CN111765889A - Pose positioning method of mobile robot in production workshop based on multi-cell-ellipsoid dual-filtering - Google Patents
Pose positioning method of mobile robot in production workshop based on multi-cell-ellipsoid dual-filtering Download PDFInfo
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Abstract
The invention discloses a pose positioning method of a mobile robot in a production workshop based on multi-cell-ellipsoid double filtering. The method is realized by the following steps: firstly, establishing a mobile robot pose positioning linearization model in a production workshop, and obtaining an input and output sequence of the mobile robot pose positioning linearization model according to a system model; carrying out dual identification on system parameters by using a holohedral symmetry multicellular body method and an ellipsoid method in the collective identification, firstly, carrying out primary identification by using the ellipsoid, and simultaneously obtaining a holohedral symmetry multicellular body with the minimum volume at the moment according to a holohedral symmetry multicellular body iterative formula; then updating the fully symmetric multicellular bodies to contain the changed parameters; and finally dispersing the dimensionality-reduced fully-symmetrical multicellular bodies into constraint conditions to update ellipsoids for the second time to obtain system parameter values. The dimensionality of the fully-symmetrical multicellular body is not increased all the time through singular value decomposition, and is maintained at an initial given dimensionality all the time, so that the computational complexity is reduced, and the identification precision is improved while the identification conservatism is reduced through two times of ellipsoid updating.
Description
Technical Field
The invention relates to a multi-cell-ellipsoid filtering technology for positioning the pose of a mobile robot in a production workshop, belonging to the technical field of advanced manufacturing process control.
Background
With social progress and scientific technological development, automation technology has gradually replaced manpower and is widely applied to intelligent manufacturing, agricultural production and national defense industry. Robotics with higher integration of automation technology has also been used in production and life. In the era of intelligent factories, the application of robots gradually replaces the labor, and the productivity is greatly improved and the defective rate of production is reduced.
Compared with a high-precision robot in the medical field, the self-positioning of the mobile robot used in the production workshop at present has the problem of low positioning precision due to the requirements of manufacturing process and cost. In the research of positioning the mobile robot for the workshop, the documents Zhou B, Qian K, Ma X, et al, the objective, the floor, the application and the application to the mobile robots [ J ] (english edition), 2017(5), B, and Zhou, the X, z, the objective, the distribution, the interaction, the analysis, 2011: 2195. and the like, position the pose of the mobile robot using the elliptical method, which increases the positioning error in the process of obtaining the center-to-constraint plane distance and then normalizing the center-to-constraint plane distance, and causes the problem of not increasing the iterative error. Alamo T, Bravo J M, Camacho E F. guarded state estimation by zonanotopes [ C ]// IEEEConference on Decision & control. IEEE,2005. the method adopts a multisomal filtering method to realize the positioning of the pose of the robot, but because the method selects the least edge of the fully symmetrical multisomal in the iteration process, the upper and lower boundaries of the predicted value of each step of the pose of the robot are larger, the conservative prediction is high, and the positioning precision is not high.
Disclosure of Invention
The invention is based on a mobile robot in a production workshop in the intelligent manufacturing process, and aims to improve the precision, accuracy and efficiency of parameter estimation, establish a more accurate system model and improve the positioning precision. The invention aims to provide a pose positioning method of a mobile robot between production vehicles based on multi-cell-ellipsoid double filtering, which effectively reduces algorithm conservation and improves identification precision while reducing calculated amount.
The purpose of the invention is realized by the following technical scheme: a pose positioning method of a mobile robot in a production workshop based on multi-cell-ellipsoid double filtering comprises the following steps:
step 1: discretizing a kinematic model of a mobile robot into a discrete continuous model yk＝φk Tθ*+ekWherein phi iskFor the observation vector, theta is the pose positioning parameter, ekRepresenting system bounded noise;
step 2: obtaining an observation vector phi according to a kinematic model of the mobile robot given unknown but bounded noise and an applied excitation signalkAnd output sequence ykAnd by observing the vector phikAnd output sequence ykObtaining the constraint condition of the parameter feasible set in the k step;
step 3: obtaining a first ellipsoid identification minimum trace ellipsoid according to the constraint condition of the step k and the ellipsoid of the step k-1;
step 4: obtaining the fully-symmetrical multicellular body with the minimum volume in the k step according to the constraint condition in the k step and the fully-symmetrical multicellular body in the k-1 step;
step 5: expanding the fully-symmetrical multicellular bodies obtained in the fourth step by considering the change of system parameters;
step 6: performing singular value decomposition dimension reduction on the expanded holohedral symmetry to obtain a dimension-reduced holohedral symmetry;
the method is characterized in that:
step 7: dispersing the fully-symmetrical multicellular bodies after dimensionality reduction into constraint conditions, carrying out second-time ellipsoid identification to obtain a minimum trace ellipsoid, and taking the central value of the minimum trace ellipsoid as a kth step posture estimation value.
Further, Step 1: discretizing a kinematic model of a mobile robot into a discrete continuous model yk＝φkTθ*+ekWherein phi iskFor the observation vector, theta is the pose positioning parameter, ekRepresenting system bounded noise; the method comprises the following specific steps:
the crawler-type mobile robot model of the production workshop:
wherein (x)kyk)TIndicating the position of the robot, #kRepresenting the robot angle, which can be measured by a sensor, omega1,k、ω2,kRepresenting rotational angular velocities of left and right driving wheels, r representing a wheel radius, b representing a distance between the left and right wheels, Δ T representing a time interval, s1,k、s2,kThe slip ratio of the robot is shown.
Obtaining a discrete continuous system:
wherein ekRepresents system bounded noise and ek|≤，v1＝ω1,k+ω2,k/2、v2＝-ω1,k+ω2,k， θk＝[s1,krsin(2πΔT)s2,kr/bsin(πΔT)]T。
Further, Step 2: under the condition of given unknown but bounded noise and external excitation signal, obtaining observation vector phi according to kinematic model of mobile robotkAnd output sequence yk，
Constraints for the feasible set of parameters for step k.
Further, Step 3: ellipsoid of step k-1k-1(ck-1,Pk-1) And the constraint condition S of the kth step is { theta: | bTTheta-d | ≦ sigma } to obtain the first ellipsoid identification minimum trace ellipsoid, where S ═ C,
d＝ykσ ═ σ; the method comprises the following specific steps:
(1) first, a predicted walking ellipsoid E is obtained by considering parameter variationk,k-1(ck,k-1,Pk,k-1)：
Wherein
Is a diagonal matrix formed by the maximum value of each parameter variation;
(2) calculating and predicting the center c of the step ellipsoidk,k-1Distance to S of the constraint plane:
if it is not
Or
Ending identification, otherwise normalizing distance
If it is not
ck＝ck,k-1,Pk＝Pk,k-1Otherwise
Wherein
gi＝bTPkk-1b
λiIs the positive root of the following equation
Obtaining the first ellipsoid update minimum trace ellipsoid Ek(ck,Pk)，nθIs the dimension of the parameter to be identified, nθ＝2。
Further, the k-1 th holosymmetric multicellular body in Step 4:
and the k step constraint condition: s ═ θ: | bTθ -d ≦ σ } resulting in a minimally volumetrically all-symmetric multicellular body containing a feasible set of parameters, where S ═ C,
d＝ykj is an integer and satisfies 0 ≦ j ≦ l, l is the number of columns of the matrix H, and the specific steps are:
obtaining a volume-minimized fully-symmetric multicellular body containing a feasible set of parameters
nθIs the dimension of the parameter to be identified.
Further, in Step5, the change of system parameters is considered, and the fully symmetrical multicellular body obtained in Step four is expanded
Wherein, the parameter variation is a diagonal matrix formed by the maximum value of each parameter variation;
further, the expanded fully symmetric multicellular bodies are dimensionality reduced in Step6 [ T (j)*)]＝UΣVTWhere U and V are unitary matrices, and Σ is a main diagonal element [ T (j)*)]The remaining elements are a matrix of 0 s,
where D is a diagonal matrix and the diagonal elements are Di＝||σiVi||1，σiIs [ T (j)*)]Ith singular value, ViIs the ith column of V, and the k-th step holosymmetric multicellular body after dimensionality reduction is obtained
Wherein
Further, dispersing the dimensionality-reduced fully-symmetrical multicellular bodies into constraint conditions in Step7, and performing second-time ellipsoid identification to obtain a minimum trace ellipsoid, wherein the dimensionalities of the fully-symmetrical multicellular bodies after dimensionality reduction are consistent with those of parameters to be identified, so that the fully-symmetrical multicellular bodies are parallel quadrilaterals;
where the dotted line is the first ellipsoid estimate, the dashed line is the holosymmetric polytope constraint, and the solid line is the second ellipsoid estimate. The vertex coordinates can be obtained according to the holohedral symmetry multilocular formula, and the vertex coordinates are assumed to be
By line segment l12,l34For example, a pair of constraints is obtained, l12,l34The equations are respectively
a12θ1+b12θ2＝f12，a34θ1+b34θ2＝f34
Wherein
Then the parameters in the constraint are
And performing second ellipsoid identification according to the obtained constraint condition and the ellipsoid identified by the first ellipsoid to obtain a final ellipsoid, and taking the central value of the final ellipsoid as the k-th step attitude estimation value.
The invention has the beneficial effects that: according to the pose positioning method, the mobile robot is positioned by the ellipsoid and the fully-symmetrical multi-cell collective filtering method, the ellipsoid is updated twice, and the fully-symmetrical multi-cell is dispersed into new constraint conditions after dimensionality reduction, so that identification conservatism is effectively reduced, and the accuracy of robot pose positioning is improved. Furthermore, dimensionality reduction is carried out on the fully-symmetrical multicellular bodies through singular value decomposition, the final calculated amount is simplified, the calculation burden brought by dimension increase is avoided, and the calculation efficiency is greatly improved. The pose positioning method is applied to pose positioning of the mobile robot in the production workshop, positioning accuracy and state estimation efficiency are improved, and accordingly productivity can be improved; the method of the application also gives technical suggestions for the following intelligent manufacturing.
The scheme has high identification efficiency and accuracy in the aspect of parameter identification of pose positioning of the mobile robot in a production workshop, lays a foundation for the next intelligent manufacturing and provides powerful guarantee.
Drawings
Fig. 1 is a schematic flow chart of the pose positioning method of the invention.
FIG. 2 is a diagram of pose positioning parameters of the pose positioning method of the present invention
Get
The identification result is compared with that of the prior ellipsoid and holohedral symmetry multicellular body method.
FIG. 3 shows pose positioning parameters of the pose positioning method of the present invention
Get
The identification result is compared with that of the prior ellipsoid and holohedral symmetry multicellular body method.
FIG. 4 shows the second ellipsoid identification to obtain the minimum trace ellipsoid according to the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
Example 1: a pose positioning method of a mobile robot in a production workshop based on multi-cell-ellipsoid double filtering comprises the following steps:
the method comprises the following steps: passing through a typical kinematic model of a production shop tracked mobile robot, and then discretizing into a discrete continuous system yk＝φk Tθ*+ek(ii) a The method comprises the following specific steps:
the crawler-type mobile robot model of the production workshop:
wherein (x)kyk)TIndicating the position of the robot, #kRepresenting the robot angle, which can be measured by means of a sensor. Omega1,k、ω2,kRepresenting rotational angular velocities of left and right driving wheels, r representing a wheel radius, b representing a distance between the left and right wheels, Δ T representing a time interval, s1,k、s2,kThe slip ratio of the robot is shown.
Obtaining a discrete continuous system:
wherein ekRepresents system bounded noise and ek≤，v1＝ω1,k+ω2,k/2、v2＝-ω1,k+ω2,k， θk＝[s1, krsin(2πΔT) s2,kr/bsin(πΔT)]T。
Step two: obtaining an observation vector phi according to a typical kinematic model of a production workshop crawler type mobile robot under the condition of given unknown but bounded noise and an external excitation signalkAnd output sequence yk，
Constraint conditions for the feasible set of parameters in the k step;
step three: ellipsoid E of the last stepk-1(ck-1,Pk-1) And the constraint condition S of the kth step is { theta: | bTTheta-d | ≦ sigma } to obtain the first ellipsoid identification minimum trace ellipsoid, where S ═ C,
d＝ykand σ ═ o. Firstly, a prediction ellipsoid E is obtained by considering parameter variationk,k-1(ck,k-1,Pk,k-1)
Wherein
Is a diagonal matrix formed by the maximum value of each parameter variation. Calculating and predicting the center c of the step ellipsoidk,k-1Distance to S of constraint plane
If it is not
Or
Ending identification, otherwise normalizing distance
If it is not
ck＝ck,k-1,Pk＝Pk,k-1. Otherwise
Wherein
gi＝bTPk,k-1b
λiIs the positive root of the following equation
Obtaining the first ellipsoid update minimum trace ellipsoid Ek(ck,Pk)，nθIs the dimension of the parameter to be identified, n θ2; step four: the former step of fully symmetrical multicellular bodies is known
And the constraint condition S of the kth step is { theta: | cTTheta-d | < sigma } obtaining the k-th fully symmetric multicellular body with the minimum volume and containing parameter feasible set
Where S is C, j is an integer and satisfies 0 ≦ j ≦ l, and l is the number of columns in matrix H
nθIs the dimension of the parameter to be identified;
step five: expanding the fully symmetrical multicellular bodies obtained in the fourth step by considering the change of system parameters
Wherein the diagonal is formed by the maximum value of each parameter variationArraying;
step six: for the expanded holosymmetric multicellular dimensionality reduction, [ T (j)*)]＝UΣVTWhere U and V are unitary matrices, and Σ is a main diagonal element [ T (j)*)]The remaining elements are a matrix of 0 s,
where D is a diagonal matrix and the diagonal elements are Di＝||σiVi||1，σiIs [ T (j)*)]Ith singular value, ViIs the ith column of V, and the fully symmetric multicellular body of the kth step after dimensionality reduction is obtained
Wherein
Step seven: and step seven, dispersing the dimensionality reduced fully-symmetrical multicellular bodies into constraint conditions, and performing second ellipsoid identification to obtain a minimum trace ellipsoid as shown in figure 4.
Where the dotted line is the first ellipsoid estimate, the dashed line is the holosymmetric polytope constraint, and the solid line is the second ellipsoid estimate. The vertex coordinates can be obtained according to the holohedral symmetry multilocular formula, and the vertex coordinates are assumed to be
By line segment l12,l34For example, a pair of constraints is obtained, l12,l34The equations are respectively
a12θ1+b12θ2＝f12，a34θ1+b34θ2＝f34
Wherein
Then the parameters in the constraint are
And performing second ellipsoid identification according to the obtained constraint condition and the ellipsoid identified by the first ellipsoid to obtain a final ellipsoid, and taking the central value of the final ellipsoid as the k-th step attitude estimation value.
Assume that the initial position of the robot is set to [ 000 ]]T，r＝0.1m，b＝0.35m， ω1,k＝1rad/s，ω2,k＝7rad/s，ΔT＝0.01s，s1,k＝s2,k1, the initial holosymmetric multicellular body is
According to a typical kinematic model of a crawler-type mobile robot in a production workshop, the identification result is obtained as follows, and the holosymmetric multicellular body is a document Alamo T, Bravo J M, Camacho E F]//IEEE Conference on Decision&IEEE,2005, the ellipsoids of which are the documents Zhou B, Qiank, Ma X, et al, Ellipsoidal bounding set-membership identification for early detection of robust failure errors to mobile robots [ J]System engineering and electronics (english edition), 2017(5). The method has the advantages of lower conservation and higher identification accuracy, and the calculated amount is greatly reduced according to singular value decomposition.
The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solution of the present invention by those skilled in the art should fall within the protection scope defined by the claims of the present invention without departing from the spirit of the present invention.
Claims (8)
1. A pose positioning method of a mobile robot in a production workshop based on multi-cell-ellipsoid double filtering comprises the following steps:
step 1: discretizing a kinematic model of a mobile robot into a discrete continuous model yk＝φk Tθ*+ekWherein phi iskFor the observation vector, theta is the pose positioning parameter, ekRepresenting system bounded noise;
step 2: obtaining an observation vector phi according to a kinematic model of the mobile robot under the given unknown but bounded noise and an applied excitation signalkAnd output sequence ykAnd by observing the vector phikAnd output sequence ykObtaining the constraint condition of the parameter feasible set in the k step;
step 3: obtaining a first ellipsoid identification minimum trace ellipsoid according to the constraint condition of the step k and the ellipsoid of the step k-1;
step 4: obtaining the fully-symmetrical multicellular body with the minimum volume in the k step according to the constraint condition in the k step and the fully-symmetrical multicellular body in the k-1 step;
step 5: expanding the fully-symmetrical multicellular bodies obtained in the fourth step by considering the change of system parameters;
step 6: performing singular value decomposition dimension reduction on the expanded holohedral symmetry to obtain a dimension-reduced holohedral symmetry;
the method is characterized in that:
step 7: dispersing the fully-symmetrical multicellular bodies after dimensionality reduction into constraint conditions, carrying out second-time ellipsoid identification to obtain a minimum trace ellipsoid, and taking the central value of the minimum trace ellipsoid as a kth step posture estimation value.
2. The production workshop mobile robot pose positioning method based on multi-cell-ellipsoid dual-filtering as claimed in claim 1, wherein: step 1: discretizing a kinematic model of a mobile robot into a discrete continuous model yk＝φk Tθ*+ekWherein phi iskFor the observation vector, theta is the pose positioning parameter, ekRepresenting system bounded noise; the method comprises the following specific steps:
the crawler-type mobile robot model of the production workshop:
wherein (x)kyk)TIndicating the position of the robot, #kRepresenting the angle of the robot, and measuring omega by a sensor1,k、ω2,kRepresenting rotational angular velocities of left and right driving wheels, r representing a wheel radius, b representing a distance between the left and right wheels, Δ T representing a time interval, s1,k、s2,kThe slip ratio of the robot is shown.
Obtaining a discrete continuous system:
wherein ekRepresents system bounded noise and ek|≤，v1＝ω1,k+ω2,k/2、v2＝-ω1,k+ω2,k，θk＝[s1,krsin(2πΔT) s2,kr/bsin(πΔT)]T。
3. The production workshop mobile robot pose positioning method based on multi-cell-ellipsoid dual-filtering as claimed in claim 1, wherein: step 2: under the condition of given unknown but bounded noise and external excitation signal, an observation vector phi is obtained according to a kinematic model of the mobile robotkAnd output sequence yk，
Constraints for the feasible set of parameters for step k.
4. The multi-production-shop mobile robot of claim 1The pose positioning method of the cell-ellipsoid double filtering is characterized by comprising the following steps: step 3: ellipsoid of step k-1k-1(ck-1,Pk-1) And the constraint condition S of the kth step is { theta: | bTTheta-d | ≦ sigma } to obtain the first ellipsoid identification minimum trace ellipsoid, where S ═ C,
d＝ykσ ═ σ; the method comprises the following specific steps:
(1) first, a predicted walking ellipsoid E is obtained by considering parameter variationk,k-1(ck,k-1,Pk,k-1)：
Wherein
Is a diagonal matrix formed by the maximum value of each parameter variation;
(2) calculating and predicting the center c of the step ellipsoidk,k-1Distance to S of the constraint plane:
if it is not
Or
Ending identification, otherwise normalizing distance
If it is not
ck＝ck,k-1,Pk＝Pk,k-1Otherwise
Wherein
gi＝bTPk,k-1b
λiIs the positive root of the following equation
Obtaining the first ellipsoid update minimum trace ellipsoid Ek(ck,Pk)，nθIs the dimension of the parameter to be identified, nθ＝2。
5. The production workshop mobile robot pose positioning method based on multi-cell-ellipsoid dual-filtering as claimed in claim 1, wherein: step4, k-1 th holosymmetric multicellular body:
and the k step constraint condition: s ═ θ: | bTθ -d ≦ σ } resulting in a minimally volumetrically all-symmetric multicellular body containing a feasible set of parameters, where S ═ C,
d＝ykj is an integer and satisfies 0 ≦ j ≦ l, l is the number of columns of the matrix H, and the specific steps are:
obtaining a volume-minimized fully-symmetric multicellular body containing a feasible set of parameters
nθIs the dimension of the parameter to be identified.
6. The production workshop mobile robot pose positioning method based on multi-cell-ellipsoid dual-filtering as claimed in claim 1, wherein: step5, taking system parameter change into consideration, expanding the fully symmetrical multicellular body obtained in Step four
Wherein is a diagonal matrix composed of the maximum value of each parameter variation.
7. The production workshop mobile robot pose positioning method based on multi-cell-ellipsoid dual-filtering as claimed in claim 1, wherein: dimension reduction of expanded holosymmetric multicellular bodies [ T (j) in Step6*)]＝UΣVTWherein U and V are unitary matrices respectively,Σ is the main diagonal element of [ T (j)*)]The remaining elements are a matrix of 0 s,
where D is a diagonal matrix and the diagonal elements are Di＝||σiVi||1，σiIs [ T (j)*)]Ith singular value, ViIs the ith column of V, and the k-th step holosymmetric multicellular body after dimensionality reduction is obtained
Wherein
8. The production workshop mobile robot pose positioning method based on multi-cell-ellipsoid dual-filtering as claimed in claim 1, wherein: dispersing the dimensionality-reduced fully-symmetrical multicellular bodies into constraint conditions in Step7, and performing second ellipsoid identification to obtain a minimum trace ellipsoid, wherein the dimensionality of the fully-symmetrical multicellular bodies subjected to dimensionality reduction is consistent with that of the parameters to be identified, so that the fully-symmetrical multicellular bodies are a parallelogram; where the dotted line is the first ellipsoid estimate, the dashed line is the holosymmetric polytope constraint, and the solid line is the second ellipsoid estimate. The vertex coordinates can be obtained according to the holohedral symmetry multilocular formula, and the vertex coordinates are assumed to be
By line segment l12,l34For example, a pair of constraints is obtained, l12,l34The equations are respectively
a12θ1+b12θ2＝f12，a34θ1+b34θ2＝f34
Wherein
Then the parameters in the constraint are
And performing second ellipsoid identification according to the obtained constraint condition and the ellipsoid identified by the first ellipsoid to obtain a final ellipsoid, and taking the central value of the final ellipsoid as the k-th step attitude estimation value.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117910201A (en) * | 2023-10-31 | 2024-04-19 | 湖南盛鼎科技发展有限责任公司 | Multi-cell double-filtering state estimation algorithm for radar data |
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