CN107122568A - A kind of flexible cable traction dirt extraction robot kinetic stability evaluation method - Google Patents
A kind of flexible cable traction dirt extraction robot kinetic stability evaluation method Download PDFInfo
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Abstract
The invention discloses a kind of flexible cable traction dirt extraction robot kinetic stability evaluation method, the stability that flexible cable draws dirt extraction robot motion is evaluated in terms of dirt extraction robot end grabs bucket the movement velocity of flexible cable pulling force and end grab bucket of current location point on the relative position residing for working space, most weak constraint direction etc. three, a kind of Trinity kinetic stability evaluation method for integrating robot end position, restraining force and tip speed is proposed, and then reference is provided for lifting flexible cable traction dirt extraction robot stability approach.
Description
Technical field
Dirt extraction robot field is drawn the present invention relates to flexible cable, and in particular to a kind of flexible cable traction dirt extraction robot motion is steady
Qualitative evaluating method.
Background technology
Dirt extraction robot is the class in flexible cable traction parallel robot, and the motion of its end grab bucket is not by ground obstacle
Influence, it is possible to achieve the Arbitrary 3 D motion in working space, and with working space is big, the speed of service is fast, stability is high,
The advantages of simple installation.However, dirt extraction robot draws a type of parallel robot, also inherent tool as flexible cable
Standby flexible cable draws some shortcomings of parallel robot, for example：The unidirectional constraint of flexible rope, relative to rigid bar parallel manipulator
For people, its end poing rigidity is weak, kinetic stability difference and system control difficulty etc..Meanwhile, relative to the traction of existing flexible cable
Parallel robot, the work of dirt extraction robot has certain particularity.(a) in the moment of crawl spoil, the grab bucket of its end
Movement velocity must be synchronous with the movement velocity of belt conveyer, completion crawl work that so could be more reliable and more stable；(b)
The moment end grab bucket of spoil and the synchronism of belt conveyer are captured, it is necessary to design a kind of effective trajectory planning in order to realize
And the control method of stable crawl；(c) because dirt extraction robot is that a class has certain requirements flexible cable to end movement speed
Parallel robot is drawn, the unidirectional constraint of flexible cable and flexible meeting cause inevitable influence to the stability that it is moved.Therefore need
Effective kinetic stability evaluation method and evaluation index is set up to dirt extraction robot, its kinetic stability is entered with realizing
Row is evaluated, and then finds out the method and strategy for lifting its stability.
Firstly, since dirt extraction robot drives end to grab bucket using the rope of light soft, so when it is by the external world
In the case of interference or motion state change acutely, it is possible to the change under the forcing that external interference or motion state are mutated
The current position of its end grab bucket.If external interference changes the current location of dirt extraction robot end grab bucket, robot
It is unstable.So, the stability of dirt extraction robot is referred to when robot is mutated by external interference or motion state
When, it constrains the ability that external interference is resisted on most weak direction.By the theoretical research and experimental verification of early stage, dirt extraction machine
The kinetic stability of people is mainly influenceed by three aspects：Robot end grabs bucket in the location of working space, currently
There is the movement velocity that pulling force minimum flexible cable is subject in flexible cable Suo Lali and end grab bucket at location point.Therefore, it can from
Its kinetic stability is studied in terms of above three, proposition dirt extraction robot multi-parameter kinetic stability evaluation method and its
Index, the kinetic stability for weighing robot end's grab bucket, also provides thinking to improve its kinetic stability.
The content of the invention
To solve the above problems, the invention provides a kind of flexible cable traction dirt extraction robot kinetic stability evaluation method.
To achieve the above object, the technical scheme taken of the present invention is：
A kind of flexible cable traction dirt extraction robot kinetic stability evaluation method, comprises the following steps：
S1, according to dirt extraction robot kinematics model, try to achieve flexible cable vector O ' BiLength in global coordinate systemAnd then end grab bucket is obtained 4 at working space any location point
The direction of the minimum flexible cable of pulling force and angle theta=arcsin ((H- of horizontal plane in flexible cableozo′)/ρi), (wherein,ozo′For end
Actuator and the height coordinate of plane where rope pin joint；H is the height of Sarasota；ρiFor 4 flexible cables at location point P, Q, M
The length of flexible cable minimum middle Suo Lali；θP、θQ、θMθ angles at respectively point P, Q, M)；Meanwhile, in dirt extraction robot redundancy rope
Pulling force solving model formula:(wherein matrix J is the Jacobian matrix of dirt extraction robot on the basis of JT=W；Vector T is picker
The rope tensility vector of each flexible cable of device people；Vectorial W is broad sense force vector), try to achieve the Suo La that end is grabbed bucket at the point of current location
Force vector, and then the meter of the minimum Suo Lali by following formula progress robot end's grab bucket in working space at any location point
Calculate：
Tmin=min (T) (1)
In formula, min () represents that rope draws the minimum component of force vector；
S2, the dynamic analysis based on dirt extraction robot and redundancy rope pulling force optimization solution, propose two positions respectively
Performance factor and two rope pulling force characteristic factors, current location point is grabbed bucket in working space institute for describing dirt extraction robot end
Influences of the Suo Lali to end effector kinetic stability on the position and the most weak direction of constraint at place；Specifically, figure is neutral
Cube is the working space of dirt extraction robot；Any position of the end grab bucket in working space is represented with point P；Dirt extraction machine
People's working space vertical center line is represented with a；The intersection point of horizontal plane and vertical center line a where the point P of optional position is represented with Q；It is perpendicular
The straight uppermost location points of center line a are represented with M；Minimum Suo Li at position P, Q and M uses T respectivelyP,min,TQ,minAnd TM,minTable
Show；There are the rope of Suo Lali minimums and the angle of horizontal plane in rope to use γ respectively at position P, Q and MP,γQAnd γMRepresent；
Movement velocity of the dirt extraction robot end grab bucket at location point P, Q and M uses v respectivelyP、vQAnd vMRepresent；It is therefore proposed that
Two position performance factorsWithCome weigh current location point away from planar central where the location point and coboundary away from
From being expressed as：
Further by formula (1), two rope pulling force characteristic factors are proposedWithFor studying minimum Suo Lali in work
Distribution situation on the horizontal section and vertical center line in space, is expressed as：
In formula, XPFor the coordinate vector at the point P of current location；The span of 4 power location factors is all interval for [0,1]；
S3, in order to quantify influence of the dirt extraction robot end grab bucket movement velocity to its kinetic stability, propose speed shadow
Ring function f (vP) be used to characterize end grab bucket in the movement velocity being presently at location point to dirt extraction robot kinetic stability
Influence；Speed influence function f (vP) must possess following property：
1) end grab bucket stability, function f (v at the point of current location are quantified to use the positive number of interval [0,1]P)
Codomain f (vP)∈[0,1]；
2) stability of the end grab bucket at the point of current location reduces with the increase of its speed at the location point；
3) speed of the end grab bucket at the point P of current location is vP, work as vPWhen=0, that is, in current location Dian Chu, no
Consider the situation of end grab bucket speed influence；Work as vP=vmaxWhen, that is, in current location Dian Chu, the motion speed of end grab bucket
Degree reaches maximum, and we provide that at the maximum location point of end grab bucket speed its motion stabilization degree is 0；At remaining location point
Stability between above two limiting case；
S4, composite type (2), (3), (4), (5) and dirt extraction robot end grab bucket speed influence function f (vP), propose
Flexible cable traction dirt extraction robot end is evaluated to grab bucket the Trinity stability indicator Ω of dynamic stabilityd, its numerical value it is big
It is small to be referred to as motion stabilization degree, it is formulated as：
Ωd(XP)=Ωm(XP)f(vP) (6)
In formula,p1、p2、q1And q2For weight coefficient, and p1+p2=1,
q1+q2=1；Usually, Ωm(XP) span be Ωm∈[0,1]。
Preferably due toWithRespectively represent working space vertical center line on minimum Suo Lali distribution and vertically
Distance of any location point away from working space coboundary on center line, but due to vertical center line in full working space in completely right
The position of title, so, weight coefficient q1And q2All take 0.5；
Preferably for weight coefficient p1And p2If, the contribution phase of the rope pulling force characteristic factor and location factor to terminal stabilization
When can elect them as 0.5；If the contribution of rope pulling force characteristic factor pair terminal stabilization is larger, corresponding weight coefficient p1
More than 0.5, and corresponding weight coefficient p2Less than 0.5；If contribution of the location factor to terminal stabilization is larger, corresponding power system
Number p2More than 0.5, and corresponding weight coefficient p1Less than 0.5.
Preferably, speed influence function f (vP) take function
The speed influence function for choosing above-mentioned form is to be moved to describe dynamic stability evaluation index with end's platform
Relation between kinetic energy；In formula, vPGrabbed bucket for end in the speed of current location point；vmaxFor dirt extraction robot maximal work feelings
The lower maximal rate that can be reached of condition, when the movement velocity of dirt extraction robot is more than or equal to vmaxWhen, it is believed that it is dynamic that it is moved
State stability is 0.
The invention has the advantages that：
Current location point is grabbed bucket on the relative position residing for working space, most weak constraint direction from dirt extraction robot end
Suo Lali and three aspects such as movement velocity of end grab bucket analyze the stability that flexible cable draws dirt extraction robot motion,
A kind of Trinity kinetic stability evaluation method for integrating position, power and speed is proposed, to lift its stability
Method with strategy provide reference.
Brief description of the drawings
Fig. 1 is location factor, the Suo Lali factors and velocity factor accompanying drawings in the embodiment of the present invention.
Fig. 2 is that dirt extraction robot end grabs bucket current location point in the location of working space and about in the embodiment of the present invention
Influence schematic diagrames of the Suo Lali to end effector kinetic stability on the most weak direction of beam.
Embodiment
In order that objects and advantages of the present invention are more clearly understood, the present invention is carried out with reference to embodiments further
Describe in detail.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to limit this hair
It is bright.
The embodiments of the invention provide a kind of flexible cable traction dirt extraction robot kinetic stability evaluation method, including following step
Suddenly：
S1, one side, according to dirt extraction robot kinematics model as shown in Figure 1, try to achieve flexible cable vector O ' BiIn the overall situation
Length in coordinate systemAnd then end grab bucket is obtained in working space
The direction of the minimum flexible cable of pulling force and angle theta=arcsin ((H- of horizontal plane in 4 flexible cables at any location pointozo′)/ρi),
(wherein,ozo′The height coordinate of plane where end effector and rope pin joint；H is the height of Sarasota；ρiFor in position
The length of flexible cable minimum Suo Lali in 4 flexible cables at point P, Q, M；θP、θQ、θMθ angles at respectively point P, Q, M)；The opposing party
Face, (wherein matrix J is the Ya Ke of dirt extraction robot on the basis of dirt extraction robot redundancy rope pulling force solving model formula JT=W
Compare matrix；Vector T is vectorial for the rope tensility of each flexible cable of dirt extraction robot；Vectorial W is broad sense force vector), try to achieve end grab bucket
Rope at the point of current location draws force vector, and then carries out robot end's grab bucket any position in working space by following formula
The calculating of minimum Suo Lali at point：
Tmin=min (T) (1)
In formula, min () represents that rope draws the minimum component of force vector；
S2, the dynamic analysis based on dirt extraction robot and redundancy rope pulling force optimization solution, propose two positions respectively
Performance factor and two rope pulling force characteristic factors, current location point is grabbed bucket in working space institute for describing dirt extraction robot end
Influences of the Suo Lali to end effector kinetic stability on the position and the most weak direction of constraint at place；Specifically, figure is neutral
Cube is the working space of dirt extraction robot；Any position of the end grab bucket in working space is represented with point P；Dirt extraction machine
People's working space vertical center line is represented with a；The intersection point of horizontal plane and vertical center line a where the point P of optional position is represented with Q；It is perpendicular
The straight uppermost location points of center line a are represented with M；Minimum Suo Li at position P, Q and M uses T respectivelyP,min,TQ,minAnd TM,minTable
Show；There are the rope of Suo Lali minimums and the angle of horizontal plane in rope to use γ respectively at position P, Q and MP,γQAnd γMRepresent；
Movement velocity of the dirt extraction robot end grab bucket at location point P, Q and M uses v respectivelyP、vQAnd vMRepresent；It is therefore proposed that
Two position performance factorsWithCome weigh current location point away from planar central where the location point and coboundary away from
From being expressed as：
Further by formula (1), two rope pulling force characteristic factors are proposedWithFor studying minimum Suo Lali in work
Distribution situation on the horizontal section and vertical center line in space, is expressed as：
In formula, XPFor the coordinate vector at the point P of current location；The span of 4 power location factors is all interval for [0,1]；
S3, in order to quantify influence of the dirt extraction robot end grab bucket movement velocity to its kinetic stability, propose speed shadow
Ring function f (vP) be used to characterize end grab bucket in the movement velocity being presently at location point to dirt extraction robot kinetic stability
Influence；Speed influence function f (vP) must possess following property：
1) end grab bucket stability, function f (v at the point of current location are quantified to use the positive number of interval [0,1]P)
Codomain f (vP)∈[0,1]；
2) stability of the end grab bucket at the point of current location reduces with the increase of its speed at the location point；
3) speed of the end grab bucket at the point P of current location is vP, work as vPWhen=0, that is, in current location Dian Chu, no
Consider the situation of end grab bucket speed influence；Work as vP=vmaxWhen, that is, in current location Dian Chu, the motion speed of end grab bucket
Degree reaches maximum, and we provide that at the maximum location point of end grab bucket speed its motion stabilization degree is 0；At remaining location point
Stability between above two limiting case；
S4, composite type (2), (3), (4), (5) and dirt extraction robot end grab bucket speed influence function f (vP), propose
Flexible cable traction dirt extraction robot end is evaluated to grab bucket the Trinity stability indicator Ω of dynamic stabilityd, its numerical value it is big
It is small to be referred to as motion stabilization degree, it is formulated as：
Ωd(XP)=Ωm(XP)f(vP) (6)
In formula,p1、p2、q1And q2For weight coefficient, and p1+p2=1, q1+
q2=1；Usually, Ωm(XP) span be Ωm∈[0,1]。
There is following selection principle for weight coefficient：Every group of weight coefficient p1、p2、q1And q2Corresponding to a kind of structure parameters and superfluous
The stability of remaining Suo Lali optimization aims；In the solution procedure to dirt extraction robot stability, weight coefficient p1、p2、q1And q2Instead
The contribution of the rope pulling force characteristic factor and location factor to terminal stabilization is reflected, they are smaller than 1 positive number, and p1+p2=1,
q1+q2=1.
Due toWithRespectively represent working space vertical center line on minimum Suo Lali distribution and vertical center line on
Distance of any location point away from working space coboundary, and because vertical center line is in full symmetric position in full working space
Put, so, weight coefficient q1And q2All take 0.5；
For weight coefficient p1And p2If, the rope pulling force characteristic factor and location factor to the contribution of terminal stabilization quite, can be by
They elect 0.5 as；If the contribution of rope pulling force characteristic factor pair terminal stabilization is larger, corresponding weight coefficient p1More than 0.5,
And corresponding weight coefficient p2Less than 0.5；If contribution of the location factor to terminal stabilization is larger, corresponding weight coefficient p2It is more than
0.5, and corresponding weight coefficient p1Less than 0.5.
The speed influence function f (vP) take function
The speed influence function for choosing above-mentioned form is to be moved to describe dynamic stability evaluation index with end's platform
Relation between kinetic energy；In formula, vPGrabbed bucket for end in the speed of current location point；vmaxFor dirt extraction robot maximal work feelings
The lower maximal rate that can be reached of condition, when the movement velocity of dirt extraction robot is more than or equal to vmaxWhen, it is believed that it is dynamic that it is moved
State stability is 0.It is as follows that we provide its proof：
Prove：∵vP≤vmax,Property 1 must be demonstrate,proved.
∵vmaxFor constant, ∴ functionsWith the increase of end grab bucket speed at the point of current location
And reduce, property 2 must be demonstrate,proved.
As speed v of the end grab bucket at location point PPWhen=0, f (vP)=1, i.e. Ωd(XP)=Ωm(XP)f(vP)=Ωm
(XP)；As speed v of the end grab bucket at location point PP=vmaxWhen, f (vP)=0, i.e. Ωd(XP)=Ωm(XP)f(vP)=0.Property
Matter 3 must be demonstrate,proved.
In summary, grab bucket movement velocity in end is taken as to the influence function of stabilityIt can expire
Sufficient speed influence function f (vP) the required property possessed, therefore be rational.
As seen through the above analysis, because speed influence function f (vP) and Ωm(XP) span be [0,
1].So, the span for the Trinity dynamic stability evaluation method that the application is proposed also is Ωd(XP)∈[0,1]。
Wherein Ωd=0 location point corresponded to outside working space or the maximum locus point of end grab bucket movement velocity.Because
It is in outside working space or end grab bucket has reached the limit of the speed of service at this point, it is believed that its motion stabilization degree
For 0；Ωd=1 corresponds to the best location point of kinetic stability in full working space；Fortune in working space at remaining location point
Dynamic stability is all between 0 and 1.Therefore, the Trinity dynamic stability evaluation method can be using between interval [0,1]
Numerical value come quantify dirt extraction robot end grab bucket at the point of current location move degree of stability.
Described above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should
It is considered as protection scope of the present invention.
Claims (4)
1. a kind of flexible cable traction dirt extraction robot kinetic stability evaluation method, it is characterised in that comprise the following steps：
S1, according to dirt extraction robot kinematics model, try to achieve flexible cable vector O ' BiLength in global coordinate systemI=1,2,3,4, and then end grab bucket is obtained 4 at working space any location point
The direction of the minimum flexible cable of pulling force and angle theta=arcsin ((H- of horizontal plane in root flexible cableozo′)/ρi), wherein,ozo′For end
Hold actuator and the height coordinate of plane where rope pin joint；H is the height of Sarasota；ρiFor at location point P, Q, M 4 it is soft
The length of flexible cable minimum Suo Lali in rope；θP、θQ、θMθ angles at respectively point P, Q, M；Meanwhile, in dirt extraction robot redundancy
On the basis of Suo Lali solving model formulas JT=W, (wherein matrix J is the Jacobian matrix of dirt extraction robot；Vector T is dirt extraction
The rope tensility vector of each flexible cable of robot；Vectorial W is broad sense force vector) try to achieve the Suo La that end is grabbed bucket at the point of current location
Force vector, and then carry out minimum Suo Lali of the dirt extraction robot end grab bucket at working space any location point by following formula
Calculate：
Tmin=min (T) (1)
In formula, min () represents that rope draws the minimum component of force vector；
S2, based on dirt extraction Kinetic Analysis of Robots and redundancy rope pulling force optimization solve, two position performance factors are proposed respectively
With two rope pulling force characteristic factors, current location point is grabbed bucket in the location of working space for describing dirt extraction robot end
And influences of the Suo Lali on the most weak direction of constraint to end effector kinetic stability；Cube is the work of dirt extraction robot
Make space；Any position of the end grab bucket in working space is represented with point P；Dirt extraction robot working space vertical center line is used
A is represented；The intersection point of horizontal plane and vertical center line a where end grab bucket optional position point P is represented with Q；Vertical center line a is topmost
Location point represented with M；Minimum Suo Li at position P, Q and M uses T respectivelyP,min,TQ,minAnd TM,minRepresent；At position P, Q and M
The angle of rope minimum Suo Lali and horizontal plane uses γ respectively in all ropesP,γQAnd γMRepresent；Dirt extraction robot end
The movement velocity at location point P, Q and M of grabbing bucket uses v respectivelyP、vQAnd vMRepresent.On the basis of the above, two positions are proposed
Put performance factorWithTo weigh end grab bucket current location point away from planar central where the location point and coboundary
Distance, is expressed as：
Further by formula (1), two rope pulling force characteristic factors are proposedWithFor studying minimum Suo Lali in working space
Horizontal section and vertical center line on distribution situation, be expressed as：
In formula, XPFor the coordinate vector at the point P of current location；The span of 4 power location factors is all interval for [0,1]；
S3, in order to quantify influence of the dirt extraction robot end grab bucket movement velocity to its kinetic stability, propose speed influence letter
Number f (vP) it is used to characterize end grab bucket in shadow of the movement velocity being presently at location point to dirt extraction robot kinetic stability
Ring, speed influence function f (vP) must possess following property：
1) end grab bucket stability, function f (v at the point of current location are quantified to use the positive number of interval [0,1]P) value
Domain f (vP)∈[0,1]；
2) stability of the end grab bucket at the point of current location reduces with the increase of its speed at the location point；
3) speed of the end grab bucket at the point P of current location is vP, work as vPWhen=0, that is, in current location Dian Chu, do not consider
The situation of end grab bucket speed influence；Work as vP=vmaxWhen, that is, in current location Dian Chu, the movement velocity of end grab bucket reaches
To maximum, we provide that at the maximum location point of end grab bucket speed its motion stabilization degree is 0；It is steady at remaining location point
Spend calmly between above two limiting case；
S4, composite type (2), (3), (4), (5) and dirt extraction robot end grab bucket speed influence function f (vP), it is proposed that evaluate
The Trinity stability indicator Ω of flexible cable traction dirt extraction robot end's grab bucket dynamic stabilityd, the size of its numerical value is referred to as
For motion stabilization degree, it is formulated as：
Ωd(XP)=Ωm(XP)f(vP) (6)
In formula,p1、p2、q1And q2For weight coefficient, and p1+p2=1, q1+q2=
1；Usually, Ωm(XP) span be Ωm∈[0,1]。
2. a kind of flexible cable traction dirt extraction robot kinetic stability evaluation method as claimed in claim 1, it is characterised in that right
There is following selection principle in weight coefficient：Every group of weight coefficient p1、p2、q1And q2It is excellent corresponding to a kind of structure parameters and redundancy rope pulling force
Change the stability of target；Be smaller than 1 positive number, and p1+p2=1, q1+q2=1.
3. a kind of flexible cable traction dirt extraction robot kinetic stability evaluation method as claimed in claim 1, it is characterised in that right
In weight coefficient p1And p2If the contribution of the rope pulling force characteristic factor and location factor to terminal stabilization is suitable, can elect them as
0.5；If the contribution of rope pulling force characteristic factor pair terminal stabilization is larger, corresponding weight coefficient p1More than 0.5, and weigh accordingly
Coefficient p2Less than 0.5；If contribution of the location factor to terminal stabilization is larger, corresponding weight coefficient p2More than 0.5, and it is corresponding
Weight coefficient p1Less than 0.5.
4. a kind of flexible cable traction dirt extraction robot kinetic stability evaluation method as claimed in claim 1, it is characterised in that speed
Spend influence function f (vP) take function
In formula, vPThe speed of current location point is gripped in for end；vmaxFor institute in the case of Wire driven robot dirt extraction robot maximal work
The maximal rate that can be reached, when the movement velocity of dirt extraction robot is more than or equal to vmaxWhen, it is believed that its motion stabilization degree is 0.
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| CN115070771A (en) * | 2022-07-19 | 2022-09-20 | 中国科学技术大学 | Elastic double-ring synchronous control method for rope traction parallel robot |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110948481A (en) * | 2019-11-05 | 2020-04-03 | 佛山科学技术学院 | Stability evaluation method of rope-traction parallel robot based on pose cable force stiffness |
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| CN111938989B (en) * | 2020-07-20 | 2022-05-17 | 哈尔滨工程大学 | Motion stability evaluation method of rigid-flexible hybrid lower limb gait rehabilitation training robot |
| CN115070771A (en) * | 2022-07-19 | 2022-09-20 | 中国科学技术大学 | Elastic double-ring synchronous control method for rope traction parallel robot |
| CN115070771B (en) * | 2022-07-19 | 2022-12-30 | 中国科学技术大学 | Elastic double-ring synchronous control method for rope traction parallel robot |
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