CN106744389A

CN106744389A - A kind of efficient single cylinder bolt-type multistage sequential telescopic method for optimizing route

Info

Publication number: CN106744389A
Application number: CN201611214033.1A
Authority: CN
Inventors: 毛艳; 成凯
Original assignee: Jilin University
Current assignee: Jilin University
Priority date: 2016-12-22
Filing date: 2016-12-22
Publication date: 2017-05-31
Anticipated expiration: 2036-12-22
Also published as: CN106744389B

Abstract

The present invention relates to a kind of efficient single cylinder bolt-type multistage sequential telescopic method for optimizing route, belong to single cylinder bolt-type multistage sequential telescopic method for optimizing route.Range, required minimum stroke, operational process judge needed for by calculating, and draw contracting arm limiting condition collection；The principle that all contracting arm limiting condition collection that will be drawn stretch in order carry out step sequence act, it is necessary to walk sequence it is minimum be optimal contracting arm limiting condition collection.The present invention is general, universality algorithm, it is adaptable to n sections telescopic arm, per there is m snibbing position in joint arm, and algorithm logic is clear, expression is clear and definite, integrated level is high, establish one's own system, depth optimal solution can be found, whether to being that optimal solution possesses evaluation criterion, generally, optimization measure is up to more than 10%.

Description

A kind of efficient single cylinder bolt-type multistage sequential telescopic method for optimizing route

Technical field

The present invention provides a kind of single cylinder bolt-type multistage sequential telescopic method for optimizing route, and the multistage order of single cylinder bolt-type is stretched Contracting is to promote multi-stage telescopic arms/set with a section driving cylinder order, per joint arm/put several pin-and-hole positions, the arm of arm joint afterbody Pin is locked with the pin-and-hole of its outside arm joint, so that telescopic arm/set is elongated to the length of demand step by step.The single cylinder of autocrane Bolt-type multistage telescopic arm is typical multistage sequential telescopic mechanism.

Background technology

" single cylinder bolt-type sequential telescopic " refers to：With a telescopic oil cylinder, successively top stretch or bounce back each arm joint to certain Arm pin-and-hole position, the stroke of oil cylinder only has a joint arm long.It is flexible according to：The principle of " contract from outside to inside, stretch from inside to outside ".With five As a example by section telescopic arm, when stretching according to the five, the four, three, two, the order of a joint arm；According to first, second, third and fourth, five joint arms during contracting Order, " first-in last-out " or " first going out laggard ", be similar to stack mechanism.As shown in Figure 1.

Because the total kilometres of telescopic oil cylinder be equal to a joint arm it is long, can with per joint arm take oil cylinder stroke length, while It is also the snibbing position of the arm joint, represents arm joint length；And the combination of all arm joint length, it is brachium.If with numeral 1, 2nd, 3,4 0%, 45%, 90%, the 100% of oil cylinder total kilometres are represented respectively, can be combined with an array representation brachium, i.e. brachium, Also referred to as brachium state set.Array { 11111 }, represents that five joint arms are full reduced (see Fig. 1-a)；Array { 44444 } represents five Joint arm is stretched (see Fig. 1-c) entirely；Array { 33221 }, indicates five section telescopic arms, since arm 1, the overhang point of each joint arm It is not：90%, 90%, 45%, 45%, 0% oil cylinder total kilometres (see Fig. 1-b).

Therefore, the characteristics of sequential telescopic：

(1)：Brachium is discrete combined value, is discontinuous；

(2)：Brachium combination is limited.For example：Five section telescopic arms, have four pin-and-hole positions in every joint arm, then theoretical group It is 4 to close number⁵=1024, i.e., be up to 1024 kinds brachiums.

(3)：Change brachium trouble, it is necessary to be fully retracted into arm joint section by section, new brachium combination is then extended section by section, because This flexible efficiency is low, and speed is slow.

In fact, changing brachium, the combination of another brachium is switched to from the combination of brachium, sometimes and need not be full reduced Arm, some arm section positions can keep, or extend target location in advance, can so save flexible step number, shorten flexible Time.

Save a step and often mean improved efficiency more than 10%, therefore, flexible step number how is simplified, flexible efficiency is improved, Any flexible path optimization of brachium combination is realized, it is very meaningful to sequential telescopic class problem.

At present, the research of sequential telescopic routing problem is very few, though for example, single-cylinder bolt technology is found broad application, It is all no preferable method for optimizing route of domestic and international main engine plants.

Document 1《The optimal control method and control system of single-cylinder bolt type telescopic boom trail》, publication number CN 101670984A.By the way of judging immediately, contract a joint arm every time, and program judges whether the oil cylinder stroke of the position meets and wants AskAbove arm joint can be kept if requirement is met；If being unsatisfactory for length requirement, it is necessary to which contract a joint arm again, then judges once；Such as After this multiple contracting arm, the length of oil cylinder of requirement is reached, just the semi-girder since most end joint arm.This " make a move, calculate a step ", is one Program Realizing Method is planted, is not the algorithm model for characterizing features, it is impossible to which advance plan optimization path, effect of optimization is limited.

Document 2《The control method of single-cylinder bolt type telescopic boom, equipment, system and engineering machinery》, application publication number CN Although 104340884 A propose the core of multistage sequential telescopic routing problem：The combination of the contracting arm limit is found, but to calculating Method pool of overall importance and logic globality are held and are weak.Show as：

One, flow chart are complicated：By the position that oil cylinder is stopped, the n-th joint arm is parked in, then calls n-th subprogram, subprogram Module is more；Meanwhile, it is afterbody algorithm and head algorithm two parts by procedure division by oil cylinder stop place.Algorithm is numerous and diverse, program The scale of construction is big, takes resource.

Secondly, its greatest drawback be：Because the understanding to routing problem is not up to basic aspect, adopted without exception during optimization With " contracting 1 " treatment, other positions possibility is not accounted for, therefore for random combine, it is difficult to reach depth or extremely optimize；It is right Whether the combination of paths for drawing is optimal, and does not have evaluation criterion.

For example：Be can be seen that for extending brachium dbjective state from brachium current state collection { 22222 } from accompanying drawing 2a Collection { 21 21 2 }, document 2 can realize optimization, 4 steps are only needed to after optimization and completes flexible switching；7 steps are needed before optimization.But Knowable to accompanying drawing 2b, for extending dbjective state collection { 22222 } from current state collection { 14411 }, document 2 can not be real Now optimize, it is still necessary to which 7 steps are completed.

The content of the invention

The present invention provides a kind of efficient single cylinder bolt-type multistage sequential telescopic method for optimizing route；

It is a kind of Program Realizing Method different from document 1, it is impossible to advance path planning, can only " contract a step, calculates a step "； The present invention gives the system solution methods of routing problem, single-cylinder bolt type telescopic boom present combination and target are simply entered Combination, system can just cook up optimal path.

It is big for the flow of document 2 complexity, the program scale of construction；Understanding to routing problem is not up to basic aspect, optimization Shi Yilv does not account for other positions possibility, therefore be difficult to reach depth optimization for random combine using " contracting 1 " treatment Shortcoming, present invention finds the inherent law that contracting arm limit combination process judges, the contracting arm limit flow for creating layering judges Network, is the connection condition of interlayer with " valve ", and algorithm effect can reach depth optimization.

The present invention can effectively reduce flexible step number, so as to lift flexible efficiency.

The present invention is adopted the technical scheme that：Telescopic arm has n joint arms, comprises the following steps：

Step (1)：Receive telescopic arm current state collection { A [1], A [2] ... A [n] }, telescopic arm dbjective state collection { T [1], T [2]…T[n]}；Wherein：

N is telescopic arm joint number；A [i] is the current state of the i-th joint arm, and the value of A [i] is m, and m is positive integer, represents arm joint The pin-and-hole position of upper distribution, such as：1st pin-and-hole, m-th pin-and-hole of the 2nd pin-and-hole ..., the different oil cylinder row of each pin-and-hole correspondence Journey；Arm joint latch in different pin-and-holes, so as to there is different extension elongations；

T [i] is the dbjective state of the i-th joint arm, and the value of T [i] is m, and m is positive integer, represents the pin-and-hole position being distributed in arm joint Put, such as：1st pin-and-hole, m-th pin-and-hole of the 2nd pin-and-hole ..., the different oil cylinder stroke of each pin-and-hole correspondence；Arm joint latch exists In different pin-and-holes, so as to there is different extension elongations；

Step (2)：According to the telescopic arm current state collection, the telescopic arm dbjective state collection, and can be used to stretch Telescopic oil cylinder stroke, calculate contracting arm limiting condition collection { O [1], O [2] ... O [n] }；

Contracting arm limiting condition collection refers to：It is that first order is retracted by arm joint when multistage sequential telescopic changes brachium, it is then suitable again Sequence is stretched out；Judged by oil cylinder effective travel, some arm joints can be without retracting, it is possible to crosses its sequential telescopic other arms Section；Or some arm joints can directly be extended target position without first contracting, and the flexible of follow-up arm joint is not influenceed；These can be with The arm joint of reservation, the arm joint and other arm joints that need to be retracted that can first extend target position, add the most end for initiating a switch to stretch out The combination of arm joint state, referred to as contracting arm limiting condition collection；The total length one of contracting arm limiting condition collection is scheduled on telescopic oil cylinder total kilometres That is in joint arm scope long；

O [i] is the contracting arm limiting condition of the i-th joint arm, and the value of O [i] is m, and m is positive integer, represents the pin being distributed in arm joint Hole site, such as：1st pin-and-hole, m-th pin-and-hole of the 2nd pin-and-hole ..., the different oil cylinder stroke of each pin-and-hole correspondence；Arm joint is inserted Sell in different pin-and-holes, so as to there are different extension elongations；

Step (3)：According to the telescopic arm current state collection, the telescopic arm dbjective state collection and calculated Contracting arm limiting condition collection, the principle of telescopic arm in sequence, the flexible path of planning：From the telescopic arm current state collection --- The contracting arm limiting condition collection, is order contracting arm；From the contracting arm limiting condition collection --- the telescopic arm dbjective state collection, it is Order semi-girder；

Order contracting arm refer to：First contracting Section 1 arm, again contracting Section 2 arm ... most joint arm of retraction n-th；

Order semi-girder refers to：The n-th joint arm is first stretched, the (n-1)th joint arm ... is stretched again finally is stretched Section 1 arm；

The contracting arm limiting condition collection that step (2) draws is probably one, it is also possible to multiple, if drawing multiple, The multiple described contracting arm limiting condition collection that will be drawn is by the flexible path of step 3 methods described planning；Then therefrom select, from institute State telescopic arm current state collection --- the telescopic arm dbjective state collection uses the minimum contracting arm limiting condition collection of step number, makees It is optimal path.

The positive effect of the present invention is：

1st, the present invention provides the system solution methods of the method for optimizing route of single cylinder bolt-type multistage sequential telescopic

The complete resolving ideas for giving single cylinder bolt-type multistage sequential telescopic routing problem of present system：Seek Look for the core objective that contracting arm limiting condition collection is algorithm；Range, required minimum stroke, operational process are sentenced needed for by calculating It is disconnected, draw contracting arm limiting condition collection；The principle that all contracting arm limiting condition collection that will be drawn stretch in order carries out step sequence act, Need walk sequence it is minimum be optimal contracting arm limiting condition collection.

The method is general, universality algorithm, it is adaptable to have m snibbing position in n sections telescopic arm, every joint arm, algorithm is patrolled Volume clear, expression is clearly, integrated level is high, establish one's own system.

2nd, create and ask for the layering of contracting arm limiting condition collection and judge flow through a network, be the connection condition of interlayer with " valve ", As long as addition judges water valve, just can increase feasible path, so as to further approach depth optimal path, algorithm effect can reach Depth optimization.

Present invention finds the inherent law that contracting arm limit combination process judges, to ask for contracting arm limiting condition collection, build The judgement flow network of multilayer.The solution of optimization problem is not often unique；Also, whether feasible solution is optimal, it is necessary to evaluation criterion. With the analogy of canal water valve, the course that can be judged with pictute flow meets unlocking condition by opening or closing Water valve, draws a plurality of feasible path, and optimal path is finally selected wherein, therefore, this patent can find depth optimal solution.Together When, to whether being that optimal solution possesses evaluation criterion.Generally, optimization measure is up to more than 10%.

3rd, T-shaped water valve and A type water valve concepts are proposed, the flow of T-shaped and A types multiplexing can increase optimization depth

T-shaped water valve refers to carry out water valve unlatching judgement as the principle of fixed arm joint to extend target position；A type water valves are Refer to, water valve unlatching judgement is carried out to retain the principle as fixed arm joint in situ.It is provided simultaneously with T-shaped and A type water valves judgement stream Journey increased possible path optimizing, accordingly, it is possible to reach more depth optimization.

Brief description of the drawings

Fig. 1 is sequential telescopic principle schematic；

Fig. 2 a are the examples that document 2 can realize optimization；

Fig. 2 b are the not good examples of the effect of optimization of document 2；

Fig. 3 is that the stroke for asking for contracting arm limiting condition collection judges general flow chart；

Fig. 4 is that the stroke for asking for contracting arm limiting condition collection judges general flow chart, the compound canal water valve method of T-shaped and A types；

Fig. 5 is that the canal water valve method contracting arm limit combines corresponding telescopic step sequence figure；

Fig. 6 is Different Optimization method effect contrast figure.

Specific embodiment

Telescopic arm has n joint arms, comprises the following steps：

In the present embodiment, 4 pin-and-holes are had in arm joint, m values are 1,2,3,4, correspond to respectively oil cylinder stroke 0%, 45%th, 90,100%；Telescopic arm current state collection { A [1], A [2] ... A [n] } is：There is n to save telescopic arm, currently stretched out per joint arm Length set；

In the present embodiment, 4 pin-and-holes are had in arm joint, m values are 1,2,3,4, correspond to respectively oil cylinder stroke 0%, 45%th, 90,100%；Telescopic arm dbjective state collection { T [1], T [2] ... T [n] } is：There is n to save telescopic arm, stretched out per joint arm target Length set；

Contracting arm limiting condition collection refers to：It is that first order is retracted by arm joint when multistage sequential telescopic changes brachium, it is then suitable again Sequence is stretched out；Judged by oil cylinder effective travel, some arm joints can be without retracting, it is possible to crosses its sequential telescopic other arms Section；Or some arm joints can directly be extended target position without first contracting, and the flexible of follow-up arm joint is not influenceed；These can be with The arm joint of reservation, the arm joint and other arm joints that need to be retracted that can first extend target position, add the most end for initiating a switch to stretch out The combination of arm joint state, referred to as contracting arm limiting condition collection；The total length one of contracting arm limiting condition collection is scheduled on telescopic oil cylinder total kilometres That is in joint arm scope long, the purpose of path optimization's algorithm is to find contracting arm limiting condition collection；

In the present embodiment, 4 pin-and-holes are had in arm joint, m values are 1,2,3,4, correspond to respectively oil cylinder stroke 0%, 45%th, 90,100%；Telescopic arm contracting arm limiting condition collection { O [1], O [2] ... O [n] } is：There is n to save telescopic arm, per joint arm contracting arm The set of limiting length；

The present invention performs following steps in step (2)：

Step (20)：Compare the current state A [n] and dbjective state T [n] of least significant end arm joint, judge A [n] ≠ T [n], If A [n] and T [n] are equal, A [n-1] ≠ T [n-1] is compared forward；Compare A [n-2] ≠ T [n-2] by that analogy…；If Unequal, then flow is down performed；

Step (21)：Establish range judgment formula and minimum stroke judgment formula；Assignment x, i, derive different x, i values Corresponding range judgment formula and minimum stroke judgment formula；

The range judgment formula (formula)：

n:Telescopic arm joint number；

L:Oil cylinder total kilometres (are equal to a joint arm long), are defined as 100%；

C_A[i]:The current stroke of i-th joint arm, value is 0%-100%；

Such as：C_A [2]=2, represents Section 2 arm, currently stretches out 45% oil cylinder total kilometres, and oil cylinder total kilometres are equal to a joint arm It is long；

C_T[i]:I-th joint arm target stroke, value is 0%-100%；

Such as：C_T [4]=3, represents Section 4 arm, and target stretches out 90% oil cylinder total kilometres, and oil cylinder total kilometres are equal to a joint arm It is long；

C[i]:I-th joint arm is stretched the maximum oil cylinder stroke of needs, and value is 0%-100%；C [i]=max (C_A [i], C_T [i]) such as：C [2]=max (C_A [2], C_T [2])=3, maximum oil cylinder stroke needed for representing flexible Section 2 arm is 90%；

Minimum stroke judgment formula (formula)：

CC_i(i+1)(i+2):Flexible i-th section, (i+1) section, the minimum value of oil cylinder stroke needed for (i+2) joint arm, CC_i (i+1) (i+2)=max (C [i], C [i+1], C [i+2])；

X is represented：When flow is performed from top to bottom, the quantity (contracting 1 refers to full reduced) of 1 arm joint that contracts.Wherein：X=1, represents one Start no arm joint contracting 1；X=2, represents Section 1 arm contracting 1；…；X=n-1 is represented：Since Section 1 arm, until the n-th -2 joint arm All contract 1；

I is represented：When flow is performed from left to right, the number of plies that flow is launched to the right, because flow is except by step (22) --- step (24) is performed from top to bottom, when step (23) are gone to, if meeting minimum stroke judgment formula --- it is public Formula (2), flow can also be launched from left to right；

I=1, represents：Program circuit is performed in the 1st layer, only one of which main flow from top to bottom at the beginning；

I=2, represents：When the 1st layer of main flow goes to step (23), certain minimum stroke judgment formula meets condition, Now program may be selected to enter or do not enter the branch's flow launched to the right, if input is opened, flow is entered into be launched to the right The 2nd layer of branch's flow；If input is closed, flow cannot flow into the 2nd layer of branch's flow, can only be in the 1st laminar flow journey from upper past Lower order is performed；

I=n-2, represents：When the n-th -2 layers branch's flow go to step (23), certain minimum stroke judgment formula is expired Sufficient condition, now program may be selected to enter or do not enter the branch's flow launched to the right；If input is opened, flow is entered into The (n-1)th layer of branch's flow launched to the right；If input is closed, flow cannot flow into (n-1)th layer of branch's flow, can only be the 1st To in the n-th -2 layers branch's flow, order is performed layer from left to right, from top to bottom；

For the traveling mode of pictute flow, liken the path of flow, if i=1, only one layer with " canal stream " herein Flow from top to bottom, referred to as main canal stream；If i=2, flow can expand one level to the right branch, altogether two-layer canal stream；If ... i =n-1, flow can to the right be expanded to (n-1)th layer, common n-1 layers of canal stream；

When each layer of canal stream goes to step (23), whether minimum stroke judgment formula meets condition, if meeting condition, together When " selection open ", then flow chart can increase to the right one layer of sublateral canal stream；" selection is opened ", is compared with " water valve " herein Analogy, " water valve " is opened, and meaning " canal stream " can to the right flow into branch's flow, and " water valve " is closed, and meaning " canal stream " can only be current The operation of layer path；

" canal stream " correspondence " flow ", " water valve " correspondence " selection is opened ", both of which does not have actual physical meaning, is simply The traveling of pictute " flow ", and " selection is opened " enters the condition of branch's flow；

Step (22)：Required range judges, if required range formula meets, directly exports contracting arm limiting condition Collection O { }；Otherwise, step (23) is performed；

By step (21), initially only one layer of main canal stream, takes i=1；This layer of all arm joint of canal stream do not contract 1；Note x= 1；

Range judgment formula (1) needed for described is write as：

C[1]+C[2]+...+C[n]≤L (1.1)

If meeting, all arm joints directly extend target position, contracting arm limiting condition collection O={ T [1], T to formula (1.1) [2],…,T[n]}；If it is not satisfied, performing step (23) downwards；

Step (23)：Required minimum stroke judges, if required minimum stroke formula meets, can choose whether to enter to the right Branch's flow, if selection " water valve " is opened, flow enters next layer of branch's " canal stream ", meanwhile, i=i+1；If required minimum row Journey formula is unsatisfactory for, and flow is performed downwards, performs step (24)；

Minimum stroke judgment formula (2) needed for described is write as：

C_T[1]+CC_234...n≤L (2.1)

Formula (2.1) can select to open if meeting to next layer " water valve ", and into step (231), i=2 is similar to follow Ring performs step (21) --- step (23)；If it is not satisfied, step (24) can only be performed downwards；

Step (24)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=1, x=2, weight Multiple step (21)；

By step (21), initially only one layer of main canal stream, takes i=1；Since Section 1 arm, Section 1 arm is contracted 1, then x= 2；Step (25) is performed downwards；

Step (25)：Required range judgement, repeat step (22)；

By step (22), i=1, during x=2, required range judgment formula (1) is write as：

0+C[2]+...+C[n]≤L (1.2)

If meeting range judgment formula (1.2), there is contracting arm limiting condition collection to export O={ 1, T [2] ..., T [n] }； If it is not satisfied, then carrying out minimum stroke judgement, step (26) is performed；

Step (26)：Required minimum stroke judgement, repeat step (23)；

By step (23), i=1, during x=2, required minimum stroke judgment formula (2) is write as：

0+C_T[2]+CC_34...n≤L (2.2)

If meeting, " water valve " can select to open formula (2.2), and into step (261), i=2, similar cycle performs step Suddenly (21) --- step (23)；If it is not satisfied, step (27) can only be performed downwards；

Step (27)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=1, x=3, weight Multiple step (21) ... is until to range judgment formula (1) and minimum stroke judgment formula (2), assignment i=1, x=(n- 1), repeat step (21)；

By step (21), initially only one layer of main canal stream, takes i=1；Since Section 1 arm, Section 1, Section 2 arm are contracted 1, then x=3；

... the like,

Until by step (21), initially only one layer of main canal stream, takes i=1；Since Section 1 arm, by Section 1 --- the (n-3) joint arm contracting 1, then x=(n-2)；Step (28) is performed downwards；

Step (28)：Required range judgement, repeat step (22)；

By step (22), when i=1, x=(n-2), required range judgment formula (1) is write as：

0+...0+C[n-2]+C[n-1]+C[n]≤L (1.(n-2))

If meeting range judgment formula (1. (n-2)), contracting arm limiting condition collection output O={ 1,1 ..., 1, T [n- 2],T[n-1],T[n]}；If it is not satisfied, then carrying out minimum stroke judgement, step (29) is performed；

Step (29)：Required minimum stroke judgement, repeat step (23), and obtain flow end product；

By step (23), when i=1, x=(n-2), required minimum stroke judgment formula (2) is write as：

0+...+0+C_T[n-2]+C[n-1]+C[n]≤L (2.(n-2))

If meeting, " water valve " can select to open formula (2. (n-2)), and into step (291), i=2, similar cycle is held Row step (21) --- step (23)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1), now, range formula For：

0+...0+C[n-1]+C[n]≤L (1.(n-1))

If range formula (1. (n-1)) meets, output contracting arm limiting condition collection output O={ 1,1,1 ..., 1, T [n-1],T[n]}；If it is not satisfied, (n-1) joint arm then contracted into 1, x=n, output contracting arm limiting condition collection export O=1,1, 1,…,1,1,T[n]}。

The present invention performs following steps in step (23)：

If meeting, the second layer " water valve " can select to open formula (2.1), into step (231), now, second layer canal Stream is designated as：I=2；

Step (231)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=1, weight Multiple step (21)；

By step (21), it is initially：I=2, there is two-layer canal stream；X=1, represents that Section 1 arm extends target invariant position, from the 2 joint arms start contracting 1, do not have arm joint contracting 1 when initial, and step (232) is performed downwards；

Step (232)：Required range judgement, repeat step (22)；

By step (22), i=2；X=1；It is described needed for range judgment formula (1) write C [2]+...+C [n]≤L-C_ T[1](1.1.1)

Section 1 arm is extended target position by formula (1.1.1) if meeting, and since Section 2 arm, all arm joints are directly stretched To target position, contracting arm limiting condition collection O={ T [1], T [2] ..., T [n] }；If it is not satisfied, performing (233) downwards；

Step (233)：Required minimum stroke judgement, repeat step (23)；

By step (23), i=2, during x=1, required minimum stroke judgment formula (2) is write as：

C_T[2]+CC_34...n≤L-C_T[1] (2.1.1)

If meeting, third layer " water valve " can select to open formula (2.1.1), and into step (2331), i=3 is similar to follow Ring performs step (21) --- step (23)；If it is not satisfied, step (234) can only be performed downwards；

Step (234)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=2, weight Multiple step (21)；

By step (21), i=2, there is two-layer canal stream；X=2, represents that Section 1 arm extends target invariant position, opened from Section 2 arm Begin, by Section 2 arm contracting 1, step (235) is performed downwards；

Step (235)：Required range judgement, repeat step (22)；

By step (22), i=2；X=2；Range judgment formula (1) needed for described is write as：

0+C[3]+...+C[n]≤L-C_T[1] (1.1.2)

Formula (1.1.2) if meet, Section 1 arm extend target position, Section 2 arm contracting 1, in addition all arm joints directly extend Target position, contracting arm limiting condition collection O={ T [1], 1, T [3] ..., T [n]；If it is not satisfied, performing (236) downwards；

Step (236)：Required minimum stroke judgement, repeat step (23)；

By step (23), i=2, during x=2, required minimum stroke judgment formula (2) is write as：

0+C_T[3]+CC_34...n≤L-C_T[1] (2.1.2)

If meeting, the 2nd third layer " water valve " can select to open formula (2.1.2), into step (2361), i=3, Similar cycle performs step (21) --- step (23)；If it is not satisfied, step (237) can only be performed downwards；

Step (237)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=3, weight Multiple step (21) ... is until to range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=(n- 1), repeat step (21)；

By step (21), i=2, there is two-layer canal stream；X=3, represents that Section 1 arm extends target invariant position, opened from Section 2 arm Begin, by Section 2, Section 3 arm contracting 1；... the like, until by step (21), i=2 has two-layer canal stream；X=(n-2), table Show Section 1 arm extend target invariant position, since Section 2 arm, by Section 2 --- (n-3) joint arm contracting 1；

Step (238)：Required range judgement, repeat step (22)；

By step (22), when i=2, x=(n-2), required range judgment formula (1) is write as：

0+...+0+C[n-2]+C[n-1]+C[n]≤L-C_T[1] (1.1.(n-2))

If meeting range judgment formula (1.1. (n-2)), contracting arm limiting condition collection output O={ T [1], 1 ... 1, T [n-2],T[n-1],T[n]}；If it is not satisfied, then carrying out minimum stroke judgement, step (239) is performed；

Step (239)：Required minimum stroke judgement, repeat step (23), and obtain this layer of branch's flow end product；

By step (23), when i=2, x=(n-2), required minimum stroke judgment formula (2) is write as：

0+...+0+C_T[n-2]+C[n-1]+C[n]≤L-C_T[1] (2.1.(n-2))

If meeting, " water valve " can select to open formula (2.1. (n-2)), into step (2391), i=3, similar cycle Perform step (21) --- step (23)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1), now, range is public Formula is：

0+...+0+C[n-1]+C[n]≤L-C_T[1] (1.1.(n-1))

If range formula (1.1. (n-1)) meets, output contracting arm limiting condition collection output O=T [1], 1 ..., 1,T[n-1],T[n]}；If it is not satisfied, then by (n-1) joint arm contracting 1, x=n, output contracting arm limiting condition collection output O={ T [1],1,…,1,1,T[n]}。

The present invention performs following steps in step (26)：

If meeting, the second layer " water valve " can select to open formula (2.2), into step (261), now, second layer canal Stream is designated as：I=2；

Step (261)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=1, weight Multiple step (21)；

By step (21), it is initially：I=2, there is two-layer canal stream；X=1, represents Section 1 arm contracting 1, Section 2 arm is extended into mesh Mark, in addition all arms do not contract 1, step (262) is performed downwards；

Step (262)：Required range judgement, repeat step (22)；

By step (22), i=2；X=1；Range judgment formula (1) needed for described is write as：

C[3]+...+C[n]≤L-C_T[2] (1.2.1)

Formula (1.2.1) if meet, Section 1 arm contracting 1, Section 2 arm is extended target position, all arm joints are directly stretched in addition To target position, contracting arm limiting condition collection O={ 1, T [2], T [3], T [4] ..., T [n] }；If it is not satisfied, performing (263) downwards；

Step (263)：Required minimum stroke judgement, repeat step (23)；

C_T[3]+CC_45...n≤L-C_T[2] (2.2.1)

If meeting, the 3rd third layer " water valve " can select to open formula (2.2.1), into step (2631), i=3, Similar cycle performs step (21) --- step (23)；If it is not satisfied, step (264) can only be performed downwards；

Step (264)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=2, weight Multiple step (21)；

By step (21), i=2, there is two-layer canal stream；X=2, represents that the contracting 1, Section 2 arm of Section 1 arm extends target position, by the 3 joint arms contracting 1, in addition all arms do not contract 1.Step (265) is performed downwards；

Step (265)：Required range judgement, repeat step (22).

0+C[4]+...+C[n]≤L-C_T[2] (1.2.2)

If meeting, the contracting 1, Section 2 arm of Section 1 arm extends target position to formula (1.2.2), and Section 3 arm is contracted 1, institute in addition There is arm joint directly to extend target position, contracting arm limiting condition collection O={ 1, T [2], 1, T [4] ..., T [n] }；If it is not satisfied, holding downwards Row (266)；Step (266)：Required minimum stroke judgement, repeat step (23)；

0+C_T[4]+CC_56...n≤L-C_T[2] (2.2.2)

If meeting, the 4th third layer " water valve " can select to open formula (2.2.2), into step (2661), i=3, Similar cycle performs step (21) --- step (23)；If it is not satisfied, step (267) can only be performed downwards；

Step (267)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=3, weight Multiple step (21) ... is until to range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=(n- 1), repeat step (21)；

By step (21), i=2, there is two-layer canal stream；X=3, represents Section 1 arm contracting 1, Section 2 arm is extended target position, will Section 3, Section 4 arm contracting 1；... the like, until by step (21), i=2 has two-layer canal stream；X=(n-2), represents the 1st Joint arm contracting 1, Section 2 arm is extended target position, since Section 3 arm, by Section 3 --- (n-3) joint arm contracting 1；

Step (268)：Required range judgement, repeat step (22)；

0+...+0+C[n-2]+C[n-1]+C[n]≤L-C_T[2] (1.2.(n-2))

If meeting range judgment formula (1.2. (n-2)), contracting arm limiting condition collection O={ 1, T [2], 1 ..., 1, T [n-2],T[n-1],T[n]}；If it is not satisfied, then carrying out minimum stroke judgement, step (269) is performed；

Step (269)：Required minimum stroke judgement, repeat step (23), and obtain this layer of branch's flow end product；

0+...+0+C_T[n-2]+C[n-1]+C[n]≤L-C_T[2] (2.2.(n-2))

If meeting, " water valve " can select to open formula (2.2. (n-2)), into step (2691), i=3, similar cycle Perform step (21) --- step (23)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1), now, range is public Formula is：

0+...+0+C[n-1]+C[n]≤L-C_T[2] (1.2.(n-1))

If range formula (1.2. (n-1)) meets, contracting arm limiting condition collection O=1, T [2], 1 ..., 1, T [n-1], T[n]}；If it is not satisfied, (n-1) joint arm is contracted 1, then x=n, output contracting arm limiting condition collection O=1, T [2], 1 ..., 1,1, T[n]}。

The present invention performs following steps in step (29)：

If meeting, the second layer " water valve " can select to open formula (2.2), into step (291), now, second layer canal Stream is designated as：I=2；

Step (291)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=1, weight Multiple step (21)；

By step (21), it is initially：I=2, there is two-layer canal stream；X=1, represents Section 1 arm contracting 1, Section 2 arm is extended into mesh Mark, in addition all arms do not contract 1, step (292) is performed downwards；

Step (292)：Required range judgement, repeat step (22)；

C[n-1]+C[n]≤L-C_T[n-2] (1.(n-2).1)

Formula (1. (n-2) .1) if meet, Section 1 arm --- (n-3) joint arm contracting 1, (n-2) joint arm is extended into mesh Mark, in addition all arm joints directly extend target position, then contracting arm limiting condition collection O={ 1,1 ..., 1, T [n-2], T [n-1], T [n]}；If it is not satisfied, performing (293) downwards；

Step (293)：Required minimum stroke judgement, repeat step (23), and obtain this layer of branch's flow end product；

C_T[n-1]+C[n]≤L-C_T[n-2] (2.(n-2).1)

Formula (2. (n-2) .1) if meet, Section 1 arm --- (n-3) joint arm contracting 1, (n-2) joint arm is extended into mesh Mark, in addition all arm joints directly extend target position, then contracting arm limiting condition collection O={ 1,1 ..., 1, T [n-2], T [n-1], T [n]}；If it is not satisfied, by (n-1) joint arm contracting 1, then exporting dbjective state collection O={ 1,1 ..., 1, T [n-2], 1, T [n] }.

The present invention performs following steps in step (233)：

If meeting, third layer " water valve " can select to open formula (2.1.1), into step (2331)；

Step (2331)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=3, x=1, Repeat step (21)；

By step (21), it is initially：I=3, there is three layers of canal stream；X=1, represents that Section 1, Section 2 arm extend target position not Become, the contracting 1 since Section 3 arm, there is no arm joint contracting 1 when initial.Step (2332) is performed downwards；

Step (2332)：Required range formula judgement, repeat step (22)；

By step (22), i=3；X=1；Range judgment formula (1) is expressed as：

C[3]+...+C[n]≤L-C_T[1]-C_T[2] (1.1.1.1)

If meeting, Section 1, Section 2 arm extend target invariant position to formula (1.1.1.1), since Section 3 arm, own Arm joint directly extends target position, contracting arm limiting condition collection O={ T [1], T [2], T [3] ..., T [n] }；If it is not satisfied, holding downwards Row (2333)；

Step (2333)：Required minimum stroke formula judgement, repeat step (23)；

By step (23), i=3；X=1；Minimum stroke judgment formula (1) is expressed as：

C_T[3]+CC_45...n≤L-C_T[1]-C_T[2] (2.1.1.1)

If meeting, the 4th layer " water valve " can select to open formula (2.1.1.1), into step (23331), i=4, class Step (21) is performed like circulation --- step (23)；... by that analogy, can be with recursion to i=n-2 layers, similar cycle performs step Suddenly (21) --- step (23)；If it is not satisfied, step (2334) can only be performed downwards；

Step (2334)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=3, x=2, Repeat step (21)；

By step (21), it is initially：I=3, there is three layers of canal stream；X=2, represents that Section 1, Section 2 arm extend target position not Become, Section 3 arm contracting 1 performs downwards step (2335).

Step (2335)：Required range formula judgement, repeat step (22)；

By step (22), i=3；X=2；Range judgment formula (1) is expressed as：

C[4]+...+C[n]≤L-C_T[1]-C_T[2] (1.1.1.2)

If meeting, Section 1, Section 2 arm extend target position, Section 3 arm contracting 1, in addition all arm joints to formula (1.1.1.2) Directly extend target position, contracting arm limiting condition collection O={ T [1], T [2], 1, T [4] ..., T [n] }；If it is not satisfied, performing downwards (2336)；

Step (2336)：Required minimum stroke formula judgement, repeat step (23)；

By step (23), i=3；X=2；Minimum stroke judgment formula (1) is expressed as：

C_T[4]+CC_56...n≤L-C_T[1]-C_T[2] (2.1.1.2)

If meeting, the 4th layer " water valve " can select to open formula (2.1.1.2), into step (23361), i=4, class Step (21) is performed like circulation --- step (23)；... by that analogy, can be with recursion to i=n-2 layers, similar cycle performs step Suddenly (21) --- step (23)；If it is not satisfied, step (2337) can only be performed downwards；

Step (2337)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=3, x=3, Repeat step (21)；

By step (21), it is initially：I=3, there is three layers of canal stream；X=3, represents that Section 1, Section 2 arm extend target position not Become, Section 3, Section 4 arm contracting 1；... the like, until by step (21), i=3 has three layers of canal stream；X=(n-2), represents Section 1, Section 2 arm extend target invariant position, Section 3 --- (n-3) joint arm contracting 1；

Step (2338)：Required range judgement, repeat step (22).

By step (22), when i=3, x=(n-2), required range judgment formula (1) is write as：

C[n-2]+C[n-1]+C[n]≤L-C_T[1]-C_T[2] (1.1.1.(n-2))

If meeting, Section 1, Section 2 arm extend target position, Section 3 --- (n-3) arm to formula (1.1.1. (n-2)) Contracting 1, in addition all arm joints directly extend target position, contracting arm limiting condition collection O={ T [1], T [2], 1,1 ..., 1, T [n-2], T [n-1],T[n]}；If it is not satisfied, performing (2339) downwards；

Step (2339)：Required minimum stroke formula judgement, repeat step (23)；

By step (23), i=3；X=(n-2)；Minimum stroke judgment formula (1) is expressed as：

C_T[n-2]+CC_(n-1)n≤L-C_T[1]-C_T[2] (2.1.1.(n-2))

If meeting, " water valve " can select to open formula (2.1.1. (n-2)), and into step (23391), i=4 is similar to Circulation performs step (21) --- step (23)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1), now, maximum row Journey formula is：

0+...+0+C[n-1]+C[n]≤L-C_T[1]-C_T[2] (1.1.1.(n-1))

If range formula (1.1.1. (n-1)) meets, contracting arm limiting condition collection O={ T [1], T [2], 1 ..., 1, T [n-1],T[n]}；If it is not satisfied, (n-1) joint arm is contracted 1, then x=n, output contracting arm limiting condition collection O=T [1], T [2], 1,…,1,1,T[n]}。

The present invention adds A type minimum strokes to sentence between all required ranges judge and required minimum stroke judges It is disconnected, as a example by adding A types minimum stroke to judge between step (23) and step (24), minimum stroke judgment formula needed for A types For：

It is to show difference：Formula (2) is referred to as T-shaped required minimum stroke judgment formula below；

The process step for adding A types minimum stroke to judge is as follows：

Range judgment formula (formula)：

T-shaped minimum stroke judgment formula (formula)：

A type minimum strokes judgment formula (formula)：

Range judgment formula (1) needed for described is write as：

C[1]+C[2]+...+C[n]≤L (1.1)

Step (23)：Minimum stroke judges needed for T-shaped, if minimum stroke formula meets needed for T-shaped, can choose whether to Right entrance branch flow, if selection " water valve " is opened, flow enters next layer of branch's " canal stream ", meanwhile, i=i+1；If T-shaped Required minimum stroke formula is unsatisfactory for, and flow is performed downwards, performs step (24)；

Minimum stroke judgment formula (2) needed for described is write as：

C_T[1]+CC_234...n≤L (2.1)

Formula (2.1) can select to open if meeting to next layer T-shaped " water valve ", and into step (231), i=2 is similar to Circulation performs step (21) --- step (24)；If it is not satisfied, step (25) can only be performed downwards；

Step (24)：Needed for A types minimum stroke judge, if needed for A types minimum stroke formula meet, can choose whether to Right entrance branch flow, if selection " water valve " is opened, flow enters next layer of branch's " canal stream ", meanwhile, i '=i '+1；If A Minimum stroke formula is unsatisfactory for needed for type, and flow is performed downwards, performs step (25)；

Minimum stroke judgment formula (3) needed for described is write as：

C_A[1]+CC_234...n≤L (3.1)

Formula (3.1) can select to open if meeting to next layer of A type " water valve ", and into step (241), i=2 is similar to Circulation performs step (21) --- step (24)；If it is not satisfied, step (25) can only be performed downwards；

Step (25)：Range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A type minimum strokes are sentenced Disconnected formula (3), assignment i=1, x=2, repeat step (21)；

By step (21), initially only one layer of main canal stream, takes i=1；Since Section 1 arm, Section 1 arm is contracted 1, then x= 2；Step (26) is performed downwards；

Step (26)：Required range judgement, repeat step (22)；

0+C[2]+...+C[n]≤L (1.2)

If meeting range judgment formula (1.2), there is contracting arm limiting condition collection to export O={ 1, T [2] ..., T [n] }； If it is not satisfied, then carrying out minimum stroke judgement, step (27) is performed；

Step (27)：Minimum stroke judges needed for T-shaped, repeat step (23)；

By step (23), i=1, during x=2, T-shaped required minimum stroke judgment formula (2) is write as：

0+C_T[2]+CC_34...n≤L (2.2)

If meeting, T-shaped " water valve " can be selected to open formula (2.2), and into step (271), i=2, similar cycle is performed Step (21) --- step (24)；If it is not satisfied, step (27) can only be performed downwards；

Step (28)：Minimum stroke judgement, repeat step (24) needed for A types；

By step (23), i=1, during x=2, minimum stroke judgment formula (3) is write as needed for the A types：

0+C_T[2]+CC_34...n≤L (3.2)

If meeting, A types " water valve " can be selected to open formula (3.2), and into step (281), i=2, similar cycle is performed Step (21) --- step (24)；If it is not satisfied, step (29) can only be performed downwards；

Step (29)：Range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A type minimum strokes are sentenced Disconnected formula (3), assignment i=1, x=3, repeat step (21) ... is until to range judgment formula (1), T-shaped minimum stroke Judgment formula (2) and A type minimum strokes judgment formula (3), assignment i=1, x=(n-1), repeat step (21)；

By step (21), initially only one layer of main canal stream, takes i=1；Since Section 1 arm, Section 1, Section 2 arm are contracted 1, then x=3；... the like, until by step (21), initially only one layer of main canal stream, takes i=1；Since Section 1 arm, By Section 1 --- (n-3) joint arm contracting 1, then x=(n-2)；Step (2A) is performed downwards；

Step (2A)：Required range judgement, repeat step (22)；

0+...0+C[n-2]+C[n-1]+C[n]≤L (1.(n-2))

If meeting range judgment formula (1. (n-2)), contracting arm limiting condition collection output O={ 1,1 ..., 1, T [n- 2],T[n-1],T[n]}；If it is not satisfied, then carrying out minimum stroke judgement, step (2B) is performed；

Step (2B)：Minimum stroke judges needed for T-shaped, repeat step (23)；

By step (23), when i=1, x=(n-2), T-shaped required minimum stroke judgment formula (2) is write as：

0+...+0+C_T[n-2]+C[n-1]+C[n]≤L (2.(n-2))

If meeting, T-shaped " water valve " can select to open formula (2. (n-2)), into step (2B1), i=2, similar cycle Perform step (21) --- step (24)；If it is not satisfied, performing step (2C) downwards；

Step (2C)：Minimum stroke judgement, repeat step (24) needed for A types, and obtain flow end product；

By step (24), when i=1, x=(n-2), minimum stroke judgment formula (3) is write as needed for the A types：

0+...+0+C_A[n-2]+C[n-1]+C[n]≤L (3.(n-2))

If meeting, A types " water valve " can select to open formula (3. (n-2)), into step (2C1), i=2, similar cycle Perform step (21) --- step (23)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1).Now, range is public Formula is：

0+...0+C[n-1]+C[n]≤L (1.(n-1))

The present invention performs following steps in step (23)：

If meeting, the second layer T-shaped " water valve " can select to open formula (2.1), into step (231), now, the second layer Canal stream is designated as：I=2；

Step (231)：Range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A type minimum strokes are sentenced Disconnected formula (3), assignment i=2, x=1, repeat step (21)；

Step (232)：Required range judgement, repeat step (22)；

C[2]+...+C[n]≤L-C_T[1] (1.1.1)

Section 1 arm is extended target position by formula (1.1.1) if meeting, and since Section 2 arm, all arm joints are directly stretched To target position, contracting arm limiting condition collection O={ T [1], T [2] ..., T [n] }；If it is not satisfied, performing step (233) downwards；

Step (233)：Minimum stroke judges needed for T-shaped, repeat step (23),

By step (23), i=2, during x=1, T-shaped required minimum stroke judgment formula (2) is write as：

C_T[2]+CC_34...n≤L-C_T[1] (2.1.1)

If meeting, third layer T-shaped " water valve " can select to open formula (2.1.1), into step (2331), i=3, class Step (21) is performed like circulation --- step (24)；If it is not satisfied, step (234) can only be performed downwards；

Step (234)：Minimum stroke judgement needed for A types, repeat step (24),

By step (24), i=2, during x=1, minimum stroke judgment formula (3) is write as needed for the A types：

C_A[2]+CC_34...n≤L-C_T[1] (3.1.1)

If meeting, third layer A types " water valve " can select to open formula (3.1.1), into step (2341), i=3, class Step (21) is performed like circulation --- step (24)；If it is not satisfied, step (235) can only be performed downwards；

Step (235)：Range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A type minimum strokes are sentenced Disconnected formula (3), assignment i=2, x=2, repeat step (21)；

By step (21), i=2, there is two-layer canal stream；X=2, represents that Section 1 arm extends target invariant position, opened from Section 2 arm Begin, by Section 2 arm contracting 1, step (236) is performed downwards；

Step (236)：Required range judgement, repeat step (22)；

0+C[3]+...+C[n]≤L-C_T[1] (1.1.2)

Formula (1.1.2) if meet, Section 1 arm extend target position, Section 2 arm contracting 1, in addition all arm joints directly extend Target position, contracting arm limiting condition collection O={ T [1], 1, T [3] ..., T [n]；If it is not satisfied, performing (237) downwards；

Step (237)：Minimum stroke judges needed for T-shaped, repeat step (23)；

By step (23), i=2, during x=2, T-shaped required minimum stroke judgment formula (2) is write as：

0+C_T[3]+CC_34...n≤L-C_T[1] (2.1.2)

If meeting, the 2nd third layer T-shaped " water valve " can select to open formula (2.1.2), into step (2371), i= 3, similar cycle performs step (21) --- step (24)；If it is not satisfied, step (238) can only be performed downwards；

Step (238)：Minimum stroke judgement, repeat step (24) needed for A types；

By step (23), i=2, during x=2, minimum stroke judgment formula (3) is write as needed for the A types：

0+C_A[3]+CC_34...n≤L-C_T[1] (3.1.2)

If meeting, the 2nd third layer A types " water valve " can select to open formula (3.1.2), into step (2381), i= 3, similar cycle performs step (21) --- step (24)；If it is not satisfied, step (239) can only be performed downwards；

Step (239)：Range judgment formula (1), T-shaped minimum stroke judgment formula (2), A type minimum strokes are sentenced Disconnected formula (3), assignment i=2, x=3, repeat step (21) ... is until to range judgment formula (1), T-shaped minimum stroke Judgment formula (2) and A type minimum strokes judgment formula (3), assignment i=2, x=(n-1), repeat step (21)；

By step (21), i=2, there is two-layer canal stream；X=3, represents that Section 1 arm extends target invariant position, is opened from Section 2 arm Begin, by Section 2, Section 3 arm contracting 1；... the like, until by step (21), i=2 has two-layer canal stream；X=(n-2), table Show that Section 1 arm extends target invariant position, since Section 2 arm, by Section 2 --- (n-3) joint arm contracting 1；Step is performed downwards (23A)；

Step (23A)：Required range judgement, repeat step (22)；

0+...+0+C[n-2]+C[n-1]+C[n]≤L-C_T[1] (1.1.(n-2))

If meeting range judgment formula (1.1. (n-2)), contracting arm limiting condition collection output O={ T [1], 1 ... 1, T [n-2],T[n-1],T[n]}；If it is not satisfied, then carrying out minimum stroke judgement, step (23B) is performed；

Step (23B)：Minimum stroke judges needed for T-shaped, repeat step (23)；

By step (23), when i=2, x=(n-2), T-shaped required minimum stroke judgment formula (2) is write as：

0+...+0+C_T[n-2]+C[n-1]+C[n]≤L-C_T[1] (2.1.(n-2))

If meeting, T-shaped " water valve " can select to open formula (2.1. (n-2)), and into step (23B1), i=3 is similar to Circulation performs step (21) --- step (24)；If it is not satisfied, performing step (23C)；

Step (23C)：Minimum stroke needed for A types judges, repeat step (24), and obtains this layer of branch's flow and finally tie Really；

By step (24), when i=2, x=(n-2), minimum stroke judgment formula (3) is write as needed for the A types：

0+...+0+C_A[n-2]+C[n-1]+C[n]≤L-C_T[1] (3.1.(n-2))

If meeting, A types " water valve " can select to open formula (3.1. (n-2)), and into step (23C1), i=3 is similar to Circulation performs step (21) --- step (24)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1), now, maximum row Journey formula is：

0+...+0+C[n-1]+C[n]≤L-C_T[1] (1.1.(n-1))

The present invention performs following steps in step (233)：

If meeting, third layer T-shaped " water valve " can select to open formula (2.1.1), into step (2331)；

Step (2331)：To range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A type minimum strokes Judgment formula (3), assignment i=3, x=1, repeat step (21),

Step (2332)：Required range formula judgement, repeat step (22)；

By step (22), i=3；X=1；Range judgment formula (1) is expressed as：

C[3]+...+C[n]≤L-C_T[1]-C_T[2] (1.1.1.1)

Step (2333)：Minimum stroke formula judges needed for T-shaped, repeat step (23)；

By step (23), i=3；X=1；T-shaped minimum stroke judgment formula (2) is expressed as：

C_T[3]+CC_45...n≤L-C_T[1]-C_T[2] (2.1.1.1)

If meeting, the 4th layer T-shaped " water valve " can select to open formula (2.1.1.1), into step (23331), i=4, Similar cycle performs step (21) --- step (24)；... by that analogy, can be performed with recursion to i=n-2 layers, similar cycle Step (21) --- step (24)；If it is not satisfied, step (2334) can only be performed downwards；

Step (2334)：The judgement of minimum stroke formula, repeat step (24) needed for A types；

By step (24), i=3；X=1；A type minimum strokes judgment formula (3) is expressed as：

C_A[3]+CC_45...n≤L-C_T[1]-C_T[2] (3.1.1.1)

If meeting, the 4th layer of A type " water valve " can select to open formula (3.1.1.1), into step (23341), i=4, Similar cycle performs step (21) --- step (24)；... by that analogy, can be performed with recursion to i=n-2 layers, similar cycle Step (21) --- step (24)；If it is not satisfied, step (2335) can only be performed downwards；

Step (2335)：To range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A type minimum strokes Judgment formula (3), assignment i=3, x=2, repeat step (21)；

By step (21), i=3, there are three layers of canal stream；X=2, represents that Section 1, Section 2 arm extend target invariant position, from the 3rd Joint arm starts, and by Section 3 arm contracting 1, step (2336) is performed downwards；

Step (2336)：Required range judgement, repeat step (22)；

By step (22), i=3；X=2；Range judgment formula (1) needed for described is write as：

C[4]+...+C[n]≤L-C_T[1]-C_T[2] (1.1.1.2)

If meeting, Section 1, Section 2 arm extend target position, Section 3 arm contracting 1, in addition all arm joints to formula (1.1.1.2) Directly extend target position, contracting arm limiting condition collection O={ T [1], T [2], 1, T [4] ..., T [n]；If it is not satisfied, performing downwards (2337)；

Step (2337)：Minimum stroke judges needed for T-shaped, repeat step (23),

By step (23), i=3, during x=2, T-shaped required minimum stroke judgment formula (2) is write as：

C_T[4]+CC_45...n≤L-C_T[1]-C_T[2] (2.1.1.2)

If meeting, the 2nd third layer T-shaped " water valve " can select to open formula (2.1.1.2), into step (23371), I=4, similar cycle performs step (21) --- step (24)；If it is not satisfied, step (2338) can only be performed downwards；

Step (2338)：Minimum stroke judgement needed for A types, repeat step (24),

By step (23), i=3, during x=2, minimum stroke judgment formula (3) is write as needed for the A types：

C_A[4]+CC_45...n≤L-C_T[1]-C_T[2] (3.1.1.2)

If meeting, the 2nd third layer A types " water valve " can select to open formula (3.1.1.2), into step (23381), I=4, similar cycle performs step (21) --- step (24)；If it is not satisfied, step (2339) can only be performed downwards；

Step (2339)：Range judgment formula (1), T-shaped minimum stroke judgment formula (2), A type minimum strokes are sentenced Disconnected formula (3), assignment i=3, x=3, repeat step (21) ... is until to range judgment formula (1), T-shaped minimum stroke Judgment formula (2) and A type minimum strokes judgment formula (3), assignment i=2, x=(n-1), repeat step (21),

By step (21), i=3, there are three layers of canal stream；X=3, represents that Section 1, Section 2 arm extend target invariant position, from the 3rd Joint arm starts, by Section 3, Section 4 arm contracting 1；... the like, until by step (21), i=3 has three layers of canal stream；X= (n-2), represent that Section 1, Section 2 arm extend target invariant position, since Section 3 arm, by Section 3 --- (n-3) joint arm contracts 1；

Step (233A)：Required range judgement, repeat step (22)；

C[n-2]+C[n-1]+C[n]≤L-C_T[1]-C_T[2] (1.1.1.(n-2))

If meeting range judgment formula (1.1.1. (n-2)), the output of contracting arm limiting condition collection

O=T [1], T [2], 1 ... 1, T [n-2], T [n-1], T [n] }；If it is not satisfied, minimum stroke judgement is then carried out, Perform step (233B)；

Step (233B)：Minimum stroke judges needed for T-shaped, repeat step (23)；

By step (23), when i=3, x=(n-2), T-shaped required minimum stroke judgment formula (2) is write as：

C_T[n-2]+C[n-1]+C[n]≤L-C_T[1]-C_T[2] (2.1.1.(n-2))

If meeting, T-shaped " water valve " can select to open formula (2.1.1. (n-2)), into step (233B1), i=4, class Step (21) is performed like circulation --- step (24)；If it is not satisfied, performing step (233C)；

Step (233C)：Minimum stroke needed for A types judges, repeat step (24), and obtains this layer of branch's flow and finally tie Really；

By step (24), when i=3, x=(n-2), minimum stroke judgment formula (3) is write as needed for the A types：

C_A[n-2]+C[n-1]+C[n]≤L-C_T[1]-C_T[2] (3.1.1.(n-2))

If meeting, A types " water valve " can select to open formula (3.1.1. (n-2)), into step (233C1), i=4, class Step (21) is performed like circulation --- step (24)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1).Now, it is maximum Stroke formula is：

C[n-1]+C[n]≤L-C_T[1]-C_T[2] (1.1.1.(n-1))

If range formula (1.1.1. (n-1)) meets, output contracting arm limiting condition collection output O={ T [1], T [2],1,…1,T[n-1],T[n]}；If it is not satisfied, then by (n-1) joint arm contracting 1, x=n, output contracting arm limiting condition collection is defeated Go out O={ T [1], T [2], 1 ... 1,1, T [n] }.

The present invention performs following steps in step (234)：

If meeting, third layer A types " water valve " can select to open formula (3.1.1), into step (2341)；

Step (2341)：To range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A type minimum strokes Judgment formula (3), assignment i=3, x=1, repeat step (21)；

By step (21), it is initially：I=3, there is three layers of canal stream；X=1, represents that Section 1 extends target position, Section 2 arm and protects Constant, the contracting 1 since Section 3 arm in situ is held, there is no arm joint contracting 1 when initial, step (2342) is performed downwards；

Step (2342)：Required range formula judgement, repeat step (22)；

By step (22), i=3；X=1；Range judgment formula (1) is expressed as：

C[3]+...+C[n]≤L-C_T[1]-C_A[2] (1.1.1.1’)

If meeting, Section 1 arm extends target position to formula (1.1.1.1 '), and Section 2 arm keeps in situ constant, from Section 3 Arm starts, and all arm joints directly extend target position, contracting arm limiting condition collection O={ T [1], A [2], T [3] ..., T [n] }；If no Meet, perform (2343) downwards；

Step (2343)：Minimum stroke formula judges needed for T-shaped, repeat step (23)；

By step (23), i=3；X=1；T-shaped minimum stroke judgment formula (1) is expressed as：

C_T[3]+CC_45...n≤L-C_T[1]-C_A[2] (2.1.1.1’)

If meeting, the 4th layer T-shaped " water valve " can select to open formula (2.1.1.1 '), into step (23431), i= 4, similar cycle performs step (21) --- step (24)；... by that analogy, can be with recursion to i=n-2 layers, similar cycle is held Row step (21) --- step (24)；If it is not satisfied, step (2344) can only be performed downwards；

Step (2344)：The judgement of minimum stroke formula, repeat step (24) needed for A types；

C_A[3]+CC_45...n≤L-C_T[1]-C_A[2] (3.1.1.1’)

If meeting, the 4th layer of A type " water valve " can select to open formula (3.1.1.1 '), into step (23441), i= 4, similar cycle performs step (21) --- step (24)；... by that analogy, can be with recursion to i=n-2 layers, similar cycle is held Row step (21) --- step (24)；If it is not satisfied, step (2345) can only be performed downwards；

Step (2345)：To range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A type minimum strokes Judgment formula (3), assignment i=3, x=2, repeat step (21)；

By step (21), i=3, there are three layers of canal stream；X=2, represents that Section 1 extends target position, Section 2 arm and keeps original position not Become, the contracting 1 since Section 3 arm, by Section 3 arm contracting 1.Step (2346) is performed downwards；

Step (2346)：Required range judgement, repeat step (22)；

C[4]+...+C[n]≤L-C_T[1]-C_A[2] (1.1.1.2’)

If meeting, Section 1 extends target position to formula (1.1.1.2 '), Section 2 arm keep in situ, Section 3 arm contracting 1, this Outer all arm joints directly extend target position, contracting arm limiting condition collection O={ T [1], A [2], 1, T [4] ..., T [n]；If it is not satisfied, Perform (2347) downwards；Step (2347)：Minimum stroke judges needed for T-shaped, repeat step (23)；

C_T[4]+CC_45...n≤L-C_T[1]-C_A[2] (2.1.1.2’)

If meeting, the 2nd the 4th layer T-shaped " water valve " can select to open formula (2.1.1.2 '), into step (23471), i=4, similar cycle performs step (21) --- step (24)；If it is not satisfied, step can only be performed downwards (2348)；

Step (2348)：Minimum stroke judgement needed for A types, repeat step (24),

C_A[4]+CC_45...n≤L-C_T[1]-C_A[2] (3.1.1.2’)

If meeting, the 2nd the 4th layer of A type " water valve " can select to open formula (3.1.1.2 '), into step (23481), i=4, similar cycle performs step (21) --- step (24)；If it is not satisfied, step can only be performed downwards (2349)；

Step (2349)：Range judgment formula (1), T-shaped minimum stroke judgment formula (2), A type minimum strokes are sentenced Disconnected formula (3), assignment i=3, x=3, repeat step (21) ... is until to range judgment formula (1), T-shaped minimum stroke Judgment formula (2) and A type minimum strokes judgment formula (3), assignment i=2, x=(n-1), repeat step (21)；

By step (21), i=3, there are three layers of canal stream；X=3, represents that Section 1 extends target position, Section 2 arm and keeps original position not Become, the contracting 1 since Section 3 arm, by Section 3, Section 4 arm contracting 1；... the like, until by step (21), i=3 has three Layer canal stream；X=(n-2), represents that Section 1 extends target position, Section 2 arm and keeps constant, the contracting 1 since Section 3 arm in situ, by the 3 sections --- (n-3) joint arm contracting 1；

Step (234A)：Required range judgement, repeat step (22)；

C[n-2]+C[n-1]+C[n]≤L-C_T[1]-C_A[2] (1.1.1.(n-2)’)

If meeting range judgment formula (1.1.1. (n-2) '), the output of contracting arm limiting condition collection

O=T [1], A [2], 1 ... 1, T [n-2], T [n-1], T [n] }；If it is not satisfied, minimum stroke judgement is then carried out, Perform step (234B)；Step (234B)：Minimum stroke judges needed for T-shaped, repeat step (23)；

C_T[n-2]+C[n-1]+C[n]≤L-C_T[1]-C_A[2] (2.1.1.(n-2)’)

If meeting, T-shaped " water valve " can select to open formula (2.1.1. (n-2) '), into step (234B1), i=4, Similar cycle performs step (21) --- step (24)；If it is not satisfied, performing step (234C)；

Step (234C)：Minimum stroke needed for A types judges, repeat step (24), and obtains this layer of branch's flow and finally tie Really；

C_A[n-2]+C[n-1]+C[n]≤L-C_T[1]-C_A[2] (3.1.1.(n-2)’)

If meeting, A types " water valve " can select to open formula (3.1.1. (n-2) '), into step (234C1), i=4, Similar cycle performs step (21) --- step (24)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1), now, most Big stroke formula is：

C[n-1]+C[n]≤L-C_T[1]-C_A[2] (1.1.1.(n-1)’)

If range formula (1.1.1. (n-1) ') meets, output contracting arm limiting condition collection output O={ T [1], A [2],1,…1,T[n-1],T[n]}；If it is not satisfied, then by (n-1) joint arm contracting 1, x=n, output contracting arm limiting condition collection is defeated Go out O={ T [1], A [2], 1 ... 1,1, T [n] }.

The present invention is further illustrated by experimental example below.

Arm joint number n=5, asks from current state collection { 14421 }, to the optimization road of dbjective state collection { 21212 } Footpath.

(1) optimal contracting arm limit combination is asked for

1st, by foregoing schemes step (21), compare：A [5] ≠ T [5], therefore perform step (22)；

2nd, by step (22), required range is judged, required range formula is：

C[1]+C[2]+...+C[5]≤L

C [1]=max (C_A [1], C_T [1])=max (0%, 45%)=45%；

C [2]=max (C_A [2], C_T [2])=max (100%, 0%)=100%；

C [3]=max (C_A [3], C_T [3])=max (100%, 45%)=100%；

C [4]=max (C_A [4], C_T [4])=max (45%, 0%)=45%；

C [5]=max (C_A [5], C_T [5])=max (0%, 45%)=45%；

C [1]+C [2]+C [3]+C [4]+C [5]=45%+100%+100%+45%+45%=335%；

L=100%；Therefore, required range is more than oil cylinder stroke, and formula is unsatisfactory for, and step (23) is performed downwards；

3rd, by step (23), required minimum stroke is judged, required minimum stroke formula is：

C_T[1]+CC_2345≤L

C_T [1]=45%；

CC_2345=max (C [2], C [3], C [4], C [5])=max (100%, 100%, 45%, 45%)=100%；

C_T [1]+CC_2345=145%；

L=100%；Therefore, required minimum stroke is more than oil cylinder stroke, and formula is unsatisfactory for, and flow continues to perform step downwards Suddenly (24)；

4th, by step (24), by Section 1 arm contracting 1, remember x=2, judge required range, required range formula is：

0+C[2]+...+C[5]≤L

C [2]+C [3]+C [4]+C [5]=100%+100%+45%+45%=290%；

L=100%；Therefore, required range is more than oil cylinder stroke, and formula is unsatisfactory for, and step (25) is performed downwards；

5th, by step (25), required minimum stroke is judged, required minimum stroke formula is：

C_T[2]+CC_345≤L

C_T [2]=0%；

CC_345=max (C [3], C [4], C [5])=max (100%, 45%, 45%)=100%；

C_T [2]+CC_345=100%；

L=100%；Therefore, required minimum stroke is equal to oil cylinder stroke, and formula meets, and by-pass flow water valve can select to open, Into step (251)；Step (26) can also downwards be performed；

6th, by step (26), by Section 1 and Section 2 arm contracting 1, x=3 is remembered, range needed for judging, required range Formula is：

C[3]+C[4]+C[5]≤L

C [3]+C [4]+C [5]=100%+45%+45%=190%；

L=100%；Therefore, required range is more than oil cylinder stroke, and formula is unsatisfactory for, and step (27) is performed downwards；

7th, by step (27), required minimum stroke is judged, required minimum stroke formula is：

C_T[3]+CC_45≤L

C_T [3]=45%；

CC_45=max (C [4], C [5])=max (45%, 45%)=45%；

C_T [3]+CC_45=90%；

L=100%；Therefore, required minimum stroke is less than oil cylinder stroke, and formula meets, and by-pass flow water valve can select to open, Into step (271)；Step (28) can also downwards be performed；

8th, it is similar to, by Section 1, Section 2, Section 3 arm contracting 1, remembers x=4, range needed for judging, required maximum row Journey formula is：

C[4]+C[5]≤L

C [4]+C [5]=45%+45%=90%；

L=100%；Therefore, required range be less than oil cylinder stroke, formula meet, the 4th and Section 5 arm can extend Target position, therefore, output contracting arm limiting condition collection O={ 11112 }.Flow terminates.Therefore, drawn by ground floor main flow Contracting arm limiting condition to integrate be O₁={ 11112 }；

If the 9, second layer by-pass flow is opened in selection, step (251) is performed, then step is：

1), by step (251), x=1 is remembered, range judgment formula is expressed as：

C[3]+C[4]+C[5]≤L-C_T[2]

C [3]+C [4]+C [5]=100%+45%+45%=190%；

L-C_T [2]=100%-0=100%；

Therefore, required range formula is unsatisfactory for, and step (252) is performed downwards；

2), by step (252), x=1, required minimum stroke formula is expressed as：

C_T[3]+CC_45≤L-C_T[2]

C_T [3]+CC_45=45%+45%=90%；

L-C_T [2]=100%-0=100%；

Therefore, required minimum stroke is less than oil cylinder effective travel, and formula meets, and by-pass flow water valve can select to open, and enter Step (2521)；Step (253) can also downwards be performed；

3), by step (253), x=2 is remembered, required range formula is expressed as：

C[4]+C[5]≤L-C_T[2]

C [4]+C [5]=45%+45%=90%；

L-C_T [2]=100%-0=100%；

Therefore, required range formula meets, the 4th and Section 5 arm can extend target position, therefore, output contracting arm pole Limit state set O={ 11112 }, flow terminates.Therefore, the 2nd contracting arm limiting condition collection for being drawn by second layer main flow It is O₂={ 11 112 }；

If the 10, second layer by-pass flow is opened in selection, step (271) is performed, then step is：

1), by step (271), x=1 is remembered, range judgment formula is expressed as：

C[4]+C[5]≤L-C_T[3]

C [4]+C [5]=45%+45%=90%；

L-C_T [3]=100%-45%=55%；

Therefore, required range formula is unsatisfactory for, and step (272) is performed downwards；

2), by step (272), x=1, required minimum stroke formula is expressed as：

C_T[4]+C5≤L-C_T[3]

C_T [4]+C [5]=0%+45%=45%；

L-C_T [3]=100%-45%=55%；

Therefore, required minimum stroke is less than oil cylinder effective travel, and formula meets, and by-pass flow water valve can select to open, and enter Step (2721)；Step (273) can also downwards be performed；

3), by step (273), x=2 is remembered, required range formula is expressed as：

C[5]≤L-C_T[3]

C [5]=45%=45%；

L-C_T [3]=100%-45%=55%；

Therefore, required range formula meets, and Section 3 arm extends target position, output contracting arm limiting condition collection O={ 11 212 }, flow terminates.Therefore, it is O that the 3rd contracting arm limiting condition for being drawn by second layer main flow integrates₃={ 1121 2}；

If the 11, third layer by-pass flow is opened in selection, step (2721) is performed, then step is：

1), by step (2721), x=1 is remembered, range judgment formula is expressed as：

C[5]≤L-C_T[3]-C_T[4]

C [5]=45%=45%；

L-C_T [3]-C_T [4]=100%-45%-0%=55%；

Therefore, required range formula meets, and Section 3 and Section 4 arm extend target position, export contracting arm limiting condition collection O={ 11 212 }, flow terminates.Therefore, it is O that the 4th contracting arm limiting condition for being drawn by second layer main flow integrates₄={ 11 2 1 2}。

By foregoing 11 process steps, 4 contracting arm limiting condition collection are tried to achieve altogether, be：O₁{ 11112 }, O₂{1 1 1 1 2 }, O₃{ 11212 }, O₄{1 1 2 1 2}.By their principles flexible in order respectively, path planning is carried out.From current State set, is order contracting to contracting arm limiting condition collection；It is that order is stretched to dbjective state collection from contracting arm limiting condition collection, sees Fig. 5.

Table 1：From current state collection { 14421 }, to the optimization disaggregation of dbjective state collection { 21212 }

Optimization solution	Flow path	The contracting arm limit is combined	Step number
				a	Flow 22-28	1-1-1-1-2	6
b	Flow 251-253	1-1-1-1-2	6
				c	Flow 271-273	1-1-2-1-2	5
d	Flow 2721	1-1-2-1-2	5

Compare all path optimization's effects to find：C () and (d) is all depth optimal solution, perform second layer by-pass flow 271-273 With execution third layer by-pass flow 2721, contracting arm limiting condition collection now is { 11212 }, and step number of stretching is five steps.

(2) with existing optimization method Contrast on effect

In this example, the contracting arm limiting condition collection for not making to optimize is { 11111 }；The method of document 2 cannot realize optimization, Its contracting arm limiting condition collection is also { 11111 }；The contracting arm limiting condition collection that this patent is obtained is { 11212 }, only Need 5 steps, such as Fig. 6.

Table 2：From current state collection { 14421 }, the distinct methods to dbjective state collection { 21212 } optimize contrast

Sequence number	Optimal way	The contracting arm limit is combined	Step number	Optimization measure
					a	It is not optimised	1-1-1-1-2	6	0%
b	Document 2	1-1-1-1-2	6	0%
					c	Canal water valve method	1-1-2-1-2	5	17%

As seen from Table 2, canal water valve method can reach optimum optimization effect in this example, and efficiency is not than making optimization lifting 17%.

(1) present invention can generally be adapted to n grades of telescopic arm, have m pin-and-hole position in every joint arm.

Steel material architectural characteristic based on current application：Steel weight, so the joint number n of arm can not be too many, single-cylinder bolt Up to 8 sections before the arm joint number of formula telescopic arm；Conventional telescopic arm joint number is 4 --- 7 sections.If being done using lightweight material in the future Arm, such as carbon fiber, arm joint number may substantially exceed 8 sections, n>8, the present invention is equally applicable.

Real case of the invention is that, with five section telescopic arms, have four arm pin-and-holes in every joint arm, and each pin-and-hole position accounts for Oil cylinder stroke be 0%, 45%, 90% and 100% as a example by, be illustrated, be actually not limited to pin-and-hole quantity, be not limited to Pin-and-hole arrangement is all generally applicable.

(2) present invention is generally applicable to the routing problem of single cylinder bolt-type multistage sequential telescopic.

The present invention is illustrated by taking single-cylinder bolt sequential telescopic arm as an example, is actually not limited to single-cylinder bolt crane and is stretched Contracting arm.

(3) T-shaped and A type water valves proposed by the present invention, are defined according to extending target or retain original position arm joint, In fact, arm joint rests on the optional position of pin-and-hole, the park path of optimization is can serve as, they are used alone, it is also possible to Compound use.Different parked positions, such as：Contract 1 valve --- full reduced position；2 type valves --- extend the 2nd pin-and-hole position；3 types Valve --- extend the 3rd pin-and-hole position ...；Different compound uses, such as：T-shaped and A is combined；T-shaped and 2 types are compound；It is T-shaped and 2 types, 3 types are combined ....

Claims

1. a kind of efficient single cylinder bolt-type multistage sequential telescopic method for optimizing route, telescopic arm has n joint arms, and its feature exists In comprising the following steps：

N is telescopic arm joint number；A [i] is the current state of the i-th joint arm, and the value of A [i] is m, and m is positive integer, represents and divide in arm joint The pin-and-hole position of cloth, such as：1st pin-and-hole, m-th pin-and-hole of the 2nd pin-and-hole ..., the different oil cylinder stroke of each pin-and-hole correspondence； Arm joint latch in different pin-and-holes, so as to there is different extension elongations；

T [i] is the dbjective state of the i-th joint arm, and the value of T [i] is m, and m is positive integer, represents the pin-and-hole position being distributed in arm joint, Such as：1st pin-and-hole, m-th pin-and-hole of the 2nd pin-and-hole ..., the different oil cylinder stroke of each pin-and-hole correspondence；Arm joint latch is in difference Pin-and-hole in, so as to there is different extension elongations；

Step (2)：According to the telescopic arm current state collection, the telescopic arm dbjective state collection, and can be used for flexible stretching Contracting oil cylinder stroke, calculates contracting arm limiting condition collection { O [1], O [2] ... O [n] }；

Contracting arm limiting condition collection refers to：It is that first order is retracted by arm joint when multistage sequential telescopic changes brachium, then sequentially stretches again Go out；Judged by oil cylinder effective travel, some arm joints can be without retracting, it is possible to crosses its sequential telescopic other arm joints；Or Some arm joints of person can directly be extended target position without first contracting, and the flexible of follow-up arm joint is not influenceed；What these can retain Arm joint, the arm joint and other arm joints that need to be retracted that can first extend target position, add the most end arm joint shape for initiating a switch to stretch out The combination of state, referred to as contracting arm limiting condition collection；The total length one of contracting arm limiting condition collection is scheduled on a telescopic oil cylinder total kilometres i.e. section In arms length；

O [i] is the contracting arm limiting condition of the i-th joint arm, and the value of O [i] is m, and m is positive integer, represents the pin-and-hole position being distributed in arm joint Put, such as：1st pin-and-hole, m-th pin-and-hole of the 2nd pin-and-hole ..., the different oil cylinder stroke of each pin-and-hole correspondence；Arm joint latch exists In different pin-and-holes, so as to there is different extension elongations；

Step (3)：According to the telescopic arm current state collection, the telescopic arm dbjective state collection and the contracting for being calculated Arm limiting condition collection, the principle of telescopic arm, plans flexible path in sequence：From the telescopic arm current state collection --- it is described Contracting arm limiting condition collection, is order contracting arm；It is order from the contracting arm limiting condition collection --- the telescopic arm dbjective state collection Semi-girder；

The contracting arm limiting condition collection that step (2) draws is probably one, it is also possible to multiple, if drawing multiple, will The multiple described contracting arm limiting condition collection for going out is by the flexible path of step 3 methods described planning；Then therefrom select, stretched from described Contracting arm current state collection --- the telescopic arm dbjective state collection uses the minimum contracting arm limiting condition collection of step number, used as most Shortest path.

2. a kind of efficient single cylinder bolt-type multistage sequential telescopic method for optimizing route according to claim 1, its feature It is that following steps are performed in step (2)：

Step (20)：Compare the current state A [n] and dbjective state T [n] of least significant end arm joint, judge A [n] ≠ T [n]If, A [n] and T [n] are equal, then compare A [n-1] ≠ T [n-1] forward；Compare A [n-2] ≠ T [n-2] by that analogy…；If no Equal, then flow is down performed；

Step (21)：Establish range judgment formula and minimum stroke judgment formula；Assignment x, i, derive different x, i value correspondences Range judgment formula and minimum stroke judgment formula；

The range judgment formula (formula)：

Σ_{i = x, i &GreaterEqual; x}^{n} C [i] \leq L - Σ_{i = 1, i \leq x - 1}^{x - 1} C_T [i - 1], x = 1, 2, ...... n; - - - (1)

n:Telescopic arm joint number；

C_A[i]:The current stroke of i-th joint arm, value is 0%-100%；

Such as：C_A [2]=2, represents Section 2 arm, currently stretches out 45% oil cylinder total kilometres, and it is long that oil cylinder total kilometres are equal to a joint arm；

C_T[i]:I-th joint arm target stroke, value is 0%-100%；

Such as：C_T [4]=3, represents Section 4 arm, and target stretches out 90% oil cylinder total kilometres, and it is long that oil cylinder total kilometres are equal to a joint arm；

C[i]:I-th joint arm is stretched the maximum oil cylinder stroke of needs, and value is 0%-100%；C [i]=max (C_A [i], C_T [i])

Such as：C [2]=max (C_A [2], C_T [2])=3, maximum oil cylinder stroke needed for representing flexible Section 2 arm is 90%；

Minimum stroke judgment formula (formula)：

C C_(i) (i + 1) ... n \leq L - Σ_{i = 1, i \leq x - 1}^{x - 1} C_T [i - 1] - - - (2)

CC_i(i+1)(i+2):Flexible i-th section, (i+1) section, the minimum value of oil cylinder stroke needed for (i+2) joint arm, CC_i (i + 1) (i+2)=max (C [i], C [i+1], C [i+2])；

X is represented：When flow is performed from top to bottom, the quantity (contracting 1 refers to full reduced) of 1 arm joint that contracts, wherein：X=1, represents at the beginning There is no arm joint contracting 1；X=2, represents Section 1 arm contracting 1；…；X=n-1 is represented：Since Section 1 arm, until the n-th -2 joint arm all contracts 1；

I is represented：When flow is performed from left to right, the number of plies that flow is launched to the right, because flow is except by step (22) --- step Suddenly (24) perform from top to bottom, when step (23) are gone to, if meeting minimum stroke judgment formula --- formula (2), flow Can also launch from left to right；

I=2, represents：When the 1st layer of main flow goes to step (23), certain minimum stroke judgment formula meets condition, now Program may be selected to enter or do not enter the branch's flow launched to the right, if input is opened, flow enters into for launching to the right 2 layers of branch's flow；If input is closed, flow cannot flow into the 2nd layer of branch's flow, can only be suitable from top to bottom in the 1st laminar flow journey Sequence is performed；

I=n-2, represents：When the n-th -2 layers branch's flow go to step (23), certain minimum stroke judgment formula meets bar Part, now program may be selected to enter or do not enter the branch's flow launched to the right；If input is opened, flow is entered into the right The (n-1)th layer of branch's flow launched；If input is closed, flow cannot flow into (n-1)th layer of branch's flow, can only be arrived at the 1st layer Order is performed from left to right, from top to bottom in the n-th -2 layers branch's flow；

For the traveling mode of pictute flow, liken the path of flow with " canal stream " herein, if i=1, only one layer from upper Flow down, referred to as main canal stream；If i=2, flow can expand one level to the right branch, altogether two-layer canal stream；If ... i=n- 1, flow can to the right be expanded to (n-1)th layer, common n-1 layers of canal stream；

When each layer of canal stream goes to step (23), whether minimum stroke judgment formula meets condition, if meeting condition, while " selection is opened ", then flow chart can increase to the right one layer of sublateral canal stream；" selection is opened ", is likened with " water valve " herein, " water valve " is opened, and meaning " canal stream " can to the right flow into branch's flow, and " water valve " is closed, and meaning " canal stream " can only be on current layer road Run in footpath；

" canal stream " correspondence " flow ", " water valve " correspondence " selection is opened ", both of which does not have actual physical meaning, is intended merely to shape Traveling as describing " flow ", and " selection is opened " enters the condition of branch's flow；

Step (22)：Required range judges, if required range formula meets, directly exports contracting arm limiting condition collection O {}；Otherwise, step (23) is performed；

By step (21), initially only one layer of main canal stream, takes i=1；This layer of all arm joint of canal stream do not contract 1；Note x=1；

Range judgment formula (1) needed for described is write as：

C[1]+C[2]+...+C[n]≤L (1.1)

If meeting, all arm joints directly extend target position, contracting arm limiting condition collection O={ T [1], T [2] ..., T to formula (1.1) [n]}；If it is not satisfied, performing step (23) downwards；

Step (23)：Required minimum stroke judges, if required minimum stroke formula meets, can choose whether to enter branch to the right Flow, if selection " water valve " is opened, flow enters next layer of branch's " canal stream ", meanwhile, i=i+1；If required minimum stroke is public Formula is unsatisfactory for, and flow is performed downwards, performs step (24)；

Minimum stroke judgment formula (2) needed for described is write as：

C_T[1]+CC_234...n≤L (2.1)

Formula (2.1) can select to open if meeting to next layer " water valve ", and into step (231), i=2, similar cycle is held Row step (21) --- step (23)；If it is not satisfied, step (24) can only be performed downwards；

Step (24)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=1, x=2 repeat to walk Suddenly (21)；

By step (21), initially only one layer of main canal stream, takes i=1；Since Section 1 arm, Section 1 arm is contracted 1, then x=2；To Lower execution step (25)；

Step (25)：Required range judgement, repeat step (22)；

0+C[2]+...+C[n]≤L (1.2)

If meeting range judgment formula (1.2), there is contracting arm limiting condition collection to export O={ 1, T [2] ..., T [n] }；If no Meet, then carry out minimum stroke judgement, perform step (26)；

Step (26)：Required minimum stroke judgement, repeat step (23)；

0+C_T[2]+CC_34...n≤L (2.2)

If meeting, " water valve " can select to open formula (2.2), and into step (261), i=2, similar cycle performs step (21) --- step (23)；If it is not satisfied, step (27) can only be performed downwards；

Step (27)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=1, x=3 repeat to walk Suddenly (21) ... until to range judgment formula (1) and minimum stroke judgment formula (2), assignment i=1, x=(n-1), weight Multiple step (21)；

By step (21), initially only one layer of main canal stream, takes i=1；Since Section 1 arm, by Section 1, then Section 2 arm contracting 1, x =3；... the like, until by step (21), initially only one layer of main canal stream, takes i=1；Since Section 1 arm, by the 1st Section --- (n-3) joint arm contracting 1, then x=(n-2)；Step (28) is performed downwards；

Step (28)：Required range judgement, repeat step (22)；

0+...0+C[n-2]+C[n-1]+C[n]≤L (1.(n-2))

If meeting range judgment formula (1. (n-2)), contracting arm limiting condition collection output O={ 1,1 ..., 1, T [n-2], T [n-1],T[n]}；If it is not satisfied, then carrying out minimum stroke judgement, step (29) is performed；

0+...+0+C_T[n-2]+C[n-1]+C[n]≤L (2.(n-2))

If meeting, " water valve " can select to open formula (2. (n-2)), and into step (291), i=2, similar cycle performs step Suddenly (21) --- step (23)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1), now, range formula is：

0+...0+C[n-1]+C[n]≤L (1.(n-1))

If range formula (1. (n-1)) meets, output contracting arm limiting condition collection output O={ 1,1,1 ..., 1, T [n- 1],T[n]}；If it is not satisfied, (n-1) joint arm then contracted into 1, x=n, output contracting arm limiting condition collection export O=1,1,1 ..., 1,1,T[n]}。

3. a kind of efficient single cylinder bolt-type multistage sequential telescopic method for optimizing route according to claim 2, its feature It is that following steps are performed in step (23)：

If meeting, the second layer " water valve " can select to open formula (2.1), into step (231), now, second layer canal stream note For：I=2；

Step (231)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=1 repeat to walk Suddenly (21)；

By step (21), it is initially：I=2, there is two-layer canal stream；X=1, represents that Section 1 arm extends target invariant position, from Section 2 Arm starts contracting 1, does not have arm joint contracting 1 when initial, and step (232) is performed downwards；

Step (232)：Required range judgement, repeat step (22)；

By step (22), i=2；X=1；Range judgment formula (1) needed for described is write

C[2]+...+C[n]≤L-C_T[1] (1.1.1)

Section 1 arm is extended target position by formula (1.1.1) if meeting, and since Section 2 arm, all arm joints directly extend mesh Mark, contracting arm limiting condition collection O={ T [1], T [2] ..., T [n] }；If it is not satisfied, performing (233) downwards；

Step (233)：Required minimum stroke judgement, repeat step (23)；

C_T[2]+CC_34...n≤L-C_T[1] (2.1.1)

If meeting, third layer " water valve " can select to open formula (2.1.1), and into step (2331), i=3, similar cycle is held Row step (21) --- step (23)；If it is not satisfied, step (234) can only be performed downwards；

Step (234)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=2 repeat to walk Suddenly (21)；

By step (21), i=2, there is two-layer canal stream；X=2, represent Section 1 arm extend target invariant position, since Section 2 arm, By Section 2 arm contracting 1, step (235) is performed downwards；

Step (235)：Required range judgement, repeat step (22)；

0+C[3]+...+C[n]≤L-C_T[1] (1.1.2)

Step (236)：Required minimum stroke judgement, repeat step (23)；

0+C_T[3]+CC_34...n≤L-C_T[1] (2.1.2)

If meeting, the 2nd third layer " water valve " can select to open formula (2.1.2), and into step (2361), i=3 is similar to Circulation performs step (21) --- step (23)；If it is not satisfied, step (237) can only be performed downwards；

Step (237)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=3 repeat to walk Suddenly (21) ... until to range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=(n-1), weight Multiple step (21)；

By step (21), i=2, there is two-layer canal stream；X=3, represent Section 1 arm extend target invariant position, since Section 2 arm, By Section 2, Section 3 arm contracting 1；... the like, until by step (21), i=2 has two-layer canal stream；X=(n-2), represents Section 1 arm extends target invariant position, since Section 2 arm, by Section 2 --- (n-3) joint arm contracting 1；

Step (238)：Required range judgement, repeat step (22)；

0+...+0+C[n-2]+C[n-1]+C[n]≤L-C_T[1] (1.1.(n-2))

If meeting range judgment formula (1.1. (n-2)), contracting arm limiting condition collection output O={ T [1], 1 ... 1, T [n- 2],T[n-1],T[n]}；If it is not satisfied, then carrying out minimum stroke judgement, step (239) is performed；

0+...+0+C_T[n-2]+C[n-1]+C[n]≤L-C_T[1] (2.1.(n-2))

If meeting, " water valve " can be selected to open formula (2.1. (n-2)), and into step (2391), i=3, similar cycle is performed Step (21) --- step (23)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1), now, range formula For：

0+...+0+C[n-1]+C[n]≤L-C_T[1] (1.1.(n-1))

If range formula (1.1. (n-1)) meets, output contracting arm limiting condition collection output O={ T [1], 1 ..., 1, T [n-1],T[n]}；If it is not satisfied, (n-1) joint arm then contracted into 1, x=n, output contracting arm limiting condition collection export O=T [1], 1,…,1,1,T[n]}。

4. a kind of efficient single cylinder bolt-type multistage sequential telescopic method for optimizing route according to claim 2, its feature It is that following steps are performed in step (26)：

If meeting, the second layer " water valve " can select to open formula (2.2), into step (261), now, second layer canal stream note For：I=2；

Step (261)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=1 repeat to walk Suddenly (21)；

By step (21), it is initially：I=2, there is two-layer canal stream；X=1, represents Section 1 arm contracting 1, Section 2 arm is extended into target Position, in addition all arms do not contract 1, step (262) is performed downwards；

Step (262)：Required range judgement, repeat step (22)；

C[3]+...+C[n]≤L-C_T[2] (1.2.1)

Formula (1.2.1) if meet, Section 1 arm contracting 1, Section 2 arm is extended target position, all arm joints directly extend mesh in addition Mark, contracting arm limiting condition collection O={ 1, T [2], T [3], T [4] ..., T [n] }；If it is not satisfied, performing (263) downwards；

Step (263)：Required minimum stroke judgement, repeat step (23)；

C_T[3]+CC_45...n≤L-C_T[2] (2.2.1)

If meeting, the 3rd third layer " water valve " can select to open formula (2.2.1), and into step (2631), i=3 is similar to Circulation performs step (21) --- step (23)；If it is not satisfied, step (264) can only be performed downwards；

Step (264)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=2 repeat to walk Suddenly (21)；

By step (21), i=2, there is two-layer canal stream；X=2, represents that the contracting 1, Section 2 arm of Section 1 arm extends target position, by Section 3 Arm contracting 1, in addition all arms do not contract 1, step (265) is performed downwards；

Step (265)：Required range judgement, repeat step (22),

0+C[4]+...+C[n]≤L-C_T[2] (1.2.2)

If meeting, the contracting 1, Section 2 arm of Section 1 arm extends target position to formula (1.2.2), and Section 3 arm is contracted 1, all arms in addition Section directly extends target position, contracting arm limiting condition collection O={ 1, T [2], 1, T [4] ..., T [n] }；If it is not satisfied, performing downwards (266)；

Step (266)：Required minimum stroke judgement, repeat step (23)；

0+C_T[4]+CC_56...n≤L-C_T[2] (2.2.2)

If meeting, the 4th third layer " water valve " can select to open formula (2.2.2), and into step (2661), i=3 is similar to Circulation performs step (21) --- step (23)；If it is not satisfied, step (267) can only be performed downwards；

Step (267)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=3 repeat to walk Suddenly (21) ... until to range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=(n-1), weight Multiple step (21)；

By step (21), i=2, there is two-layer canal stream；X=3, represents Section 1 arm contracting 1, Section 2 arm is extended target position, by the 3rd Section, Section 4 arm contracting 1；... the like, until by step (21), i=2 has two-layer canal stream；X=(n-2), represents Section 1 Arm contracting 1, Section 2 arm is extended target position, since Section 3 arm, by Section 3 --- (n-3) joint arm contracting 1；

Step (268)：Required range judgement, repeat step (22)；

0+...+0+C[n-2]+C[n-1]+C[n]≤L-C_T[2] (1.2.(n-2))

If meeting range judgment formula (1.2. (n-2)), contracting arm limiting condition collection O=1, T [2], 1 ..., 1, T [n-2], T[n-1],T[n]}；If it is not satisfied, then carrying out minimum stroke judgement, step (269) is performed；

0+...+0+C_T[n-2]+C[n-1]+C[n]≤L-C_T[2] (2.2.(n-2))

If meeting, " water valve " can be selected to open formula (2.2. (n-2)), and into step (2691), i=3, similar cycle is performed Step (21) --- step (23)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1), now, range formula For：

0+...+0+C[n-1]+C[n]≤L-C_T[2] (1.2.(n-1))

If range formula (1.2. (n-1)) meets, contracting arm limiting condition collection O={ 1, T [2], 1 ..., 1, T [n-1], T [n]}；If it is not satisfied, by (n-1) joint arm contracting 1, then x=n, exports contracting arm limiting condition collection O={ 1, T [2], 1 ..., 1,1, T [n]}。

5. a kind of efficient single cylinder bolt-type multistage sequential telescopic method for optimizing route according to claim 2, its feature It is that following steps are performed in step (29)：

If meeting, the second layer " water valve " can select to open formula (2.2), into step (291), now, second layer canal stream note For：I=2；

Step (291)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=2, x=1 repeat to walk Suddenly (21)；

By step (21), it is initially：I=2, there is two-layer canal stream；X=1, represents Section 1 arm contracting 1, Section 2 arm is extended into target Position, in addition all arms do not contract 1, step (292) is performed downwards；

Step (292)：Required range judgement, repeat step (22)；

C[n-1]+C[n]≤L-C_T[n-2] (1.(n-2).1)

Formula (1. (n-2) .1) if meet, Section 1 arm --- (n-3) joint arm contracting 1, (n-2) joint arm is extended into target , all arm joints directly extend target position in addition, then contracting arm limiting condition collection O={ 1,1 ..., 1, T [n-2], T [n-1], T [n]}；If it is not satisfied, performing (293) downwards；

C_T[n-1]+C[n]≤L-C_T[n-2] (2.(n-2).1)

Formula (2. (n-2) .1) if meet, Section 1 arm --- (n-3) joint arm contracting 1, (n-2) joint arm is extended into target , all arm joints directly extend target position in addition, then contracting arm limiting condition collection O={ 1,1 ..., 1, T [n-2], T [n-1], T [n]}；If it is not satisfied, by (n-1) joint arm contracting 1, then exporting dbjective state collection O={ 1,1 ..., 1, T [n-2], 1, T [n] }.

6. a kind of efficient single cylinder bolt-type multistage sequential telescopic method for optimizing route according to claim 3, its feature It is that following steps are performed in step (233)：

Step (2331)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=3, x=1 are repeated Step (21)；

By step (21), it is initially：I=3, there is three layers of canal stream；X=1, represents that Section 1, Section 2 arm extend target invariant position, from Section 3 arm starts contracting 1, does not have arm joint contracting 1 when initial, and step (2332) is performed downwards；

Step (2332)：Required range formula judgement, repeat step (22)；

By step (22), i=3；X=1；Range judgment formula (1) is expressed as：

C[3]+...+C[n]≤L-C_T[1]-C_T[2] (1.1.1.1)

If meeting, Section 1, Section 2 arm extend target invariant position to formula (1.1.1.1), since Section 3 arm, all arm joints Directly extend target position, contracting arm limiting condition collection O={ T [1], T [2], T [3] ..., T [n] }；If it is not satisfied, performing downwards (2333)；

Step (2333)：Required minimum stroke formula judgement, repeat step (23)；

C_T[3]+CC_45...n≤L-C_T[1]-C_T[2] (2.1.1.1)

If meeting, the 4th layer " water valve " can select to open formula (2.1.1.1), and into step (23331), i=4 is similar to follow Ring performs step (21) --- step (23)；... by that analogy, step can be performed with recursion to i=n-2 layers, similar cycle (21) --- step (23)；If it is not satisfied, step (2334) can only be performed downwards；

Step (2334)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=3, x=2 are repeated Step (21)；

By step (21), it is initially：I=3, there is three layers of canal stream；X=2, represents that Section 1, Section 2 arm extend target invariant position, the 3 joint arms contracting 1, performs downwards step (2335),

Step (2335)：Required range formula judgement, repeat step (22)；

By step (22), i=3；X=2；Range judgment formula (1) is expressed as：

C[4]+...+C[n]≤L-C_T[1]-C_T[2] (1.1.1.2)

Formula (1.1.1.2) if meet, Section 1, Section 2 arm extend target position, Section 3 arm contracting 1, all arm joints are direct in addition Extend target position, contracting arm limiting condition collection O={ T [1], T [2], 1, T [4] ..., T [n] }；If it is not satisfied, performing downwards (2336)；

Step (2336)：Required minimum stroke formula judgement, repeat step (23)；

C_T[4]+CC_56...n≤L-C_T[1]-C_T[2] (2.1.1.2)

If meeting, the 4th layer " water valve " can select to open formula (2.1.1.2), and into step (23361), i=4 is similar to follow Ring performs step (21) --- step (23)；... by that analogy, step can be performed with recursion to i=n-2 layers, similar cycle (21) --- step (23)；If it is not satisfied, step (2337) can only be performed downwards；

Step (2337)：To range judgment formula (1) and minimum stroke judgment formula (2), assignment i=3, x=3 are repeated Step (21)；

By step (21), it is initially：I=3, there is three layers of canal stream；X=3, represents that Section 1, Section 2 arm extend target invariant position, the 3 sections, Section 4 arm contracting 1；... the like, until by step (21), i=3 has three layers of canal stream；X=(n-2), represents the 1st Section, Section 2 arm extend target invariant position, Section 3 --- (n-3) joint arm contracting 1；

Step (2338)：Required range judgement, repeat step (22),

C[n-2]+C[n-1]+C[n]≤L-C_T[1]-C_T[2] (1.1.1.(n-2))

If meeting, Section 1, Section 2 arm extend target position, Section 3 to formula (1.1.1. (n-2)) --- (n-3) arm contracting 1, In addition all arm joints directly extend target position, contracting arm limiting condition collection O={ T [1], T [2], 1,1 ..., 1, T [n-2], T [n- 1],T[n]}；If it is not satisfied, performing (2339) downwards；

Step (2339)：Required minimum stroke formula judgement, repeat step (23)；

C_T[n-2]+CC_(n-1)n≤L-C_T[1]-C_T[2] (2.1.1.(n-2))

If meeting, " water valve " can select to open formula (2.1.1. (n-2)), into step (23391), i=4, similar cycle Perform step (21) --- step (23)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1), now, range is public Formula is：

0+...+0+C[n-1]+C[n]≤L-C_T[1]-C_T[2] (1.1.1.(n-1))

If range formula (1.1.1. (n-1)) meets, contracting arm limiting condition collection O={ T [1], T [2], 1 ..., 1, T [n- 1],T[n]}；If it is not satisfied, (n-1) joint arm is contracted 1, then x=n, output contracting arm limiting condition collection O=T [1], T [2], 1,…,1,1,T[n]}。

7. the multistage sequential telescopic path optimization side of a kind of efficient single cylinder bolt-type according to claim 2,3,4,5 or 6 Method, it is characterised in that between all required ranges judge and required minimum stroke judges, adds A type minimum strokes to sentence It is disconnected, as a example by adding A types minimum stroke to judge between step (23) and step (24), minimum stroke judgment formula needed for A types For：

C C_(i) (i + 1) ... n \leq L - Σ_{i = 1, i \leq x - 1}^{x - 1} C_A [i - 1] - - - (3)

The process step for adding A types minimum stroke to judge is as follows：

Range judgment formula (formula)：

Σ_{i = x, i &GreaterEqual; x}^{n} C [i] \leq L - Σ_{i = 1, i \leq x - 1}^{x - 1} C_T [i - 1], x = 1, 2, ...... n; - - - (1)

T-shaped minimum stroke judgment formula (formula)：

C C_(i) (i + 1) ... n \leq L - Σ_{i = 1, i \leq x - 1}^{x - 1} C_T [i - 1] - - - (2)

A type minimum strokes judgment formula (formula)：

C C_(i) (i + 1) ... n \leq L - Σ_{i = 1, i \leq x - 1}^{x - 1} C_A [i - 1] - - - (3)

Range judgment formula (1) needed for described is write as：

C[1]+C[2]+...+C[n]≤L (1.1)

Step (23)：Minimum stroke judges needed for T-shaped, if minimum stroke formula meets needed for T-shaped, can choose whether to enter to the right Enter branch's flow, if selection " water valve " is opened, flow enters next layer of branch's " canal stream ", meanwhile, i=i+1；If needed for T-shaped Minimum stroke formula is unsatisfactory for, and flow is performed downwards, performs step (24)；

Minimum stroke judgment formula (2) needed for described is write as：

C_T[1]+CC_234...n≤L (2.1)

Formula (2.1) can select to open, into step (231), i=2, similar cycle if meeting to next layer T-shaped " water valve " Perform step (21) --- step (24)；If it is not satisfied, step (25) can only be performed downwards；

Step (24)：Minimum stroke needed for A types judges, if minimum stroke formula needed for A types meets, can choose whether to enter to the right Enter branch's flow, if selection " water valve " is opened, flow enters next layer of branch's " canal stream ", meanwhile, i '=i '+1；If A types institute Need minimum stroke formula to be unsatisfactory for, flow is performed downwards, perform step (25)；

Minimum stroke judgment formula (3) needed for described is write as：

C_A[1]+CC_234...n≤L (3.1)

Formula (3.1) can select to open, into step (241), i=2, similar cycle if meeting to next layer of A type " water valve " Perform step (21) --- step (24)；If it is not satisfied, step (25) can only be performed downwards；

Step (25)：Public is judged to range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A types minimum stroke Formula (3), assignment i=1, x=2, repeat step (21)；

By step (21), initially only one layer of main canal stream, takes i=1；Since Section 1 arm, Section 1 arm is contracted 1, then x=2；To Lower execution step (26)；

Step (26)：Required range judgement, repeat step (22)；

0+C[2]+...+C[n]≤L (1.2)

If meeting range judgment formula (1.2), there is contracting arm limiting condition collection to export O={ 1, T [2] ..., T [n] }；If no Meet, then carry out minimum stroke judgement, perform step (27)；

Step (27)：Minimum stroke judges needed for T-shaped, repeat step (23)；

0+C_T[2]+CC_34...n≤L (2.2)

If meeting, T-shaped " water valve " can select to open formula (2.2), and into step (271), i=2, similar cycle performs step (21) --- step (24)；If it is not satisfied, step (27) can only be performed downwards；

Step (28)：Minimum stroke judgement, repeat step (24) needed for A types；

0+C_T[2]+CC_34...n≤L (3.2)

If meeting, A types " water valve " can select to open formula (3.2), and into step (281), i=2, similar cycle performs step (21) --- step (24)；If it is not satisfied, step (29) can only be performed downwards；

Step (29)：Public is judged to range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A types minimum stroke Formula (3), assignment i=1, x=3, repeat step (21) ... judges until to range judgment formula (1), T-shaped minimum stroke Formula (2) and A type minimum strokes judgment formula (3), assignment i=1, x=(n-1), repeat step (21)；

By step (21), initially only one layer of main canal stream, takes i=1；Since Section 1 arm, by Section 1, then Section 2 arm contracting 1, x =3；... the like, until by step (21), initially only one layer of main canal stream, takes i=1；Since Section 1 arm, by the 1st Section --- (n-3) joint arm contracting 1, then x=(n-2)；Step (2A) is performed downwards；

Step (2A)：Required range judgement, repeat step (22)；

0+...0+C[n-2]+C[n-1]+C[n]≤L (1.(n-2))

If meeting range judgment formula (1. (n-2)), contracting arm limiting condition collection output O={ 1,1 ..., 1, T [n-2], T [n-1],T[n]}；If it is not satisfied, then carrying out minimum stroke judgement, step (2B) is performed；

Step (2B)：Minimum stroke judges needed for T-shaped, repeat step (23)；

0+...+0+C_T[n-2]+C[n-1]+C[n]≤L (2.(n-2))

If meeting, T-shaped " water valve " can be selected to open formula (2. (n-2)), and into step (2B1), i=2, similar cycle is performed Step (21) --- step (24)；If it is not satisfied, performing step (2C) downwards；

0+...+0+C_A[n-2]+C[n-1]+C[n]≤L (3.(n-2))

If meeting, A types " water valve " can be selected to open formula (3. (n-2)), and into step (2C1), i=2, similar cycle is performed Step (21) --- step (23)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1), now, range formula For：

0+...0+C[n-1]+C[n]≤L (1.(n-1))

8. a kind of efficient single cylinder bolt-type multistage sequential telescopic method for optimizing route according to claim 7, its feature It is that following steps are performed in step (23)：

If meeting, the second layer T-shaped " water valve " can select to open formula (2.1), into step (231), now, second layer canal stream It is designated as：I=2；

Step (231)：Public is judged to range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A types minimum stroke Formula (3), assignment i=2, x=1, repeat step (21)；

Step (232)：Required range judgement, repeat step (22)；

C[2]+...+C[n]≤L-C_T[1] (1.1.1)

Section 1 arm is extended target position by formula (1.1.1) if meeting, and since Section 2 arm, all arm joints directly extend mesh Mark, contracting arm limiting condition collection O={ T [1], T [2] ..., T [n] }；If it is not satisfied, performing step (233) downwards；

Step (233)：Minimum stroke judges needed for T-shaped, repeat step (23),

C_T[2]+CC_34...n≤L-C_T[1] (2.1.1)

If meeting, third layer T-shaped " water valve " can select to open formula (2.1.1), and into step (2331), i=3 is similar to follow Ring performs step (21) --- step (24)；If it is not satisfied, step (234) can only be performed downwards；

Step (234)：Minimum stroke judgement needed for A types, repeat step (24),

C_A[2]+CC_34...n≤L-C_T[1] (3.1.1)

If meeting, third layer A types " water valve " can select to open formula (3.1.1), and into step (2341), i=3 is similar to follow Ring performs step (21) --- step (24)；If it is not satisfied, step (235) can only be performed downwards；

Step (235)：Public is judged to range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A types minimum stroke Formula (3), assignment i=2, x=2, repeat step (21)；

By step (21), i=2, there is two-layer canal stream；X=2, represent Section 1 arm extend target invariant position, since Section 2 arm, By Section 2 arm contracting 1, step (236) is performed downwards；

Step (236)：Required range judgement, repeat step (22)；

0+C[3]+...+C[n]≤L-C_T[1] (1.1.2)

Step (237)：Minimum stroke judges needed for T-shaped, repeat step (23)；

0+C_T[3]+CC_34...n≤L-C_T[1] (2.1.2)

If meeting, the 2nd third layer T-shaped " water valve " can select to open formula (2.1.2), into step (2371), i=3, class Step (21) is performed like circulation --- step (24)；If it is not satisfied, step (238) can only be performed downwards；

Step (238)：Minimum stroke judgement, repeat step (24) needed for A types；

0+C_A[3]+CC_34...n≤L-C_T[1] (3.1.2)

If meeting, the 2nd third layer A types " water valve " can select to open formula (3.1.2), into step (2381), i=3, class Step (21) is performed like circulation --- step (24)；If it is not satisfied, step (239) can only be performed downwards；

Step (239)：Public is judged to range judgment formula (1), T-shaped minimum stroke judgment formula (2), A types minimum stroke Formula (3), assignment i=2, x=3, repeat step (21) ... judges until to range judgment formula (1), T-shaped minimum stroke Formula (2) and A type minimum strokes judgment formula (3), assignment i=2, x=(n-1), repeat step (21)；

By step (21), i=2, there is two-layer canal stream；X=3, represents that Section 1 arm extends target invariant position, since Section 2 arm, By Section 2, Section 3 arm contracting 1；... the like, until by step (21), i=2 has two-layer canal stream；X=(n-2), represents Section 1 arm extends target invariant position, since Section 2 arm, by Section 2 --- (n-3) joint arm contracting 1；Step is performed downwards (23A)；

Step (23A)：Required range judgement, repeat step (22)；

0+...+0+C[n-2]+C[n-1]+C[n]≤L-C_T[1] (1.1.(n-2))

If meeting range judgment formula (1.1. (n-2)), contracting arm limiting condition collection output O={ T [1], 1 ... 1, T [n- 2],T[n-1],T[n]}；

If it is not satisfied, then carrying out minimum stroke judgement, step (23B) is performed；

Step (23B)：Minimum stroke judges needed for T-shaped, repeat step (23)；

0+...+0+C_T[n-2]+C[n-1]+C[n]≤L-C_T[1] (2.1.(n-2))

If meeting, T-shaped " water valve " can select to open formula (2.1. (n-2)), into step (23B1), i=3, similar cycle Perform step (21) --- step (24)；If it is not satisfied, performing step (23C)；

Step (23C)：Minimum stroke judgement, repeat step (24) needed for A types, and obtain this layer of branch's flow end product；

0+...+0+C_A[n-2]+C[n-1]+C[n]≤L-C_T[1] (3.1.(n-2))

If meeting, A types " water valve " can select to open formula (3.1. (n-2)), into step (23C1), i=3, similar cycle Perform step (21) --- step (24)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1), now, range is public Formula is：

0+...+0+C[n-1]+C[n]≤L-C_T[1] (1.1.(n-1))

9. a kind of efficient single cylinder bolt-type multistage sequential telescopic method for optimizing route according to claim 8, its feature It is that following steps are performed in step (233)：

Step (2331)：Range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A types minimum stroke are judged Formula (3), assignment i=3, x=1, repeat step (21),

Step (2332)：Required range formula judgement, repeat step (22)；

By step (22), i=3；X=1；Range judgment formula (1) is expressed as：

C[3]+...+C[n]≤L-C_T[1]-C_T[2] (1.1.1.1)

C_T[3]+CC_45...n≤L-C_T[1]-C_T[2] (2.1.1.1)

If meeting, the 4th layer T-shaped " water valve " can select to open formula (2.1.1.1), and into step (23331), i=4 is similar to Circulation performs step (21) --- step (24)；... by that analogy, step can be performed with recursion to i=n-2 layers, similar cycle (21) --- step (24)；If it is not satisfied, step (2334) can only be performed downwards；

C_A[3]+CC_45...n≤L-C_T[1]-C_T[2] (3.1.1.1)

If meeting, the 4th layer of A type " water valve " can select to open formula (3.1.1.1), and into step (23341), i=4 is similar to Circulation performs step (21) --- step (24)；... by that analogy, step can be performed with recursion to i=n-2 layers, similar cycle (21) --- step (24)；If it is not satisfied, step (2335) can only be performed downwards；

Step (2335)：Range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A types minimum stroke are judged Formula (3), assignment i=3, x=2, repeat step (21)；

By step (21), i=3, there are three layers of canal stream；X=2, represents that Section 1, Section 2 arm extend target invariant position, from Section 3 arm Start, by Section 3 arm contracting 1, step (2336) is performed downwards；

Step (2336)：Required range judgement, repeat step (22)；

C[4]+...+C[n]≤L-C_T[1]-C_T[2] (1.1.1.2)

Formula (1.1.1.2) if meet, Section 1, Section 2 arm extend target position, Section 3 arm contracting 1, all arm joints are direct in addition Extend target position, contracting arm limiting condition collection O={ T [1], T [2], 1, T [4] ..., T [n]；If it is not satisfied, performing downwards (2337)；

Step (2337)：Minimum stroke judges needed for T-shaped, repeat step (23),

C_T[4]+CC_45...n≤L-C_T[1]-C_T[2] (2.1.1.2)

If meeting, the 2nd third layer T-shaped " water valve " can select to open formula (2.1.1.2), into step (23371), i= 4, similar cycle performs step (21) --- step (24)；If it is not satisfied, step (2338) can only be performed downwards；

Step (2338)：Minimum stroke judgement needed for A types, repeat step (24),

C_A[4]+CC_45...n≤L-C_T[1]-C_T[2] (3.1.1.2)

If meeting, the 2nd third layer A types " water valve " can select to open formula (3.1.1.2), into step (23381), i= 4, similar cycle performs step (21) --- step (24)；If it is not satisfied, step (2339) can only be performed downwards；

Step (2339)：Public is judged to range judgment formula (1), T-shaped minimum stroke judgment formula (2), A types minimum stroke Formula (3), assignment i=3, x=3, repeat step (21) ... judges until to range judgment formula (1), T-shaped minimum stroke Formula (2) and A type minimum strokes judgment formula (3), assignment i=2, x=(n-1), repeat step (21),

By step (21), i=3, there are three layers of canal stream；X=3, represents that Section 1, Section 2 arm extend target invariant position, from Section 3 arm Start, by Section 3, Section 4 arm contracting 1；... the like, until by step (21), i=3 has three layers of canal stream；X=(n-2), Represent that Section 1, Section 2 arm extend target invariant position, since Section 3 arm, by Section 3 --- (n-3) joint arm contracting 1；

Step (233A)：Required range judgement, repeat step (22)；

C[n-2]+C[n-1]+C[n]≤L-C_T[1]-C_T[2] (1.1.1.(n-2))

If meeting range judgment formula (1.1.1. (n-2)), contracting arm limiting condition collection output O={ T [1], T [2], 1 ... 1,T[n-2],T[n-1],T[n]}；If it is not satisfied, then carrying out minimum stroke judgement, step (233B) is performed；

Step (233B)：Minimum stroke judges needed for T-shaped, repeat step (23)；

C_T[n-2]+C[n-1]+C[n]≤L-C_T[1]-C_T[2] (2.1.1.(n-2))

If meeting, T-shaped " water valve " can select to open formula (2.1.1. (n-2)), and into step (233B1), i=4 is similar to follow Ring performs step (21) --- step (24)；If it is not satisfied, performing step (233C)；

Step (233C)：Minimum stroke judgement, repeat step (24) needed for A types, and obtain this layer of branch's flow end product；

C_A[n-2]+C[n-1]+C[n]≤L-C_T[1]-C_T[2] (3.1.1.(n-2))

If meeting, A types " water valve " can select to open formula (3.1.1. (n-2)), and into step (233C1), i=4 is similar to follow Ring performs step (21) --- step (24)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1), now, range Formula is：

C[n-1]+C[n]≤L-C_T[1]-C_T[2] (1.1.1.(n-1))

If range formula (1.1.1. (n-1)) meets, output contracting arm limiting condition collection output O=T [1], T [2], 1,…1,T[n-1],T[n]}；If it is not satisfied, then by (n-1) joint arm contracting 1, x=n, output contracting arm limiting condition collection output O= {T[1],T[2],1,…1,1,T[n]}。

10. a kind of efficient single cylinder bolt-type multistage sequential telescopic method for optimizing route according to claim 8, its feature It is that following steps are performed in step (234)：

Step (2341)：Range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A types minimum stroke are judged Formula (3), assignment i=3, x=1, repeat step (21)；

By step (21), it is initially：I=3, there is three layers of canal stream；X=1, represents that Section 1 extends target position, Section 2 arm and keeps former Invariant position, the contracting 1 since Section 3 arm does not have arm joint contracting 1 when initial, step (2342) is performed downwards；

Step (2342)：Required range formula judgement, repeat step (22)；

By step (22), i=3；X=1；Range judgment formula (1) is expressed as：

C[3]+...+C[n]≤L-C_T[1]-C_A[2] (1.1.1.1’)

If meeting, Section 1 arm extends target position to formula (1.1.1.1 '), and Section 2 arm keeps in situ constant, opened from Section 3 arm Begin, all arm joints directly extend target position, contracting arm limiting condition collection O={ T [1], A [2], T [3] ..., T [n] }；If it is not satisfied, Perform (2343) downwards；

C_T[3]+CC_45...n≤L-C_T[1]-C_A[2] (2.1.1.1’)

If meeting, the 4th layer T-shaped " water valve " can select to open formula (2.1.1.1 '), into step (23431), i=4, class Step (21) is performed like circulation --- step (24)；... by that analogy, can be with recursion to i=n-2 layers, similar cycle performs step Suddenly (21) --- step (24)；If it is not satisfied, step (2344) can only be performed downwards；

C_A[3]+CC_45...n≤L-C_T[1]-C_A[2] (3.1.1.1’)

If meeting, the 4th layer of A type " water valve " can select to open formula (3.1.1.1 '), into step (23441), i=4, class Step (21) is performed like circulation --- step (24)；... by that analogy, can be with recursion to i=n-2 layers, similar cycle performs step Suddenly (21) --- step (24)；If it is not satisfied, step (2345) can only be performed downwards；

Step (2345)：Range judgment formula (1), T-shaped minimum stroke judgment formula (2) and A types minimum stroke are judged Formula (3), assignment i=3, x=2, repeat step (21)；

By step (21), i=3, there are three layers of canal stream；X=2, represents that Section 1 extends target position, Section 2 arm and keeps in situ constant, The contracting 1 since Section 3 arm, by Section 3 arm contracting 1, performs downwards step (2346)；

Step (2346)：Required range judgement, repeat step (22)；

C[4]+...+C[n]≤L-C_T[1]-C_A[2] (1.1.1.2’)

If meeting, Section 1 extends target position to formula (1.1.1.2 '), Section 2 arm keep in situ, Section 3 arm contracting 1, in addition institute There is arm joint directly to extend target position, contracting arm limiting condition collection O={ T [1], A [2], 1, T [4] ..., T [n]；If it is not satisfied, downwards Perform (2347)；

Step (2347)：Minimum stroke judges needed for T-shaped, repeat step (23)；

C_T[4]+CC_45...n≤L-C_T[1]-C_A[2] (2.1.1.2’)

If meeting, the 2nd the 4th layer T-shaped " water valve " can select to open formula (2.1.1.2 '), into step (23471), i= 4, similar cycle performs step (21) --- step (24)；If it is not satisfied, step (2348) can only be performed downwards；

Step (2348)：Minimum stroke judgement needed for A types, repeat step (24),

C_A[4]+CC_45...n≤L-C_T[1]-C_A[2] (3.1.1.2’)

If meeting, the 2nd the 4th layer of A type " water valve " can select to open formula (3.1.1.2 '), into step (23481), i= 4, similar cycle performs step (21) --- step (24)；If it is not satisfied, step (2349) can only be performed downwards；

Step (2349)：Public is judged to range judgment formula (1), T-shaped minimum stroke judgment formula (2), A types minimum stroke Formula (3), assignment i=3, x=3, repeat step (21) ... judges until to range judgment formula (1), T-shaped minimum stroke Formula (2) and A type minimum strokes judgment formula (3), assignment i=2, x=(n-1), repeat step (21)；

By step (21), i=3, there are three layers of canal stream；X=3, represents that Section 1 extends target position, Section 2 arm and keeps in situ constant, The contracting 1 since Section 3 arm, by Section 3, Section 4 arm contracting 1；... the like, until by step (21), i=3 has three layers of canal Stream；X=(n-2), represents that Section 1 extends target position, Section 2 arm and keeps constant, the contracting 1 since Section 3 arm, by the 3rd in situ Section --- (n-3) joint arm contracting 1；

Step (234A)：Required range judgement, repeat step (22)；

C[n-2]+C[n-1]+C[n]≤L-C_T[1]-C_A[2] (1.1.1.(n-2)’)

If meeting range judgment formula (1.1.1. (n-2) '), contracting arm limiting condition collection output O={ T [1], A [2], 1 ... 1,T[n-2],T[n-1],T[n]}；If it is not satisfied, then carrying out minimum stroke judgement, step (234B) is performed；

Step (234B)：Minimum stroke judges needed for T-shaped, repeat step (23)；

C_T[n-2]+C[n-1]+C[n]≤L-C_T[1]-C_A[2] (2.1.1.(n-2)’)

If meeting, T-shaped " water valve " can select to open formula (2.1.1. (n-2) '), and into step (234B1), i=4 is similar to Circulation performs step (21) --- step (24)；If it is not satisfied, performing step (234C)；

Step (234C)：Minimum stroke judgement, repeat step (24) needed for A types, and obtain this layer of branch's flow end product；

C_A[n-2]+C[n-1]+C[n]≤L-C_T[1]-C_A[2] (3.1.1.(n-2)’)

If meeting, A types " water valve " can select to open formula (3.1.1. (n-2) '), and into step (234C1), i=4 is similar to Circulation performs step (21) --- step (24)；If it is not satisfied, (n-2) joint arm is contracted 1, then x=(n-1), now, maximum row Journey formula is：

C[n-1]+C[n]≤L-C_T[1]-C_A[2] (1.1.1.(n-1)’)

If range formula (1.1.1. (n-1) ') meets, output contracting arm limiting condition collection output O=T [1], A [2], 1,…1,T[n-1],T[n]}；If it is not satisfied, then by (n-1) joint arm contracting 1, x=n, output contracting arm limiting condition collection output O= {T[1],A[2],1,…1,1,T[n]}。