CN102500498A - Optimization method for spray gun track of spraying robot on irregular polyhedron - Google Patents

Abstract

An optimization method for a spray gun track of a spraying robot on an irregular polyhedron includes the steps: triangularly dividing each face of the polyhedron according to CAD (computer-aided design) data of a polyhedral workpiece; computing the normal vector of each triangular face; generating a plurality of large pieces by means of connection according to a topological structure between each two adjacent triangular faces; and building a 'rectangular model' and generating the spraying path of each face of the polyhedron. The variance between the actual thickness of a coating and the ideal thickness of the coating serves as an objective function, and the optimal value of the width of an overlapped area is solved by a golden section method on each surface of the irregular polyhedron. In order to improve spraying efficiency, optimization and combination of the spray gun track on a curved surface are indicated by a non-directional connection diagram, and improved particle swarm algorithm is used for solving. Therefore, spraying quality is ensured, and spraying efficiency is also improved.

Description

Optimizing method of spray coating robot spray gun track on the non-regular polyhedron

Technical field

The present invention relates in the automatic spraying process of spray robot the spray gun track optimizing method when carrying out spraying operation to the polyhedron workpiece.

Background technology

Spray robot is that equipment is produced in a kind of very important advanced application, is widely used in the paint line of products such as automobile at home and abroad.For such as products such as automobile, electrical equipment and furniture, its surperficial spraying effect has considerable influence to quality.In spraying was operated automatically, the manipulator of spray robot moved around around surface of the work to be coated with, and suitable track can both make production cost obtain practicing thrift with the selection of other procedure parameter.The spraying effect and the object surface shape of spray robot are closely related.For such as products such as automobile, electrical equipment and furniture, its surperficial spraying effect has considerable influence to quality.In the actual production, the optimization aim of spray robot spraying operation mainly contains two: the one, and the coating of surface of the work is as far as possible evenly; The 2nd, spray time is short as far as possible.Yet this two optimization aim (effect and efficient) are mutual restriction normally.How under the prerequisite that guarantees spraying effect, improve spray efficiency is one of difficult point in the spray robot track optimizing problem as far as possible.

In recent years, along with the extensive use of spray robot, Control During Paint Spraying by Robot can satisfy industrial needs basically.But because many non-regular polyhedron workpiece have appearred in the continuous development of process industry.Because polyhedral complex structure is changeable, adopt general Bezier curved surface and B-spline surface formative method to be difficult to non-regular polyhedron upper surface is handled.At present, most of spray robot track optimizing methods only are applicable to the spraying operation on two dimensional surface or the curved surface, are not suitable for the spraying operation on the three-dimensional polyhedron.The system that three-dimensional polyhedron is carried out spraying operation can't carry out track optimizing; There are shortcomings such as inefficiency, robot location and velocity control accuracy are low, spraying effect is undesirable; Thereby make face coat inhomogeneous, product can not reach higher technological level.Therefore the spray gun track optimizing design on the non-regular polyhedron workpiece is another difficult point in robot trajectory planning's problem.Publication number CN 101239346 provides a kind of optimizing method of spray coating robot spray gun track on complex-curved, and the robot in the time of can realizing that complex-curved workpiece carried out spraying operation sprays automatically, but this method is for non-regular polyhedron and inapplicable.Publication number CN101367076A provides the polygonal electrostatic spraying machine of a kind of non-regulation planar people variate spray method, but this method can only be used for two dimensional surface, can not be applied on the three-dimensional polyhedron.

Therefore, during the non-regular polyhedron workpiece of spraying, the product appearance quality can not further be promoted, and can not realize the full-automatic spraying on complicacy, the multiaspect in actual production.Still need manual work to spray after the major part of Control During Paint Spraying by Robot workpiece, time-consuming, effort, take material, and the workman still is in the hostile environment.

Summary of the invention

The present invention is just in order to address the above problem; It is a kind of special in the optimizing method of spray coating robot spray gun track on the non-regular polyhedron that purpose is to provide; Under the prerequisite that guarantees spraying effect and spray efficiency; To realize the automatic spraying of robot, satisfy the needs of actual industrial production to non-regular polyhedron.

The technical solution adopted for the present invention to solve the technical problems is: the optimizing method of spray coating robot spray gun track on the non-regular polyhedron of the present invention; Cad data input GID software with the polyhedron workpiece; Through GID grid pattern output function polyhedral each face is carried out triangle division; Calculate the normal vector of each triangular facet, connect several bigger sheets of generation, set up " cuboid model " and also generate the spraying path on each face of polyhedron according to topological structure between the adjacent triangular facet; With actual coating thickness and desired coating thickness variance is object function, on each face of non-regular polyhedron, adopts Fibonacci method to find the solution the optimal value of coating overlapping region width; For improving spray efficiency, utilize nondirectional connection layout to represent the spray gun track optimizing combination on the curved surface, and adopt improved particle cluster algorithm to find the solution.

Said generation spray gun route method is following: be the section of l along making several distances perpendicular to " cuboid model " right direction at first, promptly obtain the plurality of sections intersecting lens of section and patch; And then on intersecting lens, make distance fifty-fifty and be that one group of point of d, d are the distances of two sprayings between the path, the artificial setting of the big I of this distance or draw through computation optimization; At last these points are coupled together along " cuboid model " right direction, thereby generate the spray gun space path, wherein l gets R/2～R, and R is a spray gun spraying radius.

The said method of utilizing nondirectional connection layout to represent the spray gun track optimizing combination on the curved surface is following: with nondirectional connection layout G (V, E, R, a ω: E → Z ⁺) combination of expression spray gun track optimizing; Wherein V representes vertex set, and E representes the limit collection, and R representes any sub-set of E; ω representes that the power on limit is the length of actual spray gun track, in nondirectional connection layout G, obtains all limits of process and only through once the loop with beeline; M={d _IjBy the not set formed of the shortest track between summit i on same the limit and summit j among the figure G, and i, j=1,2 ..., n, n are the number of face of a polyhedron.

The method that adopts improved particle cluster algorithm to find the solution is following:

Step1 initialization: initialization particle position

I=1,2 ..., m; Each particle's velocity of initialization

I=1,2 ..., m; Selection speed max-thresholds ε and maximum iteration time N _Max, iterations k=0;

Step2 measure the fitness value of each particle

is expressed as

order

Step3 iteration k ← k +1; update speed

Update Location

Step4 measures z _iAdaptive value, be expressed as

Get

Upgrade

With

Step5 if

And k＜N _Max, then jump to Step3; If k>=N _Max, circulation stops, output result of calculation.

The present invention has very strong practicality, can realize the robot of non-regular polyhedron workpiece is sprayed automatically, can improve the quality of spray robot operating efficiency and product.

Description of drawings

Fig. 1 cuboid model sketch map;

Spray gun space path sketch map on any face of Fig. 2 polyhedron;

Spraying sketch map on Fig. 3 plane;

The nondirectional connection layout of Fig. 4.

The specific embodiment

Below in conjunction with accompanying drawing and embodiment the present invention is further specified.Implementation step of the present invention is made up of the generation of spray coating robot spray gun space path on the polyhedron, the spray gun track optimizing on each face of polyhedron, spray gun track optimizing combination three parts, and the specific embodiment is following.

The generation of spray coating robot spray gun space path on 1 polyhedron

Spray coating robot spray gun space path concrete steps are following on the polyhedron:

(1) confirms non-regular polyhedron by the workpiece cad model; After in GID7.2 software, importing non-regular polyhedron CAD figure; Through GID grid pattern output function, obtain the triangle gridding figure (allowable error 2mm, each grid is called triangular facet or triangular plate) of non-regular polyhedron.Polyhedral each face carries out can being expressed as with mathematic(al) representation after triangle gridding is divided:

M＝{T _i：i＝1，...，M} (1)

Here T _iBe i the triangular facet (sheet) in the triangle gridding, M is total number of triangle gridding intermediate cam face.

(2) calculate the normal vector of each triangular facet, connect according to topological structure between the adjacent triangular facet and generate several bigger sheets.After supposing to spray along the optimization spraying profile on the plane, average coating layer thickness does

Certain any maximum coating layer thickness does on the whole plane

Certain any minimum cover thickness does

The maximum angle of establishing the normal vector of normal vector and each face projection plane on each face again is β _Th(only considering that the normal vector of the two points to the homonymy of each face), then the coating layer thickness q on any point s on any face of polyhedron _sPossible scope is:

${\stackrel{\‾}{q}}_{\min }\cos \left({\mathrm{\β}}_{\mathrm{th}}\right)\≤q_s\≤{\stackrel{\‾}{q}}_{\max }---\left(2\right)$

If the coating layer thickness on any 1 s on the face satisfies:

$|q_s-{\stackrel{\‾}{q}}_d|\≤q_w---\left(3\right)$

Wherein, q _wFor allowing maximum coating layer thickness deviation.So,

${\stackrel{\‾}{q}}_{\max }-q_d\≤q_w---\left(4\right)$

$q_d-{\stackrel{\‾}{q}}_{\min }\cos \left({\mathrm{\β}}_{\mathrm{th}}\right)\≤q_w---\left(5\right)$

If formula (4) is set up all the time, then can obtain β according to formula (5) _ThThis that is to say, for any face on the polyhedron, if the maximum angle β of the normal vector on the face and its projection plane satisfies β≤β _Th, then certain any coating layer thickness just can satisfy formula (3) on this face.Obtaining β _ThAfter, can generate each sheet of any face on the polyhedron.The step that each triangular facet connects into an integrated piece is following:

1. specifying any triangular facet is initial triangular facet.

2. search out from initial triangular facet central point distance all triangular facets less than spray gun spraying radius.

3. calculate the normal vector of all triangular facets of 2. finding in the step and the angle of initial triangular facet normal vector, if angle is less than β _Th, then this triangular facet is connected with initial triangular facet.

4. searching does not connect triangular facet in blocks as yet as new initial triangular facet, repeats 2., 3. goes on foot, and all connects in flakes up to all triangular facets.

Behind any face burst of polyhedron, certain a slice wherein can be expressed as:

S in the formula _iRepresent the i sheet, With

Be the normal vector of j triangular facet and k triangular facet, D (T _j, T _k) distance of expression i triangular facet and k triangular facet central point.Thus, any face of polyhedron will be divided into perhaps some of a slices.

(3) on each sheet, set up " cuboid model ", and generate the spray gun path on each sheet.On certain a slice, setting up shown in the accompanying drawing 1 " cuboid model "." cuboid model " is a cuboid that comprises whole sheet just, and it mainly has following two attributes: (i) its preceding extreme direction is in the opposite direction with the normal vector of whole sheet; (ii) the rectangular area of its each face is all minimum as much as possible.In order to generate the spray gun path; At first be the section of l (it is spray gun spraying radius that l gets

R usually), can obtain the plurality of sections intersecting lens of section and patch along make several distances perpendicular to " cuboid model " right direction; And then on intersecting lens, make fifty-fifty apart from being one group of point of d; At last these points are coupled together along " cuboid model " right direction, thereby generate spray gun space path (shown in accompanying drawing 2).

Spray gun track optimizing on each face of 2 polyhedrons

Shown in the accompanying drawing 3 is the spraying process on the plane.R representes to spray radius among the figure, and v representes the spray gun translational speed, and d is expressed as the coating overlapping region width of two spraying strokes; X representes to spray the distance of interior certain 1 s of radius to article one path; S ' is a spray gun central projection point for the projection of s point on the path, O point, and the coating layer thickness of then putting s is:

$q_s\left(x\right)=\left\{\begin{array}{cc}{q}_1\left(x\right)& 0\&le;x\&le;R-d\\ q_1\left(x\right)+q_2\left(x\right)& R-d<x\&le;R\\ q_2\left(x\right)& R<x\&le;2R-d\end{array}\right.---\left(7\right)$

q ₁(x) and q ₂The coating layer thickness that s is ordered when (x) representing respectively to spray on two adjacent path, q ₁(x) and q ₂(x) computing formula is:

$q_1\left(x\right)=2{\&Integral;}_0^{t_1}f\left(r_1\right)\mathrm{dt},$ 0≤x≤R； $q_2\left(x\right)=2{\&Integral;}_0^{t_2}f\left(r_2\right)\mathrm{dt},$ R-d≤x≤2R-d (8)

Wherein, $t_1=\sqrt{R^2-x^2}/v;$ $t_2=\sqrt{R^2-{(2R-d-x)}^2}/v$

$r_1=\sqrt{{\left(\mathrm{vt}\right)}^2+x^2};$ $r_2=\sqrt{{\left(\mathrm{vt}\right)}^2{(2R-d-x)}^2}$

t ₁And t ₂Represent half the at s point spray time of spray gun on two adjacent spraying paths respectively; r ₁And r ₂The distance of representing s o'clock to two the spray gun central projection point on the adjacent spraying path respectively; T is spray gun moves to a s ' from an O time.By (8) Shi Kede:

$q_s(x,d,v)=\frac{1}{v}J(x,d)---\left(9\right)$

Wherein J is the function of x and d.In order to make surface coating thickness even as far as possible, getting actual coating thickness and the variance between the desired coating thickness that s orders is the optimization aim function:

$\underset{d\&Element;[0,R],v}{\min }{E}_1(d,v)={\&Integral;}_0^{2R-d}{(q_d-q_s(x,d,v))}^2\mathrm{dx}---\left(10\right)$

Q in the formula _dBe desired coating thickness.Because maximum coating layer thickness q _MaxWith minimum cover thickness q _MinDetermined the uniformity of coating layer thickness on the surface of the work, therefore, q _MaxAnd q _MinAlso need be optimized:

$\underset{d\&Element;[0,R],v}{\min }{E}_2(d,v)={(q_{\max }-q_d)}^2+{(q_d-q_{\min })}^2---\left(11\right)$

Can get by formula (9), (10), (11):

$\underset{d\&Element;[0,R],v}{\min }E(d,v)=\frac{1}{2R-d}{E}_1(d,v)+E_2(d,v)---\left(12\right)$

By (7) formula, maximum coating layer thickness and minimum cover thickness expression formula can be written as again:

$q_{\max }=\frac{1}{v}{J}_{\max }\left(d\right),$ $q_{\min }=\frac{1}{v}{J}_{\min }\left(d\right)---\left(13\right)$

Make

can get by formula (8), (12), (13):

$v=\frac{\frac{1}{2R-d}{\&Integral;}_0^{2R-d}{J}^2(x,d)\mathrm{dx}-J_{\max }^2\left(d\right)-J_{\min }^2\left(d\right)}{q_d[\frac{1}{2R-d}{\&Integral;}_0^{2R-d}J(x,d)\mathrm{dx}+J_{\max }\left(d\right)+J_{\min }\left(d\right)]}$

Find out that thus spray gun speed v can be expressed as the function of d, therefore, (d, minimum of a value v) is only relevant with d for E.Can adopt Fibonacci method to obtain the d optimal value, thereby can obtain the optimization track on each face on the non-regular polyhedron.

Spray gun track optimizing combination on the 3 non-regular polyhedrons

Be the simplification problem, regard the track on each dough sheet on the non-regular polyhedron as a limit.As shown in Figure 4, available nondirectional connection layout G (V, E, R, a ω: E → Z ⁺) (wherein V representes vertex set to the combination of expression spray gun track optimizing for Tool Trajectory OptimalIntegration, TTOI) problem, and E representes the limit collection, and R representes any sub-set of E, and ω representes the power (length of actual spray gun track) on limit.The TTOI problem is exactly to obtain all limits of process among the G and only through once the loop with beeline at figure.If M={d _Ij(i, j=1,2 ..., n) by the not set formed of the shortest track between summit i on same the limit and summit j among the figure G, and the shortest distance matrix between each summit can use the Floyd algorithm to calculate.That shown in Figure 2 is a connection layout G that 5 limits are arranged, and solid line is represented the limit among the figure, and dotted line is represented from a summit to other any tracks on the summit on same limit not.

Because spray coating robot spray gun track combinatorial problem self is used particle cluster algorithm and is compared with other optimized Algorithm, is easy to realize, do not have a lot of parameters to need adjustment, and do not need gradient information, be the effective tool that solves the optimum organization problem.In the algorithm, each individuality is a particle, and each particle is being represented potential separating.If z _i=(z _I1, z _I2..., z _ID) be the D dimension position vector of i particle, calculate z according to fitness function _iCurrent adaptive value can be weighed the quality of particle position, is fitness function and can choose calculating spray gun path length minimum of a value in the TTOI problem.v _i=(v _I1, v _I2..., v _ID) be the flying speed of particle i, i.e. the distance that moves of particle; p _i=(p _I1, p _I2..., p _ID) optimal location that searches up to now for particle; p _g=(p _G1, p _G2..., p _GD) optimal location that searches up to now for whole population.In each iteration, particle can be according to following formula renewal speed and position:

$v_{\mathrm{id}}^{k+1}=v_{\mathrm{id}}^k+c_1{r}_1(p_{\mathrm{id}}-z_{\mathrm{id}}^k)+c_2{r}_2(p_{\mathrm{gd}}-z_{\mathrm{id}}^k)$

$z_{\mathrm{id}}^{k+1}=z_{\mathrm{id}}^k+v_{\mathrm{id}}^{k+1}$

Wherein, i=1,2 ..., m, d=1,2...D, r ₁And r ₂Be the random number between [0,1], c ₁And c ₂Be the study factor.

Thus, the particle cluster algorithm step of TTOI problem is:

The Step1 initialization.The initialization particle position

I=1,2 ..., m; Each particle's velocity of initialization

I=1,2 ..., m; Selection speed max-thresholds ε and maximum iteration time N _Max, iterations k=0.

Step2 measure the fitness value of each particle

is expressed as

order

Step3 iteration k ← k +1; update speed

Update Location

Step4 measures z _iAdaptive value, be expressed as

Get

Upgrade With

Step5 if And k＜N _Max, then jump to Step3; If k>=N _Max, circulation stops, output result of calculation.

Claims (4)

1. the optimizing method of spray coating robot spray gun track on the non-regular polyhedron; It is characterized in that cad data input GID software with the polyhedron workpiece; Through GID grid pattern output function polyhedral each face is carried out triangle division; Calculate the normal vector of each triangular facet, connect several bigger sheets of generation, set up " cuboid model " and also generate the spraying path on each face of polyhedron according to topological structure between the adjacent triangular facet; With actual coating thickness and desired coating thickness variance is object function, on each face of non-regular polyhedron, adopts Fibonacci method to find the solution the optimal value of coating overlapping region width; For improving spray efficiency, utilize nondirectional connection layout to represent the spray gun track optimizing combination on the curved surface, and adopt improved particle cluster algorithm to find the solution.

2. according to the optimizing method of spray coating robot spray gun track on the right 1 described non-regular polyhedron; It is characterized in that: said generation spray gun route method is following: at first be the section of l along make several distances perpendicular to " cuboid model " right direction, promptly obtain the plurality of sections intersecting lens of section and patch; And then on intersecting lens, make fifty-fifty apart from being one group of point of d; At last these points are coupled together along " cuboid model " right direction; Thereby generate the spray gun space path, wherein l gets R/2～R, and R is a spray gun spraying radius; D is two distances between the spraying path, and the big I of this distance is artificial to be set or draw through computation optimization.

3. according to the optimizing method of spray coating robot spray gun track on the right 1 described non-regular polyhedron; It is characterized in that: the said method of utilizing nondirectional connection layout to represent the spray gun track optimizing combination on the curved surface is following: with a nondirectional connection layout G (V; E, R, ω: E → Z ⁺) combination of expression spray gun track optimizing; Wherein V representes vertex set, and E representes the limit collection, and R representes any sub-set of E; ω representes that the power on limit is the length of actual spray gun track, in nondirectional connection layout G, obtains all limits of process and only through once the loop with beeline; M={d _IjBy the not set formed of the shortest track between summit i on same the limit and summit j among the figure G, and i, j=1,2 ..., n, n are the number of face of a polyhedron.

4. according to the optimizing method of spray coating robot spray gun track on right 1 and the right 3 described non-regular polyhedrons, it is characterized in that the method that adopts improved particle cluster algorithm to find the solution is following:

Step1 initialization: initialization particle position

I=1,2 ..., m; Each particle's velocity of initialization

I=1,2 ..., m; Selection speed max-thresholds ε and maximum iteration time N _Max, iterations k=0;

Step2 measure the fitness value of each particle

is expressed as

order

Step3 iteration k ← k +1; update speed

Update Location

Step4 measures z _iAdaptive value, be expressed as

Get Upgrade

With

Step5 if

And k＜N _Max, then jump to Step3; If k>=N _Max, circulation stops, output result of calculation.

Images