TWM601358U - System of workpiece inspection in path planning - Google Patents

System of workpiece inspection in path planning Download PDF

Info

Publication number
TWM601358U
TWM601358U TW109203377U TW109203377U TWM601358U TW M601358 U TWM601358 U TW M601358U TW 109203377 U TW109203377 U TW 109203377U TW 109203377 U TW109203377 U TW 109203377U TW M601358 U TWM601358 U TW M601358U
Authority
TW
Taiwan
Prior art keywords
module
path
detection
mutation
workpiece
Prior art date
Application number
TW109203377U
Other languages
Chinese (zh)
Inventor
林正堅
謝天昕
吳宇杋
林鑫佑
Original Assignee
百德機械股份有限公司
國立勤益科技大學
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 百德機械股份有限公司, 國立勤益科技大學 filed Critical 百德機械股份有限公司
Priority to TW109203377U priority Critical patent/TWM601358U/en
Publication of TWM601358U publication Critical patent/TWM601358U/en

Links

Images

Landscapes

  • Numerical Control (AREA)

Abstract

本新型提供一種工件檢測之路徑規劃系統,規劃量測機檢測工件之最佳檢測路徑。以射線檢測量測機於二檢測點之間的移動方式,並依據檢測點之複數移動方式建立座標關係矩陣。路徑最佳化模組將各檢測點編碼,然後使檢測點經複數次隨機順序排列而成為複數檢測路徑,將檢測路徑依照其總距離值的大小進行排序。依據鯨魚演算單元進行演化而產生突變檢測路徑,其包含突變總距離值,將總距離值及突變總距離值進行比較並選擇保留最小者而成為最佳檢測路徑。藉此,產生快速且安全的工件檢測最佳路徑。 This model provides a path planning system for workpiece inspection, which plans the best inspection path for workpiece inspection by measuring machine. A coordinate relationship matrix is established based on the movement mode of the ray inspection measuring machine between the two detection points and the complex movement mode of the detection points. The path optimization module encodes each detection point, and then arranges the detection points in a random order multiple times to become a complex detection path, and sorts the detection paths according to their total distance value. The mutation detection path is generated according to the evolution of the whale calculation unit, which includes the total distance value of the mutation. The total distance value and the total distance value of the mutation are compared and the smallest one is selected to be the best detection path. In this way, a fast and safe optimal path for workpiece detection is generated.

Description

工件檢測之路徑規劃系統 Path planning system for workpiece inspection

本新型是關於一種路徑規劃系統,特別是關於一種工件檢測之路徑規劃系統。 This model relates to a path planning system, especially to a path planning system for workpiece detection.

在精密製造的過程中,當工件加工完成後需要透過量測機進行量測用以確保加工後的工件精度在合理的範圍內。當需檢測的檢測點數量增加時,使用者無法憑經驗順利規劃出量測路徑,因此若能夠有效的解決路徑規劃問題,便能夠顯著的提升生產效率。 In the process of precision manufacturing, when the workpiece is processed, it needs to be measured by a measuring machine to ensure that the precision of the processed workpiece is within a reasonable range. When the number of inspection points to be inspected increases, users cannot smoothly plan the measurement path based on experience. Therefore, if the path planning problem can be effectively solved, production efficiency can be significantly improved.

當前的路徑規劃採用下列幾種方法:(1)透過軌跡最小化來減少座標測量機(Coordinate measuring machine;CMM)中測量的時間,利用蟻群演算法進行搜索。(2)以最鄰近法(nearest neighbor method)和細化法來規劃量測序列,其優化的序列用以完成整個量測過程。上述路徑規劃方法仍存在著許多問題,如收斂速度過快、求解所需的時間較長、容易陷入區域最佳解及計算量龐大需要使用大量的記憶體完成。由此可知,目前市場上缺乏一種收斂較慢、求解時長較短、不易陷入區域最佳解 的路徑規劃系統,故相關業者均在尋求其解決之道。 The current path planning uses the following methods: (1) Minimize the trajectory to reduce the measurement time in the Coordinate Measuring Machine (CMM), and use the ant colony algorithm to search. (2) The measurement sequence is planned by the nearest neighbor method and the refinement method, and the optimized sequence is used to complete the entire measurement process. The above-mentioned path planning method still has many problems, such as too fast convergence speed, long time required to solve, easy to fall into the best solution in the region, and huge amount of calculation and need to use a lot of memory to complete. It can be seen that there is currently no optimal solution in the market that has slower convergence, shorter solution time, and is not easy to fall into the region. The path planning system of China, so related businesses are seeking its solutions.

因此本新型之目的在於提供一種工件檢測之路徑規劃系統,其先檢測各檢測點之間的移動方式並生成座標關係矩陣,將各檢測點編碼並隨機排序為複數檢測路徑,計算各檢測路徑的總距離值,並將各檢測路徑依照其總距離值的大小進行排序,進而分群並選出各組別中的領袖。再以鯨魚演算單元產生突變檢測路徑及突變總距離,並從各領袖及突變檢測路徑中選出總距離值最小者成為最佳檢測路徑,以解決習知路徑規劃技術中易陷入區域最佳解之問題。 Therefore, the purpose of this new model is to provide a path planning system for workpiece inspection, which first detects the movement between the inspection points and generates a coordinate relationship matrix, encodes and randomly sorts the inspection points into a complex inspection path, and calculates the path of each inspection path. The total distance value, and each detection path is sorted according to the total distance value, and then the group is divided and the leader in each group is selected. Then use the whale calculus unit to generate the mutation detection path and the mutation total distance, and select the smallest total distance value from each leader and mutation detection path as the best detection path to solve the problem of the best solution that is easy to fall into the region in the conventional path planning technology problem.

依據本新型的結構態樣之一實施方式提供一種工件檢測之路徑規劃系統,用以規劃量測機檢測工件之最佳檢測路徑,其工件檢測之路徑規劃系統包含座標關係矩陣建立模組及路徑最佳化模組。座標關係矩陣建立模組驅動射線檢測量測機於二檢測點之間的移動方式,以生成座標關係矩陣。路徑最佳化模組訊號連接座標關係矩陣建立模組,路徑最佳化模組包含初始化編碼模組、適應值排序模組、動態分群模組、突變模組、選擇模組及迭代次數判斷模組。初始化編碼模組用以將各檢測點編碼,然後驅動檢測點複數次隨機順序排列而生成複數檢測路徑。適應值排序模組,訊號連接初始化編碼模組,係依據座標關係矩陣及各檢測路徑生成各檢測路徑的總距離值,並依照總距離值的大小 排序檢測路徑。動態分群模組,訊號連接適應值排序模組,依據總距離值將檢測路徑分群成複數組別,任一組別之複數檢測路徑之複數總距離值之差值小於等於預設差值。突變模組,訊號連接動態分群模組,組別之領袖經由鯨魚演算單元生成突變檢測路徑,突變檢測路徑包含突變總距離值。選擇模組,訊號連接突變模組,將各組別中領袖之總距離值、突變總距離值及前次迭代後的最佳檢測路徑進行比較並選擇保留最小者而成為最佳檢測路徑。迭代次數判斷模組,訊號連接選擇模組與突變模組,迭代次數判斷模組判斷突變模組的執行次數是否等於預設次數;若否,則突變模組與選擇模組重新被執行;若是,則路徑最佳化模組終止執行。 According to one of the implementations of the structural aspect of the present invention, a path planning system for workpiece inspection is provided to plan the best inspection path for the measuring machine to detect the workpiece. The path planning system for workpiece inspection includes a coordinate relationship matrix establishment module and a path Optimization module. The coordinate relationship matrix establishment module drives the movement mode of the ray inspection measuring machine between the two detection points to generate the coordinate relationship matrix. Path optimization module signal connection coordinate relationship matrix building module, path optimization module includes initialization coding module, fitness value sorting module, dynamic grouping module, mutation module, selection module and iteration number judgment module group. The initial coding module is used to code each detection point, and then drive the detection points to be arranged in random order multiple times to generate multiple detection paths. The fitness value sorting module, the signal connection initialization coding module, is based on the coordinate relationship matrix and each detection path to generate the total distance value of each detection path, and according to the size of the total distance value Sort detection paths. The dynamic grouping module, the signal connection fitness sorting module, groups the detection paths into multiple groups according to the total distance value, and the difference between the total distance values of the multiple detection paths in any group is less than or equal to the preset difference. The mutation module, the signal is connected to the dynamic grouping module, the leader of the group generates a mutation detection path through the whale calculation unit, and the mutation detection path includes the total distance value of the mutation. Select the module, connect the signal to the mutation module, compare the total distance value of the leader in each group, the total distance value of the mutation, and the best detection path after the previous iteration, and select the smallest one to be the best detection path. The iteration number judgment module, the signal connects the selection module and the mutation module, the iteration number judgment module determines whether the execution times of the mutation module is equal to the preset number; if not, the mutation module and the selection module are executed again; if yes , The path optimization module terminates execution.

藉此,本新型的工件檢測之路徑規劃系統透過動態分群模組及鯨魚演算單元逃脫區域最佳解,以解決習知路徑規劃系統存在收斂速度過快而易陷入區域最佳解之問題。 In this way, the path planning system of the new type of workpiece detection escapes the regional optimal solution through the dynamic grouping module and the whale calculation unit, so as to solve the problem that the conventional path planning system converges too fast and easily falls into the regional optimal solution.

前述實施方式之其他實施例如下:前述座標關係矩陣建立模組中,若二檢測點之間存在工件,移動方式為非直線移動。若二檢測點之間不存在工件,移動方式為直線移動。 Other examples of the foregoing embodiment are as follows: In the foregoing coordinate relationship matrix establishment module, if there is a workpiece between two detection points, the movement mode is non-linear movement. If there is no workpiece between the two detection points, the movement mode is linear movement.

前述實施方式之其他實施例如下:前述動態分群模組包含相似度計算子模組及分群子模組。相似度計算子模組計算檢測路徑之適合度閾值及距離閾值。分群子模組,訊號連接相似度計算子模組計算各檢測路徑與領袖之間的 適合度差及距離差,並依據適合度閾值及距離閾值分成組別。 Other examples of the foregoing embodiment are as follows: the foregoing dynamic grouping module includes a similarity calculation sub-module and a grouping sub-module. The similarity calculation sub-module calculates the suitability threshold and distance threshold of the detected path. The grouping sub-module, the signal connection similarity calculation sub-module calculates the difference between each detection path and the leader The fitness difference and distance difference are divided into groups according to the fitness threshold and the distance threshold.

前述實施方式之其他實施例如下:前述鯨魚演算單元包含包圍子模組、狩獵子模組及隨機搜索子模組。包圍子模組更新前次迭代後的最佳檢測路徑並找出各領袖之總距離值之最小者。狩獵子模組,訊號連接包圍子模組,找出各領袖之總距離值之最小者。隨機搜索子模組,訊號連接狩獵子模組,係以隨機順序排列檢測點而生成突變檢測路徑。 Other examples of the foregoing embodiment are as follows: the foregoing whale calculation unit includes an enclosing sub-module, a hunting sub-module, and a random search sub-module. Surround the sub-module to update the best detection path after the previous iteration and find the smallest total distance value of each leader. Hunting sub-module, the signal is connected to surround the sub-module to find the smallest total distance value of each leader. Random search sub-modules, signal connection to hunting sub-modules, arranging detection points in random order to generate mutation detection paths.

前述實施方式之其他實施例如下:前述工件檢測之路徑規劃系統,更包含重新編碼模組,訊號連接迭代次數判斷模組,重新編碼模組係將最佳檢測路徑之編碼轉換為量測機使用之量測機編碼。 Other examples of the aforementioned implementation are as follows: the aforementioned workpiece inspection path planning system further includes a re-encoding module, a signal connection iteration number judging module, and the re-encoding module converts the encoding of the best inspection path into a measuring machine for use The code of the measuring machine.

200:工件檢測之路徑規劃系統 200: Path planning system for workpiece inspection

210:座標關係矩陣建立模組 210: Coordinate relationship matrix creation module

212:路徑最佳化模組 212: Path Optimization Module

214:重新編碼模組 214: Recode module

220:初始化編碼模組 220: Initialize the coding module

230:適應值排序模組 230: fitness value sorting module

240:動態分群模組 240: Dynamic grouping module

242:相似度計算子模組 242: Similarity calculation submodule

244:分群子模組 244: Group sub-module

250:突變模組 250: mutation module

252:鯨魚演算單元 252: Whale Calculus Unit

254:包圍子模組 254: Surround submodule

256:狩獵子模組 256: Hunting submodule

258:隨機搜索子模組 258: Random Search Submodule

260:選擇模組 260: Select Module

270:迭代次數判斷模組 270: Iteration number judgment module

100:工件檢測之路徑規劃方法 100: Path planning method for workpiece inspection

152:鯨魚演算法 152: Whale Algorithm

S110:座標關係矩陣建立步驟 S110: Steps for establishing coordinate relationship matrix

S112:路徑最佳化步驟 S112: Path optimization step

S114:重新編碼步驟 S114: Recoding step

S120:初始化編碼步驟 S120: Initial coding step

S130:適應值排序步驟 S130: fitness value sorting steps

S140:動態分群步驟 S140: Dynamic grouping steps

S142:計算相似度步驟 S142: step of calculating similarity

S144:分群步驟 S144: Grouping steps

S150:突變步驟 S150: mutation step

S154:包圍步驟 S154: Bracketing step

S156:狩獵步驟 S156: Hunting Step

S158:隨機搜索步驟 S158: Random search step

S160:選擇步驟 S160: Selection steps

S170:迭代次數判斷步驟 S170: Steps to determine the number of iterations

第1圖係繪示本新型第一實施例之工件檢測之路徑規劃系統之方塊示意圖;第2圖係繪示第1圖之工件檢測之路徑規劃系統之路徑最佳化模組之方塊示意圖;第3圖係繪示第2圖之路徑最佳化模組的動態分群模組之方塊示意圖;第4圖係繪示本新型第一實施例之工件檢測之路徑規劃系統之鯨魚演算單元之方塊示意圖; 第5圖係繪示本新型第二實施例之工件檢測之路徑規劃方法之流程示意圖;第6圖係繪示第5圖之工件檢測之路徑規劃方法的路徑最佳化步驟之流程示意圖;第7圖係繪示第6圖之路徑最佳化步驟的動態分群步驟之流程示意圖;以及第8圖係繪示本新型第二實施例之工件檢測之路徑規劃方法的鯨魚演算法之流程示意圖。 Figure 1 is a block diagram of the path planning system for workpiece inspection in the first embodiment of the present invention; Figure 2 is a block diagram of the path optimization module of the path planning system for workpiece inspection in Figure 1; Figure 3 is a block diagram of the dynamic grouping module of the path optimization module of Figure 2; Figure 4 is a block diagram of the whale calculation unit of the path planning system for workpiece detection in the first embodiment of the present invention Schematic diagram Figure 5 is a schematic flow diagram of the path planning method for workpiece inspection according to the second embodiment of the present invention; Figure 6 is a schematic flow diagram of the path optimization steps of the path planning method for workpiece inspection in Figure 5; Figure 7 is a schematic flow diagram of the dynamic grouping step of the path optimization step in Figure 6; and Figure 8 is a schematic flow diagram of the whale algorithm of the path planning method for workpiece detection in the second embodiment of the present invention.

請一併參照第1圖,其中第1圖係繪示本新型第一實施例之工件檢測之路徑規劃系統200之方塊示意圖,如圖所示,此工件檢測之路徑規劃系統200規劃量測機檢測工件之最佳檢測路徑。工件檢測之路徑規劃系統200包含座標關係矩陣建立模組210、路徑最佳化模組212及重新編碼模組214。 Please also refer to Figure 1. Figure 1 is a block diagram of the workpiece inspection path planning system 200 according to the first embodiment of the present invention. As shown in the figure, the workpiece inspection path planning system 200 planning measurement machine The best inspection path for inspecting workpieces. The path planning system 200 for workpiece inspection includes a coordinate relationship matrix establishment module 210, a path optimization module 212, and a recoding module 214.

座標關係矩陣建立模組210,係驅動射線檢測量測機於二檢測點之間的移動方式,以生成座標關係矩陣。若二檢測點之間存在工件,移動方式為非直線移動;若二檢測點之間不存在工件,移動方式為直線移動。詳細地說,以射線檢測探針能否在二檢測點之間以直線方式移動,根據點與點之間的移動方式分為“0”與“1”,其中“0”代表兩點之間可進行直線移動,“1”代表兩點之間不可進行直線移動,需進行拉高Z軸的安全性移動,以避免碰撞的發生, 並將二檢測點之間的移動方式建立為座標關係矩陣。 The coordinate relationship matrix establishment module 210 is used to drive the movement of the ray inspection and measurement machine between the two detection points to generate the coordinate relationship matrix. If there is a workpiece between the two detection points, the movement mode is non-linear movement; if there is no workpiece between the two detection points, the movement mode is linear movement. In detail, whether the ray detection probe can move in a straight line between two detection points, it is divided into "0" and "1" according to the way of movement between points, where "0" represents between two points It can be moved in a straight line. "1" means that the two points cannot be moved in a straight line. The Z-axis needs to be moved safely to avoid collisions. And the movement mode between the two detection points is established as a coordinate relationship matrix.

請配合參照第2圖,第2圖係繪示第1圖之工件檢測之路徑規劃系統200之路徑最佳化模組212之方塊示意圖。路徑最佳化模組212訊號連接座標關係矩陣建立模組210,路徑最佳化模組212包含初始化編碼模組220、適應值排序模組230、動態分群模組240、突變模組250、選擇模組260及迭代次數判斷模組270。換句話說,路徑最佳化模組212用以將檢測點列出複數種排列方式,並從中找出最佳的檢測路徑。 Please refer to FIG. 2. FIG. 2 is a block diagram of the path optimization module 212 of the path planning system 200 for workpiece detection in FIG. 1. FIG. Path optimization module 212 signal connection coordinate relationship matrix establishment module 210. Path optimization module 212 includes initialization coding module 220, fitness value sorting module 230, dynamic grouping module 240, mutation module 250, selection The module 260 and the iteration number judgment module 270. In other words, the path optimization module 212 is used to list the detection points in a plurality of arrangements and find the best detection path from them.

初始化編碼模組220用以將各檢測點編碼,然後驅動此些檢測點複數次隨機順序排列而生成複數檢測路徑。換句話說,初始化編碼模組220係將各檢測點的座標編碼並產生多個隨機順序排列的檢測路徑。 The initial coding module 220 is used to code each detection point, and then drive the detection points to be arranged in a random order multiple times to generate multiple detection paths. In other words, the initialization encoding module 220 encodes the coordinates of each detection point and generates a plurality of detection paths arranged in random order.

請配合參照表一,適應值排序模組230訊號連接初始化編碼模組220,適應值排序模組230係依據座標關係矩陣及各檢測路徑生成檢測路徑的總距離值並依照總距離值的大小排序檢測路徑,並將各檢測路徑的組別預設為0。總距離值為Fitness,各檢測路徑為In。將In依照其Fitness由最小值排序至最大值,I1為總距離值最小者,INP為總距離值最大者,Group為組別。 Please refer to Table 1. The fitness value sorting module 230 is connected to the initialization coding module 220. The fitness value sorting module 230 generates the total distance value of the detection path according to the coordinate relationship matrix and each detection path, and sorts according to the total distance value. Detect paths, and preset the group of each detection path to 0. The total distance value is Fitness, and each detection path is I n . Sort I n according to its fitness from minimum to maximum, I 1 is the smallest total distance value, I NP is the largest total distance value, and Group is the group.

Figure 109203377-A0305-02-0007-1
Figure 109203377-A0305-02-0007-1

請配合參照第3圖,第3圖係繪示第2圖之路徑最佳化模組212的動態分群模組240之方塊示意圖。如圖所示,動態分群模組240訊號連接適應值排序模組230,依據總距離值將檢測路徑分群成複數組別,任一組別之複數檢測路徑之複數總距離值之差值小於等於預設差值。動態分群模組240包含相似度計算子模組242與分群子模組244。 Please refer to FIG. 3 in conjunction. FIG. 3 is a block diagram of the dynamic grouping module 240 of the path optimization module 212 in FIG. 2. As shown in the figure, the dynamic grouping module 240 is connected to the fitness sorting module 230 to group the detection paths into multiple groups according to the total distance value. The difference between the total distance values of the multiple detection paths in any group is less than or equal to The preset difference. The dynamic grouping module 240 includes a similarity calculation sub-module 242 and a grouping sub-module 244.

詳細地說,相似度計算子模組242係計算檢測路徑之適合度閾值及距離閾值。相似度計算子模組242的計算方法符合下式:

Figure 109203377-A0305-02-0008-2
In detail, the similarity calculation sub-module 242 calculates the suitability threshold and the distance threshold of the detected path. The calculation method of the similarity calculation submodule 242 conforms to the following formula:
Figure 109203377-A0305-02-0008-2

Figure 109203377-A0305-02-0008-3
Figure 109203377-A0305-02-0008-3

Figure 109203377-A0305-02-0008-4
Figure 109203377-A0305-02-0008-4

Figure 109203377-A0305-02-0008-5
其中DISg為第g組的距離差,n為檢測路徑的總數,D為檢測點的總數,g為組別,
Figure 109203377-A0305-02-0008-6
為第g組的領袖,
Figure 109203377-A0305-02-0008-7
為第i個檢測路徑,NC為當前組別的檢測路徑總數,φg為第g組的距離閾值。FITg為第g組的適合度差,Fit(τg)為第g組的領袖之適應度值,Fit(Xi)為第i個檢測路徑的適應度值,ψg為第g組的適合度閾值。
Figure 109203377-A0305-02-0008-5
Where DIS g is the distance difference of the g-th group, n is the total number of detection paths, D is the total number of detection points, and g is the group,
Figure 109203377-A0305-02-0008-6
Is the leader of group g,
Figure 109203377-A0305-02-0008-7
Is the i-th detection path, NC is the total number of detection paths in the current group, and φ g is the distance threshold of the g-th group. FIT g is the fitness difference of the g- th group, Fit(τ g ) is the fitness value of the leader of the g- th group, Fit(X i ) is the fitness value of the i-th detection path, and ψ g is the fitness value of the g-th group The fitness threshold.

分群子模組244訊號連接相似度計算子模組242,係計算各檢測路徑與領袖之間的適合度差與距離差,並依 據適合度閾值及距離閾值分成組別。分群子模組244符合下式:

Figure 109203377-A0305-02-0009-28
The grouping sub-module 244 signal connection similarity calculation sub-module 242 calculates the fitness difference and distance difference between each detection path and the leader, and divides them into groups according to the fitness threshold and the distance threshold. The grouping submodule 244 conforms to the following formula:
Figure 109203377-A0305-02-0009-28

Fit i =|Fit g )-Fit(X i )| (6)。其中Disi為第i個檢測路徑的距離差,Fiti為第i個檢測路徑的適合度差,D為檢測點的總數,

Figure 109203377-A0305-02-0009-8
為第g組的領袖,
Figure 109203377-A0305-02-0009-9
為第i個檢測路徑,Fit(τg)為第g組的領袖之適應度值,Fit(Xi)為第i個檢測路徑的適應度值。當Disig和Fitig時,表示第i個檢測路徑與第g組領袖是相似的,第i個檢測路徑會被歸入第g組,所有檢測路徑皆有組別後,分群子模組244執行終止執行。 Fit i =| Fit g )- Fit ( X i )| (6). Where Dis i is the distance difference of the i-th detection path, Fit i is the fitness difference of the i-th detection path, D is the total number of detection points,
Figure 109203377-A0305-02-0009-8
Is the leader of group g,
Figure 109203377-A0305-02-0009-9
Is the i-th detection path, Fit(τ g ) is the fitness value of the leader of the g- th group, and Fit(X i ) is the fitness value of the i-th detection path. When Dis ig and Fit ig , it means that the i-th detection path is similar to the g-th group leader, and the i-th detection path will be classified into the g-th group, and all detection paths have groups. , The grouping sub-module 244 executes termination execution.

請配合參照第4圖,第4圖係繪示本新型第一實施例之工件檢測之路徑規劃系統200之鯨魚演算單元252之方塊示意圖。突變模組250訊號連接動態分群模組240,突變模組250將此些組別之領袖經由鯨魚演算單元252生成突變檢測路徑,突變檢測路徑包含突變總距離值。鯨魚演算單元252包含包圍子模組254、狩獵子模組256及隨機搜索子模組258。 Please refer to FIG. 4, which is a block diagram of the whale calculation unit 252 of the path planning system 200 for workpiece detection according to the first embodiment of the present invention. The mutation module 250 is signaled to the dynamic grouping module 240. The mutation module 250 generates a mutation detection path through the whale arithmetic unit 252 for the leaders of these groups. The mutation detection path includes the total distance value of the mutation. The whale calculation unit 252 includes an enclosure sub-module 254, a hunting sub-module 256, and a random search sub-module 258.

包圍子模組254係更新前次迭代後的最佳檢測路徑並找出各領袖之各總距離值之最小者。包圍子模組254符合下式:

Figure 109203377-A0305-02-0009-11
The surrounding sub-module 254 updates the best detection path after the previous iteration and finds the smallest total distance value of each leader. The surrounding submodule 254 conforms to the following formula:
Figure 109203377-A0305-02-0009-11

Figure 109203377-A0305-02-0009-12
Figure 109203377-A0305-02-0009-12

Figure 109203377-A0305-02-0010-13
Figure 109203377-A0305-02-0010-13

Figure 109203377-A0305-02-0010-14
其中t為當前的迭代次數,X(t)為當前的最佳檢測路徑,X*(t)為檢測路徑的位置空間,Xτg為第g組之領袖,A、C為係數,其計算方法如第(9)式及第(10)式,a為進行迭代時從2線性下降到0的向量,r表示0到1之間的隨機數。換句話說,包圍子模組254載入前次迭代後的最佳檢測路徑及各領袖之總距離值之最小者。
Figure 109203377-A0305-02-0010-14
Where t is the current iteration number, X(t) is the current best detection path, X * (t) is the location space of the detection path, X τg is the leader of the g-th group, A and C are coefficients, and its calculation method Such as (9) and (10), a is a vector that linearly decreases from 2 to 0 when iterating, and r represents a random number between 0 and 1. In other words, the surrounding submodule 254 loads the best detection path after the previous iteration and the smallest total distance value of each leader.

狩獵子模組256訊號連接包圍子模組254,係找出各領袖之總距離值之最小者。狩獵子模組256符合下式:

Figure 109203377-A0305-02-0010-15
其中p為0到1之間的隨機數,b為用來定義螺旋形狀的常數,1為1到-1之間的隨機數。當p<0.5時,以收縮環繞方式找出各領袖之總距離值最小之檢測路徑;當p>0.5時,以螺旋運動方式找出各領袖中總距離值最小之檢測路徑。 The hunting sub-module 256 signals the surrounding sub-module 254 to find the smallest total distance value of each leader. The hunting submodule 256 conforms to the following formula:
Figure 109203377-A0305-02-0010-15
Where p is a random number between 0 and 1, b is a constant used to define the spiral shape, and 1 is a random number between 1 and -1. When p<0.5, the detection path with the smallest total distance value of each leader is found by shrinking and wrapping; when p>0.5, the detection path with the smallest total distance value of each leader is found by spiral motion.

隨機搜索子模組258訊號連接狩獵子模組256,係以隨機順序排列檢測點而生成突變檢測路徑。隨機搜索子模組258符合下式:

Figure 109203377-A0305-02-0010-16
The random search sub-module 258 is connected to the hunting sub-module 256 with a signal to arrange the detection points in a random order to generate a mutation detection path. The random search submodule 258 conforms to the following formula:
Figure 109203377-A0305-02-0010-16

Figure 109203377-A0305-02-0010-17
其中Xrand為隨機產生的檢測路徑之向量,⊕表示乘法, D向量的產生方式導入Lévy飛行策略,Lévy飛行策略從提供的概率分佈中提供隨機游動,使鯨魚演算單元252能跳脫區域最佳解。當A
Figure 109203377-A0305-02-0011-27
1時,隨機產生一個突變檢測路徑,突變檢測路徑包含突變總距離值。
Figure 109203377-A0305-02-0010-17
Where X rand is the vector of the detection path generated randomly, ⊕ represents multiplication, and the method of generating D vector is imported into the Lévy flight strategy. The Lévy flight strategy provides random walks from the probability distribution provided, so that the whale calculation unit 252 can escape the area most Good solution. When A
Figure 109203377-A0305-02-0011-27
At 1:00, a mutation detection path is randomly generated, and the mutation detection path contains the total distance value of the mutation.

選擇模組260訊號連接突變模組250,將各組別中領袖之總距離值、突變總距離值及前次迭代後的最佳檢測路徑進行比較並選擇保留最小者而成為最佳檢測路徑。選擇模組260符合下式:

Figure 109203377-A0305-02-0011-18
其中
Figure 109203377-A0305-02-0011-19
為前次迭代後的最佳檢測路徑,
Figure 109203377-A0305-02-0011-20
為隨機搜索子 模組258所產生的突變檢測路徑。選擇模組260判斷
Figure 109203377-A0305-02-0011-26
的總距離值是否比
Figure 109203377-A0305-02-0011-23
更好,若是,則
Figure 109203377-A0305-02-0011-24
取代
Figure 109203377-A0305-02-0011-25
成為最佳檢測路徑;若否,則前次迭代後的最佳檢測路徑保留至下一代。 The signal of the selection module 260 is connected to the mutation module 250, and the total distance value of the leader in each group, the total distance value of the mutation, and the best detection path after the previous iteration are compared, and the smallest remaining one is selected to become the best detection path. The selection module 260 conforms to the following formula:
Figure 109203377-A0305-02-0011-18
among them
Figure 109203377-A0305-02-0011-19
Is the best detection path after the previous iteration,
Figure 109203377-A0305-02-0011-20
The mutation detection path generated by the sub-module 258 is randomly searched. Selection module 260 judgment
Figure 109203377-A0305-02-0011-26
Is the total distance value greater than
Figure 109203377-A0305-02-0011-23
Better, if yes, then
Figure 109203377-A0305-02-0011-24
replace
Figure 109203377-A0305-02-0011-25
Become the best detection path; if not, the best detection path after the previous iteration is retained to the next generation.

迭代次數判斷模組270訊號連接選擇模組260與突變模組250,迭代次數判斷模組270用以判斷突變模組250的執行次數是否等於預設次數;若否,則突變模組250與選擇模組260重新被執行;若是,則路徑最佳化模組212終止執行。換句話說,當迭代至預設次數時,所得之最佳檢測路徑即為工件檢測之路徑規劃系統200所求之最佳檢測路徑。 The iteration number determination module 270 signals the connection selection module 260 and the mutation module 250. The iteration number determination module 270 is used to determine whether the execution times of the mutation module 250 are equal to the preset number; if not, the mutation module 250 and the selection module 250 The module 260 is executed again; if so, the path optimization module 212 terminates execution. In other words, when the iteration reaches the preset number of times, the obtained optimal inspection path is the optimal inspection path requested by the path planning system 200 for workpiece inspection.

重新編碼模組214訊號連接迭代次數判斷模組270,重新編碼模組214係將最佳檢測路徑之編碼轉換為 量測機使用之量測機編碼。詳細地說,量測機可為數控機床(Computer Numerical Control;CNC),量測機使用之量測機編碼可為G/M code。 The re-encoding module 214 signals the connection iteration number judging module 270. The re-encoding module 214 converts the encoding of the best detection path into The code of the measuring machine used by the measuring machine. In detail, the measuring machine can be a computer numerical control (CNC) machine, and the measuring machine code used by the measuring machine can be G/M code.

藉此,本新型的工件檢測之路徑規劃系統200透過動態分群模組240及鯨魚演算單元252逃脫區域最佳解,以解決習知路徑規劃系統存在收斂速度過快而易陷入區域最佳解之問題。 In this way, the path planning system 200 for workpiece detection of the present invention escapes the regional optimal solution through the dynamic grouping module 240 and the whale calculation unit 252, so as to solve the problem that the conventional path planning system converges too fast and easily falls into the regional optimal solution. problem.

請一併參照第1圖至第6圖,其中第5圖係繪示本新型第二實施例之工件檢測之路徑規劃方法100之流程示意圖;第6圖係繪示第5圖之工件檢測之路徑規劃方法100的路徑最佳化步驟S112之流程示意圖。如圖所示,此工件檢測之路徑規劃方法100用以規劃量測機檢測工件之最佳檢測路徑,檢測路徑包含複數檢測點。此工件檢測之路徑規劃方法100包含座標關係矩陣建立步驟S110、路徑最佳化步驟S112以及重新編碼步驟S114。 Please refer to Figures 1 to 6 together. Figure 5 shows the flow diagram of the workpiece inspection path planning method 100 according to the second embodiment of the present invention; Figure 6 shows the workpiece inspection of Figure 5 A schematic flowchart of the path optimization step S112 of the path planning method 100. As shown in the figure, the path planning method 100 for workpiece inspection is used to plan the best inspection path for the measuring machine to inspect the workpiece, and the inspection path includes a plurality of inspection points. The path planning method 100 for workpiece detection includes a coordinate relationship matrix establishment step S110, a path optimization step S112, and a recoding step S114.

座標關係矩陣建立步驟S110係驅動射線檢測量測機於二檢測點之間的移動方式,並依據檢測點之移動方式建立座標關係矩陣。若二檢測點之間存在工件,移動方式為非直線移動;若二檢測點之間不存在工件,移動方式為直線移動。座標關係矩陣建立步驟S110透過座標關係矩陣建立模組210執行。 The coordinate relationship matrix establishment step S110 is to drive the movement mode of the radiation inspection and measuring machine between the two detection points, and establish the coordinate relationship matrix according to the movement mode of the detection points. If there is a workpiece between the two detection points, the movement mode is non-linear movement; if there is no workpiece between the two detection points, the movement mode is linear movement. The coordinate relationship matrix creation step S110 is performed through the coordinate relationship matrix creation module 210.

路徑最佳化步驟S112包含初始化編碼步驟S120、適應值排序步驟S130、動態分群步驟S140、突變步驟S150、選擇步驟S160及迭代次數判斷步驟S170。 The path optimization step S112 includes an initialization coding step S120, an fitness ranking step S130, a dynamic grouping step S140, a mutation step S150, a selection step S160, and an iteration number determination step S170.

初始化編碼步驟S120係將各檢測點編碼,然後使檢測點經複數次隨機順序排列而成為複數檢測路徑。初始化編碼步驟S120透過初始化編碼模組220執行。 The initial coding step S120 is to code each detection point, and then arrange the detection points in a random order multiple times to form a complex detection path. The initialization coding step S120 is performed by the initialization coding module 220.

適應值排序步驟S130係依據座標關係矩陣及各檢測路徑計算各檢測路徑的總距離值。適應值排序步驟S130透過適應值排序模組230執行。 The fitness sorting step S130 is to calculate the total distance value of each detection path according to the coordinate relationship matrix and each detection path. The fitness value sorting step S130 is performed by the fitness value sorting module 230.

請參照第7圖,第7圖係繪示第6圖之路徑最佳化步驟S112的動態分群步驟S140之流程示意圖。動態分群步驟S140係將檢測路徑依據總距離值分群成複數組別,任一組別之複數檢測路徑之複數總距離值之差值小於等於預設差值,且各組別中總距離值之最小者視為領袖。動態分群步驟S140包含計算相似度步驟S142及分群步驟S144。動態分群步驟S140係透過動態分群模組240執行。 Please refer to FIG. 7, which is a schematic flowchart of the dynamic grouping step S140 of the path optimization step S112 in FIG. 6. The dynamic grouping step S140 is to group the detection paths into multiple groups according to the total distance value. The difference between the total distance values of the multiple detection paths in any group is less than or equal to the preset difference, and the total distance value in each group is The smallest is regarded as the leader. The dynamic grouping step S140 includes a similarity calculation step S142 and a grouping step S144. The dynamic grouping step S140 is executed through the dynamic grouping module 240.

計算相似度步驟S142係計算檢測路徑之適合度閾值及距離閾值。計算相似度步驟S142係透過相似度計算子模組242執行。 The similarity calculation step S142 is to calculate the suitability threshold and the distance threshold of the detected path. The similarity calculation step S142 is performed through the similarity calculation sub-module 242.

分群步驟S144係計算各檢測路徑與領袖之間的適合度差及距離差,並依據適合度閾值及距離閾值分成組別。分群步驟S144透過分群子模組244執行。 The grouping step S144 is to calculate the fitness difference and distance difference between each detection path and the leader, and divide into groups according to the fitness threshold and the distance threshold. The grouping step S144 is executed by the grouping sub-module 244.

請參照第8圖,第8圖係繪示本新型第二實施例之工件檢測之路徑規劃方法100的鯨魚演算法152之流程示意圖。突變步驟S150係將組別之領袖依據鯨魚演算法152進行演化而產生突變檢測路徑,突變檢測路徑包含突 變總距離值。鯨魚演算法152包含包圍步驟S154、狩獵步驟S156及隨機搜索步驟S158。 Please refer to FIG. 8. FIG. 8 is a flowchart of the whale algorithm 152 of the path planning method 100 for workpiece inspection according to the second embodiment of the present invention. The mutation step S150 is to evolve the leader of the group according to the whale algorithm 152 to generate a mutation detection path. The mutation detection path includes the mutation detection path. Change the total distance value. The whale algorithm 152 includes a surrounding step S154, a hunting step S156, and a random search step S158.

包圍步驟S154係更新前次迭代後的最佳檢測路徑並以收縮環繞方式找出各領袖之總距離值之最小者。包圍步驟S154透過包圍子模組254執行。 The encircling step S154 is to update the best detection path after the previous iteration and find the smallest value of the total distance of each leader in a shrinking and encircling manner. The enclosing step S154 is performed through the enclosing sub-module 254.

判斷隨機亂數p之值是否<0.5,若是,則再次執行包圍步驟S154;若否,則執行狩獵步驟S156。狩獵步驟S156係以螺旋運動方式找出各領袖之總距離值之最小者。狩獵步驟S156透過狩獵子模組256執行。 It is judged whether the value of the random random number p is less than 0.5, if it is, the encircling step S154 is executed again; if not, the hunting step S156 is executed. The hunting step S156 is to find the smallest total distance value of each leader in a spiral motion. The hunting step S156 is executed by the hunting sub-module 256.

隨機搜索步驟S158係以隨機順序排列檢測點而產生突變檢測路徑。隨機搜索步驟S158透過隨機搜索子模組258執行。 The random search step S158 is to arrange the detection points in a random order to generate a mutation detection path. The random search step S158 is performed by the random search sub-module 258.

選擇步驟S160係將各組別中領袖之總距離值、突變總距離值及前次迭代後的最佳檢測路徑進行比較並選擇保留最小者而成為最佳檢測路徑。選擇步驟S160透過選擇模組260執行。 The selection step S160 is to compare the total distance value of the leader in each group, the total distance value of the sudden change, and the best detection path after the previous iteration, and select the one that remains the smallest to become the best detection path. The selection step S160 is performed through the selection module 260.

迭代次數判斷步驟S170係判斷突變步驟S150的執行次數是否等於預設次數;若否,則重新執行突變步驟S150與選擇步驟S160;若是,則結束路徑最佳化步驟S112。迭代次數判斷步驟S170透過迭代次數判斷模組270執行。 The iteration number determination step S170 is to determine whether the execution number of the mutation step S150 is equal to the preset number; if not, the mutation step S150 and the selection step S160 are executed again; if so, the path optimization step S112 is ended. The iteration number determination step S170 is executed by the iteration number determination module 270.

重新編碼步驟S114係將最佳檢測路徑之編碼轉換為量測機使用之量測機編碼。重新編碼步驟S114透過重新編碼模組214執行。 The re-encoding step S114 is to convert the code of the best detection path into the code of the measuring machine used by the measuring machine. The re-encoding step S114 is performed by the re-encoding module 214.

藉此,本新型的工件檢測之路徑規劃方法100透過動態分群步驟S140及鯨魚演算法152逃脫區域最佳解,以解決習知路徑規劃方法存在收斂速度過快而易陷入區域最佳解之問題。 In this way, the new path planning method 100 for workpiece detection escapes the regional optimal solution through the dynamic grouping step S140 and the whale algorithm 152, so as to solve the problem that the conventional path planning method has too fast convergence speed and easily falls into the regional optimal solution. .

雖然本新型已以實施方式揭露如上,然其並非用以限定本新型,任何熟習此技藝者,在不脫離本新型之精神和範圍內,當可作各種之更動與潤飾,因此本新型之保護範圍當視後附之申請專利範圍所界定者為準。 Although the present invention has been disclosed in the above embodiments, it is not intended to limit the present invention. Anyone who is familiar with this technique can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the protection of the present invention The scope shall be subject to those defined in the attached patent scope.

200:工件檢測之路徑規劃系統 200: Path planning system for workpiece inspection

210:座標關係矩陣建立模組 210: Coordinate relationship matrix creation module

212:路徑最佳化模組 212: Path Optimization Module

214:重新編碼模組 214: Recode module

Claims (5)

一種工件檢測之路徑規劃系統,用以規劃一量測機檢測一工件之一最佳檢測路徑,該工件檢測之路徑規劃系統包含:一座標關係矩陣建立模組,係驅動一射線檢測該量測機於二檢測點之間的一移動方式,以生成一座標關係矩陣;以及一路徑最佳化模組,訊號連接該座標關係矩陣建立模組,該路徑最佳化模組包含:一初始化編碼模組,用以將各該檢測點編碼,然後驅動該些檢測點複數次隨機順序排列而生成複數檢測路徑;一適應值排序模組,訊號連接該初始化編碼模組,係依據該座標關係矩陣及各該檢測路徑生成各該檢測路徑的一總距離值,並依照該些總距離值的大小排序該些檢測路徑;一動態分群模組,訊號連接該適應值排序模組,依據該些總距離值將該些檢測路徑分群成複數組別,任一該組別之複數該檢測路徑之複數該總距離值之差值小於等於一預設差值;一突變模組,訊號連接該動態分群模組,該些組別之複數領袖經由一鯨魚演算單元生成一突變檢測路徑,該突變檢測路徑包含一突變總距離值;一選擇模組,訊號連接該突變模組,將各該組別中該 領袖之該總距離值、該突變總距離值及前次迭代後的該最佳檢測路徑進行比較並選擇保留最小者而成為該最佳檢測路徑;及一迭代次數判斷模組,訊號連接該選擇模組與該突變模組,該迭代次數判斷模組判斷該突變模組的一執行次數是否等於一預設次數;若否,則該突變模組與該選擇模組重新被執行;若是,則該路徑最佳化模組終止執行。 A path planning system for workpiece inspection, which is used to plan the best inspection path for a workpiece by a measuring machine. The path planning system for workpiece inspection includes: a standard relationship matrix establishment module that drives a ray to detect the measurement The machine moves between two detection points to generate a standard relationship matrix; and a path optimization module, the signal is connected to the coordinate relationship matrix establishment module, the path optimization module includes: an initialization code The module is used to encode the detection points, and then drive the detection points to be arranged in a random order multiple times to generate a complex detection path; a fitness value sorting module, the signal is connected to the initialization coding module, based on the coordinate relationship matrix And each detection path generates a total distance value of each detection path, and sorts the detection paths according to the size of the total distance values; a dynamic grouping module, the signal is connected to the fitness value sorting module, according to the total distance value The distance value groups the detection paths into a complex group, and the difference between the plurality of the detection paths in any one group and the total distance value is less than or equal to a preset difference; a mutation module, the signal is connected to the dynamic grouping Module, the plural leaders of the groups generate a mutation detection path through a whale calculation unit, the mutation detection path includes a total mutation distance value; a selection module, the signal is connected to the mutation module, and the group is The The total distance value of the leader, the total distance value of the sudden change, and the best detection path after the previous iteration are compared and the smallest one is selected to be the best detection path; and an iteration number judgment module, the signal is connected to the selection Module and the mutation module, the iteration number determination module determines whether an execution number of the mutation module is equal to a preset number; if not, the mutation module and the selection module are re-executed; if so, then The path optimization module terminates execution. 如請求項1所述之工件檢測之路徑規劃系統,其中在該座標關係矩陣建立模組中,若該二檢測點之間存在該工件,該移動方式為非直線移動;及若該二檢測點之間不存在該工件,該移動方式為直線移動。 The path planning system for workpiece detection according to claim 1, wherein in the coordinate relationship matrix establishment module, if the workpiece exists between the two detection points, the movement mode is non-linear movement; and if the two detection points If the workpiece does not exist between, the movement method is linear movement. 如請求項1所述之工件檢測之路徑規劃系統,其中該動態分群模組包含:一相似度計算子模組,係計算該些檢測路徑之一適合度閾值及一距離閾值;及一分群子模組,訊號連接該相似度計算子模組,係計算各該檢測路徑與該領袖之間的一適合度差及一距離差,並依據該適合度閾值及該距離閾值分成該些組別。 The path planning system for workpiece inspection according to claim 1, wherein the dynamic grouping module includes: a similarity calculation sub-module for calculating a suitability threshold and a distance threshold of the detection paths; and a grouping sub-module A module, a signal connected to the similarity calculation sub-module, calculates a fitness difference and a distance difference between each detection path and the leader, and divides them into the groups according to the fitness threshold and the distance threshold. 如請求項1所述之工件檢測之路徑規劃系統,其中該鯨魚演算單元包含:一包圍子模組,係更新前次迭代後的該最佳檢測路徑並找出各該領袖之該總距離值之最小者; 一狩獵子模組,訊號連接該包圍子模組,係找出各該領袖之該總距離值之最小者;及一隨機搜索子模組,訊號連接該狩獵子模組,係以隨機順序排列該些檢測點而生成該突變檢測路徑。 The path planning system for workpiece detection according to claim 1, wherein the whale calculation unit includes: an enveloping sub-module that updates the best detection path after the previous iteration and finds the total distance value of each leader The smallest A hunting sub-module with a signal connected to the surrounding sub-module to find the smallest value of the total distance of each leader; and a random search sub-module with a signal connected to the hunting sub-module, arranged in random order These detection points generate the mutation detection path. 如請求項1所述之工件檢測之路徑規劃系統,更包含:一重新編碼模組,訊號連接該迭代次數判斷模組,該重新編碼模組係將該最佳檢測路徑之編碼轉換為該量測機使用之一量測機編碼。 The path planning system for workpiece inspection according to claim 1, further comprising: a re-encoding module, the signal is connected to the iteration number judgment module, and the re-encoding module converts the encoding of the best inspection path into the quantity The measuring machine uses a measuring machine code.
TW109203377U 2020-03-24 2020-03-24 System of workpiece inspection in path planning TWM601358U (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
TW109203377U TWM601358U (en) 2020-03-24 2020-03-24 System of workpiece inspection in path planning

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
TW109203377U TWM601358U (en) 2020-03-24 2020-03-24 System of workpiece inspection in path planning

Publications (1)

Publication Number Publication Date
TWM601358U true TWM601358U (en) 2020-09-11

Family

ID=73644581

Family Applications (1)

Application Number Title Priority Date Filing Date
TW109203377U TWM601358U (en) 2020-03-24 2020-03-24 System of workpiece inspection in path planning

Country Status (1)

Country Link
TW (1) TWM601358U (en)

Similar Documents

Publication Publication Date Title
CN106897821B (en) Transient evaluation feature selection method and device
CN104482911B (en) Sphericity error assessment method based on error ball
CN109800288B (en) Scientific research hotspot analysis and prediction method based on knowledge graph
CN106354942B (en) Assembly contact stress distribution evaluation method based on entropy theory
CN110895333B (en) Rapid 77G vehicle-mounted radar data clustering method based on Doppler frequency
AU2018253470B2 (en) Device and method for extracting terrain boundary
Hao et al. The application of an adaptive genetic algorithm based on collision detection in path planning of mobile robots
Wen et al. An improved genetic algorithm for planar and spatial straightness error evaluation
Luo et al. A method for axis straightness error evaluation based on improved artificial bee colony algorithm
TWM601358U (en) System of workpiece inspection in path planning
EP3863020A1 (en) Crystalline material analysis device, crystalline material analysis method, and crystalline material analysis program
Zhao et al. CNC thermal compensation based on mind evolutionary algorithm optimized BP neural network
KR101462349B1 (en) Method for multi-objective optimizing based on Pareto-optimality
Guo et al. Data mining and application of ship impact spectrum acceleration based on PNN neural network
Vasudevan et al. Genetic algorithm for optimisation of A-TIG welding process for modified 9Cr–1Mo steel
CN111813669B (en) Adaptive random test case generation method based on multi-target group intelligence
Cao et al. A focal any-angle path-finding algorithm based on A* on visibility graphs
CN113447022A (en) Path planning method and system for workpiece detection
CN114117898A (en) While-drilling gamma logging forward modeling method based on machine learning algorithm
Benini et al. Comparison between Pure and Surrogate-assisted Evolutionary Algorithms for Multiobjective Optimization
CN113345005A (en) Finite random search method suitable for target ball center resolving
CN109446481B (en) Method for estimating life distribution parameters of log-normal unit
CN105404736B (en) Severity computational methods based on multi-source confidence fuzzy message
CN110070620A (en) Three-dimensional grid surface model global approximation axial symmetry decision algorithm based on genetic algorithm
Chen et al. Optimal cutter size determination for 2½-axis finish machining of NURBS profile parts