CN103394430B - A kind of complex-curved even application manufacture method based on blind area Optimization Technology between sheet - Google Patents
A kind of complex-curved even application manufacture method based on blind area Optimization Technology between sheet Download PDFInfo
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Abstract
The invention discloses a kind of complex-curved even application manufacture method based on blind area Optimization Technology between sheet, first according to the geometry of workpiece and topological characteristic, burst is carried out to STL model, original workpiece curved surface is divided into some simple almost plane sub-pieces and processes respectively; Then according to spray gun spraying forming model and corresponding process producing index, the crucial spray parameters such as the translational speed of Optimization Solution spray gun and stroke span, to generate the spraying path in sub-pieces; Again by extracting the direct of travel of position relationship between each adjacent sub-pieces edge and spray gun, adopt the numerical model of the method establishment even application of block sampling respectively for several frequently seen typical blind area situation; Finally unified employing genetic algorithm is optimized spraying path, blind area and solves.Present invention saves coating and human cost, thus be conducive to the benefit improving spraying production, there is good using value and economic outlook.
Description
Technical field
The present invention relates to the advanced manufacturing industry technical field of spray robot, particularly relate to a kind of spraying manufacture method based on blind area Optimization Technology between sheet for complex part curved surface.
Background technology
Traditional spraying operation carries out hand spray mainly through spraying workman pistol to be completed, and its coating quality is easily subject to the impact spraying workman's experience, mood etc., is difficult to keep stable.In painting environments, easily a large amount of harmful gas of volatilization can have a strong impact on the physical and mental health of spraying workman simultaneously.And spray robot as in Fundamentals of Robot Techniques in conjunction with the advanced coating equipment that spraying coating process grows up, can not by the impact of painting environments, by the spraying operation of different workpieces of having programmed, ensure the uniformity of coating quality, reduce the loss of coating, thus greatly improve spray efficiency, reduce the production cost of product, be therefore widely used in the spraying operation of the products such as boats and ships, space flight, automobile, household electrical appliances.
The application of early stage spray robot mainly adopts the mode of " teaching-reproduction " to carry out, this mode is simple and easy to realize, but also there is the shortcoming that some are difficult to overcome: the 1) experience of coating quality heavy dependence spraying workman, the spray gun track generated is difficult to combine with the parameter such as workpiece shapes, Spray gun model, is difficult to obtain best spraying profile; 2) in the process of teaching, spray robot is in the stage of stopping production for a long time, reduces production efficiency; 3) artificial teaching needs, through carrying out repeated spraying experiment, to waste a large amount of coating, improve production cost, particularly seeming especially obvious when spraying large-scale workpiece; 4) technical staff is in poisonous environment all the time in teaching process, has a strong impact on that it is healthy.For the familiar lacunas of these conventional spray paint robots, current industry starts to explore computer software and hardware platform and corresponding virtual reality technology to realize the off-line trajectory planning of spray robot, thus automatically can generate optimum spraying profile when not needing actual robot to participate in, to improve coating quality and spray efficiency.
But, the off-line method for planning track of current spray robot remains in certain difficulty in actual applications, be mainly reflected in: existing off-line method for planning track is often developed for certain specific paint application, its applicable surface is restricted, lack a kind of can for the versatility spraying method of complex part with arbitrary surface shape, particularly lack for some common such as limit, the intelligent processing method in the specific spray blind areas such as angle or dead band, cause the product quality produced not good, defect ware is more, the a large amount of manpower and materials of cost are needed to do further micronization processes, thus become the bottleneck problem of restriction spray robot manufacturing industry productivity ratio raising.
Summary of the invention
The object of the invention is the deficiency in order to overcome the existing off-line trajectory planning techniques of above-mentioned spray robot, provide a kind of complex-curved even application manufacture method based on blind area Optimization Technology between sheet, this method can carry out automatic path planning generation for the various complex part curved surface with different surfaces shape, there is good adaptability and comparatively wide application surface, and efficiently solve several typical limit, blind area, angle coating quality problem not up to standard, improve uniformity performance indications and the spraying production efficiency of integral spray, save production cost.
The technical solution used in the present invention is: a kind of complex-curved even application manufacture method based on blind area Optimization Technology between sheet, comprise the following steps: first according to the geometry of workpiece and topological characteristic, burst is carried out to STL model, original workpiece curved surface is divided into some simple almost plane sub-pieces and processes respectively; Then according to spray gun spraying forming model and corresponding process producing index, the crucial spray parameters such as the translational speed of Optimization Solution spray gun and stroke span, to generate the spraying path in sub-pieces; Again by extracting the direct of travel of position relationship between each adjacent sub-pieces edge and spray gun, adopt the numerical model of the method establishment even application of block sampling respectively for several frequently seen typical blind area situation; Finally unified employing genetic algorithm is optimized spraying path, blind area and solves.Its concrete steps comprise:
(1) importing of workpiece and complex-curved burst process: first carry out sub-pieces division based on physical dimension, emphasis considers the degree of crook of surface of the work, adopts twoly to deviate from the curved surface that complex part curved surface is divided into almost plane one by one by angle algorithm; Next is on the basis that physical dimension divides, and in conjunction with the topological property of workpiece, adopts sciagraphy it to be split further, is divided into the simple curve surface of workpiece of topological structure, so that process workpiece exists the situation of hole.
(2) the spraying coordinates measurement in sub-pieces: according to set up coating cumulative speed model, expect that thickness and coating uniformity are for hybrid optimization target with coating, set up corresponding Optimized model, then adopt golden section search to solve and obtain spraying rate and stroke span, spraying profile point in the simple sub-pieces adopting the acquisition of bounding box projecting method to optimize on this basis.
(3) numerical modeling in blind area spraying path between sheet: the finite element processing method adopting block sampling, for have arbitrarily angled relation adjacent external surfaces, there is the adjacent inner surface of vertical relation and there is three kinds, the inner corners region blind area situation of vertical relation, according to sub-pieces border and spray gun track, divide several situation: parallel-parallel, parallel-vertical and vertical-vertically to set up respectively and evenly optimize numerical model.
(4) Optimization Solution of blind area spray gun track: according to the spray gun track Optimized model set up, determines that the gene of each individuality is the spray gun track parameter needing to optimize, composition chromosome; Set up fitness function according to coating layer thickness, then adopt genetic algorithm for solving spray gun track Optimized model.
Beneficial effect: compared with prior art, the present invention compensate for the deficiencies in the prior art, provide a kind of complex-curved even application manufacture method based on blind area Optimization Technology between sheet, automatic coating Track Pick-up can be carried out for any complex part curved surface, and carry out corresponding optimization process for common spraying blind area, thus improve spraying uniformity, enhance coating quality, reach the target optimizing spraying, meet the requirement that different spraying is produced.
Accompanying drawing explanation
Fig. 1 is: based on the complex-curved even application schematic flow sheet of blind area Optimization Technology between sheet;
Fig. 2 is: geometry burst flow chart;
Fig. 3 is: projection approximation slicing algorithm schematic diagram;
Fig. 4 is: Fibonacci method solves optimum travel parameters flow chart;
Fig. 5 is: OBBs algorithm flow chart;
Fig. 6-8 is: position relationship schematic diagram between sub-pieces;
Fig. 9 is: spray gun track is parallel-parallel schematic diagram;
Figure 10 is: spray gun track is vertical-parallel schematic diagram;
Figure 11 is: spray gun track is vertical-vertical schematic diagram;
Figure 12 is: genetic algorithm flow chart.
Detailed description of the invention
Below in conjunction with the drawings and specific embodiments, the present invention will be further described.
Fig. 1 is the complex-curved even application manufacture method based on blind area Optimization Technology between sheet that the present invention proposes.As shown in the figure, comprise the following steps:
1, the importing of workpiece and complex-curved burst process
1) workpiece STL model imports:
The importing of part model mainly completes selects part model file from part model storehouse, and whether the form judging file is STL form.If so, then direct file reading, and be presented in the left side tree that the present invention develops software, otherwise be converted to the file of STL form, then part model is imported.
2) geometry burst:
According to the STL part model imported, its sprayed surface adopts triangle to be similar to.Define angle between adjacent two sub-pieces for deviating from angle, carry out the geometric properties (i.e. the curvature of curved surface) of approximate surface of the work thus, thus employing deviates from based on the two of region growing the Preliminary division burst that angle slicing algorithm completes surface of the work, as shown in Figure 2, two concrete steps deviating from angle algorithm are as follows:
The first step: β is set
thand β
maxtwo threshold parameters;
Second step: obtain the triangle T that area is maximum
seedsub-pieces S is built as seed triangle
i;
3rd step: choose S
iany one adjacent sub-pieces T
jif adjacent sub-pieces cannot be found, then turn the 6th step, otherwise deviate from angle β both calculating
ij;
4th step: if β
ijbe less than and maximumly deviate from angle β
th, then the 5th step is turned; Otherwise turn second step;
5th step: calculate T
jwith S
ithe angle of interior all triangular facets, tries to achieve maximum.If this maximum is less than β
max, then by T
jbe incorporated to S
i, otherwise turn second step;
6th step: if all sub-pieces divide complete, then algorithm terminates, otherwise turns second step.
3) topological burst:
Curved surface topology burst is mainly in order to solve in curved surface the problem that there is hole or forbid spraying area.By curved surface topology burst, curved surface is divided into and there is no hole and the simple sub-pieces of topological structure, thus can coating be saved, reduce spraying cost, avoid forbidding that spraying area is affected.As shown in Figure 3, concrete steps are as follows for Slicing procedure:
The first step: curved surface is projected in the other direction along its method of average vector, is converted into two dimensional surface.
Second step: key point is carried out to free form surface border and is similar to, be converted to shape changeable.
3rd step: after acquisition approximate polygon, whether be included within outer boundary according to the borderline point of hole and border is judged, obtain outer boundary and hole;
4th step: each article of boundary sections extending approximate polygon inner and outer boundary, is divided into unit polygon (i.e. unit sheet) one by one by polygon;
5th step: after acquisition unit sheet, adjacent side figure being set up to each unit sheet, different characteristics can be considered emphatically by setting different systems.Each unit sheet is combined into satisfactory sub-pieces by the principle the smaller the better according to fitness;
6th step: the burst result on perspective plane is mapped back former curved surface, obtains final burst result.
2, the spraying coordinates measurement in sub-pieces
The spray gun spraying path that sub-pieces trajectory planning is exactly geometric properties according to sub-pieces, spraying model and spraying parameter etc. determine to reach spraying effect.First to set up the spraying profile Optimized model in each sub-pieces for optimization aim with spraying coating process requirement, then adopt the Numerical Methods Solve such as Fibonacci method to be optimized the key parameter of track, finally adopt the travel paths that bounding box projecting method obtains in each sub-pieces.Concrete steps are as follows:
(1) derivation of multiple-pass coating layer thickness Accumulation Model
Because Spray gun model is constant in spraying process, the speed simultaneously sprayed also is constant, therefore on any one cross section between stroke, its coating distribution situation is also identical.Therefore can only discuss to single cross section.The then coating layer thickness of arbitrfary point between stroke, by this point apart from the analysis of distance more closely spraying path, must the coating layer thickness Accumulation Model of this point.
(2) Optimization Modeling of travel parameters
The coating layer thickness of arbitrfary point s is except outside the Pass having with model itself, only relevant with stroke span d with the movement speed v of spray gun, so just can set up the optimization problem of v and d.When considering spraying effect, with the expectation thickness of coating and thickness evenness, for target, to set up optimization object function as follows:
After establishing optimization problem, adopt golden cut algorithm to carry out optimizing to d and v, its flow chart as shown in Figure 4.
(3) generate based on spraying profile in the sub-pieces of bounding box sciagraphy
According to stroke key parameter v and d that optimizing obtains, adopt bounding box sciagraphy to generate spraying profile in sub-pieces, this algorithm utilizes the outsourcing box of curved surface to carry out trajectory planning, and its flow process as shown in Figure 5.Step is as follows:
The first step: the method for average vector n asking for spraying surface of the work S, at the opposite direction n of method of average vector n
pupper structure plane P
1, by each point on surface of the work along vector n
pproject to plane P
1on, obtain subpoint S set
2;
Second step: for point set S
2, ask for its minimum outer rectangular, by this rectangle in vector n
pdirection stretches and obtains minimum outsourcing rectangle.Two vertical edges of definition rectangle are respectively R, F; Definition R place, limit plane is RIGHT plane, and F place, limit plane is FRONT plane;
3rd step: the length comparing R, F, otherwise assuming that R>F(in like manner), then choosing RIGHT plane is the plane of reference, set up cluster distance for d(stroke span) parallel plane, here to get RIGHT plane be the object of the plane of reference is ensure that spray gun stroke is minimum, i.e. the least number of times of turning round of spray gun on path;
4th step: the size comparing R, F, supposes F>R here, now still getting RIGHT plane is the plane of reference.Then with RIGHT plane for reference planes, set up one group of plane, the distance now between plane is no longer stroke span d, can be arbitrary value, and distance less precision higher;
5th step: utilize the bundle of planes of generation and curve surface of workpiece to ask for intersection, according to path forms spacing d, some sections are divided into for each intersection, thus constitute many sampled points;
6th step: connect by the direction perpendicular to RIGHT plane sampled point, forms independent stroke.These independent strokes then form the incident point path of spray gun on curved surface, fix and the hypothesis of lance ejection direction perpendicular to surface of the work according to spray gun height, can push away to obtain the attained pose of spray gun further;
7th step: to adopting semicircle migration path to connect between each stroke, thus form the complete spraying profile in each sub-pieces.
3, the numerical modeling in blind area spraying path between sheet
For adjacent area between sheet, owing to there is no the spraying impact considered each other in spraying process above, often cause the coating quality in this region not good, easily there is overweight coating or excessively thin, therefore the spraying blind area of spray robot is called as, often need through artificial after-treatment, thus become the crucial problem of the restriction Control During Paint Spraying by Robot quality of production.Contemplated by the invention the Automatic Optimal problem of spray gun track between sheet, three kinds of situations are mainly divided into improve related sputtering processes: the spray gun track optimization in the inner corners region that the spray gun track optimization with any acute angle relation adjacent external surfaces, the spray gun track optimization of two adjacent inner surface with vertical relation and three adjacent inner surface with vertical relation are formed, as shown in figs 6-8.Basic ideas first adopt the method for sampling based on finite element theory to set up spraying Optimized model, thus be optimized adjustment to the spraying path of blind area.The spraying Optimization Modeling of various situation is as follows respectively:
(1) there is the spray gun track optimization of any acute angle relation adjacent external surfaces
After complex-curved burst, obtain two adjacent outer surfaces, as shown in Figure 6.According to the relation between spray gun track and sub-pieces border, the spray gun track optimization problem of adjacent external surfaces is converted into parallel-parallel, parallel-vertical, vertical-vertical three kinds of situations and is discussed, set up spray gun track Optimized model respectively.Setting up in Optimized model process, suppose that spray gun gait of march v in each sub-pieces and stroke span d remains unchanged, spray gun is respectively a, b at the major and minor axis of the oval spraying area that surface of the work is formed.
1) spray gun track Optimization Modeling when spray gun track is parallel-parallel with the position relationship on border
As Fig. 9, suppose that sheet 1 is β with the angle of sheet 2, spray gun track is h to the distance on border, the optimization of the spray gun track then between two panels can be converted into the coating layer thickness optimization in the cross section of any side, border, now two panels intersection any point p (x, y), then now the coating layer thickness of p point can be expressed as:
q
p(y,h)=q(y)+q(h+(h-y)cosβ)cosβ(2)
According to formula (2), then can calculate the coating layer thickness of any point p, then layer thickness uniformity can be expressed as:
Wherein q
drepresent and expect coating layer thickness.
2) spray gun track Optimization Modeling when spray gun track is parallel-vertical with the position relationship on border
As can be known from Fig. 10, according to the symmetry of coating layer thickness distribution, highlight regions is the characteristic area that can represent the coating layer thickness distribution of both sides, border, and coating layer thickness and the highlight regions in other regions are similar.By the spray gun track segmentation of vertical end, set up rectangular coordinate system as shown in the figure.As we know from the figure, suppose that the spray gun track on sheet 1 is d apart from the distance on border
1, the distance on the spray gun track distance border on sheet 2 is d
2, the p (x, y) of highlight regions any point in figure, the angle between sub-pieces is β.
By Modling model, the coating cumulative thickness q of spray gun track in a p (x, y) in the sheet 1 that is easy to get
1the coating cumulative thickness q of spray gun track in a p (x, y) in (x, y) and sheet 2
2(y
1), wherein y
1represent the distance of some p to the spray gun track of sheet 2 end.Then can obtain the coating cumulative thickness of highlighted characteristic area any point p (x, y), be shown below:
Now spray gun track optimization problem can be modeled as:
Wherein v=(v
0..., v
i+j-1), qd represents expectation coating layer thickness, and d represents stroke span.
3) spray gun track Optimization Modeling when spray gun track is vertical-vertical with the position relationship on border
According to the symmetry of coating layer thickness distribution, choose the object of characteristic area wherein as spray gun track Optimization Modeling, as shown in highlight regions in Figure 11, the coating layer thickness distribution in other regions is similar with the coating layer thickness of highlight regions.According to symmetry, spray gun track 1 is equal to the distance on border with spray gun track 2, and be set to h, the angle between two panels is β.
Spray gun track 1 p point coating layer thickness accumulation and 2) in identical.Spray gun track 2 pairs of p (x, y) are put coating layer thickness impact and are tried to achieve by segmentation in such as Figure 11, are designated as q
2(x, y).Then in characteristic area, the coating layer thickness of any point p (x, y) is:
q
p(x,y)=q
1(x,y)+q
2(x,y)cosβ(6)
Now spray gun track optimization problem can be expressed as:
Wherein v=(v
0..., v
i+j-1), q
drepresent and expect coating layer thickness, d represents stroke span.
(2) there is the spray gun track optimization problem modeling of two adjacent inner surface of vertical relation
For the spray gun track optimization of adjacent inner surface with vertical relation, now β=90o, equally according to the position relationship between spray gun track and sub-pieces border, be divided into parallel-parallel, parallel-vertical, vertical-vertical three kinds of situations, set up Optimized model respectively.
1) spray gun track is parallel-parallel
When spray gun track position relationship is parallel-parallel, mutually vertical between shown sub-pieces, as Fig. 7.Its modeling analysis process is the same when being parallel-parallel with the spray gun track of outer surface, and suppose that spray gun track is h to the distance on border, now two panels intersection any point p (x, y), then now the coating layer thickness of p point can be expressed as:
q
p(y,h)=q(y)+q(2h-y)(8)
Then coating layer thickness Optimized model as the formula (3).
2) spray gun track is parallel-vertical
When spray gun track position relationship is parallel-vertical, mutually vertical between shown sub-pieces, as Fig. 7.Its optimization method is also carry out segmentation to vertical end spray gun track, consistent with outer surface analytical method, is discussed in two kinds of situation: one be p in sheet 1, two is that p point is in sheet 2.To try to achieve in two kinds of situation bottom sheet 1 spray gun track respectively at the coating layer thickness q of p point
1the coating cumulative thickness q of spray gun track in a p in (x, y) and sheet 2
2(y
1), wherein y
1=d
1+ d
2+ h-y.So the coating layer thickness of p point can be expressed as:
q
p(x,y)=q
1(x,y)+q
2(d
1+d
2+h-y)(9)
Then coating layer thickness Optimized model as the formula (5).
3) spray gun track is vertical-vertical
When spray gun track position relationship is vertical-vertical, mutually vertical between shown sub-pieces, as Fig. 7.Its optimization method is also carry out segmentation to vertical end spray gun track, consistent with outer surface analytical method.To try to achieve in sheet 1 spray gun track respectively at the coating layer thickness q of p point
1the coating cumulative thickness q of spray gun track in a p in (x, y) and sheet 2
2(x, y).The coating layer thickness then putting p is accumulated as:
q
p(x,y)=q
1(x,y)+q
2(x,y)(10)
Then coating layer thickness Optimized model as the formula (7).
The spray gun track Optimization Modeling in the inner corners region that (3) three adjacent inner surface with vertical relation are formed
Three spraying workpiece with the adjacent inner surface of vertical relation are workpiece common during actual spraying is produced, as shown in Figure 8, " dead band " that this workpiece three adjacent inner surface are formed is the difficult point of spraying, the spraying effect of spray robot is often not ideal enough, need to be optimized spray gun track, to improve coating quality.For this kind of situation, the thinking taked herein is substep track optimizing, first the spray gun track between orthogonal any two inner surfaces is optimized according to the modeling method provided in (2), in this, as an entirety, optimize the spray gun track between the 3rd vertical plane, thus improve the coating quality in " dead band ", spray gun track is optimized.
4, the Optimization Solution of blind area spray gun track
According to spray gun track Optimized model, be optimization aim, set up genetic algorithm for solving with layer thickness uniformity, as Figure 12, its concrete solution procedure is as follows:
The first step: according to the spray gun track Optimized model set up, determines that the gene of each individuality is the spray gun track parameter (spray gun gait of march and stroke span) needing to optimize, composition chromosome;
Second step: determine fitness function, shown in 3,5,7, asks for minimum of a value.
3rd step: determine population scale, and initialize population.Be all real number according to the variable needing herein to be optimized, take real coding herein, the population scale of setting is 100, utilizes random fashion to produce first generation population according to the excursion of variable.
4th step: the fitness value calculating each individuality in population, select the individuality that wherein fitness is high to carry out cross and variation operation, the selection strategy taked herein is roulette.
5th step: the individuality high according to the fitness selecting to obtain, carries out cross and variation operation, to obtain population of future generation.The crossover probability arranged herein is 0.8, and mutation probability is 0.2, once the probability of variation is too high will cause the unstability of population.
6th step: judge whether population meets end condition, otherwise return the 4th step according to the new population produced.The end condition arranged herein is | f
i-f
i+1| <1e-6, otherwise return, until meet the demands.
It should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.The all available prior art of each part not clear and definite in the present embodiment is realized.
Claims (1)
1., based on a complex-curved even application manufacture method for blind area Optimization Technology between sheet, it is characterized in that: comprise the following steps:
(1) first carry out sub-pieces division based on physical dimension, emphasis considers the degree of crook of surface of the work, and employing is two deviates from the curved surface that complex part curved surface is divided into almost plane one by one by angle algorithm; Next is on the basis that physical dimension divides, and in conjunction with the topological property of workpiece, adopts sciagraphy it to be split further, is divided into the simple curve surface of workpiece of topological structure, so that process workpiece exists the situation of hole;
(2) according to set up coating cumulative speed model, expect that thickness and coating uniformity are for hybrid optimization target with coating, set up corresponding Optimized model, then adopt golden section search to solve and obtain spraying rate and stroke span, spraying profile point in the simple sub-pieces adopting the acquisition of bounding box projecting method to optimize on this basis;
(3) by extracting the direct of travel of position relationship between each adjacent sub-pieces edge and spray gun, respectively for the spray gun track optimization with any acute angle relation adjacent external surfaces, there is the typical blind area situation that spray gun track optimization in the inner corners region that the spray gun track optimization of two adjacent inner surface of vertical relation and three adjacent inner surface with vertical relation are formed etc. three kinds is common, according to sub-pieces border and spray gun track, divide several situation: parallel-parallel, parallel-vertically with vertical-vertical, adopt the block sampling method based on finite element theory to set up spraying respectively and optimize numerical model, thus adjustment is optimized to the spraying path of blind area,
(4) according to the spray gun track Optimized model set up, determine that the gene of each individuality is the spray gun track parameter needing to optimize, composition chromosome; Set up fitness function according to coating layer thickness, then adopt genetic algorithm for solving spray gun track Optimized model.
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| CN101239346A (en) * | 2008-03-10 | 2008-08-13 | 江苏大学 | Optimizing method of spray coating robot spray gun track on complex curved surface |
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| CN102909148A (en) * | 2012-08-13 | 2013-02-06 | 东南大学 | Spraying path automatic generating method for adaptive modeling of multiple spray guns |
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2013
- 2013-08-15 CN CN201310355020.6A patent/CN103394430B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101239346A (en) * | 2008-03-10 | 2008-08-13 | 江苏大学 | Optimizing method of spray coating robot spray gun track on complex curved surface |
| CN102831306A (en) * | 2012-08-13 | 2012-12-19 | 东南大学 | Layered spraying track planning method used for spraying robot |
| CN102909148A (en) * | 2012-08-13 | 2013-02-06 | 东南大学 | Spraying path automatic generating method for adaptive modeling of multiple spray guns |
Non-Patent Citations (1)
| Title |
|---|
| 面向复杂曲面的喷涂机器人喷枪轨迹优化;赵德安，陈伟，汤养;《江苏大学学报（自然科学版）》;20070930;第28卷(第5期);425-429 * |
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