CN112051796A - Planning method for generating shortest path by connecting two-dimensional random closed graphs - Google Patents

Planning method for generating shortest path by connecting two-dimensional random closed graphs Download PDF

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CN112051796A
CN112051796A CN202010819357.8A CN202010819357A CN112051796A CN 112051796 A CN112051796 A CN 112051796A CN 202010819357 A CN202010819357 A CN 202010819357A CN 112051796 A CN112051796 A CN 112051796A
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梅雪松
李钦
刘斌
王晓东
张勇
王新田
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Xian Jiaotong University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
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Abstract

The invention discloses a planning method for connecting two-dimensional random closed graphs to generate a shortest path, which takes a plurality of randomly generated two-dimensional closed graphs (the graphs are not intersected and have longer distance) as a basis for sequencing a data point set P, firstly determines a certain graph centroid as a starting point, connects the rest two-dimensional graphs one by one, optimizes the path, takes the shortest path as a target output, and adopts an improved greedy algorithm to obtain an optimal path; the relevant parameters include path length L, point PiAnd PjA distance D betweenijPoint PiTotal distance S to other pointsiCurve equation l. The invention realizes the path planning of the open-loop two-dimensional processing graph, reduces the time complexity, improves the optimality of the path planning and greatly improves the processing efficiency compared with a general intelligent algorithm.

Description

Planning method for generating shortest path by connecting two-dimensional random closed graphs
Technical Field
The invention belongs to the technical field of numerical control machining, and particularly relates to a planning method for connecting a large number of two-dimensional closed graphs to generate a shortest path in numerical control machining.
Background
In numerical control machining, path planning is an important component in data processing, and reasonable machining path planning can well improve machining efficiency. The processing path generated by the CAM generally adopts a nearest neighbor search algorithm, and because the algorithm has the defect of short visibility, global optimization is difficult to achieve. The solving time of the accurate solving algorithm increases exponentially along with the complexity of the problem, and is not practical enough for the actual complex problem. At present, an algorithm for planning a two-dimensional processing track generally adopts an intelligent optimization algorithm, such as a genetic algorithm, an ant colony algorithm, an annealing algorithm and the like, and the algorithm has a good effect in a specific application occasion, but has high time complexity, is easy to fall into local optimization, has a large possibility of a difference from an optimal solution, and has a non-ideal solving effect.
Disclosure of Invention
The invention provides a planning method for connecting a large number of two-dimensional closed graphs to generate a shortest path in numerical control machining, aiming at numerical control machining.
The invention is realized by adopting the following technical scheme:
a planning method for connecting two-dimensional random closed graphs to generate shortest paths comprises the steps of taking centroids of a plurality of randomly generated two-dimensional closed graphs as a basis for sequencing a data point set P, firstly determining a certain graph centroid as a starting point, connecting the rest two-dimensional graphs one by one, optimizing paths, outputting by taking the shortest paths as targets, and obtaining optimal paths by adopting an improved greedy algorithm; the relevant parameters include path length L, point PiAnd PjA distance D betweenijPoint PiTotal distance S to other pointsiCurve equation l.
The invention has the further improvement that the method specifically comprises the following steps:
1) selection of starting point
Centroid set points P, D for n graphsijIs a point PiAnd point PjA distance between, wherein DiiSi is point P ═ 0iThe sum of the distances to other points is as follows:
Figure BDA0002633920630000021
get max { SiObtaining a certain point Pi as a starting point;
2) point-to-point optimization of initial paths
Obtaining an initial optimized path by utilizing a nearest neighbor search algorithm, wherein the nearest neighbor search algorithm has short visibility, traversing the initial optimized path, if two paths are crossed, exchanging the point sequences of two points, regenerating the path, if other point sequences exist between the two points, turning the sequence, regenerating the path, traversing again until no crossing condition exists in the path, and storing a new optimized path;
3) point-to-line segment re-optimization path
For the optimized point sequence of 2), selecting PiI 1,2, … n-2, the remaining path
Figure BDA0002633920630000022
Processing in reverse order to obtain new path
Figure BDA0002633920630000023
Judging whether the total path length L is shortened, if so, determining a new point sequence and storing, and repeating the steps; if not, continuing the next point until the last third point Pn-2(ii) a Selecting P in turnjJ is 1,2, … n, and is inserted into the sequence between the other two points to form a new point sequence, and whether the total path length L is shortened is judged; if the path is shortened, generating a new point sequence and storing the new point sequence, repeating the steps after generating the new point sequence until all points are traversed and L is not changed any more, and storing a new optimized path;
4) line segment to line segment further optimizing path
For the point sequence path generated in step 3), obtaining an optimal road section to obtain the optimal path
Figure BDA0002633920630000024
And as a whole, reordering according to the steps of 3) until L is not reduced any more, and storing a new optimized path.
The invention is further improved in that the method also comprises the following steps:
5) fitting a graphical contour
Performing curve fitting on the contour of the processing graph to obtain a curve equation of each processing graph;
6) connecting graphics paths
Obtaining 5) the sorted processing pattern sequence, and three adjacent processing patterns Qi-1，Qi，Qi+1As a group, first calculating the processing pattern QiThe knife entering point; get Qi-1And Qi+1Center of mass Pi-1：(xi-1,yi-1) And Pi+1：(xi+1,yi+1) When Q isiIn the case of a quadratic curve: li:ax2+bxy+cy2+dx+ey+f＝0；
Figure BDA0002633920630000031
Figure BDA0002633920630000032
Simultaneous is K1，K2，K3Equation, solve to (x, y), replace QiThe centroid point sequence Pi, the new path sequence is saved, and the processes are sequentially carried out (Q)2,Q3,…Qn-1) Replacing the center of mass point with the knife entering point on the pattern; by Q2The distance Q is obtained from the cutting point1Point of entry of the upper shortest path, Qn-1Finding Q from the cutting edgenAnd (4) entering the tool point with the shortest path, repeating the process until the change of L is within 0.5%, and storing the processing path.
The invention further improves the method that the optimal road section definition in the step 4) comprises the following steps: refers to a section of road formed by several adjacent points, if the section of road
Figure BDA0002633920630000033
Smaller than any other road section length, define
Figure BDA0002633920630000034
Is the optimal road section.
The invention further improves the method for fitting the figure outline in the step 5) as follows: if the machined pattern is a simple geometric figure, the straight line profile of the pattern is fitted with a linear function: l1Y + ax + b is 0, and the curve profile is piecewise fitted with a quadratic curve: l2:ax2+bxy+cy2+ dx + ey + f ═ 0, and this is stored in the corresponding pattern QiPerforming the following steps; if the processed pattern is complex, the pattern is subjected to segment fitting: li:ax2+bxy+cy2+ dx + ey + f is 0 with an error < 0.5%.
The invention has the following beneficial technical effects:
1. the time complexity is low: the general genetic algorithm has high time complexity for solving the TSP problem and long calculation time, and the algorithm is optimized according to steps, so that the time complexity is far lower than that of the general genetic algorithm.
2. The optimization degree is high: compared with the general genetic algorithm, the genetic algorithm is likely to be involved in local optimization and cannot be better optimized continuously, and the average optimization degree is lower than that of the analytical solution algorithm.
3. The accuracy is improved: compared with a method of replacing a machining graph with a node, the contour fitting can shorten a machining path.
4. Certainty: there is randomness to the genetic algorithm so that the results are not stable at each time, while the analytical solution algorithm has a definite unique solution.
5. The expandability is strong: the method can also be applied to other non-closed-loop travel planning problems, such as bus travel planning and the like, and has a wide application range.
Drawings
Fig. 1 is a flowchart of a method for generating shortest path planning in connecting random data points according to the present invention.
Fig. 2 is a schematic diagram of a simple multi-geometry machining path planning.
In the figure: 1 is a two-dimensional data point, 2 is a two-dimensional plane, 3 is a planned path, 4 is a point, 5 is a cross path, 6 is an optimized cross path result, 7 is a point-to-line segment path non-optimized end part, 8 is a point-to-line segment path non-optimized middle part, 9 is a point-to-line segment path end part optimized result, 10 is a point-to-line segment path middle part optimized result, 11 is an optimal line segment, and 12 is a line segment-to-line segment path optimized result;
13 is an initial graph centroid, 14-21 are processing graphs, 22 is an initial optimization path, 23 is an optimization path after Lagrange optimization iteration, 24 is an optimization node after optimization iteration, and 25 is an end graph centroid.
Detailed Description
The invention is further illustrated below with reference to the figures and examples. Because the two-dimensional point trajectory planning and the two-dimensional closed graph are not easy to combine and represent, the two methods are separately represented by the attached graph.
As shown in fig. 1: the invention provides a planning method for a shortest path of data points connected with a two-dimensional plane, which takes a two-dimensional data point 1 as input, obtains an open-loop shortest path L on a two-dimensional plane 2 as output and optimizes a total path by using a modified greedy algorithm. The parameters include path length L, point PiAnd PjA distance D betweenijPoint PiTotal distance S to other pointsiCurve equation l.
The two-dimensional data point path planning method specifically comprises the following steps:
1) selection of starting point
Set point P of centroids for n figures, where Dii＝0；
Figure BDA0002633920630000051
Get max { SiGet a point POIs the starting point.
2) Optimizing initial Path (Point-to-Point)
With the point 4 as the starting point,obtaining an initial optimized path 3 by utilizing a nearest neighbor search algorithm, traversing the initial optimized path 3 due to the short visibility of the nearest neighbor search algorithm, and crossing the path 5 in the case of path crossing
Figure BDA0002633920630000052
And
Figure BDA0002633920630000053
cross, exchange PXAnd PNDue to PXAnd PNAnd other points exist between the two points, the sequence of the other points is inverted, the path is regenerated again, for example, the result 6 of the optimized cross path is traversed again until no cross condition exists in the path, and a new optimized path is stored.
3) Optimize the path again (Point to line segment)
For the optimized point sequence of 2), selecting P for the non-optimized end part 7 of the point-to-line segment pathi(i-1, 2, … n-2), the remaining paths
Figure BDA0002633920630000054
Reversing the sequence to obtain an optimization result 9 of the end part of the point-to-line segment path, judging whether the total length of the path is shortened, if so, determining a new point sequence and storing, and repeating the steps again; if not, continuing to the next point until P is reachedn-2. For the point-to-line segment path non-optimized middle part 8, P is selected in turnj(j ═ 1,2, … n), and the sequence between the remaining two points is inserted to form a new point sequence, and it is determined whether or not the total path length L has shortened. If the path is shortened, generating a new point sequence and storing the optimization result 10 of the middle part of the point-to-line segment path, repeating the steps after generating the new point sequence until all points are traversed and L is not changed, and storing a new optimization path.
4) Further optimize path (line segment to line segment)
And 3) searching an optimal road section for the generated point sequence path. Route of travel
Figure BDA0002633920630000061
Than itIf the length of any path is small, define
Figure BDA0002633920630000062
Is the optimal path. And (3) reordering the optimal road section 11 as a whole according to the steps in 3) until L is not reduced any more, obtaining a line segment-to-line segment path optimization result 12, and storing a new optimization path.
As shown in fig. 2: the invention provides a shortest path planning method applied to connecting two-dimensional plane processing graphs, which takes a connecting shortest path L obtained by two-dimensional processing graphs 14-21 sequenced according to a mass center as output and optimizes a total path by using a local Greenland multiplier method. The parameters include the curve equation L, path length L.
5) Fitting a graphical contour
The machined patterns 14-21 are simple two-dimensional machined patterns, the straight line profiles for the patterns 14,17,21 are fitted with a linear function: l1Y + ax + b is 0, and the curve profiles of the graphs 15,16,18,19,20 are piecewise fitted with quadratic curves: l2:ax2+bxy+cy2+ dx + ey + f ═ 0, and this is stored in the corresponding graph QiIn (1). If the processed graph is complex, the graph can be considered to be subjected to segment fitting: li:ax2+bxy+cy2+ dx + ey + f is 0 and requires an error of < 5%.
6) Connecting graphics paths
Obtaining 5) the ordered processing pattern sequence, and firstly calculating the tool feeding point of the processing pattern 15 by taking three adjacent processing patterns 14, 15 and 16 as a group. The centroid (x) of the processed pattern 14 and the processed pattern 16 is takeni-1,yi-1)，(xi+1,yi+1) Taking the processing pattern 15 as a quadratic curve as an example: li:ax2+bxy+cy2+dx+ey+f＝0。
Figure BDA0002633920630000063
Figure BDA0002633920630000064
Simultaneous K1，K2，K3Solving an equation to obtain (x, y), replacing the centroid point of the processing graph 15 in the processing sequence by the optimization node 24 after optimization iteration, saving a new path sequence, sequentially processing the processing graphs 16,17,18,19 and 20, and replacing the centroid point by the tool entering point on the graphs to obtain an initial optimization path 22. And (3) solving a tool entering point which is the shortest path on the distance processing graph 14 by using the tool entering point of the processing graph 15 to replace the centroid 13 of the initial graph, solving a tool entering point which is the shortest path on the processing graph 21 by using the tool entering point of the processing graph 20 to replace the centroid 25 of the tail graph, and obtaining the optimized path 23 after Lagrange optimization iteration. Repeating the above process until the change of the path length L is within 0.5%, and obtaining the preserved processing path.

Claims (5)

1. A planning method for connecting two-dimensional random closed graphs to generate the shortest path is characterized in that the method takes the centroids of a plurality of randomly generated two-dimensional closed graphs as the basis of ordering a data point set P, firstly, a certain graph centroid is determined as the initial point, the rest two-dimensional graphs are connected one by one, the path is optimized, the shortest path is taken as the target output, and an improved greedy algorithm is adopted to obtain the optimal path; the relevant parameters include path length L, point PiAnd PjA distance D betweenijPoint PiTotal distance S to other pointsiCurve equation l.
2. The planning method for connecting a two-dimensional random closed graph to generate a shortest path according to claim 1 is characterized by comprising the following steps:
1) selection of starting point
Centroid set points P, D for n graphsijIs a point PiAnd point PjA distance between, wherein DiiSi is point P ═ 0iThe sum of the distances to other points is as follows:
Figure FDA0002633920620000011
get max { SiObtaining a certain point Pi as a starting point;
2) point-to-point optimization of initial paths
Obtaining an initial optimized path by utilizing a nearest neighbor search algorithm, wherein the nearest neighbor search algorithm has short visibility, traversing the initial optimized path, if two paths are crossed, exchanging the point sequences of two points, regenerating the path, if other point sequences exist between the two points, turning the sequence, regenerating the path, traversing again until no crossing condition exists in the path, and storing a new optimized path;
3) point-to-line segment re-optimization path
For the optimized point sequence of 2), selecting PiI 1,2, … n-2, the remaining path
Figure FDA0002633920620000012
Processing in reverse order to obtain new path
Figure FDA0002633920620000013
Judging whether the total path length L is shortened, if so, determining a new point sequence and storing, and repeating the steps; if not, continuing the next point until the last third point Pn-2(ii) a Selecting P in turnjJ is 1,2, … n, and is inserted into the sequence between the other two points to form a new point sequence, and whether the total path length L is shortened is judged; if the path is shortened, generating a new point sequence and storing the new point sequence, repeating the steps after generating the new point sequence until all points are traversed and L is not changed any more, and storing a new optimized path;
4) line segment to line segment further optimizing path
For the point sequence path generated in step 3), obtaining an optimal road section to obtain the optimal path
Figure FDA0002633920620000021
And as a whole, reordering according to the steps of 3) until L is not reduced any more, and storing a new optimized path.
3. The planning method for connecting two-dimensional random closed graphs to generate shortest paths according to claim 2, further comprising the steps of:
5) fitting a graphical contour
Performing curve fitting on the contour of the processing graph to obtain a curve equation of each processing graph;
6) connecting graphics paths
Obtaining 5) the sorted processing pattern sequence, and three adjacent processing patterns Qi-1，Qi，Qi+1As a group, first calculating the processing pattern QiThe knife entering point; get Qi-1And Qi+1Center of mass Pi-1：(xi-1,yi-1) And Pi+1：(xi+1,yi+1) When Q isiIn the case of a quadratic curve: li:ax2+bxy+cy2+dx+ey+f＝0；
Figure FDA0002633920620000022
Figure FDA0002633920620000023
Simultaneous is K1，K2，K3Equation, solve to (x, y), replace QiThe centroid point sequence Pi, the new path sequence is saved, and the processes are sequentially carried out (Q)2,Q3,…Qn-1) Replacing the center of mass point with the knife entering point on the pattern; by Q2The distance Q is obtained from the cutting point1Point of entry of the upper shortest path, Qn-1Finding Q from the cutting edgenAnd (4) entering the tool point with the shortest path, repeating the process until the change of L is within 0.5%, and storing the processing path.
4. A planning method for connecting two-dimensional random closed patterns to generate shortest path according to claim 2 or 3,defining the optimal road section in the step 4): refers to a section of road formed by several adjacent points, if the section of road
Figure FDA0002633920620000031
Smaller than any other road section length, define
Figure FDA0002633920620000032
Is the optimal road section.
5. The planning method for connecting two-dimensional random closed patterns to generate the shortest path according to claim 4, wherein in the step 5), a specific method for fitting the graph contour is as follows: if the machined pattern is a simple geometric figure, the straight line profile of the pattern is fitted with a linear function: l1Y + ax + b is 0, and the curve profile is piecewise fitted with a quadratic curve: l2:ax2+bxy+cy2+ dx + ey + f ═ 0, and this is stored in the corresponding pattern QiPerforming the following steps; if the processed pattern is complex, the pattern is subjected to segment fitting: li:ax2+bxy+cy2+ dx + ey + f is 0 with an error < 0.5%.
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