and be connected with initial triangular facet and be connected into a sheet;

(3) whether the sheet that judgement connects into meets the feature of planar chip;

The determination methods of the feature of planar chip is:

A. calculate the method for average vector of sheet

$\stackrel{\→}{n_a}=\frac{{\mathrm{\Σ}}_{i=1}^p{s}_i\stackrel{\→}{n_i}}{{\mathrm{\Σ}}_{i=1}^p{s}_i}/\left|\right|\frac{{\mathrm{\Σ}}_{i=1}^p{s}_i\stackrel{\→}{n_i}}{{\mathrm{\Σ}}_{i=1}^p{s}_i}\left|\right|$

Wherein,

mean T _ithe normal vector of individual triangular facet, s _imean T _ithe area of individual triangular facet, P means the quantity of this curved surface triangle division Vee formation face;

B. calculate the normal vector of the maximum projection plane of sheet, i.e. the sail angle normal vector

the steps include:

Write maximum projection plane's area expression formula of slice

order

solving equation draws the normal vector of maximum projection plane

C. the method for average vector of sheet

with its sail angle normal vector

between angle be maximum normal vector bias angle theta _mDA,

If θ _mDA≤ θ _th, meet the feature of planar chip, confirm to connect effectively;

If θ _mDA﹥ θ _th, do not meet the feature of planar chip, it is invalid to connect, and abandons this connection;

(4) seek and being connected with this sheet all over all new triangular facets adjacent with this sheet, and the feature that whether meets planar chip is judged;

4) find and not yet connect triangular facet in blocks as new initial triangular facet, by described triangular facet connection method, triangular facet is connected into to less planar chip, until all triangular facets all connect into planar chip;

5) set up the planar chip connection layout; Concrete steps are:

(1) each planar chip on a spraying curved surface is expressed as to a node, and with a nondirectional connection layout G=(V, E) mean the topological structure of this curved surface, nondirectional connection layout G is the planar chip connection layout on this spraying curved surface, wherein, V means the node in connection layout, and E means the boundary line of the figure that this group node forms, and

(2) normal vector of establishing the represented planar chip of any i node vi in the planar chip connection layout is

the planar chip area is A _i, the maximum normal vector drift angle on planar chip is θ _mDAi, can be by node v _ibe expressed as

(3) establish e _ijfor node v _iwith node v _jlimit, ω (i, j) means limit e _ijweights, weights are the angle of the normal vector of every two, two of normal vector angle minimum sheets are the minimum limit of weights ω (i, j) in the planar chip connection layout;

Certain planar chip connection layout of setting up need to meet following characteristics:

A. a planar chip connection layout is a connected graph;

B. after the arbitrary node in a planar chip connection layout merges an other node, resulting new nondirectional connection layout remains a planar chip connection layout;

C. merging process can only merge a node in the planar chip connection layout each time;

6) according to planar chip connection layout merge algorithm, each is merged into to new larger planar chip than the facet sheet, concrete steps are:

(1) find two node (v of adjacent normal vector angle minimum in the planar chip connection layout _i, v _j);

(2) calculate limit e _ijweights ω (i, j), establish BV=2 θ _th, and judge whether ω (i, j)≤BV sets up, and if set up, enter next step, otherwise merge, stop;

(3) by node v _iwith node v _jmerge into new sheet v _ijafter, by this sheet v _ijwith mathematic(al) representation, be expressed as:

$v_{\mathrm{ij}}=v_i\⊕v_j=\{\stackrel{\→}{n_{\mathrm{pi}}},A_i,{\mathrm{\θ}}_{\mathrm{MDAi}}\}\⊕\{\stackrel{\→}{n_{\mathrm{pj}}},A_j,{\mathrm{\θ}}_{\mathrm{MDAj}}\}=\{\frac{\stackrel{\→}{n_{\mathrm{pi}}}{A}_i+\stackrel{\→}{n_{\mathrm{pj}}}{A}_j}{A_i+A_j},A_i+A_j,{\mathrm{\θ}}_{\mathrm{MDAij}}\}$

In above formula, A _iwith A _jthe area that means respectively i and j planar chip, θ _mDAijmean new sheet v _ijmaximum normal vector drift angle;

(4) judge v _ijwhether be planar chip, if, enter (5) step, otherwise make BV, be 2 initial θ _thto 3 θ _thbetween an artificial setting value, then proceed to (1) step;

(5) upgrade the planar chip connection layout and recalculate according to (1)-(4) step;

(6) in Judge plane sheet connection layout, whether all nodes all merge, if finish, otherwise forward step (1) to.

Purpose of the present invention can also further realize by following technical measures:

Aforementioned machines people sprays curve surface of workpiece formative method, wherein step 2) described maximum normal vector threshold value θ _thbe located between 15 °～20 °.

Compared with prior art, the invention has the beneficial effects as follows: on the basis of triangulation method, propose a kind of based on planar chip connection layout (Flat Patch Adjacency Graph, abbreviation FPAG) spraying curve surface of workpiece formative method, the method can be applicable to various complex part curved surfaces, especially be applied to curvature and change curve surface of workpiece moulding greatly, and computational speed is very fast, thereby the spray robot path planning and the track optimizing work that can be back are ready, to meet the spray robot requirements of one's work, can improve the quality of spray robot operating efficiency and product.

The accompanying drawing explanation

Fig. 1 sets up planar chip connection layout FPAG schematic diagram;

The planar chip merge algorithm flow chart of Fig. 2 based on planar chip connection layout FPAG;

Fig. 3 is all the 3D solid of convex surface;

Fig. 4 has the 3D solid of concave surface.

The specific embodiment

Below in conjunction with the drawings and specific embodiments, the invention will be further described.

The invention process step is mainly connected into less planar chip, sets up planar chip connection layout FPAG, merged into some new larger planar chip three parts than the facet sheet and form by triangular facet, and the specific embodiment is as follows:

1. triangular facet connects into less planar chip

In engineering application software (as GID7.2), after input workpiece cad data, use the triangular facet output function of software directly workpiece to be carried out to triangle division.Curve surface of workpiece triangulation concrete steps are as follows:

1. according to the cad model of workpiece, surface of the work is carried out to triangulation;

2. remove to approach original surface of the work with obtaining triangle mesh curved surface after having divided.

Curved surface carries out can being expressed as with mathematic(al) representation after triangulation:

M=｛T _i:i=1,…,P｝

Here T _ibe i triangular facet in triangle gridding, P is total number of triangle gridding intermediate cam face.Set maximum normal vector threshold value θ in system _th, θ generally _that 15 degree between 20 degree.According to the triangular facet connection method, triangular facet is connected into to less planar chip, concrete steps are:

(1) specifying any one triangular facet is initial triangular facet.

(2) find with the triangular facet of initial triangular facet vicinity and be connected with initial triangular facet and be connected into a sheet.

(3) verify whether the sheet connected in (2) step meets the feature of planar chip, and seek and being connected with this sheet all over all new triangular facets adjacent with this sheet.Here planar chip is defined as: after curved surface carries out triangulation, by some, adjacent triangular facet connects in flakes, if this sheet is a part and its method of average vector of curved surface

with its sail angle normal vector

between angle be less than maximum normal vector threshold value θ _th, claim that this sheet is a planar chip.In this definition, the method for average vector on certain sheet

computational methods are:

$\stackrel{\→}{n_a}=\frac{{\mathrm{\Σ}}_{i=1}^p{s}_i\stackrel{\→}{n_i}}{{\mathrm{\Σ}}_{i=1}^p{s}_i}/\left|\right|\frac{{\mathrm{\Σ}}_{i=1}^p{s}_i\stackrel{\→}{n_i}}{{\mathrm{\Σ}}_{i=1}^p{s}_i}\left|\right|$

Wherein,

mean T _ithe normal vector of individual triangular facet, s _imean T _ithe area of individual triangular facet, P means the quantity of this curved surface triangle division Vee formation face.In the planar chip definition, the sail angle normal vector of planar chip refers to the normal vector of the maximum projection plane of a sheet, uses symbol

mean, its calculation procedure is:

1. write out maximum projection plane's area expression formula of a sheet

2. order $\frac{\mathrm{dS}}{d\stackrel{\→}{v_a}}=0;$

3. 2. solving equation can obtain the normal vector of maximum projection plane

If establish

normal vector with its maximum projection plane

between angle be θ _mDA, claim θ _mDAfor maximum normal vector drift angle, on planar chip, must have: θ _mDA≤ θ _th, what meet just can be called planar chip.

(4) find and not yet connect triangular facet in blocks as new initial triangular facet, repeat (2), (3) step, until all triangular facets all connect in flakes.

2. set up planar chip connection layout FPAG

After in the spraying curve surface of workpiece, all triangular facets all connect in flakes, each first needs to set up planar chip connection layout FPAG before merging into some new larger planar chips than the facet sheet, and concrete steps are:

(1) each planar chip on a spraying curved surface is expressed as to a node, and with a nondirectional connection layout G=(V, E) mean the topological structure of this curved surface, nondirectional connection layout G is the planar chip connection layout on this spraying curved surface (Flat Patch Adjacency Graph is called for short FPAG).Wherein, V means the node in connection layout, and E means the boundary line of the figure that this group node forms, and

(2) establish any i node v in planar chip connection layout FPAG _i, the normal vector that resets the planar chip represented with this node is

the planar chip area is A _i, the maximum normal vector bias angle theta on planar chip _mDAi, can be by node v _ibe expressed as $V_i=\{\stackrel{\→}{n_{\mathrm{pi}}},A_i,{\mathrm{\θ}}_{\mathrm{MDAi}}\}.$

(3) suppose e _ijfor node v _iwith node v _jlimit, ω (i, j) means limit e _ijweights (being the angle of the normal vector of every two), two of normal vector angle minimum sheets are the minimum limit of weights ω (i, j) in FPAG.

As shown in example in accompanying drawing 1, after some curved surfaces are divided into 5 less planar chips, wherein A sheet and C sheet normal vector angle are θ, this curved surface are converted to the length ω (A, C) of FPAG back AC=θ.Thus, as node v _iwith node v _jmerge into new sheet v _ijafter, this sheet v _ijavailable mathematic(al) representation is expressed as:

$v_{\mathrm{ij}}=v_i\⊕v_j=\{\stackrel{\→}{n_{\mathrm{pi}}},A_i,{\mathrm{\θ}}_{\mathrm{MDAi}}\}\⊕\{\stackrel{\→}{n_{\mathrm{pj}}},A_j,{\mathrm{\θ}}_{\mathrm{MDAj}}\}=\{\frac{\stackrel{\→}{n_{\mathrm{pi}}}{A}_i+\stackrel{\→}{n_{\mathrm{pj}}}{A}_j}{A_i+A_j},A_i+A_j,{\mathrm{\θ}}_{\mathrm{MDAij}}\}$

In above formula, A _iwith A _jthe area that means respectively i and j planar chip, θ _mDAijthe v that means new sheet _ijmaximum normal vector drift angle.

And certain planar chip connection layout FPAG of foundation need to meet following characteristics:

(1) planar chip connection layout FPAG is a connected graph;

(2) after the arbitrary node in a planar chip connection layout FPAG merges an other node, resulting new nondirectional connection layout remains a FPAG;

(3) merging process can only merge a node in planar chip connection layout FPAG each time.

3. merge into some new larger planar chips than the facet sheet

After planar chip connection layout FPAG has set up, each can be merged into to some new larger planar chips than the facet sheet, its flow chart as shown in Figure 2.The concrete steps that planar chip merges are:

(1) find two node (v of adjacent normal vector angle minimum in FPAG _i, v _j).

(2) calculate limit e _ijweights ω (i, j), establish BV=2 θ _th, and judge whether ω (i, j)≤BV sets up, and if set up, enter (3) step, otherwise merge, stop.

(3) by node v _iwith node v _jmerge into new sheet v _ijafter, and by this sheet v _ijwith mathematic(al) representation, be expressed as:

(4) judge v _ijwhether be planar chip, if, enter (5) step, otherwise make BV, be 2 initial θ _thto 3 θ _thbetween an artificial setting value after proceed to again (1) step.

(5) upgrade FPAG and recalculate according to (1)-(4) step.

(6) judge in FPAG, whether all nodes all merge, if finish, otherwise forward step (1) to.

In actual industrial production, many spraying workpiece shapes are more complicated all, the normal vector angle that can run into a plurality of spray-coating surfaces and each spray-coating surface when it is sprayed is larger, for example all face is all the 3D solid of convex surface, as shown in Figure 3, use in this case the spraying curve surface of workpiece formative method based on the planar chip connection layout of the present invention can obtain good effect.And, for the 3D solid with concave surface as shown in Figure 4, because its face shaping is very complicated, and need robot to there is extremely good flexibility during automatic spraying, therefore need further research.

In addition to the implementation, the present invention can also have other embodiments, and all employings are equal to the technical scheme of replacement or equivalent transformation formation, all drop in the protection domain of requirement of the present invention.

Claims (2)

1. a Control During Paint Spraying by Robot curve surface of workpiece formative method, is characterized in that, comprises the following steps:

1) curve surface of workpiece triangulation; Curved surface carries out with mathematic(al) representation, being expressed as after triangulation:

M=｛T _i:i=1,…,P｝

T wherein _ibe i triangular facet in triangle gridding, P is total number of triangle gridding intermediate cam face;

2) set maximum normal vector threshold value θ _th;

3) according to the triangular facet connection method, triangular facet is connected into to less planar chip; Described triangular facet connection method comprises the following steps:

(1) specifying any one triangular facet is initial triangular facet;

(2) find the triangular facet contiguous with initial triangular facet and be connected with initial triangular facet and be connected into a sheet;

(3) whether the sheet that judgement connects into meets the feature of planar chip;

The determination methods of the feature of planar chip is:

A. calculate the method for average vector of sheet

$\stackrel{\→}{n_a}=\frac{{\mathrm{\Σ}}_{i=1}^p{s}_i\stackrel{\→}{n_i}}{{\mathrm{\Σ}}_{i=1}^p{s}_i}/\left|\right|\frac{{\mathrm{\Σ}}_{i=1}^p{s}_i\stackrel{\→}{n_i}}{{\mathrm{\Σ}}_{i=1}^p{s}_i}\left|\right|$

Wherein, mean T _ithe normal vector of individual triangular facet, s _imean T _ithe area of individual triangular facet, P means the quantity of this curved surface triangle division Vee formation face;

B. calculate the normal vector of the maximum projection plane of sheet, i.e. the sail angle normal vector

the steps include:

Write maximum projection plane's area expression formula of slice order

solving equation draws the normal vector of maximum projection plane

C. the method for average vector of sheet with its sail angle normal vector

between angle be maximum normal vector bias angle theta _mDA,

If θ _mDA≤ θ _th, meet the feature of planar chip, confirm to connect effectively;

If θ _mDA﹥ θ _th, do not meet the feature of planar chip, it is invalid to connect, and abandons this connection;

(4) seek and being connected with this sheet all over all new triangular facets adjacent with this sheet, and the feature that whether meets planar chip is judged;

4) find and not yet connect triangular facet in blocks as new initial triangular facet, by described triangular facet connection method, triangular facet is connected into to less planar chip, until all triangular facets all connect into planar chip;

5) set up the planar chip connection layout; Concrete steps are:

(1) each planar chip on a spraying curved surface is expressed as to a node, and with a nondirectional connection layout G=(V, E) mean the topological structure of this curved surface, nondirectional connection layout G is the planar chip connection layout on this spraying curved surface, wherein, V means the node in connection layout, and E means the boundary line of the figure that this group node forms, and

(2) establish any i node v in the planar chip connection layout _ithe normal vector of represented planar chip is

the planar chip area is A _i, the maximum normal vector drift angle on planar chip is θ _mDAi, can be by node v _ibe expressed as

(3) establish e _ijfor node v _iwith node v _jlimit, ω (i, j) means limit e _ijweights, weights are the angle of the normal vector of every two, two of normal vector angle minimum sheets are the minimum limit of weights ω (i, j) in the planar chip connection layout;

Certain planar chip connection layout of setting up need to meet following characteristics:

A. a planar chip connection layout is a connected graph;

B. after the arbitrary node in a planar chip connection layout merges an other node, resulting new nondirectional connection layout remains a planar chip connection layout;

C. merging process can only merge a node in the planar chip connection layout each time;

6) according to planar chip connection layout merge algorithm, each is merged into to new larger planar chip than the facet sheet, concrete steps are:

(1) find two node (v of adjacent normal vector angle minimum in the planar chip connection layout _i, v _j);

(2) calculate limit e _ijweights ω (i, j), establish BV=2 θ _th, and judge whether ω (i, j)≤BV sets up, and if set up, enter next step, otherwise merge, stop;

(3) by node v _iwith node v _jmerge into new sheet v _ijafter, by this sheet v _ijwith mathematic(al) representation, be expressed as:

$v_{\mathrm{ij}}=v_i\⊕v_j=\{\stackrel{\→}{n_{\mathrm{pi}}},A_i,{\mathrm{\θ}}_{\mathrm{MDAi}}\}\⊕\{\stackrel{\→}{n_{\mathrm{pj}}},A_j,{\mathrm{\θ}}_{\mathrm{MDAj}}\}=\{\frac{\stackrel{\→}{n_{\mathrm{pi}}}{A}_i+\stackrel{\→}{n_{\mathrm{pj}}}{A}_j}{A_i+A_j},A_i+A_j,{\mathrm{\θ}}_{\mathrm{MDAij}}\}$

In above formula, A _iwith A _jthe area that means respectively i and j planar chip, θ _mDAijmean new sheet v _ijmaximum normal vector drift angle;

(4) judge v _ijwhether be planar chip, if, enter (5) step, otherwise make BV, be 2 initial θ _thto 3 θ _thbetween an artificial setting value, then proceed to (1) step;

(5) upgrade the planar chip connection layout and recalculate according to (1)-(4) step;

(6) in Judge plane sheet connection layout, whether all nodes all merge, if finish, otherwise forward step (1) to.

2. Control During Paint Spraying by Robot curve surface of workpiece formative method as claimed in claim 1, is characterized in that described step 2) maximum normal vector threshold value θ _thbe located between 15 °～20 °.

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