CN107563050A - A kind of method for being used for the fast searching Optimal Curve in figure layer is collided - Google Patents

A kind of method for being used for the fast searching Optimal Curve in figure layer is collided Download PDF

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CN107563050A
CN107563050A CN201710766425.7A CN201710766425A CN107563050A CN 107563050 A CN107563050 A CN 107563050A CN 201710766425 A CN201710766425 A CN 201710766425A CN 107563050 A CN107563050 A CN 107563050A
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curve
list
cutter
optimal curve
point
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CN107563050B (en
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张铁
苏杰汶
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South China University of Technology SCUT
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Abstract

The invention provides a kind of method for being used for the fast searching Optimal Curve in figure layer is collided, including step：1）To the step of asking at impact-free interval midpoint, i.e., starting point of the midpoint of the impact-free interval of cutter-contact point sequence number as new Optimal Curve corresponding to joining place when intersecting during Optimal Curve is advanced with collision area border；2）Unidirectional Optimal Curve based on Neighbor search finds step, i.e., from some impact-free interval midpoint, Optimal Curve is found in reliable area in the case where not generating complete collision figure layer；3）Bidirectional optimistic curve based on recurrence method finds step；4）Optimal Curve is generated in whole collision collision figure layer.The present invention has the characteristics of flexibly practical, substantially increases and the speed of Optimal Curve is being found in colliding figure layer and is significantly reducing the operand during finding Optimal Curve.

Description

A kind of method for being used for the fast searching Optimal Curve in figure layer is collided
Technical field
The present invention relates to a kind of method for being used for the fast searching Optimal Curve in figure layer is collided, including to collisionless area Between midpoint to ask for algorithm, the unidirectional Optimal Curve finding algorithm based on Neighbor search, the bidirectional optimistic based on recurrence method bent Line finding algorithm.
Background technology
Robot to workpiece when being processed, it will usually by the machining path of CAM Software Create workpiece, then machine People end clamping workpiece or cutter perform the machining path, and workpiece is processed.But it is increasingly complicated with workpiece shapes, During performing machining path, often collide phenomenon, as robot and cutter collide, cutter and workpiece generation Collision etc..This can make the workpiece of processing scrap or be caused damage to robot.Row when therefore to the machining path of robot Collisionless optimization just seems particularly significant, and optimization method is typically to be realized using collision figure layer method.By adding to robot The emulation of work process and collision detection, the collision figure layer in processing of robots path is obtained, pass through the reliable area in collision figure layer One Optimal Curve of middle searching, and Optimal Curve is converted into the machining path of robot, realize that robot touches to the nothing of workpiece Hit processing.But the complete collision figure layer of generation needs to carry out substantial amounts of collision detection, and operand is huge, takes longer.Now One kind is needed rapidly to find an Optimal Curve in figure layer is collided in the case where not generating complete collision figure layer, it is real The collisionless optimization of the machining path of existing robot.
The content of the invention
The invention provides a kind of method for being used for the fast searching Optimal Curve in figure layer is collided.Including to collisionless area Between midpoint to ask for algorithm, the unidirectional Optimal Curve finding algorithm based on Neighbor search, the bidirectional optimistic based on recurrence method bent Line finding algorithm.The acquiring method at wherein impact-free interval midpoint solves to be determined newly when Optimal Curve runs into collision area The bright problem of Optimal Curve starting point, the unidirectional Optimal Curve finding algorithm based on Neighbor search are solved in not complete Collision diagram The problem of Optimal Curve is found in the case of layer, the bidirectional optimistic curve finding algorithm based on recurrence method, which solves, entirely to be collided The problem of whole piece Optimal Curve is found in figure layer.The present invention has the characteristics of flexibly practical, substantially increases in figure layer is collided Find the speed of Optimal Curve and significantly reduce the operand during searching Optimal Curve.
The purpose of the present invention is realized by following technical proposals：
A kind of method for being used for the fast searching Optimal Curve in figure layer is collided, including step：
1) to the step of asking at impact-free interval midpoint, i.e., intersect during Optimal Curve is advanced with collision area border When joining place corresponding to cutter-contact point sequence number impact-free interval starting point of the midpoint as new Optimal Curve；
2) unidirectional Optimal Curve based on Neighbor search finds step, i.e., from some impact-free interval midpoint, Optimal Curve is found in reliable area in the case of not generating complete collision figure layer；
3) the bidirectional optimistic curve based on recurrence method finds step；
4) Optimal Curve is generated in whole collision collision figure layer.
Further, described step 1) specifically includes：
11) initial curve is set as a first, last point difference (1,0), the straight line of (N, 0), when representing initial, whole cutter-contact points Corresponding Cutter coordinate system { M ' } is in reference axisIn position be d=0；
12) robot polishes emulation since the 1st cutter-contact point, when being polished to i-th of cutter-contact point PiWhen, if detecting work During the collision of part or robot and cutter, obtain being located at i-th of cutter-contact point PiCutter coordinate system { the M ' at placeiIn reference axisIn Several impact-free intervals；
13) and then the midpoint of each impact-free interval is asked for, when asking for impact-free interval midpoint, it is necessary to positioned at i-th Cutter coordinate system { the M ' of cutter-contact pointiΔ d is gone through all over whole seat at certain intervals from area of feasible solutions d=-A-W/2 to d=A+W/2 ParameterAnd collision detection is carried out to point (i, d), the Origin And Destination of each impact-free interval is sequentially found, and ask for its section Midpoint, W are the width in abrasive band, and A is maximum of the Cutter coordinate system { M ' } around abrasive band tangent line rotation alpha angle；
Further, in described step 13), if i is current cutter-contact point, list listmidFor storing impact-free interval Midpoint, Δ d be Cutter coordinate system { M ' } adjustment step-length, doFor the starting point of impact-free interval, null is one and is more than A+W/2 An integer, work as doDuring ≠ null, represent that Cutter coordinate system { M ' } comes intoImpact-free interval, then find i-th of knife The specific steps at the impact-free interval midpoint of contact include：
131) { M ' } is from reference axisInterval limit d=-A-W/2 start to go through all over reference axis
If 132) d ∈ [- A-W/2, A+W/2], then collision detection is carried out to (i, d) in figure layer is collided；Otherwise go to Step 136)；
133) (if i, d) ∈ CA and do≠ null, then make dm=(do+ d- Δs d)/2, by dmIt is added to list listmid In, make do=null, d=d+ Δ d, go to step 132)；
134) (if i, d) ∈ CA and do=null, or ifAnd do≠ null, then go to step 132)；
If 135)And do=null, then make do=d, goes to step 132)；
If 136) do=null, then terminate to find, otherwise make dm=(do+ d)/2, by dmIt is added to list listmidIn, Make do=null, terminate to find.
Further, in described step 2),
21) impact-free interval midrange mid, hunting zone n=i of the input as Optimal Curve starting pointo→it, integer m, Robot initial joint position list Joints, cutter-contact point list points, the point list curve on initial curve, in list I-th of value curve [i] represent { M 'i On position；
22) the growth step delta i (being 1 or -1) of cutter-contact point sequence number is calculated, makes curve [io- Δ i]=mid, i=io, d =mid；
If 23) i ≠ it+ Δ i, then seeking neighborhood U, (d, m Δ d), by neighborhood U, (value in d, m Δ d) is suitable by size Sequence is put into a list list={ d-m Δs ..., d, d+ Δ ... d+m Δs }, wherein：
In formula, diIt is the point p of i-th point in initial curveiOrdinate, d 'i+1It is the i+1 point p ' in initial curvei+1 Ordinate；Otherwise i is returnedlast=it, represent that Optimal Curve is found successfully, terminate to find；
If 24)Then jump to step 25)；Otherwise to (i, curve in figure layer is collided [i]) collision detection is carried out, ifThen Optimal Curve is found successfully, returns to ilast=it, terminate to find； IfThen jump to step 25)；
25) go through from the beginning to the end all over list and collision detection is carried out, see with the presence or absence of d ' ∈ list andAnd count Joint of robot pose θ now is calculated, if it is present making curve [i]=d=d ', Joints [i]=θ, i=i+ Δ i, is jumped To step 23)；Otherwise represent that Optimal Curve finds failure, returns to ilast=i, terminate to find.
Further, described step 3) specifically includes：
31) the cutter-contact point sequence number i to collide is inputtedF, and ask for i-thFThe middle point list of the impact-free interval of individual cutter-contact point list；
If 32) list listmidFor sky, then i is returnedr=-1, show that bidirectional optimistic curve finds failure, terminate to find； Otherwise, the first element for taking out list is assigned to mid, and deletes the first element in list, makes io=iF- 1, it=0；With mid For starting point, by n=io→itOrder, by it is unmarried searching Optimal Curve the step of, find Optimal Curve backward, and return to optimization As a result with ilast；
33) if curve is found successfully, step 34) is jumped to；Otherwise the cutter-contact point to collide is made to index n=ilast, Recursive call bidirectional optimistic curve finds step, and returns to irIf ir≠ -1, then step 34) is jumped to, otherwise jumps to step 32)；
34) i is madeo=iF+ 1, it=imax, wherein imaxFor maximum cutter-contact point sequence number, using mid as starting point, by n=io→it Order, find Optimal Curve backward, and return to optimum results and ilast；
If 35) optimized successfully, step 36) is jumped to；Otherwise the index for making the cutter-contact point to collide is n=ilast, Recursive call bidirectional optimistic curve finds step, and returns to irIf ir≠ -1, then distance Step6, otherwise jumps to Step2；
36) i is returnedr=ilast, terminate to find.
Further, described step 4) specifically includes：
41) initial manufacture coordinate system { M ' is inputtedO, the cutter-contact point list points to polish on path；
42) according to { M 'OAnd all joint positions of points generation robots, and it is sequentially placed into joint list Joints In；
43) it is the list of the point on initial curve to generate axial path list curve, curve, and each point represents respectively Cutter coordinate system { M ' } is in reference axis corresponding to cutter-contact point in pointsOn position, the initial value of all elements in list For 0；Make i=1；
If 44) i≤Joint.size, wherein Joint.size is the number of element in list Joints, then is emulating Moved the robot into scene in joint position joint [i], carry out collision detection；Otherwise represent to optimize successfully, terminate step Suddenly；
If 45) do not collided, i=i+1 is made, jumps to step 44)；Otherwise using i as collision cutter-contact point sequence number, Call bidirectional optimistic curve to find step, and return to ir；
If 46) ir≠ -1, then make i=ir, i=i+1, and jump to step 44)；Otherwise optimization failure, end step.
Compared with prior art, the present invention has the characteristics of flexibly practical, substantially increases and optimization is found in figure layer is collided The speed of curve and significantly reducing finds the operand during Optimal Curve, have it is simple, efficiently, the advantages of easily realizing.
Brief description of the drawings
Fig. 1 asks for schematic diagram to collide in figure layer to impact-free interval midpoint.
Fig. 2 is that the unidirectional Optimal Curve based on Neighbor search finds schematic diagram.
Fig. 3 a are to work as di≤d′i+1When, the descending arrangement schematic diagram of value in list.
Fig. 3 b are to work as di>d′i+1When, the descending arrangement schematic diagram of value in list.
Fig. 4 a be initial curve in the contiguous range of Optimal Curve when Optimal Curve find schematic diagram.
Fig. 4 b be initial curve not in the contiguous range of Optimal Curve when Optimal Curve find schematic diagram.
Fig. 5 is to be worked into the collisionless that motion path during the collision of workpiece or robot and cutter occurs for i-th cutter-contact point Optimize schematic diagram.
Fig. 6 is recursive call bidirectional optimistic curve finding algorithm schematic diagram when bidirectional optimistic curve is found.
Fig. 7 is to build processing of robots simulated environment schematic diagram.
Embodiment
Below in conjunction with drawings and examples, the present invention is described in further detail, but embodiments of the present invention are not It is limited to this.
In CAM softwares generate workpiece machining path, in the present embodiment be generate workpiece polishing path, and by its Motion path during processing of robots is converted into, as shown in fig. 7, processing of robots simulated environment is built, including robot, workpiece And belt sander, then processing of robots workpiece is emulated, and generation collision figure layer while emulation, in figure layer is collided Find Optimal Curve.
A kind of method for being used for the fast searching Optimal Curve in figure layer is collided, including step：
1) to the step of asking at impact-free interval midpoint, i.e., intersect during Optimal Curve is advanced with collision area border When joining place corresponding to cutter-contact point sequence number impact-free interval starting point of the midpoint as new Optimal Curve；
2) unidirectional Optimal Curve based on Neighbor search finds step, i.e., from some impact-free interval midpoint, Optimal Curve is found in reliable area in the case of not generating complete collision figure layer；
3) the bidirectional optimistic curve based on recurrence method finds step；
4) Optimal Curve is generated in whole collision collision figure layer.
Specifically, as shown in figure 1, described step 1) specifically includes：
11) initial curve is set as a first, last point difference (1,0), the straight line of (N, 0), when representing initial, whole cutter-contact points Corresponding Cutter coordinate system { M ' } is in reference axisIn position be d=0；
12) robot polishes emulation since the 1st cutter-contact point, when being polished to i-th of cutter-contact point PiWhen, if detecting work During the collision of part or robot and cutter, obtain being located at i-th of cutter-contact point PiCutter coordinate system { the M ' at placeiIn reference axisIn Several impact-free intervals, such as the section S in accompanying drawing 11With S2；
13) midpoint of each impact-free interval, point m as shown in Figure 1 are asked for and then1With m2, asking for impact-free interval , it is necessary to Cutter coordinate system { M ' positioned at i-th of cutter-contact point during midpointiFrom area of feasible solutions d=-A-W/2 to d=A+W/2 with one Fixed interval delta d is gone through all over whole reference axisAnd collision detection is carried out to point (i, d), sequentially find rising for each impact-free interval Point and terminal, and its interval midpoint is asked for, W is the width in abrasive band, and A is Cutter coordinate system { M ' } around abrasive band tangent line rotation alpha angle Maximum；
Specifically, in described step 13), if i is current cutter-contact point, list listmidFor storing impact-free interval Midpoint, Δ d be Cutter coordinate system { M ' } adjustment step-length, doFor the starting point of impact-free interval, null is one and is more than A+W/2 An integer, work as doDuring ≠ null, represent that Cutter coordinate system { M ' } comes intoImpact-free interval, then find i-th of knife The specific steps at the impact-free interval midpoint of contact include：
131) { M ' } is from reference axisInterval limit d=-A-W/2 start to go through all over reference axis
If 132) d ∈ [- A-W/2, A+W/2], then collision detection is carried out to (i, d) in figure layer is collided；Otherwise go to Step 136)；
133) (if i, d) ∈ CA and do≠ null, then make dm=(do+ d- Δs d)/2, by dmIt is added to list listmid In, make do=null, d=d+ Δ d, go to step 132)；
134) (if i, d) ∈ CA and do=null, or ifAnd do≠ null, then go to step 132)；
If 135)And do=null, then make do=d, goes to step 132)；
If 136) do=null, then terminate to find, otherwise make dm=(do+ d)/2, by dmIt is added to list listmidIn, Make do=null, terminate to find.
Step is found on the unidirectional Optimal Curve based on Neighbor search, as shown in Fig. 2 being touched when searching out i-th of knife Behind the impact-free interval midpoint of point, one of interval midpoint is selected as starting point, m as shown in Figure 11Point.From m1Point sets out, In n=io→itIn the range of, find an Optimal Curve (red imaginary curve), avoid collision area, with i-th point after just Beginning curve is connected (red solid line in figure), point of intersection n=n1.Optimal Curve is substituted into n=i in initial curveo→itPortion Point, make robot not collided when processing these cutter-contact points.
When finding Optimal Curve, the Cutter coordinate system { M ' } corresponding to two neighboring cutter-contact point existsIn distance can not It is excessive, because once apart from excessive, when processing the two cutter-contact points, amplitude that Robot contact wheel can be caused to move axially Suddenly increase, influence crudy.Therefore the point on Optimal Curve is found using Neighbor search, makes Optimal Curve more flat It is slow.
As shown in figure 3, Optimal Curve reaches i-th of point pi=(i, di), asking for i+1 point pi+1When, i+1 point Ordinate span should be dsM Δ d neighborhood U (di, m Δs d)={ di-m·Δd,…,di,di+Δd,…di+ m·Δd}(Δd>0), so that { M ' } corresponding to adjacent two cutter-contact point be existedOn distance be limited to ± m Δ d scopes It is interior.
, can be by U (d in order to improve the efficiency of searchi, the value in m Δs d) is sequentially put into a list list=by size {di-m·Δ,…,di,di+Δ,…di+ m Δs } in, wherein：
In formula, d 'i+1It is the i+1 point p ' in initial curvei+1Ordinate.Work as di≤d′i+1When, value in list by Minispread is arrived greatly, as depicted in figure 3 a, vice versa, as shown in fig. 3b.The value d all over list is gone through from the beginning to the end and to point (i+ 1, d) collision detection is carried out, ifThe then point p on Optimal Curvei+1=(i+1, d).IfThere is (i+ 1, d) ∈ CA, then Optimal Curve, which is found, fails.This searching method can ensure that Optimal Curve is close until intersecting to initial curve.
As shown in figure 4, work as d 'i+1∈U(di, during m Δ d), represent initial curve in the contiguous range of Optimal Curve It is interior, then preferentially to (i+1, d 'i+1If) carry out collision detectionAs shown in accompanying drawing 4a, then on Optimal Curve Point pi+1=(i+1, d 'i+1), and be connected with initial curve, Optimal Curve is found successfully；Otherwise list go through time, such as accompanying drawing Shown in 4b.
Therefore, described step 2) specifically includes,
21) impact-free interval midrange mid, hunting zone n=i of the input as Optimal Curve starting pointo→it, integer m, Robot initial joint position list Joints, cutter-contact point list points, the point list curve on initial curve, in list I-th of value curve [i] represent { M 'i On position；
22) the growth step delta i (being 1 or -1) of cutter-contact point sequence number is calculated, makes curve [io- Δ i]=mid, i=io, d =mid；
If 23) i ≠ it+ Δ i, then seeking neighborhood U, (d, m Δ d), by neighborhood U, (value in d, m Δ d) is suitable by size Sequence is put into a list list={ d-m Δs ..., d, d+ Δ ... d+m Δs }, wherein：
In formula, diIt is the point p of i-th point in initial curveiOrdinate, d 'i+1It is the i+1 point p ' in initial curvei+1 Ordinate；Otherwise i is returnedlast=it, represent that Optimal Curve is found successfully, terminate to find；
If 24)(d, m Δ d), then jump to step 25)；Otherwise to (i, curve in figure layer is collided [i]) collision detection is carried out, if (i, curve [i]) ∈ CA, then Optimal Curve is found successfully, returns to ilast=it, terminate to seek Look for；IfThen jump to step 25)；
25) go through from the beginning to the end all over list and collision detection is carried out, see with the presence or absence of d ' ∈ list andAnd count Joint of robot pose θ now is calculated, if it is present making curve [i]=d=d ', Joints [i]=θ, i=i+ Δ i, is jumped To step 23)；Otherwise represent that Optimal Curve finds failure, returns to ilast=i, terminate to find.
As shown in Fig. 2 work as io<itWhen, the algorithm can find n forward since mid>The Optimal Curve of i cutter-contact point, If it is desired to find n<During the Optimal Curve of i cutter-contact point, only i need to be madeo>it.
Specifically, described step 3) specifically includes：
31) the cutter-contact point sequence number i to collide is inputtedF, and ask for i-thFThe middle point list of the impact-free interval of individual cutter-contact point list；
If 32) list listmidFor sky, then i is returnedr=-1, show that bidirectional optimistic curve finds failure, terminate to find； Otherwise, the first element for taking out list is assigned to mid, and deletes the first element in list, makes io=iF- 1, it=0；With mid For starting point, by n=io→itOrder, by it is unmarried searching Optimal Curve the step of, find Optimal Curve backward, and return to optimization As a result with ilast；
33) if curve is found successfully, step 34) is jumped to；Otherwise the cutter-contact point to collide is made to index n=ilast, Recursive call bidirectional optimistic curve finds step, and returns to irIf ir≠ -1, then step 34) is jumped to, otherwise jumps to step 32)；
34) i is madeo=iF+ 1, it=imax, wherein imaxFor maximum cutter-contact point sequence number, using mid as starting point, by n=io→it Order, find Optimal Curve backward, and return to optimum results and ilast；
If 35) optimized successfully, step 36) is jumped to；Otherwise the index for making the cutter-contact point to collide is n=ilast, Recursive call bidirectional optimistic curve finds step, and returns to irIf ir≠ -1, then distance Step6, otherwise jumps to Step2；
36) i is returnedr=ilast, terminate to find.
As shown in figure 5, when being worked into i-th of cutter-contact point, there occurs the collision of workpiece or robot and cutter, then need An impact-free interval midpoint at n=i, such as the m in Fig. 51, connection initial curve is found respectively forwardly, backward Optimal Curve, make whole piece curve avoid collision area, realize the collisionless optimization of motion path.
The process of basic bidirectional optimistic curve finding algorithm is：First ask for the impact-free interval midpoint of i-th of cutter-contact point List listmid, go through all over listmidIn point m, using m as starting point, respectively forwardly, Optimal Curve is found backward, if two curves Find successfully, then terminate algorithm, if wherein a curve finds failure, continue to go through all over listmid, until listmidGo through All over completion.
As shown in fig. 6, in bidirectional optimistic curve finding algorithm, if from m1Point starts to meet when finding Optimal Curve forward To collision area, if the curve c in Fig. 6 is in n=ilastPlace enters collision area 1.In order to allow Optimal Curve to avoid the impact zone Domain, recurrence method can be used.In cutter-contact point sequence number n=ilastPlace, recursive call bidirectional optimistic curve finding algorithm, with collisionless Interval midpoint m '1Set out, find Optimal Curve junction curve c backward, find Optimal Curve connection initial curve forward.From m1Point When starting to run into collision area when finding Optimal Curve backward, also using same method.
Finally, described step 4) specifically includes：
41) initial manufacture coordinate system { M ' is inputtedO, the cutter-contact point list points to polish on path；
42) according to { M 'OAnd all joint positions of points generation robots, and it is sequentially placed into joint list Joints In；
43) it is the list of the point on initial curve to generate axial path list curve, curve, and each point represents respectively Cutter coordinate system { M ' } is in reference axis corresponding to cutter-contact point in pointsOn position, the initial value of all elements in list For 0；Make i=1；
If 44) i≤Joint.size, wherein Joint.size is the number of element in list Joints, then is emulating Moved the robot into scene in joint position joint [i], carry out collision detection；Otherwise represent to optimize successfully, terminate step Suddenly；
If 45) do not collided, i=i+1 is made, jumps to step 44)；Otherwise using i as collision cutter-contact point sequence number, Call bidirectional optimistic curve to find step, and return to ir；
If 46) ir≠ -1, then make i=ir, i=i+1, and jump to step 44)；Otherwise optimization failure, end step.
After robot motion path collisionless optimized algorithm optimizes successfully, the joint of robot pose row after optimization can be generated Table Joints, as long as robot performs the pose in the list successively, you can to realize that the collisionless to workpiece is polished.
In summary, compared with prior art, the present invention has advantage prominent as follows：
Ask for impact-free interval of the current Optimal Curve corresponding to the cutter-contact point corresponding to the intersection point on collision area border Midpoint, and the starting point using the point as new Optimal Curve section, can so ensure the big possibility of new Optimal Curve Duan Yougeng Property bypasses collision area.
Optimal Curve is found using neighborhood search strategy, collision detection number is greatly reduced, significantly reduces computing Measure and improve the searching efficiency of curve.
When searching Optimal Curve when, Optimal Curve encounters collision area again, and recursive call bidirectional optimistic curve is found Algorithm, can neatly make Optimal Curve bypass collision area, and this method has the advantages of simple, efficient, easily to realize.
Above example is used for illustrative purposes only, rather than limitation of the present invention, the technology people about technical field Member, without departing from the spirit and scope of the present invention, can also make various conversion or modification, therefore all equivalent Technical scheme should also belong to scope of the invention, should be limited by each claim.

Claims (6)

  1. A kind of 1. method for being used for the fast searching Optimal Curve in figure layer is collided, it is characterised in that including step：
    1) to the step of asking at impact-free interval midpoint, i.e., when intersecting during Optimal Curve is advanced with collision area border Starting point of the midpoint of the impact-free interval of cutter-contact point sequence number as new Optimal Curve corresponding to joining place；
    2) the unidirectional Optimal Curve based on Neighbor search finds step, i.e., from some impact-free interval midpoint, is not giving birth to Into finding Optimal Curve in reliable area in the case of complete collision figure layer；
    3) the bidirectional optimistic curve based on recurrence method finds step；
    4) Optimal Curve is generated in whole collision collision figure layer.
  2. 2. the method according to claim 1 for being used for the fast searching Optimal Curve in figure layer is collided, it is characterised in that institute The step 1) stated specifically includes：
    11) initial curve is set as a first, last point difference (1,0), the straight line of (N, 0), and when representing initial, whole cutter-contact points institutes are right The Cutter coordinate system { M ' } answered is in reference axisIn position be d=0；
    12) robot polishes emulation since the 1st cutter-contact point, when being polished to i-th of cutter-contact point PiWhen, if detect workpiece or During the collision of robot and cutter, obtain being located at i-th of cutter-contact point PiCutter coordinate system { the M at placei' in reference axisIn if Dry impact-free interval；
    13) and then the midpoint of each impact-free interval is asked for, when asking for impact-free interval midpoint, it is necessary to be touched positioned at i-th of knife Cutter coordinate system { the M of pointi' Δ d is gone through all over whole reference axis at certain intervals from area of feasible solutions d=-A-W/2 to d=A+W/2And collision detection is carried out to point (i, d), the Origin And Destination of each impact-free interval is sequentially found, and its interval midpoint is asked for, W is the width in abrasive band, and A is maximum of the Cutter coordinate system { M ' } around abrasive band tangent line rotation alpha angle.
  3. 3. the method according to claim 2 for being used for the fast searching Optimal Curve in figure layer is collided, it is characterised in that institute In the step 13) stated, if i is current cutter-contact point, list listmidFor storing the midpoint of impact-free interval, Δ d sits for processing The step-length of mark system { M ' } adjustment, doFor the starting point of impact-free interval, null is an integer for being more than A+W/2, works as do≠ During null, represent that Cutter coordinate system { M ' } comes intoImpact-free interval, then find the impact-free interval of i-th of cutter-contact point The specific steps at midpoint include：
    131) { M ' } is from reference axisInterval limit d=-A-W/2 start to go through all over reference axis
    If 132) d ∈ [- A-W/2, A+W/2], then collision detection is carried out to (i, d) in figure layer is collided；Otherwise step is gone to 136)；
    133) (if i, d) ∈ CA and do≠ null, then make dm=(do+ d- Δs d)/2, by dmIt is added to list listmidIn, order do=null, d=d+ Δ d, go to step 132)；
    134) (if i, d) ∈ CA and do=null, or ifAnd do≠ null, then go to step 132)；
    If 135)And do=null, then make do=d, goes to step 132)；
    If 136) do=null, then terminate to find, otherwise make dm=(do+ d)/2, by dmIt is added to list listmidIn, make do =null, terminate to find.
  4. 4. the method according to claim 1 for being used for the fast searching Optimal Curve in figure layer is collided, it is characterised in that institute In the step 2) stated,
    21) impact-free interval midrange mid, hunting zone n=i of the input as Optimal Curve starting pointo→it, integer m, machine The initial joint position list Joints of people, cutter-contact point list points, the point list curve on initial curve, i-th in list Individual value curve [i] represents { Mi'On position；
    22) the growth step delta i of cutter-contact point sequence number is calculated, makes curve [io- Δ i]=mid, i=io, d=mid；
    If 23) i ≠ it+ Δ i, then seeking neighborhood U, (d, m Δ d), by neighborhood U, (value in d, m Δ d) is sequentially put into by size In one list list={ d-m Δs ..., d, d+ Δ ... d+m Δs }, wherein：
    In formula, diIt is the point p of i-th point in initial curveiOrdinate, di′+1It is the i+1 point p ' in initial curvei+1It is vertical Coordinate；Otherwise i is returnedlast=it, represent that Optimal Curve is found successfully, terminate to find；
    If 24)Then jump to step 25)；Otherwise (i, curve [i]) is entered in figure layer is collided Row collision detection, if (i, curve [i]) ∈ CA, then Optimal Curve is found successfully, returns to ilast=it, terminate to find；IfThen jump to step 25)；
    25) go through from the beginning to the end all over list and collision detection is carried out, see with the presence or absence of d ' ∈ list andAnd calculate this When joint of robot pose θ, if it is present making curve [i]=d=d ', Joints [i]=θ, i=i+ Δ i, jump to step It is rapid 23)；Otherwise represent that Optimal Curve finds failure, returns to ilast=i, terminate to find.
  5. 5. the method according to claim 1 for being used for the fast searching Optimal Curve in figure layer is collided, it is characterised in that institute The step 3) stated specifically includes：
    31) the cutter-contact point sequence number i to collide is inputtedF, and ask for i-thFThe middle point list of the impact-free interval of individual cutter-contact point list；
    If 32) list listmidFor sky, then i is returnedr=-1, show that bidirectional optimistic curve finds failure, terminate to find；Otherwise, The first element for taking out list is assigned to mid, and deletes the first element in list, makes io=iF- 1, it=0；Using mid as rise Point, by n=io→itOrder, by it is unmarried searching Optimal Curve the step of, find Optimal Curve backward, and return to optimum results With ilast；
    33) if curve is found successfully, step 34) is jumped to；Otherwise the cutter-contact point to collide is made to index n=ilast, recurrence tune Step is found with bidirectional optimistic curve, and returns to irIf ir≠ -1, then step 34) is jumped to, otherwise jumps to step 32)；
    34) i is madeo=iF+ 1, it=imax, wherein imaxFor maximum cutter-contact point sequence number, using mid as starting point, by n=io→itIt is suitable Sequence, Optimal Curve is found backward, and return to optimum results and ilast；
    If 35) optimized successfully, step 36) is jumped to；Otherwise the index for making the cutter-contact point to collide is n=ilast, recurrence tune Step is found with bidirectional optimistic curve, and returns to irIf ir≠ -1, then distance Step6, otherwise jumps to Step2；
    36) i is returnedr=ilast, terminate to find.
  6. 6. the method according to claim 1 for being used for the fast searching Optimal Curve in figure layer is collided, it is characterised in that institute The step 4) stated specifically includes：
    41) initial manufacture coordinate system { M ' is inputtedO, the cutter-contact point list points to polish on path；
    42) according to { M 'OAnd all joint positions of points generation robots, and be sequentially placed into joint list Joints；
    43) it is the list of the point on initial curve to generate axial path list curve, curve, and each point is represented in points respectively Cutter-contact point corresponding to Cutter coordinate system { M ' } in reference axisOn position, in list the initial value of all elements be 0；Make i= 1；
    If 44) i≤Joint.size, wherein Joint.size is the number of element in list Joints, then in simulating scenes In move the robot into joint position joint [i], carry out collision detection；Otherwise represent to optimize successfully, end step；
    If 45) do not collided, i=i+1 is made, jumps to step 44)；Otherwise using i as collision cutter-contact point sequence number, call Bidirectional optimistic curve finds step, and returns to ir；
    If 46) ir≠ -1, then make i=ir, i=i+1, and jump to step 44)；Otherwise optimization failure, end step.
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