CN107627305A - A kind of optimal locking angle method for solving in space manipulator failure joint - Google Patents
A kind of optimal locking angle method for solving in space manipulator failure joint Download PDFInfo
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- CN107627305A CN107627305A CN201711007220.7A CN201711007220A CN107627305A CN 107627305 A CN107627305 A CN 107627305A CN 201711007220 A CN201711007220 A CN 201711007220A CN 107627305 A CN107627305 A CN 107627305A
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Abstract
The embodiments of the invention provide a kind of space manipulator for meeting integrated motion performance requirement freely swing failure joint it is optimal locking angle method for solving, including：By the way that minimum singular value, conditional number, operable degree index are normalized, space manipulator joint space integrated motion performance indications are constructed；Configuration during different angle is locked in based on Analytic Method space manipulator failure joint, meets the configuration of integrated motion performance requirement using the screening of integrated motion performance indications to form space manipulator preferred configuration collection；Solve failure joint and be locked in variable locking angle time space mechanical arm degeneration working space volume corresponding to preferred configuration collection, it is the optimal locking angle in space manipulator failure joint to select locking angle corresponding to maximum volume.The technical scheme provided according to embodiments of the present invention, it is possible to achieve space manipulator freely swing failure joint it is optimal locking angle solution.
Description
【Technical field】
Freely swing the optimal lock in failure joint the present invention relates to a kind of space manipulator for meeting integrated motion performance requirement
Determine angle method for solving, belong to space manipulator troubleshooting technical field.
【Background technology】
The complexity of the severe and articulation structure of space environment, makes the space manipulator of long service inevitably close
Save failure.Knuckle failure type is broadly divided into locking with freely swinging, the space mechanism for the failure that freely swings for generation joint
Arm, failure joint is locked in the angle of manipulator motion performance satisfaction requirement, remained to after being broken down for space manipulator
It is most important to continue to complete in-orbit operation task.Therefore, the correlation for carrying out the optimal locking angle in space manipulator failure joint is ground
Study carefully, it is very crucial to complete space probation to the mankind.
It is existing for space manipulator freely swing failure joint it is optimal locking angle solve research it is seldom, due to locking
Angle difference causes space manipulator integrated motion performance different, and when failure joint is locked in some special angles, mechanical arm closes
Section space and operating space exercise performance can become very low, and then degeneration mechanical arm may be caused can not to continue to complete follow-up behaviour
Make task, therefore, on the premise of ensureing that joint space and operating space exercise performance are all as high as possible, complete space manipulator
The solution of the optimal locking angle in the failure that freely swings joint, for space manipulator occur joint freely swing remain to after failure after
The continuous follow-up space tasks of completion have vital realistic meaning.
【The content of the invention】
In view of this, the embodiments of the invention provide a kind of optimal locking angle solution side in space manipulator failure joint
Method, institute's extracting method can be that the freely swing processing of failure of space mechanism shoulder joint provides safeguard.
In the solution procedure of the above-mentioned optimal locking angle in space manipulator failure joint, the method used comprises at least：
According to the characteristic features of joint space different motion performance indications, as minimum singular value can characterize the worst fortune of mechanical arm
Locomitivity, conditional number on dynamic direction can characterize degree of closeness of exercise performance etc. in mechanical arm all directions, choose multiple
Index, makes it to characterize the integrated motion performance of space manipulator joint space after integrating, and normalizing is carried out to selected index
Change is handled, so that each index span is identical, and is an index by each index comprehensive, i.e. space manipulator joint space is comprehensive
Resultant motion performance indications；
Space manipulator configuration corresponding during different angle is locked according to the inverse solution failure joint of analytic method, combination is all
Configuration, based on the integrated motion performance indications constructed, calculates gained structure to form simple joint defective space mechanical arm configuration collection
Type concentrates space manipulator integrated motion performance corresponding to all configurations, chooses the configuration for meeting integrated motion performance requirement with shape
Into space manipulator preferred configuration collection；
Failure joint, which is solved, according to Monte Carlo method is locked in variable locking angle time space machine corresponding to preferred configuration collection
The degeneration working space of tool arm, the volume of degeneration working space, chooses maximum degeneration work as obtained by solving rasterizing processing
Optimal locking angle of the locking angle as failure joint corresponding to spatial volume, to realize that space manipulator freely swings failure
The solution of the optimal locking angle in joint.
In above-mentioned solution procedure, the process of construction space manipulator joint space integrated motion performance indications includes：
The first step：Based on the characteristic features of joint space different motion performance indications, multiple indexs are chosen, can table
Levy the integrated motion performance of space manipulator joint space；The exercise performance index of space manipulator joint space includes minimum strange
Different value, conditional number, operable degree etc., wherein, minimum singular value is defined as the minimum value in Jacobian matrix singular value, conditional number
Maximum singular value and the ratio of minimum singular value in Jacobian matrix singular value are defined as, operable degree is defined as Jacobian matrix
The product of all non-zero singular values；
Using the Jacobian matrix of J representation space mechanical arms, singular value decomposition is carried out to Jacobian matrix J, such as following formula institute
Show：
J=U Σ V
In above formula, U represents dimension of m m orthogonal matrix, and V represents n × n orthogonal dimension matrixes, and m represents working space dimension, n tables
Show space manipulator number of degrees of freedom, Σ represents that diagonal ties up diagonal matrix for m × n of nonnegative real number, and Σ has following form：
Understood based on singular value decomposition characteristic, the σ in Σ1,σ2,…,σmMeet σ1＞ σ2＞ ... ＞ σm, wherein, σmRepresent
Minimum singular value；
Based on required Jacobian matrix singular value σ1,σ2,…,σmAnd the definition of each index of space manipulator, can will be minimum strange
The indexs such as different value, conditional number, operable degree are represented sequentially as：
Understood based on above formula, minimum singular value s can be used for characterizing the locomitivity in the worst direction of motion of mechanical arm, and s is got over
Greatly, the exercise performance in the worst direction of motion of representation space mechanical arm is higher；Conditional number c can be used for characterizing mechanical arm all directions
The degree of closeness of upper exercise performance, c is smaller, and the exercise performance in each direction of motion of representation space mechanical arm is closer；It can grasp
Degree of work ω can be used for the height for characterizing the comprehensive operation flexibility ratio of mechanical arm, and ω is bigger, the comprehensive operation of representation space mechanical arm
Flexibility ratio is higher；
Characteristic features based on different indexs understand that three minimum singular value, conditional number, operable degree indexs can integrate
Characterize the exercise performance of space manipulator joint space；When being in view of space manipulator under certain configuration, by calculating space
The minimum singular value of mechanical arm, conditional number, operable degree, and judge whether these three indexs meet threshold requirement respectively, and then
Determine whether the space manipulator under the configuration meets the requirement of joint space exercise performance, the calculating involved by this process with
Judgement is extremely cumbersome, therefore, necessary that three minimum singular value, conditional number, operable degree indexs are configured into an index,
That is space manipulator joint space integrated motion performance indications；
Second step：Based on normalized, space manipulator joint space integrated motion performance indications are constructed；Can in completion
After the selecting index of comprehensive characterization space manipulator joint space exercise performance and expression, it is contemplated that the minimum of space manipulator
Singular value, conditional number, the distribution of operable degree value are different, the space mechanism as obtained by being directly added three indexs
Arm integrated motion performance, it is impossible to equilibrium embody selected by the respective characteristic of index, therefore, need to minimum singular value, conditional number, can grasp
It is normalized, and then is added to complete to characterize three the balanced of index as degree；
If minimum singular value s span is if [a, b], then as s=x, at corresponding minimum singular value s normalization
Managing result is：
Normal (s)=(x-a)/(b-a) ∈ [0,1]
In above formula, normal () represents that minimum singular value s is normalized；Can similarly complete to conditional number and
The normalized of operable degree index；
Because the value of minimum singular value and operable degree is bigger, the value of conditional number is smaller, and space manipulator corresponds to motility
Can be better, therefore, the integrated motion performance indications u of space manipulator joint space is represented by：
U=normal (s)+normal (- c)+normal (ω) ∈ [0,3]
In above formula, the integrated motion performance in the bigger representation space joint of mechanical arm spaces of u is better；It can be completed based on above formula
The construction of space manipulator joint space integrated motion performance indications.
In above-mentioned calculating process, choose and meet the configuration of integrated motion performance requirement to form space manipulator preferred configuration
The process of collection includes：
The first step：Based on Analytic Method space manipulator configuration collection；In view of actual performing for the task of space manipulator
There should be continuity, therefore, the end pose P of space manipulator before and after failure joint lockingE(x, y, z, α, β, γ) needs to keep
It is constant；
On the premise of space manipulator end pose keeps constant, because failure joint lock angle degree is different, based on solution
The inverse solution gained space manipulator configuration of analysis method is different；The failure if space mechanism shoulder joint k freely swings, makes its joint angle θk
With step delta θkTravel through its slewing area [θk_min,θk_max], m=(θ can be obtainedk_max-θk_min)/ΔθkIndividual failure joint locking
Angle；Failure joint k is locked in a certain angle of traversal gained, make the pose P during holding knuckle failure of space manipulator endE
(x, y, z, α, beta, gamma) is constant, then space manipulator configuration, i.e. joint of mechanical arm angle sequence corresponding to solution, to complete to sky
The inverse kinematics of room machine arm, it is as follows that corresponding space manipulator configuration can be tried to achieve：
qe=(θ1,θ2,...,θk,...,θn) e=1,2 ..., j
In above formula, j represents inverse solution number, n representation space mechanical arm number of degrees of freedom,s；
Failure joint is locked in into the inverse solution gained space manipulator configuration of different angle to be combined, you can obtain space machine
Configuration collection after tool shoulder joint fault locking：
Q={ q1_j,q2_j,...,qi_j,...,qm_jI=1,2 ..., m
In above formula, m represents failure joint lock angle degree number.
Second step：Based on integrated motion performance indications, configuration required by screening concentrates the structure for meeting integrated motion performance requirement
Type；
After k breaks down when joint, degeneration minimum singular value s need to be based ond, degenerative conditions number cd, degenerate operable degree ωd
Reconfiguring for space manipulator integrated motion performance indications is carried out, it is as a result as follows：
ud=normal (sd)+normal(-cd)+normal(ωd)∈[0,3]
Wherein, subscript d represents to degenerate；Based on construction gained integrated motion performance indications ud, calculate space manipulator and be in
Various configuration qi_jWhen integrated motion performanceThe space manipulator that can similarly obtain in configuration collection q corresponding to all configurations is comprehensive
Resultant motion performance：
If degeneration minimum singular value sd, degenerative conditions number cd, degenerate operable degree ωdScreening threshold value be respectively χ, λ, κ,
The screening threshold value μ that space manipulator integrated motion performance indications can be obtained based on normalized is：
Define integrated motion performance numberMore than screening threshold value μ, expression meets integrated motion performance requirement；Utilize screening
Threshold value μ judges u successivelydThe middle integrated motion performance number for meeting to require, to form preferred integrated motion performance setSetIn space manipulator configuration corresponding to each integrated motion performance number, with shape
Into space manipulator preferred configuration collection qopt：
qopt={ q1_j,q2_j,...,qt_j}
Wherein, t represents preferred configuration number, and meets t≤m.
In above-mentioned calculating process, solution room mechanical arm freely swing failure joint it is optimal locking angle process include：
The first step：The variable locking angle that preferred configuration concentrates failure joint is chosen, forms the preferred lock angle in failure joint
Degree collection θopt：
θopt={ θk_1,θk_2,...,θk_g}
In above formula, g represents locking angle number, and meets g≤t；
Preferred locking transform angle set θ is locked in based on Monte Carlo method solution room mechanical arm failure joint respectivelyoptMiddle difference
During angle, the degeneration working space W of space manipulator：
W={ W1,W2,...,Wg}
Second step：The volume of gained space manipulator degeneration working space is solved based on rasterizing processing；
It is respectively l with length, width and heighta,lb,lcCuboid Q outsourcing space manipulators degeneration working space Wr, wherein, r=
1,2,...,g；With(wherein,For the operation that rounds up, Δ is the grid length of side
Coefficient is determined, and has Δ ∈ (0,1)) it is the grid length of side, rasterizing processing is carried out to cuboid Q, then cuboid Q can be rasterized into
It is Δ l small cubes grid set into the length of side, and grid sum can be obtained and be：
Because the degeneration working space of space manipulator is typically in state is randomly distributed, it is big can not accurately to calculate its volume
It is small, therefore its grid is turned into the minimum small square set of volume, and define：Grid quantity of the inside comprising scatterplot is multiplied by grid
Lattice volume acquired results are the volume V of degeneration working spaceW, based on this definition, space manipulator degeneration working space can be tried to achieve
The volume of each degeneration working space in set W：
VW={ VW_1,VW_2,...,VW_g}
3rd step：Bigger based on degeneration working space volume, space manipulator operating space exercise performance gets over the principle of sorrow,
Degeneration working space volume set V required by selectionWMiddle maximum volume VbiggestCorresponding failure joint lock angle degree θk, as
Space manipulator freely swings the optimal locking angle, θ in failure jointopt, and then complete the optimal lock in space manipulator failure joint
Determine the solution of angle.
The technical scheme of the embodiment of the present invention has the advantages that：
(1) characteristic features of the invention based on each exercise performance index of space manipulator joint space, it is determined that can be comprehensive
The multiple indexs for characterizing space manipulator joint space exercise performance are closed, and each index is normalized, pass through phase
Add each index to complete the construction of space manipulator joint space integrated motion performance indications, the integrated motion performance constructed refers to
Mark can characterize the integrated motion performance of space manipulator joint space, solve space manipulator joint space integrated motion
Can the selection of characteristic index, index comprehensive application, the problems such as performance characterization is cumbersome.
(2) the optimal locking angle method for solving in the failure joint proposed by the present invention that freely swings, mechanical arm can ensured
On the premise of end pose is constant, pass through solution room joint of mechanical arm space and operating space exercise performance while optimal when institute
Corresponding failure joint lock angle degree, the solution of the optimal locking angle in the failure joint that freely swings is realized, solves space mechanism
Arm occur joint freely swing failure when how quick handling failure, mechanical arm integrated motion Performance Evaluation, failure joint locking
The problems such as angle-determining.
According to advantages of the present invention, being freely swung by application, failure joint is optimal to lock angle method for solving, can be complete
Solved into the space manipulator that can the make integrated motion best performance optimal locking angle in failure joint that freely swings, the technology can answer
For the space manipulator troubleshooting stage.
【Brief description of the drawings】
In order to illustrate the technical solution of the embodiments of the present invention more clearly, below by embodiment it is required use it is attached
Figure is briefly described, it is therefore apparent that drawings in the following description are only some embodiments of the present invention, common for this area
For technical staff, do not pay it is creative and laborious on the premise of, other accompanying drawings can also be obtained according to these accompanying drawings.
Fig. 1 is freely swung the optimal lock in space manipulator failure joint of failure for joint in the embodiment of the present invention
Determine the schematic flow sheet of angle analysis method；
Fig. 2 is that building for research object is figure in the embodiment of the present invention；
Fig. 3 is that the variable locking angle of joint 2 corresponds to space manipulator degeneration working space and includes grid in the embodiment of the present invention
Lattice number figure.
【Specific embodiment】
1st, seven freedom space manipulator kinematics model is established as shown in Fig. 2 its D-H parameter declaration is as shown in table 1.
The failure if joint 2 of space manipulator freely swings, now, each joint angles of space manipulator be followed successively by [-
21,45,177,119,140,60, -120] (unit for degree), corresponding mechanical arm tail end pose for [- 4.72, -3.92,0.15, -
48.81, -14.20,77.77] (unit is rice or degree).
The seven freedom space manipulator D-H parameters of table 1
If the 2, the slewing area of joint 2 is [- 180,180] (unit is degree), makes it travel through its with 1 degree for step-length and rotate model
Enclose, then can obtain 361 locking angles；With [- 4.72, -3.92,0.15, -48.81, -14.20,77.77] (unit is rice or degree)
For space manipulator end pose, joint 2 is made to be locked in different angle successively, the inverse fortune based on Analytic Method space manipulator
It is dynamic to learn solution, 2384 groups of joint angle sequences can be obtained, and then space manipulator configuration collection q can be formed.
3rd, the space manipulator degeneration minimum singular value s in solution room mechanical arm configuration collection q corresponding to each configurationd, move back
Change conditional number cd, degenerate operable degree ωdValue, the space manipulator integrated motion performance indications u constructed based on the present inventiond, meter
Calculate space manipulator integrated motion performance number corresponding to 2384 configurations；If degeneration minimum singular value sd, degenerative conditions number cd, move back
Change operable degree ωdThreshold value be respectively χ=0.85, λ=9, κ=100, integrated motion performance can be obtained by normalized and referred to
Target threshold value μ=1.3, it can be obtained using the threshold value as according to the integrated motion performance number corresponding to 2384 groups of configurations of screening, wherein 119
Group configuration meets integrated motion performance requirement；Failure joint variable locking angle corresponding to enumerating 119 groups of configurations successively, can shape
The failure joint for including 79 locking angles into space manipulator preferably locks transform angle set θopt。
4th, joint 2 is made to be locked in preferred locking transform angle set θ successivelyoptIn different angle, based on Monte Carlo method by time
Degeneration working space corresponding to 50000 groups of joint configurations solutions is gone through, then the variable locking angle of joint 2 can be tried to achieve based on rasterizing processing
The corresponding degeneration working space of degree includes grid number, as shown in Figure 3；From the figure 3, it may be seen that correspond to space when joint 2 is locked in 92 degree
The volume of mechanical arm degeneration working space is maximum (the grid number included is most), it follows that when the end position of space manipulator
When appearance is [- 4.72, -3.92,0.15, -48.81, -14.20,77.77] (unit is rice or degree), joint 2 freely swings
Optimal locking angle is 92 degree corresponding to failure.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
God any modification, equivalent substitution and improvements done etc., should be included within the scope of protection of the invention with principle.
The content not being described in detail in description of the invention belongs to the known technology of those skilled in the art.
Claims (4)
1. a kind of optimal locking angle method for solving in space manipulator failure joint, it is characterised in that this method includes following step
Suddenly：
(1) characteristic features according to joint space different motion performance indications, choose multiple indexs, make it being capable of table after integrating
The integrated motion performance of space manipulator joint space is levied, selected index is normalized, and is integrated as one
Index, i.e. space manipulator joint space integrated motion performance indications；
(2) space manipulator configuration corresponding during different angle is locked according to the inverse solution failure joint of analytic method, obtains single close
Defective space mechanical arm configuration collection is saved, based on integrated motion performance corresponding to all configurations of integrated motion performance Index Calculation, choosing
The configuration for meeting to require is taken to form space manipulator preferred configuration collection；
(3) solve failure joint according to Monte Carlo method and be locked in variable locking angle space-time room machine corresponding to preferred configuration collection
The degeneration working space of arm, gained degeneration working space volume is solved, choose and locked corresponding to maximum degeneration working space volume
Optimal locking angle of the angle as failure joint.
2. according to the method for claim 1, it is characterised in that the space manipulator joint space integrated motion performance refers to
The process of mark construction comprises at least：
(1) Jacobian matrix J singular value σ is utilized1,σ2,…,σm, complete space manipulator joint space different motion performance and refer to
Target represents；
(2) according to the characteristic features of different indexs, tri- minimum singular value s, conditional number c, operable degree ω indexs are chosen, are carried out
The comprehensive characterization of space manipulator joint space exercise performance；
(3) according to the span of each index, three selected indexs are normalized respectively；
(4) result of three index normalizeds is added, obtains space manipulator joint space integrated motion performance indications u=
normal(s)+normal(-c)+normal(ω)∈[0,3]。
3. according to the method for claim 1, it is characterised in that the structure for meeting integrated motion performance requirement by choosing
Type is comprised at least with forming the process of space manipulator preferred configuration collection：
(1) failure joint k is made with step delta θkTravel through its slewing area [θk_min,θk_max], and make it be locked in certain obtained by traversal
One angle, make the pose P during holding knuckle failure of space manipulator endE(x, y, z, α, beta, gamma) is constant, inverse based on analytic method
Solution failure joint k is locked in the space manipulator configuration q during anglee=(θ1,θ2,...,θk,...,θn), e=1,2 ...,
j；
(2) combined fault joint k is locked in inverse solution gained space manipulator configuration during different angle, obtains space mechanism shoulder joint
Configuration collection q={ q after fault locking1_j,q2_j,...,qi_j,...,qm_j, i=1,2 ..., m；
(3) it is based on degeneration minimum singular value sd, degenerative conditions number cdWith the operable degree ω that degeneratesd, construct space machine after knuckle failure
The integrated motion performance indications u of tool armd=normal (sd)+normal(-cd)+normal(ωd)∈[0,3]；
(4) it is based on integrated motion performance indications ud, calculate the space manipulator integrated motion corresponding to all configurations in configuration collection q
Performance
(5) threshold value based on normalized solution room mechanical arm integrated motion performance indicationsJudge u using threshold value μdThe middle integrated motion performance for meeting to require
Value, to form preferred integrated motion performance set
(6) combineIn space manipulator configuration corresponding to each integrated motion performance number, to form the preferred structure of space manipulator
Type collection qopt={ q1_j,q2_j,...,qt_j}。
4. according to the method for claim 1, it is characterised in that the space manipulator freely swings the optimal lock in failure joint
The process for determining angle solution comprises at least：
(1) preferred configuration collection q is chosenoptMiddle failure joint k variable locking angle, composition failure joint preferably lock transform angle set
θopt={ θk_1,θk_2,...,θk_g}；
(2) preferred locking transform angle set θ is locked in based on Monte Carlo method solution room mechanical arm failure joint respectivelyoptMiddle difference
During angle, the degeneration working space W={ W of space manipulator1,W2,...,Wg, and gained space is solved based on rasterizing processing
The volume V of mechanical arm degeneration working spaceW={ VW_1,VW_2,...,VW_g}；
(3) degeneration working space volume set V required by choosingWMiddle maximum volume VbiggestCorresponding failure joint lock angle degree
θk, the optimal locking angle, θ in the failure joint that freely swings as space manipulatoropt, and then complete space manipulator failure joint
The solution of optimal locking angle.
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