CN103714242A - Singularity-avoiding input parameter value space method for avoiding kinematic singularity in parallel mechanisms - Google Patents

Abstract

The invention relates to a singularity-avoiding input parameter value space method for avoiding kinematic singularity in parallel mechanisms and belongs to technologies of avoiding parallel mechanisms kinematic singularity in the field of robotic mechanism. The method mainly includes: constructing parallel mechanism singularity position space distribution surfaces using input parameters as all coordinate axes; constructing inscribed envelope surface of the space distribution surfaces to obtain singularity-avoiding input parameter value space distribution surfaces; selecting proper operating points in the singularity-avoiding input parameter value space distribution surfaces, and determining the value ranges of input parameters meeting the operation requirements; determining the value ranges of the input parameters are in the singularity-avoiding input parameter value space distribution surfaces, and eliminating kinematic singularity in the parallel mechanisms during a design phase. The method is simple, universal and easy to implement; the method is directly applicable to eliminating kinematic singularity of operating space of the parallel mechanisms during the design phase and preventing the parallel mechanisms from running into a state of kinematic singularity during a control phase.

Description

The unusual input parameter value space-wise of exempting from of evading parallel institution Kinematics singularity

Technical field

The present invention relates to a kind of method of evading parallel institution Kinematics singularity, particularly a kind of unusual input parameter value space-wise of exempting from of evading parallel institution Kinematics singularity.

Background technology

Kinematics singularity is the inherent characteristic of parallel institution.Mostly occur different on border from serial mechanism Kinematics singularity, the Kinematics singularity of parallel institution mainly occurs in work space inside, and prominent feature is: lock drive device length, and moving platform still can obtain one or several degree of freedom, moving platform is out of control, and its load-carrying ability sharply declines.The Kinematics singularity of parallel institution has seriously restricted it in Important Project, as the application in the fields such as Aero-Space.Therefore, eliminate the impact of Kinematics singularity on parallel institution, for improving parallel institution performance, expand its application, there is important value.

Negative influence parallel institution performance and work space being brought in order to overcome Kinematics singularity, people have proposed to evade redundant member method, paths planning method, sensing Measurement Method and the forcing function method etc. of parallel institution Kinematics singularity.Mohamed and Gosselin be at IEEE Transactions on Robotics in 2005, and 21 (3): in 277-287 literary composition, proposed a kind of redundant member method of evading parallel institution Kinematics singularity.By adding motion redundant member or drive redundancy member, change the local singular position distributional pattern of former parallel institution, realize the unusual motion of local work space and evade.But the introducing due to redundant member, make solving of parallel institution kinematics problem become extremely difficult, and utilize drive redundancy member to evade parallel institution Kinematics singularity, when kinematic pair exists gap and driver to have execution error, cause parallel institution to occur great internal stress.Particularly, a redundant drive can only solve near the Kinematics singularity evasion a certain singular configuration, and can not solve the Kinematics singularity evasion at all singular configurations place in overall work space.Dasgupta and Mruthyunjaya be based on robot path planning's principle, at Mechanism and Machine Theory in 1998, and 33 (6): in 711-725 literary composition, provided a kind of method of exempting from singular path of constructing in work space.But when work space do not exist connection exempt from singular space time, the paths planning method proposing can not construct one and exempt from singular path, method lost efficacy.

For preventing that in the control stage parallel institution is absorbed in Kinematics singularity state, Ranganath etc. are at Mechanism and Machine Theory in 2004, and 39 (9): in 971-998 literary composition, provided a kind of sensing Measurement Method.By install power/torque sensor additional on parallel institution connecting rod, the degree of closeness of prediction parallel institution current location and singular position, prevents that parallel institution is absorbed in unusual motion state.Because the relation of heat transfer agent and singular position is very complicated, when heat transfer agent setting value is larger, under the impact of parallel institution hinge gap, be easy to cause parallel institution to be absorbed in Kinematics singularity state; And when heat transfer agent setting value hour, be easy to again cause erroneous judgement, cause the discontinuous of work space.Wang etc. were at ASME Journal of Mechanical Design in 2008,130 (5): the forcing function method proposing in 052305-1-8 literary composition, though can solve parallel institution at the Kinematics singularity evasion at singular position place, but because forcing function structural anormaly is complicated, and only for a singular position, cause the versatility of the method poor, be difficult to specifically apply in the control stage.

Although people, as St-Onge, Bandyopadhyay, Huang etc. have provided the parallel institution singular position spatial distribution model with pose parametric description.But because such spatial distribution model can not dimensionality reduction, must some pose parameter value of supposition, just can obtain spatial distribution model intuitively, as three-dimensional spatial distribution model.Similarly, Jiang and Gosselin be at ASME Journal of Mechanical Design in 2008, and 130 (11): in 112304-1-8 literary composition, drawn given three direction pose parameters by the singular space of exempting from of three position pose parametric descriptions.Singular position spatial distribution model for such by pose parametric description, or exempt from singular space, when assumed conditions changes, distributed model also changes thereupon, especially, because of moving platform pose monitoring with measure and have huge difficulty, and such distributed model or exempt from singular space and the reason such as parallel institution input parameter is irrelevant, make such distributed model can not be used directly in design phase and the elimination of control stage or prevent the Kinematics singularity of parallel institution.

Liu etc. are at Mechanism and Machine Theory in 2006, and 41 (5): in 145-169 literary composition, the special relationship by between supposition plane 5R mechanism yardstick, has provided the unusual track characteristic collection of illustrative plates of different institutions Scaling interval.The approximate description of the unusual track characteristic of Yin Qijinwei mechanism, and there is non-connected region etc. in unusual track characteristic collection of illustrative plates inside, given unusual track characteristic collection of illustrative plates can not solve the elimination problem of parallel institution Kinematics singularity, particularly, for comparatively complicated parallel institution, obtaining such unusual track characteristic collection of illustrative plates is complex and unpractical.3D curved surface drawing command based in Mathematica mathematical tool, Wang and Li were at Proc.IMechE Part C:J.Mechanical Engineering Science in 2011,225(1): in 204-215 literary composition, drawn and take the singular position space distribution curved surface that input parameter is coordinate axis.Because singular equation is the higher-dimension equation about input parameter, for same group of input parameter, there are some groups of singular position solutions, therefore, the space distribution of singular position should be space many curved surfaces distribution mode, i.e. a space distribution curved surface not only, but a plurality of space distribution curved surface.Because the 3D curved surface drawing command in Mathematica only can be drawn one of them space distribution curved surface, and can not guarantee that drawn singular position space distribution curved surface inside no longer exists other singular position distribution surfaces, therefore, this article is given take the singular position space distribution curved surface that input parameter is coordinate axis, can not eliminate or prevent for design phase and control stage the Kinematics singularity of parallel institution.

Summary of the invention

The object of the invention is to evade for existing the deficiency that parallel institution Kinematics singularity method exists, provide a kind of simple general-purpose, can effectively evade parallel institution in the unusual method of overall work spatial movement in design phase and control stage.

The object of the present invention is achieved like this: build and take input parameter as the whole parallel institution singular position space distribution curved surface of coordinate axis; Do these space distribution curved surfaces in connect envelope surface, obtain exempting from unusual input parameter value space distribution curved surface; In exempting from unusual input parameter value space distribution curved surface, select appropriate working point, and according to the job requirement of parallel institution, determine the span of each input parameter that meets job requirement; Check character closes the span of each input parameter of parallel institution job requirement, within whether being all positioned at and exempting from unusual input parameter value space distribution curved surface, if so, in the design phase, eliminates the Kinematics singularity of parallel institution; The input parameter span that meets job requirement when existence exceeds while exempting from unusual input parameter value space distribution curved surface, suitably adjusts working point, within being located at and exempting from unusual input parameter value space distribution curved surface.Using each input parameter span that meets job requirement as exempting from unusual input parameter value space, in the control stage, by detect each input parameter whether be positioned at separately exempt from unusual value space, prevent that parallel institution is absorbed in unusual motion state.

Specific implementation process is:

(1) first, the parallel institution configuration equation that foundation comprises whole input parameters, according to Singular Condition, the singular equation that obtains being expressed by input parameter, secondly, adopt numerical methods such as expanding equation method (or homotopy Method), from the singular equation of being expressed by input parameter building, obtain all singular positions of expressing with input parameter, then, continuously change the value of input parameter, obtain the singular position of all correspondences under a series of different input parameters, finally, take in the space that input parameter is coordinate axis, connect respectively successively the singular position point that these are expressed with input parameter, obtain take input parameter as the whole parallel institution singular position space distribution curved surface of coordinate axis.

(2) do these parallel institution singular position space distribution curved surfaces in connect envelope surface, obtain exempting from unusual input parameter value space distribution curved surface.

(3) in exempting from unusual input parameter value space distribution curved surface, select appropriate working point, and take this working point as basis, according to the work requirements of parallel institution, determine the span of each input parameter that meets parallel institution job requirement.

(4) check character closes the span of each input parameter of parallel institution job requirement, within whether being all positioned at and exempting from unusual input parameter value space distribution curved surface, if so, in the design phase, eliminates the Kinematics singularity of parallel institution.

(5) when existing the input parameter span meet job requirement to exceed to exempt from unusual input parameter value space distribution curved surface, rationally adjust working point, within finally making the span of each input parameter all fall into exempt from unusual input parameter value space distribution curved surface.

(6) by exempting to meet in unusual input parameter value space distribution curved surface the input parameter span of job requirement, as input parameter, exempt from unusual value space, for control procedure, monitor and prevent that parallel institution is absorbed in Kinematics singularity state.

Described Singular Condition can be Jacobi matrix or Screw spiral matrix contraction condition, how much comeplex conditions etc.; Described take the parallel institution singular position space distribution curved surface that input parameter is coordinate axis, dimension is sextuple at most, but generally can be according to the symmetry of structure and motion, can obtain the spatial distribution model of dimensionality reduction, as three-dimensional space model, for the design phase is eliminated Kinematics singularity, provide directly perceived, vivid distributed model.

Beneficial effect: owing to adopting such scheme, by within the span that meets each input parameter of work requirements be arranged in exempt from unusual input parameter value space distribution curved surface, can in the design phase, eliminate the Kinematics singularity of parallel institution, guarantee that parallel institution has definite movement output and higher load-carrying ability in overall work space.Particularly, in the control stage, by detecting within whether input parameter be positioned at and exempt from unusual input parameter value space, can promptly judge and prevent that parallel institution is absorbed in Kinematics singularity state.Owing to exempting from unusual input parameter value space distribution curved surface, be the space of an internal communication, relative redundancy drive member method and paths planning method, method proposed by the invention, can solve the parallel institution Kinematics singularity evasion in overall work space.With with the singular position spatial distribution model of parallel institution pose parametric description, compare, given exempt from unusual input parameter value space distribution curved surface, the Kinematics singularity that can be used directly in design phase elimination parallel institution, prevents that in the control stage parallel institution is absorbed in Kinematics singularity state.Therefore, the unusual input parameter value space-wise of exempting from based on exempting from unusual input parameter value space distribution curved surface, reached object of the present invention, that is: in the design phase, eliminated the negative influence of Kinematics singularity to parallel institution, in the control stage, prevented that parallel institution is absorbed in Kinematics singularity state.

Advantage is: method is simple, general, be easy to realize, and can directly apply to the Kinematics singularity of eliminating parallel institution overall work space in the design phase, in the control stage, prevents that parallel institution is absorbed in Kinematics singularity state.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of exempting from unusual input parameter value space-wise that structure is evaded parallel institution Kinematics singularity.

Fig. 2 implements an example 3SPS-3PRS parallel institution of the present invention (2a) and job requirement (2b) thereof.

Fig. 3 be take the parallel institution singular position space distribution curved surface that input parameter is coordinate axis, and exempts from unusual input parameter value space distribution curved surface.

Fig. 4 is the setting of parallel institution working point, and meet job requirement exempt from determining of unusual input parameter value space.

Embodiment

Below in conjunction with accompanying drawing, embodiments of the invention are elaborated.

The present embodiment is implemented take technical solution of the present invention under prerequisite, provided detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

In the invention process, as shown in Figure 1, the parallel institution configuration equation that foundation comprises structure parameters and whole input parameters, and according to Singular Condition, the singular equation that obtains being expressed by input parameter, adopt numerical methods such as expanding equation method or homotopy Method, obtain take input parameter as the whole singular position space distribution curved surface of coordinate axis; Then, construct these space distribution curved surfaces in connect envelope surface, obtain exempting from unusual input parameter value space distribution curved surface; According to the job requirement of parallel institution, in exempting from unusual input parameter value space distribution curved surface, rationally determine the working point of parallel institution, provide the span of each input parameter of parallel institution that meets accordingly job requirement; In the time of within the span of each input parameter is being exempted from unusual input parameter value space distribution curved surface, determined working point and meet job requirement exempt from unusual input parameter value space, can eliminate the negative influence of Kinematics singularity to parallel institution in the design phase.That exports that these meet job requirement exempts from unusual input parameter value space, for control procedure, whether parallel institution to be approached the monitoring of singular position.When having input parameter span to exceed to exempt from unusual input parameter value space distribution curved surface, rationally adjust working point, make the input parameter value space that exceeds distribution surface to the direction adjustment that is conducive to not exceed, finally, make to meet respectively the exempting within unusual input parameter value space all falls into and exempt from unusual input parameter value space distribution curved surface of job requirement.

Embodiment

The 3SPS-3PRS parallel institution shown in Fig. 2 a of take is below example, elaborates specific embodiment of the invention process.

The job requirement of this 3SPS-3PRS parallel institution as shown in Figure 2 b.When moving platform center is during at P point, moving platform can be realized universal deflection (around the resultant deflection of x axle and the y axle) θ of the relative stationary platform axis of its normal (z axle) ₂; When Q point, the universal corner of moving platform is θ ₁; In other positions of point-to-point transmission, the universal deflection angle of moving platform is between θ ₁～θ ₂between.

Step 1: build and take input parameter as the whole parallel institution singular position space distribution curved surface of coordinate axis.

Set up configuration equation F (x, μ)=0 of this parallel institution.Structure parameters x can be the pose parameter of parallel institution, can be also moving platform hinge coordinate, or both part combinations.In this example, x=[x ₀, y ₀, z ₀, x ₁, y ₁, z ₁, x ₂, y ₂, z ₂] ^tcoordinate for moving platform centre coordinate and two adjacent ball pivot contacts.μ is whole input parameters of parallel institution, in this example, and μ=[l ₂, l ₄, l ₆] ^t.According to condition of singular position:

$\left\{\begin{array}{c}F(x,\mathrm{\μ})=0\\ \left|F_{\mathrm{\μ}}(x,\mathrm{\μ})\right|=0\end{array}\right.---\left(1\right)$

Give the value of two input parameters in fixed pattern (1), as l ₄, l ₆, utilize homotopy Method, can from formula (1), try to achieve space input parameter l to be asked in stationary platform ₂four respective value at singular position place

continuously change the value of these two input parameters profit uses the same method, and obtains input parameter to be asked

a series of values of four singular positions in singular position place

take in the space that input parameter is coordinate axis, connect respectively successively the singular position point that these are expressed with input parameter

obtain take input parameter as the whole parallel institution singular position space distribution curved surface of coordinate axis, amount to four curved surfaces.

Be subject to formula (1) in the impact of singular position place Jacobian matrix contraction, near the solution efficiency of Homotopy Method singular position is very low.For improving the solution efficiency of singular position, the expansion equation of structure (1) formula:

$\mathrm{\Γ}\left(\mathrm{\Ω}\right):=\left\{\begin{array}{c}{f}_i=f_i(x,\mathrm{\μ})=0\\ f_{\mathrm{jx}}=\left[\frac{{\∂f}_j}{\∂x}\right]v=0\\ \underset{k=1}{\overset{9}{\mathrm{\Σ}}}{v}_k^2-1=0\end{array}\right.---\left(2\right)$

Vague generalization, for the parallel institution with n input parameter, given input parameter l _i, i=1 ..., n, a class value of i ≠ j, utilizes numerical method, can promptly from (2) formula, try to achieve singular position input parameter l to be asked _jall m homographic solution values

continuously change input parameter

value, obtain a series of singular positions place input parameter

all m homographic solution values take input parameter as coordinate axis, connect respectively successively m the singular position point that these are expressed with input parameter $(l_{{\mathrm{jM}}_1}^k,l_i^k,i=1,...,n,i\≠j),\·\·\·,(l_{{\mathrm{jM}}_m}^k,l_i^k,i=1,...,n,i\≠j),$ Obtain take input parameter as the whole singular position space distribution curved surface of coordinate axis, amount to m distribution surface.

Implementation process of the present invention is described for simplicity, makes l ₄=l ₆(this condition is corresponding with moving platform maximum deflection angle), now, the dimension of singular position equation is bidimensional, i.e. l ₂, l _4,6, corresponding singular position space distribution curved surface changes distribution curve into.Based on formula (2), adopt the homotopy Method based on expanding equation, be fixed space on platform and take the singular position distribution curve that input parameter is coordinate axis, M ₁, M ₂, M ₃, M ₄, amount to four, as shown in Figure 3.

Step 2: obtain exempting from unusual input parameter value space distribution curve.

Make four singular position distribution curve M in Fig. 3 ₁, M ₂, M ₃, M ₄in connect enveloping curve, obtain parallel institution and exempt from unusual input parameter value space distribution curve, as shown in Fig. 3 hatched example areas.When meeting within the parallel institution input parameter span of job requirement is positioned at this hatched example areas, parallel institution does not move unusual.Because configuration equation is continuously differentiable function about input parameter, within exempting from unusual input parameter value space distribution curve, there is not isolated point and non-connected domain.

Step 3: within exempting from unusual input parameter value space distribution curve, choose appropriate working point, and determine the input parameter span that meets parallel institution job requirement.

As a reference point with 3SPS-3PRS parallel institution moving platform center point P, shown in Fig. 3 exempt from unusual input parameter value space distribution curve within, hatched example areas, chooses the working point of ordering as P in appropriate position, as shown in Figure 4.

According to the job requirement shown in Fig. 2 b, at this working point P, input parameter l ₄=l ₆minimum value be

here R ₁for moving platform hinge point distribution radius, corresponding input parameter l ₂maximum occurrences scope be: (l _2minP, l _2maxP)=[z ₁₀-R ₁sin (θ ₂), z ₁₀+ R ₁sin (θ ₂)].At working position Q, meet the input parameter l of job requirement ₂span be (l _2minQ, l _2maxQ)=[z ₁₀+ a ₀-R ₁sin (θ ₁), z ₁₀+ a ₀+ R ₁sin (θ ₁)].

Step 4: check character closes the span of each input parameter of parallel institution job requirement, within whether being all positioned at and exempting from unusual input parameter value space distribution curved surface, if so, eliminates the Kinematics singularity of parallel institution in the design phase.

At working point P, l ₄=l ₆=l _4,6minPvertical line meet at respectively P with the border of exempting from unusual input parameter value space distribution curve (oblique line part) ₁point and P ₂point, corresponding l ₂maximum exempt from unusual value space and be

in like manner, as input parameter l ₄=l ₆for maximal value

time, corresponding l ₂maximum exempt from unusual value space and be

obviously, due to $({\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="DEST\_PATH\_HDA0000438380670000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_{2\min P},{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="DEST\_PATH\_HDA0000438380670000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_{2\max P})\&Element;(l_{2P_1},l_{2P_2})$ With $({\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="DEST\_PATH\_HDA0000438380670000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_{2\min P},{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="DEST\_PATH\_HDA0000438380670000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_{2\max P})\&Element;(l_{2P_1^{\&prime;}},l_{2{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="DEST\_PATH\_HDA0000438380670000022.png"\; state="\{\{state\}\}">P</figure-callout>}}_2^{\&prime;}}),$ Within the span that meets each input parameter of work requirements is all positioned at and exempts from unusual input parameter value space distribution curve, 3SPS-3PRS parallel institution can not move unusual at working point P.

Step 5: adjust working point, within the span that makes to meet each input parameter of work requirements is all positioned at and exempts from unusual input parameter value space distribution curved surface.

When occurring meeting the input parameter value space of job requirement and exceed the situation of exempting from unusual input parameter value space distribution curved surface, need to adjust working point.For example, the working position Q shown in Fig. 2, as input parameter l ₄=l ₆get maximal value

time, exempt from the definite l of unusual input parameter value space distribution curve ₂maximum is exempted from unusual value space

and meet the input parameter l of job requirement ₂span (l _2minQ, l _2maxQ), at l _2minQplace, has exceeded l ₂maximum exempt from unusual value space

lower boundary.In this working position, as input parameter l ₂approach minimum value l _2minQtime, parallel institution will move unusual appearance., working point P suitably need to be moved to upper right side for this reason, until

thus, by each input parameter span that meets job requirement being arranged within parallel institution exempts from unusual input parameter value space distribution curved surface, in the design phase, eliminate the Kinematics singularity of parallel institution.

Step 6: will exempt to meet in unusual input parameter value space distribution curved surface the input parameter span of job requirement, as input parameter, exempt from unusual value space, in the control stage, currency by detecting each input parameter whether each input parameter exempt from unusual value space within, prevent that parallel institution is absorbed in Kinematics singularity state.

As mentioned above, in conjunction with 3SPS-3PRS parallel institution, provided and implemented detailed process of the present invention.The present invention is effective to the elimination of platform class parallel institution Kinematics singularity problem, and method is simple, general, be easy to realize, can directly apply to the Kinematics singularity of eliminating parallel institution overall work space in the design phase, and in the control stage, by the currency of direct-detection input parameter, prevent that parallel institution is absorbed in unusual motion state.

Claims (1)

1. the unusual input parameter value space-wise of exempting from of evading parallel institution Kinematics singularity, is characterized in that, comprises the following steps:

The first step, builds and take input parameter as the whole parallel institution singular position space distribution curved surface of coordinate axis;

Second step, do these parallel institution singular position space distribution curved surfaces in connect envelope surface, obtain exempting from unusual input parameter value space distribution curved surface;

The 3rd step, in exempting from unusual input parameter value space distribution curved surface, selects appropriate working point, and determines each input parameter span that meets parallel institution job requirement;

The 4th step, check character closes the span of each input parameter of parallel institution job requirement, within whether being all positioned at and exempting from unusual input parameter value space distribution curved surface, if so, in the design phase, eliminates the Kinematics singularity of parallel institution;

The 5th step, the input parameter span that meets job requirement when existence exceeds while exempting from unusual input parameter value space distribution curved surface, rationally adjust working point, within finally making the span of each input parameter all fall into exempt from unusual input parameter value space distribution curved surface;

The 6th step, by exempting to meet in unusual input parameter value space distribution curved surface the input parameter span of job requirement, exempts from unusual value space as input parameter, for control procedure, monitors and prevents that parallel institution is absorbed in Kinematics singularity state.

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