CN111765889B - Pose positioning method of mobile robot in production workshop based on multi-cell-ellipsoid double filtering - Google Patents
Pose positioning method of mobile robot in production workshop based on multi-cell-ellipsoid double 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 comprises the following steps: firstly, establishing a mobile robot pose positioning linearization model in a production workshop, and obtaining an input and output sequence according to a system model; double identification is carried out on system parameters by utilizing a full-symmetry multicellular body method and an ellipsoid method in member identification, firstly, the ellipsoid is utilized for carrying out first identification, and meanwhile, the full-symmetry multicellular body with the minimum volume at the moment is obtained according to a full-symmetry multicellular body iterative formula; then updating the holohedral system to contain the changed parameters; singular value decomposition dimension reduction is carried out on the updated full-symmetrical multicellular bodies to obtain the full-symmetrical multicellular bodies containing the feasible parameter sets after dimension reduction, and finally the full-symmetrical multicellular bodies after dimension reduction are discretized into constraint conditions to update ellipsoids for the second time to obtain system parameter values. The dimension of the fully symmetrical multicellular body is not always increased through singular value decomposition and is always maintained at the initially given dimension, so that the calculation complexity is reduced, and the identification conservatism is reduced and the identification precision is improved through updating the ellipsoid twice.
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 technology development, automated technology has gradually replaced manpower and has been widely applied to intelligent manufacturing, agricultural production and defense industries. Robot technology with higher integration level of automation technology is also applied to production and living. In the intelligent factory age, the application of robots gradually replaces manual work, and the productivity is greatly improved, and the production defective rate is reduced.
Compared with the high-precision robots in the medical field, the mobile robots used in production workshops at present have the problem of low positioning precision due to the requirements of manufacturing process and cost. In the research of the positioning of the mobile robots for workshops, documents Zhou B, qian K, maX, et al Ellipsoidal bounding set-membership identification approach for robust fault diagnosis with application to mobile robots [ J ]. System engineering and electronic technology (English edition), 2017 (5) B. And Zhou, X.Z. Dai. Robust fault detection of mobile robots using an ellipsoid bounding identification algorithm, proc. Of the IEEE International Conference on Mechatronics and Automation, 2011:2195-2200. And the like utilize an ellipse method to position the pose of the mobile robots for workshops, errors of the method increase along with the increase of iteration times in the process of solving the distance from the ellipse center to the constraint plane and then normalizing, so that the positioning precision is not high, and the problem of large calculation amount exists in the method caused by continuous iteration. Alamo T, bravo J M, camahho E F Guaranteed state estimation by zonotopes [ C ]// IEEE Conference on Decision & control IEEE 2005, provides a multi-cell filtering method for positioning the pose of the robot, but the method has a large upper and lower boundary of the predicted value of each step of the pose of the robot and high prediction conservation because the least-sided full-symmetrical multi-cell is selected in the iterative process, and thus the positioning accuracy is not high.
Disclosure of Invention
The invention aims to improve the precision and accuracy and efficiency of parameter estimation, build a more accurate system model and improve the positioning precision by taking a production workshop mobile robot as a background in the intelligent manufacturing process. The invention aims to provide a pose positioning method of a mobile robot in a production workshop based on multi-cell-ellipsoid double filtering, which effectively reduces algorithm conservation and improves identification precision while reducing calculated amount.
The aim 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:
step1: discretizing a kinematic model of a mobile robot into a discrete continuous modelWherein->For observing vector, +.>Positioning parameters for pose +_>Representing system bounded noise;
step2: obtaining an observation vector according to a kinematic model of the mobile robot given unknown but bounded noise and an externally applied excitation signalAnd output sequence->And by observing vector->And output sequence->Obtaining constraint conditions of a k-th parameter feasible set;
step3: obtaining a first ellipsoid identification minimum trace ellipsoid according to the k-step constraint condition and the k-1 step ellipsoid;
step4: obtaining the minimum fully symmetrical multicellular body of the kth step volume according to the constraint condition of the k step and the fully symmetrical multicellular body of the k-1 step;
step5: expanding the fully symmetrical multicellular bodies obtained in the fourth step by considering the change of system parameters;
step6: performing singular value decomposition dimension reduction on the expanded fully-symmetrical multicellular bodies to obtain the fully-symmetrical multicellular bodies after dimension reduction;
the method is characterized in that:
step7: and dispersing the dimension-reduced full-symmetrical multicellular bodies into constraint conditions, carrying out secondary ellipsoid identification to obtain a minimum trace ellipsoid, and taking the central value of the minimum trace ellipsoid as a kth step pose estimated value.
Further, step1: discretizing a kinematic model of a mobile robot into a discrete continuous modelWherein->For observing vector, +.>Positioning parameters for pose +_>Representing system bounded noise; the method comprises the following specific steps:
crawler-type mobile robot model in production workshop:
wherein the method comprises the steps ofIndicating robot position->Indicating the robot angle, which can be measured by a sensor, -can be measured>、Represents the rotational angular velocity of the left and right driving wheels, +.>Represents the radius of the wheel>Indicating the distance between the left and right wheels +.>Indicates the time interval, +.>、/>The slip ratio of the robot is indicated.
A discrete continuous system is obtained:
wherein the method comprises the steps ofRepresents system bounded noise and +.>，/>、/>，。
Further, step2: obtaining an observation vector according to a kinematic model of the mobile robot given unknown but bounded noise and an externally applied excitation signalAnd output sequence->，/>Is a constraint on the feasible set of k-th parameters.
Further, step3: k-1 step ellipsoidAnd the kth step constraint->Obtaining a first ellipsoid identifying the smallest trace ellipsoid, wherein +.>，/>，/>，/>(II), (III), (V), (; the method comprises the following specific steps:
(1) Firstly, obtaining a predicted step ellipsoid by considering parameter variation：
Wherein the method comprises the steps of，/>Is a diagonal array formed by the maximum value of each parameter variation;
(2) Calculating a predicted step ellipsoid centerDistance to S of constraint plane:
，/>
if it isOr->Ending the identification, otherwise normalizing the distance +.>；
If it is，/>Otherwise
Wherein the method comprises the steps of
Is the positive root of the following equation
Obtaining a first ellipsoid updated minimum trace ellipsoid，/>Is the dimension of the parameter to be identified, +.>。
Further, the k-1 holomorphic multicellular bodies in Step4:and a kth constraint:obtaining a volume-minimized holohedral multicellular body comprising a viable set of parameters, wherein +.>，/>，，/>J is an integer and satisfies->，/>Is the column number of the matrix H, and comprises the following specific steps:
obtaining the volume minimum full-symmetrical multicellular body containing the feasible set of parameters，Is the dimension of the parameter to be identified.
Further, in Step5, considering the system parameter variation, expanding the holohedral symmetry multicellular bodies obtained in the fourth StepWherein->Is a diagonal array formed by the maximum value of each parameter variation;
further, in Step6, the dimension of the expanded holohedral symmetry multicellular bodies is reduced,wherein U, V are unitary matrices, < ->Is a major diagonal element +.>Matrix with singular values of 0 for the remaining elements, +.>Wherein D is a diagonal matrix and the diagonal elements are +.>，/>Is->Ith singular value, +.>Is V column i, and the k step holomorphic multicellular body after dimension reduction is obtained>Wherein->。
Further, in Step7, the fully-symmetrical multicellular bodies after dimension reduction are discretized into constraint conditions, and secondary ellipsoid identification is carried out to obtain minimum trace ellipsoids, wherein the dimensions of the fully-symmetrical multicellular bodies after dimension reduction are known to be consistent with those of parameters to be identified, so that the fully-symmetrical multicellular bodies are a parallelogram;
wherein the dash-dot line is the first ellipsoid estimate, the dashed line is the fully symmetric multicellular constraint, and the solid line is the second ellipsoid estimate. The vertex coordinates of the cells can be calculated according to the holohedral symmetry multicellular formula, and the vertex coordinates are assumed to beThe method comprises the steps of carrying out a first treatment on the surface of the With line segments->Obtaining a pair of constraints for example, +.>Equations are respectively
，/>
Wherein the method comprises the steps of
，/>
The parameters in the constraint are
And carrying out secondary ellipsoid identification according to the obtained constraint condition and the ellipsoids identified by the primary ellipsoids to obtain a final ellipsoid, and taking the central value of the final ellipsoid as the kth step pose estimated value.
The invention has the beneficial effects that: according to the pose positioning method, the mobile robot is positioned by adopting the ellipsoid and the full-symmetry multicellular body member-gathering filtering method, and the full-symmetry multicellular body after dimension reduction is discretized into a new constraint condition by updating the ellipsoid twice, so that identification conservation is effectively reduced, and the accuracy of the pose positioning of the robot is improved. Furthermore, the dimension of the fully-symmetrical multicellular bodies is reduced through singular value decomposition, so that the final calculated amount is simplified, the calculation burden caused by the increase of the dimension 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 therefore productivity can be improved; the method also provides technical teaching for the following intelligent manufacturing.
The scheme has high identification efficiency and accuracy in the aspect of parameter identification of the pose positioning of the mobile robot in the production workshop, lays an advantageous foundation for the next intelligent manufacturing, and provides powerful guarantee.
Drawings
FIG. 1 is a flow chart of the pose positioning method of the present invention.
FIG. 2 is a position and orientation parameter of the position and orientation method of the present inventionGet->And comparing with the identification results of the existing ellipsoid and holohedral symmetry multicellular methods.
FIG. 3 is a position and orientation parameter of the position and orientation method of the present inventionGet->And comparing with the identification results of the existing ellipsoid and holohedral symmetry multicellular methods.
FIG. 4 is a diagram showing the identification of a second ellipsoid as a minimum trace ellipsoid according to the present invention.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples.
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:
step one: by a typical kinematic model of a production plant crawler mobile robot, and then discretized into a discrete continuous systemThe method comprises the steps of carrying out a first treatment on the surface of the The method comprises the following specific steps:
crawler-type mobile robot model in production workshop:
wherein the method comprises the steps ofIndicating robot position->Representing the robot angle, can be measured by a sensor. />、Represents the rotational angular velocity of the left and right driving wheels, +.>Represents the radius of the wheel>Indicating the distance between the left and right wheels +.>Indicates the time interval, +.>、/>The slip ratio of the robot is indicated.
A discrete continuous system is obtained:
wherein the method comprises the steps ofRepresents system bounded noise and +.>，/>、/>，。
Step two: obtaining an observation vector from a typical kinematic model of a production plant crawler mobile robot given unknown but bounded noise and an externally applied excitation signalAnd output sequence->，/>Constraint conditions of a k-th parameter feasible set;
step three: the ellipsoid of the last step is knownAnd the kth step constraint->Obtaining a first ellipsoid identifying the smallest trace ellipsoid, wherein +.>，/>，/>，/>,. Firstly, obtaining a predicted step ellipsoid by considering parameter variation>
Wherein the method comprises the steps of，/>Is a diagonal array of maximum values of each parameter variation. Calculating predicted step ellipsoid center>Distance to S of constraint plane
，/>
If it isOr->Ending the identification, otherwise normalizing the distance +.>。
If it is，/>. Otherwise
Wherein the method comprises the steps of
Is the positive root of the following equation
Obtaining a first ellipsoid updated minimum trace ellipsoid，/>Is the dimension of the parameter to be identified, +.>；
Step four: the last step of holomorphic multicellular body is knownAnd the kth step constraint->Obtaining the k-th step of the minimum volume holohedral symmetry multicellular bodies containing the feasible set of parameters>WhereinJ is an integer and satisfies->，/>Is the column number of matrix H
Is the dimension of the parameter to be identified;
step five: taking system parameter changes into consideration, expanding the holohedral symmetry multicellular bodies obtained in the fourth stepWherein->Is a diagonal array formed by the maximum value of each parameter variation;
step six: the dimension of the expanded full-symmetrical multicellular body is reduced,wherein->，/>Respectively unitary matrix>Is a major diagonal element +.>Matrix with singular values of 0 for the remaining elements, +.>Wherein D is a diagonal matrix and the diagonal elements are +.>，/>Is->Ith singular value, +.>Is->Is to obtain the holohedral symmetry multicellular bodies of the kth step after dimension reduction ∈>Wherein->；
Step seven: in the seventh step, the fully-symmetrical multicellular body after dimension reduction is discretized into constraint conditions, and the second ellipsoid identification is carried out to obtain a minimum trace ellipsoid, as shown in fig. 4, wherein the dimensions of the fully-symmetrical multicellular body after dimension reduction are known to be consistent with those of parameters to be identified, so that the fully-symmetrical multicellular body is a parallelogram.
Wherein the dash-dot line is the first ellipsoid estimate, the dashed line is the fully symmetric multicellular constraint, and the solid line is the second ellipsoid estimate. The vertex coordinates of the cells can be calculated according to the holohedral symmetry multicellular formula, and the vertex coordinates are assumed to be. With line segments->Obtaining a pair of constraints for example, +.>Equations are respectively
，/>
Wherein the method comprises the steps of
，/>
The parameters in the constraint are
And carrying out secondary ellipsoid identification according to the obtained constraint condition and the ellipsoids identified by the primary ellipsoids to obtain a final ellipsoid, and taking the central value of the final ellipsoid as the kth step pose estimated value.
Assume that the initial position of the robot is set to，/>，/>，/>，/>，，/>The initial holohedral symmetry is +.>According to a typical kinematic model of a crawler-type mobile robot in a production workshop, the identification result is as follows, and the holohedral symmetry multicellular bodies are the documents Alamo T, bravo J M, camahho E F. Guaranteed state estimation by zonotopes [ C ]]// IEEE Conference on Decision & Control. IEEE, 2005.In (B), ellipsoids are the documents Zhou B, qian K, ma X, et al Ellipsoidal bounding set-membership identification approach for robust fault diagnosis with application to mobile robots [ J ]]System engineering and electronics (english edition), 2017 (5). The invention has lower conservation and higher identification accuracy, and the calculated amount is greatly reduced according to singular value decomposition.
The foregoing examples are merely illustrative of the preferred embodiments of the present invention and are not intended to limit the scope of the invention, and various modifications and improvements made by those skilled in the art to which the invention pertains will fall within the scope of the invention as defined by the appended claims without departing from the spirit of the 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:
step1: discretizing a kinematic model of a mobile robot into a discrete continuous modelWherein phi is k For observing vector, θ is pose positioning parameter, e k Representing system bounded noise;
step2: obtaining an observation vector phi according to a kinematic model of the mobile robot given unknown but bounded noise and an externally applied excitation signal k And output sequence y k And by observing the vector phi k And output sequence y k Obtaining constraint conditions of a k-th parameter feasible set;
step3: obtaining a first ellipsoid identification minimum trace ellipsoid according to the k-step constraint condition and the k-1 step ellipsoid;
step4: obtaining the minimum fully symmetrical multicellular body of the kth step volume according to the constraint condition of the k step and the fully symmetrical multicellular body of the k-1 step;
step5: taking the change of system parameters into consideration, expanding the obtained full-symmetry multicellular bodies in Step 4;
step6: performing singular value decomposition dimension reduction on the expanded fully-symmetrical multicellular bodies to obtain the fully-symmetrical multicellular bodies after dimension reduction;
the method is characterized in that:
step7: and dispersing the dimension-reduced full-symmetrical multicellular bodies into constraint conditions, carrying out secondary ellipsoid identification to obtain a minimum trace ellipsoid, and taking the central value of the minimum trace ellipsoid as a kth step pose estimated value.
2. The pose positioning method for the mobile robot in the production workshop based on multi-cell-ellipsoid double filtering according to claim 1, wherein the pose positioning method is characterized by comprising the following steps of: step1: discretizing a kinematic model of a mobile robot into a discrete continuous modelWherein phi is k For observing vector, θ is pose positioning parameter, e k Representing system bounded noise; the method comprises the following specific steps:
crawler-type mobile robot model in production workshop:
wherein the method comprises the steps ofRepresents the robot position, ψ k Representing the robot angle, ω can be measured by a sensor 1,k 、ω 2,k The rotational angular velocity of the left and right driving wheels, r the wheel radius, b the distance between the left and right wheels, Δt the time interval, s 1,k 、s 2,k The slip rate of the robot is represented;
a discrete continuous system is obtained:
wherein e k Represents system bounded noise and |e k |≤δ,v 1 ＝ω 1,k +ω 2,k /2、v 2 ＝-ω 1,k +ω 2,k ，
3. The pose positioning method for the mobile robot in the production workshop based on multi-cell-ellipsoid double filtering according to claim 2, wherein the pose positioning method is characterized by comprising the following steps of: step2: obtaining an observation vector phi according to a kinematic model of the mobile robot under the given unknown but bounded noise and an externally applied excitation signal k And output sequence y k ，Is a constraint on the feasible set of k-th parameters.
4. A workshop mobile robot as defined in claim 2, wherein the pose positioning party is based on multi-cell-ellipsoid dual-filteringThe method is characterized in that: step3: k-1 step ellipsoid E k-1 (c k-1 ,P k-1 ) And the kth constraintObtaining a first ellipsoid identifying minimum trace ellipsoid, wherein S=C, < >>d＝y k Sigma=δ; the method comprises the following specific steps:
(1) Firstly, obtaining a predicted step ellipsoid E by considering parameter variation k,k-1 (c k,k-1 ,P k,k-1 )：
Wherein the method comprises the steps ofΓ is the diagonal matrix of each parameter variation maxima;
(2) Calculating a predicted step ellipsoid center c k,k-1 Distance to S of constraint plane:
if it isOr->Ending the identification, otherwise normalizing the distance +.>
If it isc k ＝c k，k-1 ，P k ＝P k，k-1 Otherwise
c k ＝c k，k-1 +
Wherein the method comprises the steps of
Lambda is the positive root of the following equation
Obtaining a first ellipsoid updated minimum trace ellipsoid E k (c k ,P k )，n θ Is the dimension of the parameter to be identified, n θ ＝2。
5. The pose positioning method for the mobile robot in the production workshop based on multi-cell-ellipsoid double filtering according to claim 2, wherein the pose positioning method is characterized by comprising the following steps of: the k-1 th holomorphic multicellular body in Step4:and a kth constraint: />Obtaining a volume-minimized holohedral system comprising a feasible set of parameters, wherein S = C,/->d＝y k Sigma=delta, j is an integer and satisfies 0.ltoreq.j.ltoreq.l, l being the number of columns of the matrix H, the specific steps are:
obtaining the volume minimum full-symmetrical multicellular body containing the feasible set of parametersn θ Is the dimension of the parameter to be identified.
6. The pose positioning method based on multi-cell-ellipsoid double filtering for the mobile robot in the production workshop according to claim 5, wherein the pose positioning method is characterized by comprising the following steps of: considering system parameter variation in Step5, expanding the holo-symmetrical multicellular bodies obtained in Step4Where Γ is the diagonal matrix of the maximum of each parameter variation.
7. A production plant mover as claimed in claim 5The pose positioning method based on multi-cell-ellipsoid double filtering for the robot is characterized by comprising the following steps of: in Step6, the dimension of the expanded full-symmetrical multicellular body is reduced,wherein U, V are unitary matrices, respectively, Σ is the principal diagonal element [ T (j) * )Γ]Matrix with singular values of 0 for the remaining elements, +.>Wherein D is a diagonal matrix and the diagonal element is D i ＝||σ i V i || 1 ，σ i Is [ T (j) * )Γ]Ith singular value, V i Is V column i, and the k step holomorphic multicellular body after dimension reduction is obtained>Wherein->
8. The pose positioning method based on multi-cell-ellipsoid double filtering for the mobile robot in the production workshop according to claim 4, wherein the pose positioning method is characterized by comprising the following steps of: in Step7, dispersing the dimension-reduced full-symmetrical multicellular bodies into constraint conditions, and carrying out secondary ellipsoid identification to obtain minimum trace ellipsoids, wherein the dimension of the dimension-reduced full-symmetrical multicellular bodies is known to be consistent with that of parameters to be identified, so that the full-symmetrical multicellular bodies are a parallelogram; the vertex coordinates of the cells can be calculated according to the holohedral symmetry multicellular formula, and the vertex coordinates are assumed to beBy line segment l 12 ,l 34 To obtain a pair of constraint conditions for example, l 12 ,l 34 Equations are respectively
a 12 θ 1 +b 12 θ 2 ＝f 12 ，a 34 θ 1 +b 34 θ 2 ＝f 34
Wherein the method comprises the steps of
The parameters in the constraint are
And carrying out secondary ellipsoid identification according to the obtained constraint condition and the ellipsoids identified by the primary ellipsoids to obtain a final ellipsoid, and taking the central value of the final ellipsoid as the kth step pose estimated value.
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