CN117681213A - Method and device for planning and evaluating motion trail of industrial robot - Google Patents
Method and device for planning and evaluating motion trail of industrial robot Download PDFInfo
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Abstract
The invention discloses a method and a device for planning and evaluating a motion trail of an industrial robot, which belong to the technical field of industrial robot control and comprise the following steps: the method comprises the steps of taking DH model parameters of an industrial robot and joint angles of track starting points and stopping points as input data, generating a track control point set through a binary tree model with random control points, carrying out B spline interpolation calculation on the track control point set to obtain a smooth track space curve, and calculating characterization data such as energy, curvature, flexibility rate and the like of the track curve so as to evaluate the movement efficiency, the bending degree and the space torsion amplitude of the track, so that the movement track planning and evaluation of the industrial robot are realized. According to the invention, the parameter model, the random control point binary tree model, the B-spline curve interpolation model and the track evaluation model of the industrial robot are orderly integrated to form a complete motion track planning and evaluation system, so that simple, convenient, low-cost and high-precision motion track planning and optimal path output service can be provided for users.
Description
Technical Field
The invention belongs to the technical field of industrial robot control, and particularly relates to a method and a device for planning and evaluating a motion trail of an industrial robot.
Background
Along with continuous popularization of automation, intellectualization and internet of things in industrial fields, the demand of industrial robots in the fields of automobile manufacturing, electronic manufacturing, food and beverage, medical manufacturing, logistics storage and the like is also increasing. The motion track planning and evaluation are very important technical links of the industrial robot, and the track is required to be planned and evaluated in the motion process of the industrial robot so as to meet corresponding operation requirements.
The track planning needs to ensure that the speed and the acceleration of the robot are in a proper range, and the acceleration and the speed mutation in the track are reduced as much as possible so as to reduce jolt and vibration of the robot in operation, and ensure the stability and the high efficiency of the robot in operation. In actual operation, the robot needs to continuously perform repeated actions in an optimal track, so that no large error is generated in continuous reciprocating operation, namely, high repeated positioning accuracy is required.
The existing industrial robot track planning method mostly adopts the modes of programming control, sensor feedback or dynamic compensation and the like. Specifically, the motion trail of the robot is generated offline by using the robot programming language, so that the method has higher efficiency and can save time cost, but the method has higher requirements on programming skills and lacks intuitiveness, on the other hand, when the robot programming language is adopted to realize the offline planning of the motion trail of the robot, the method is difficult to deal with a dynamic environment, in the dynamic environment, the motion trail of the robot needs to be adjusted in real time, and the programming language may not be capable of rapidly responding to changes.
In addition, with the gradual perfection of models such as a neural network and deep learning, the motion track planning of a robot based on the model is also a mainstream track planning mode, the motion track of the robot is calculated by utilizing a path planning algorithm according to the position information of a target object and the dynamic model of the robot, the method is generally suitable for complex tasks, the motion of the robot can be accurately controlled, but the method has higher requirement on the precision of the model and has higher complexity than other track planning modes.
In view of the above problem, patent document publication No. CN113190021a discloses an industrial robot small line segment trajectory planning algorithm, which includes: s01, inputting paths, carrying out smoothing treatment on each small line segment path in the paths, and simultaneously determining characteristic points of each small line segment path subjected to the smoothing treatment; s02, solving the joint limiting speed of each characteristic point determined in the step S01 by using a numerical method; s03, backtracking speed, namely backtracking by taking a path end point as a backtracking start point and reversely backtracking by upwards one characteristic point, so as to solve the distance limiting speed of each characteristic point; if the distance limiting speed of the feature point is smaller than the joint limiting speed, removing the feature point, continuing to trace back the speed to the next feature point, otherwise, reserving the feature point, and using the feature point as a tracing starting point to trace back the speed to the next feature point, wherein the rest feature point is finally marked as an initial key point; s04, forward looking at the speed, forward looking at the next initial key point from the starting point of the path, so as to solve the distance limiting speed of each initial key point; if the distance limiting speed of the initial key point is smaller than the joint limiting speed, removing the initial key point, continuing to look forward to the next initial key point, otherwise, reserving the initial key point, and taking the initial key point as a starting point to look forward to the next initial key point, and finally marking the rest initial key point as an actual key point; s05, performing speed planning by using a motion planning algorithm according to the actual key points obtained in the step S04, and solving the time law of motion among the actual key points.
The invention provides a robot speed planning method based on characteristic points and key points, but in actual operation, the selection of the characteristic points and the key points is a subjective process, and when the joint limiting speed and the distance limiting speed are calculated, the physical characteristics and the environmental factors of the robot are not considered, so that the application scene of the robot speed planning method is obviously limited, and the final planning result has poor adaptability.
Patent document publication No. CN106338966a discloses an industrial robot trajectory planning programming method, comprising: obtaining D-H parameter information of the industrial robot through a structural drawing of the industrial robot; performing track planning and deducing work on each joint of the industrial robot by adopting a method of three times of uniform B spline curve difference values of joint space; designing a general element for track planning of the industrial robot; carrying out industrial robot track planning graphical programming by adopting a general element and a directional connecting line according to a deduced cubic uniform B spline curve formula; adopting a graphical programming mode to construct a simulation model of the industrial robot, and completing the simulation work of the control strategy; and downloading the correct control strategy verified by simulation into an actual controller to control the actual industrial robot to complete the work task.
However, the technical scheme provided by the invention requires that relevant technicians have deep robot programming capability, high technical cost and no intuitiveness, and in addition, the invention builds a model in a graphical programming mode, so that the problem of insufficient precision or flexibility is easy to occur when facing a complex control strategy.
Therefore, a simple, convenient and efficient method is needed to realize high-precision planning of the motion trail of the industrial robot.
Disclosure of Invention
The invention aims to provide a method and a device for planning and evaluating the motion trail of an industrial robot, which are based on an industrial robot ginseng number model, a control point set is generated through a random control point binary tree model, a plurality of smooth motion trail curves are obtained through a B-spline curve interpolation model, and an optimal trail is obtained by setting a trail evaluation model.
In order to achieve the above purpose, the technical scheme provided by the invention is as follows:
in a first aspect, the method for planning and evaluating the motion trail of the industrial robot provided by the embodiment of the invention comprises the following steps:
step 1: under the joint angle space, a relative transformation matrix from a base to an end rod is obtained according to a relative pose transformation matrix of a front connecting rod to a rear connecting rod of the industrial robot, and an industrial robot ginseng number model in Cartesian space is obtained according to the relative transformation matrix;
step 2: setting motion trail planning parameters to obtain a motion trail set, and generating a motion trail control point set containing a plurality of control points in a joint angle space by adopting a random control point binary tree model according to the start-stop joint angles and the motion trail set of the industrial robot;
step 3: performing interpolation operation on the motion track control point set by adopting a B spline interpolation model to obtain a smooth curve in a joint angle space, and performing coordinate transformation on the smooth curve according to an industrial machine ginseng number model to obtain a three-dimensional track curve in a Cartesian space;
step 4: and (3) repeating the steps 1-3, inputting the three-dimensional track curve generated in batch into a track evaluation model to perform quality scoring comprising energy, curvature and flexibility rate, and obtaining an optimal movement track for guiding the movement of the industrial robot.
According to the method, DH model parameters of the industrial robot and joint angles of track starting and stopping points are used as input data, a track control point set (comprising the joint angles of the track starting and stopping points) is generated through a binary tree model of random control points, B spline interpolation calculation is conducted through the track control point set to obtain a smooth track space curve, and then characterization data such as energy, curvature and flexibility rate of the track curve are calculated so as to evaluate the movement efficiency, the bending degree and the space distortion amplitude of the track, so that the planning and evaluation of the movement track of the industrial robot are realized.
Further, in step 1, the industrial machine ginseng number model is expressed as:
，
wherein,representing Cartesian homogeneous coordinate vectors, +.>Representing the first joint angle spaceiThe transformation relation of the space angles of each joint to the corresponding coordinates in the Cartesian three-dimensional space is 1 used for ensuring consistency in the homogeneous coordinate transformation of three-dimensional space points, and the transformationThe relationship is used for describing the ginseng number model of the industrial machine,mindicating the degree of freedom of the joints of the industrial robot, +.>Representing the relative transformation matrix of the industrial robot from the base to the end bar,q i,j representing the first of the relative transformation matricesiFirst joint space pointjThe angle value of each joint is calculated,xyzVthe base coordinate offset vector is represented as such,。
further, in step 2, the motion trail set includes:
aggregate sizeMThe method is used for representing the number of the motion trail finally generated by the motion trail planning method;
control point binary tree layer numbern，The binary tree model is used for limiting the random control points to generate a plurality of random control points;
track curve point numberT，The interpolation points are used for representing the B spline interpolation model;
evaluation of Curve parametersβ，The method is used for participating in a track evaluation model and scoring the generated plurality of motion tracks.
Further, in step 2, according to the start-stop joint angle and the motion track set of the industrial robot, a binary tree model of random control points is adopted to generate a motion track control point set including a plurality of control points in a joint angle space, including:
according to the control point binary tree layer number in the motion trail setnThe total number of control points generated by the binary tree model of the random control points is obtained asNExpressed by the formula:
，
creation ofN×mJoint angle control point matrixThArrAccording to the initial joint angleAnd termination joint angle->Obtaining a joint angle control point matrixThArrStarting point in (a)ThArr(0)=Th 0 And end pointThArr(N-1)=Th e ；
Will start the pointThArr(0)=Th 0 And end pointThArr(N-1)=Th e Inputting the random control point binary tree model, traversing through a stack structure according to initialization parameters s and e of the random control point binary tree model, and controlling a point matrix by joint angles in the traversing processThArrIntermediate state of (2)ThArr(k) Expressed by the formula:
，
wherein,λe (0, 1) is a randomly generated number,ThArr(k)represent the firstk+1 row joint angle;
after the traversing is completed, a motion trail control point set containing a plurality of control points is generated.
Further, in step 3, the interpolation operation is performed on the motion track control point set by using the B-spline interpolation model to obtain a smooth curve under the joint angle space, which includes:
solving tri-diagonal matrix equations using chase methodA Coefficient matrix of B-spline interpolation model in (a)pvThe first of (3)jIndividual elementspv j Wherein, the method comprises the steps of, wherein,Afor a pre-set tri-diagonal matrix,bn j for vectors constructed from a set of motion trajectory control points, a coefficient matrixpvExpressed by the formula:
，
obtaining the motion of the B spline interpolation model according to the coefficient matrixInterpolation result matrix after track control point set interpolationQvConnecting the interpolation result matrixQvThe nodes in the matrix obtain a smooth curve and an interpolation result matrixQvExpressed by the formula:
，
wherein,representing the first of the interpolation result matricesiLine 1jOne node of the column,/>、/>，/>Representation ofkA single-row matrix of the order polynomial,QCV j representation ofmDegree of freedomkSub-index position transformation matrixQCVThe first of (3)jThe column elements are arranged in a row,Brepresentation ofkThe coefficient matrix of the secondary polynomial is expressed as:
，
wherein,，/>and->。
Further, in step 3, the coordinate transformation is performed on the smooth curve according to the industrial robot parameter model to obtain a three-dimensional track curve in cartesian space, which includes:
the interpolation node is used for generating the interpolation node according to the industrial machine ginseng digital model in the Cartesian spaceFruit matrixQvPerforming space conversion to obtain a three-dimensional track curve in Cartesian space, wherein a three-dimensional coordinate matrix corresponding to the three-dimensional track curve is expressed as follows by a formula:
，
wherein,ip3Dthe three-dimensional coordinate matrix is corresponding to the three-dimensional track curve.
Further, in the track evaluation model, according to the three-dimensional coordinate matrix corresponding to the three-dimensional track curveip3DThe energy vector, curvature vector and deflection rate vector of the track curve are obtained by the step change of the track curve, and the method specifically comprises the following steps:
separately calculateip3DIs the first order derivative of (2)ip3Dd1. Second derivativeip3Dd2 and third order guidesip3Dd3；
According toip3Dd1 mould lengthip3DnsCalculating the energy vector of the trajectory curvep3DEnergy，p3DEnergyExpressed by the formula:
，
wherein,eg i =ns i ，ns i representing the length of the mouldip3DnsThe first of (3)iAn element;
calculating a first order derivativeip3Dd1 and second derivativeip3DdCross product of 2ip3DvsIs longer than the die length of (2)ip3DncAccording toip3DncAndip3Dns，calculating curvature vector of motion trail curvep3DCurvity，p3DCurvityExpressed by the formula:
，
wherein the method comprises the steps ofcv i =nc i /(ns i ) 3 ，nc i Representing the length of the mouldip3DncThe first of (3)iAn element;
calculating third order guidesip3Dd3 andip3Dvsdot product of (2)ip3DesAccording toip3DesAndip3Dnscalculating the deflection rate vector of the motion trail curvep3DTorsion：
,
Wherein,tv i =de i /(ns i ) 2 ，de i representation ofip3DesThe first of (3)iThe number of elements to be added to the composition,。
further, further computing a quality score from the energy vector, the curvature vector, and the deflection vector of the three-dimensional trajectory curve, comprising:
calculating track energy according to the energy vector, curvature vector and deflection rate vector of the three-dimensional track curvetrackEnergyTrack curvaturetrackCurvityFlexibility of tracktrackTorsionExpressed by the formula:
，/>，/>，
respectively giving track energytrackEnergyTrack curvaturetrackCurvityFlexibility of tracktrackTorsionWeighting is given、/>、/>Obtaining an evaluation indexestIndexExpressed by the formula:
，
outputting final quality scores according to the evaluation indexes by the track evaluation modelestScoreExpressed by the formula:
，
wherein,βthe evaluation curve parameters are shown.
In a second aspect, in order to achieve the above object, an embodiment of the present invention further provides an industrial robot motion trajectory planning and evaluating device, including an industrial robot ginseng number model building unit, a control point set generating unit, a trajectory curve generating unit, and a trajectory scoring unit;
the industrial robot ginseng model construction unit is used for obtaining a relative transformation matrix from a base to a tail end rod according to a relative pose transformation matrix of a front connecting rod to a rear connecting rod of the industrial robot under the joint angle space, and obtaining an industrial robot ginseng model in Cartesian space according to the relative transformation matrix;
the control point set generating unit is used for setting motion trail planning parameters to obtain a motion trail set, and generating a motion trail control point set containing a plurality of control points in a joint angle space by adopting a random control point binary tree model according to the start-stop joint angles of the industrial robot and the motion trail set;
the track curve generating unit is used for carrying out interpolation operation on the motion track control point set by adopting a B spline interpolation model to obtain a smooth curve in a joint angle space, and carrying out coordinate transformation on the smooth curve according to an industrial machine ginseng number model to obtain a three-dimensional track curve in a Cartesian space;
the track scoring unit is used for repeating the industrial robot ginseng number model construction unit, the control point integration generation unit and the track curve generation unit, inputting the three-dimensional track curve generated in batch into the track evaluation model to perform quality scoring comprising energy, curvature and flexibility rate, and obtaining an optimal motion track for guiding the motion of the industrial robot.
In order to achieve the above object, the embodiment of the present invention further provides an industrial robot motion trajectory planning and evaluating device, including a memory and a processor, where the memory is configured to store a computer program, and the processor is configured to implement the industrial robot motion trajectory planning and evaluating method provided by the embodiment of the first aspect when the computer program is executed.
The beneficial effects of the invention are as follows:
(1) According to the method provided by the invention, a control point set is generated by a random control point binary tree model through a starting point of a given motion track, and then interpolation is carried out on the control point set by a B spline interpolation model, so that a large quantity of smooth motion tracks which accurately pass through the control point set are generated, and the accurate planning of the motion track of the industrial robot is realized;
(2) According to the method, the resolvable performances of the first-order derivative, the second-order derivative and the third-order derivative of the track curve are analyzed, so that the motion track planning method provided by the invention has good stability on the position change of any motion track in the joint space and the corresponding Cartesian space;
(3) The invention provides a track evaluation model for a motion track of an industrial robot, which is characterized in that the working efficiency, the motion precision and the fluency of the industrial robot under the motion track curve given by the method are judged by carrying out weight summation on an energy vector, a curvature vector and a deflection vector of a track curve, and finally an optimal track is obtained by scoring, so that the industrial robot is ensured to have higher repeated positioning precision under the optimal track;
(4) The method provided by the invention can be used for providing simple, convenient, low-cost and high-precision motion track planning and optimal path output service for users.
Drawings
Fig. 1 is a flowchart of an industrial robot motion trajectory planning method according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a specific flow for planning and evaluating a motion trajectory of an industrial robot according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of a result of a control point set generated by a random control point binary tree model according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of a differential change of several derivatives of a trajectory curve provided by an embodiment of the present invention.
FIG. 5 is a schematic diagram of the spatial distribution of track energy, track curvature and track flexibility of a track curve provided by an embodiment of the present invention.
Fig. 6 is a schematic diagram of a smooth trajectory planned by the trajectory planning model according to the embodiment of the present invention.
Fig. 7 is a schematic structural diagram of an industrial robot motion trajectory planning device according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the detailed description is presented by way of example only and is not intended to limit the scope of the invention.
The technical conception of the invention is as follows: for the purpose ofmFreedom degree industrial robot, and joint space control point set is generated by utilizing random control point binary tree modelThArr(also a manually set of joint control points); joint control point set using B-spline interpolation modelThArrInterpolation result matrix of joint space is obtained by interpolation operationQvThen the ginseng is processed by an industrial machine ginseng number modelQvThree-dimensional coordinate matrix converted into Cartesian spaceip3DThe method comprises the steps of carrying out a first treatment on the surface of the Will beip3DObtaining a final score of the motion track through track evaluation model processing; data analysis is carried out on the motion track set generated in batches to obtain an optimal track curve and output the optimal track curve。
Fig. 1 is a flowchart of an industrial robot motion trajectory planning and evaluating method according to an embodiment of the present invention. As shown in fig. 1, an embodiment provides a method for planning and evaluating a motion trajectory of an industrial robot, including the following steps:
s110, under the joint angle space, a relative transformation matrix from a base to a tail end rod is obtained according to a relative pose transformation matrix of a front connecting rod to a rear connecting rod of the industrial robot, and a ginseng number model of the industrial robot in Cartesian space is obtained according to the relative transformation matrix.
In the present embodiment, the parameter data of the industrial robot mainly includes the degree of freedom of the jointsmAnd D-H parameters and start-stop joint angles, wherein the D-H parameters include joint anglesθ j Offset distance of jointd j Length of connecting roda j And the torsion angle of the connecting rod，θ j Is variable, the others are constant,>，jrepresent the firstjAnd a plurality of links as shown in (1) (2) of fig. 2.
According to the parameter data in the joint angle space, converting the industrial robot in the joint angle space into an industrial robot model in the Cartesian space through a transformation relation, wherein the industrial robot model in the Cartesian space is used as a general transformation relation for realizing the space transformation of the industrial robot model. The process of solving the industrial robot model in cartesian space is as follows:
(1) Connecting rod of industrial robot in joint angle spacej-1 pair of connecting rodsjIs expressed as:
，
wherein,represented in the connecting rodjThe corresponding joint angle isθ j Lower connecting rodj-1 pair of connecting rodsjIs a relative pose transformation matrix of (a).
(2) From the relative pose transformation matrix, it is possible to obtain a motion from the industrial robot base (base coordinate link 0) to the end bar (link)m) Is formulated as:
，
wherein,representing the base coordinate from link 0 to linkmIn the present embodiment, the base coordinate offset vector is set asxyzZExpressed by the formula:
。
(3) Setting parameter variable bits in a relative transformation matrixTh i ，Th i Representing the first under the angular space of the jointiThe individual joint space angles are expressed as:
，
wherein,q i,j represent the firstiFirst joint space pointjIndividual joint angle values;
according to the base coordinate offset vectorxyzZAnd a relative transformation matrix, theniThe respective joint space angles correspond to the Cartesian space three-dimensional coordinate system expressed as:
，
wherein,representing Cartesian homogeneous coordinatesVector (S)>Representing the first joint angle spaceiA transformation relationship from the space angle of each joint to the corresponding coordinates in the Cartesian three-dimensional space, 1 for ensuring consistency in performing homogeneous coordinate transformation on three-dimensional space points, said transformation relationship being used for describing a ginseng number model of an industrial machine,mindicating the degree of freedom of the joints of the industrial robot, +.>Representing the relative transformation matrix of the industrial robot from the base to the end bar,q i,j representing the first of the relative transformation matricesiFirst joint space pointjThe angle value of each joint is calculated,xyzVthe base coordinate offset vector is represented as such,。
s120, setting motion trail planning parameters to obtain a motion trail set, and generating a motion trail control point set containing a plurality of control points in a joint angle space by adopting a random control point binary tree model according to the start-stop joint angles and the motion trail set of the industrial robot.
As shown in fig. 2 (3) (4) (5), in the present embodiment, the motion trajectory planning parameter includes a set sizeM(track number) control point binary tree layer numbernTrack curve point numberTEvaluation of Curve parametersβ. Wherein the aggregate sizeMThe method is used for representing the number of the motion trail finally generated by the motion trail planning method; control point binary tree layer numbernThe method comprises the steps that a binary tree model used for limiting random control points is used for generating a plurality of random control points, so that a motion track control point set under a joint angle space is obtained; track curve point numberTThe interpolation points are used for representing the B spline interpolation model; evaluation of Curve parametersβThe method is used for participating in a track evaluation model and scoring the generated plurality of motion tracks.
Inputting the motion track set and the start-stop joint angles into a random control point binary tree model to obtain a motion track control point set of a joint space, wherein the specific process is as shown in fig. 3:
(1) In the present embodiment of the present invention,mthe initial joint angle of the motion trail planning of the freedom degree industrial robot is set asThe termination joint angle is set to +>。
(2) According to the binary tree layer number of the control pointnThe total number of control points generated by the binary tree model of the random control points is obtained asNExpressed by the formula:
。
(3) Creation ofN×mJoint angle control point matrixThArr，ThArr(i) Represent the firsti+1 row joint angle) According to the initial joint angle and the final joint angle, letThArr(0)=Th 0 ，ThArr(N-1)=Th e ，ThArr(0) AndThArr(N-1) representing a start point and an end point of a motion trajectory of the industrial robot, respectively.
(4) Will start and stop pointsThArr(0)=Th 0 ，ThArr(N-1)=Th e Inputting the random control point binary tree model to generate control points, and initializing index parameters of the random control point binary tree model to be respectivelysAndeas shown in FIG. 3, N1.1 in FIG. 3 refers to the index parametersAndea new control point, N2.1, etc., generated randomly between the corresponding two control points, wherein,s=0，e=N-1, calculate indexk=(s+e) 2, create stack node stacknode. Id=k, stacknode. Parentid= -1, stacknode. Val= [ske]Push (stack node) is performed.
(5) Judging whether stack isIf the node is idle (7), otherwise, a node is popped out of stack=stack.pop (), and index data corresponding to the node of the stack is obtained, namelys=stackNode.val(0)，e=stackNode.val(2)，k=jacknode. Val (1), calculating joint angle corresponding to jacknode node, and controlling joint angle control point matrix in traversal processThArrIntermediate state of (2)ThArr(k) Expressed by the formula:，
wherein,λe (0, 1) is a randomly generated number,ThArr(k) The specific formula is as follows:
and (6) turning.
(6) Iterating in a binary tree model of random control points, for eachThArr(k) Generating corresponding control points:
fori=0:1
s=stackNode.val(i),e= stackNode.val(i+1)
if (s+e)%2==0
k=(s+e)/2
newStackNode.id=k
newStackNode. parentId = stackNode.id
newStackNode.val =[ske]
stack.push(newStackNode)
end
end
turning to (5), and performing loop iteration between (5) and (6).
(7) After the traversal is finished, finally obtainingThArrThe output joint angle control point matrix is that the set of all row vectors in the matrix is that of the motion trail control point, and the head row and the tail row respectively correspond to the initial joint angle and the termination joint angle, as shown in fig. 3.
S130, performing interpolation operation on the motion track control point set by adopting a B spline interpolation model to obtain a smooth curve in the joint angle space, and performing coordinate transformation on the smooth curve according to the industrial machine ginseng number model to obtain a three-dimensional track curve in the Cartesian space.
(1) The product obtained in S120mThe motion trail control point set of the freedom degree industrial robot is described as。
(2) Constructing a tri-diagonal matrixAExpressed as:
，
in this embodiment, a tri-diagonal matrix is selectedAElements of (a)a i,j The following values were used:
，
construction No.jJoint angle expansion vectorbn j ：
，
Solving tri-diagonal matrix equations using chase methodA The specific process is as follows:
(a) Order theAnd initializing the matrixATElements of (a)at i,j =a i,j Wherein->；
(b)iFrom 1 toN+1 performs the iterative calculation in succession:and；/>
(c) Order theAnd initializing the matrixALElement->Performing calculation, assigning->And->；
(d) Order theAnd initializing the matrixAUElement->Performing calculation, assigning->And->;
(e) First calculatey=bn j AL, recalculatepv j =y/AU。
The first of the coefficient matrices obtained from (a) (b) (c) (d) (e)jThe row vector of a row is formulated as:wherein->Thereby obtaining a coefficient matrix:
。
(3) Calculating distance matrixWherein->，/>。
(4) For the followingkB-spline interpolation of 3 times, initializing a distance proportional vector between track curve points (interpolation points)uThe method comprises the following steps:。
(5) Determining a node vector corresponding to an interpolation point in the track curve by utilizing Hadley-JarrettuFor distance matrixAnd (3) summing:
；
obtaining a distance proportion vector according to the summation resultuThe values of (a), namely:
whereink=3。
(6) Setting the number of track curve pointsT(interpolation points)TNode step size =300s=1/(T-1) calculating each interpolation node according to the following steps:
(a) Setting interpolation node step size vectorWherein->，；
(b) When (when)us i Greater than or equal tou score When the index position is obtainedscoreIf there are a plurality of equal andus i the last index position is taken if the index position is less than 1; if it isus i When the number of the index positions is equal to 1, the index position before the first index position is taken and then the index position is calculated according toscore=score-k，k=3 is the number of B-spline interpolations;
(c) Construction matrixCalculation ofWherein is a coefficient matrixpvElement values of corresponding subscripts;
(d) Calculation of，kOne-row matrix of secondary polynomialsAndmIn the degree of freedomkSub-index position transformation matrixQCV，QCVExpressed by the formula: />
，
Wherein,QCVthe first of (3)jColumn elementQCV j Expressed as:
，
then the interpolation result matrixQVMiddle (f)iLine 1jElements of columnsWherein B representskA matrix of coefficients of the polynomial of degree +_>、/>B is formulated as:
，
wherein,，/>and->In this embodiment, the number of the first and second electrodes,k=3, so:
，
an interpolation result matrix is obtained from (a) (b) (c) (d)QVThe method comprises the following steps:
。
(7) Using the spatial transformation relationship obtained in S110, the interpolation result matrix of the joint spaceQvConverting into a three-dimensional coordinate matrix in Cartesian space:
，
ip3Dnamely a three-dimensional coordinate matrix of the B-spline interpolation model, and a matrix description corresponding to a smooth three-dimensional track curve generated by the B-spline interpolation model, as shown in (6) (7) in fig. 2.
S140, repeating the steps S110-S130, inputting the three-dimensional track curves generated in batches into a track evaluation model to perform quality scoring comprising energy, curvature and flexibility rate, and obtaining an optimal motion track for guiding the motion of the industrial robot.
The trajectory evaluation model procedure is included in (8) (9) in fig. 2, and is output according to the B-spline interpolation model in S130ip3DIs subjected to a derivative of the energy comprising the trajectory curveQuality assessment of rate and flex rate. In the present embodiment, according toip3DThe first order guide, the second order guide and the third order guide of the track curve are calculated, the track energy, the track curvature and the track flexibility are respectively obtained according to the energy vector, the curvature vector and the flexibility vector, the track energy, the track curvature and the track flexibility are respectively weighted, the score mapping is carried out through fuzzy probability, the score of the track curve is obtained, and the scoring range is 0-100 minutes. The specific process is as follows:
(1) In a three-dimensional coordinate system of Cartesian space, pairip3DSolving first order derivativesip3Dd1, first order guideip3Dd1 is expressed as:
wherein, the method comprises the steps of, wherein,；/>
in the same way, the processing method comprises the steps of,ip3Dis the second derivative of (2)ip3Dd2 is:wherein；
ip3DThird order guide of (2)ip3Dd3 is:wherein, the method comprises the steps of, wherein,。
(2) Computing the cross product of the first and second derivativesip3Dvs：
Wherein->，/>；
Similarly, in a Cartesian space three-dimensional coordinate system,yandzthe elements in the corresponding cross product in the direction are respectively:，/>。
(3) Calculating third order derivatives and cross productsip3DvsDot product of (2)ip3Des：
，
Wherein,，/>，/>representation ofip3DA kind of electronic deviceyElements in the third order guide of the directional line vector, are->Representation ofip3DA kind of electronic devicezElements in the third order derivative of the directional row vector.
(4) Computing the cross product of the first and second derivativesip3DvsIs longer than the die length of (2)ip3Dnc：
，
Wherein,；
similarly, first order guideip3Dd1 mould lengthip3DnsThe method comprises the following steps:
，
wherein,，/>。
FIG. 4 shows the present inventionip3DA differential change schematic of a number of derivatives of (c), wherein,ip3Dthe spatial coordinates X, Y, Z in (c) represent joint angles,ip3Dis the first order derivative of (2)ip3Dd1 denotes the velocity of the joint and,ip3Dis the second derivative of (2)ip3Dd2 denotes the acceleration of the joint,ip3Dthird order guide of (2)ip3Dd3 represents joint jerk, and the spatial distribution along with the different control points is shown in fig. 4. The method has good stability on any motion trail in the aspects of joint space and corresponding Cartesian space position change, and the differential (first, second and third order guide) change also has good stability.
(5) According to first order guidesip3Dd1 mould lengthip3DnsCalculating the energy vector of the motion trail curvep3DEnergy：Whereineg i =ns i ；
Cross product based on first and second derivativesip3DvsIs longer than the die length of (2)ip3Dnc、First order guideip3Dd1 mould lengthip3DnsCalculating curvature vector of motion trail curvep3DCurvity：Whereincv i =nc i /(ns i ) 3 ；
According to third-order derivatives and cross productsip3DvsDot product of (2)ip3Des、First order guideip3Dd1 mould lengthip3DnsCalculating the deflection rate vector of the motion trail curvep3DTorsion：Wherein, the method comprises the steps of, wherein,tv i =de i /(ns i ) 2 ，/>。
(6) Calculation of trajectory energytrackEnergyAnd is given weight，trackEnergyExpressed by the formula:；
calculating track curvaturetrackCurvityAnd is given weight，trackCurvityExpressed by the formula:；
calculating the track flexibility ratetrackTorsionAnd is given weight，trackTorsionExpressed by the formula:；
in the present embodiment, track energy is respectively giventrackEnergyTrack curvaturetrackCurvityAnd track flexibilitytrackTorsionThe weight values of (2) are:、/>、/>。
FIG. 5 shows a schematic view of the spatial distribution of the track energy, track curvature and track flexibility of a smooth track curve with different control points according to a track evaluation model, and the horizontal axis represents the control points in the smooth track curve. As can be seen from fig. 5, the same smooth track curve has different property distributions at different control points, and a high track energy indicates that the industrial robot has higher working efficiency at the control point, a high track curvature indicates that the motion track of the industrial robot has larger curvature at the control point, and a high track flexibility rate indicates that the motion track of the industrial robot has larger bending degree at the control point.
Energy to tracktrackEnergyTrack curvaturetrackCurvityAnd track flexibilitytrackTorsionPerforming weighted summation to obtain an evaluation indexestIndex：。
(7) Calculating final comprehensive evaluation score of trackestScore：WhereinβRepresenting the parameters of the evaluation curve which, in this embodiment,β=0.5。
and (3) carrying out quality evaluation on the generated track curves by adopting the track evaluation model, repeating S110-S130, generating a large number of track curves to be evaluated, judging whether the number of the generated motion curves is larger than the set size M, continuing to generate if the number of the generated motion curves is smaller than M, and grading, sorting and screening if the number of the generated motion curves is larger than or equal to M. After scoring by the track evaluation model, a track curve corresponding to the highest score is screened out, as ⑪ in fig. 2, and is used as the optimal motion track of the target industrial robot, and the industrial robot completes industrial operation according to the optimal motion track.
The quality scores of a group of motion trajectories are calculated by the method provided by the invention, and are shown in tables 1-5, wherein the corresponding trajectory ID of the group with the highest score is 60, and the score is 79.1. The distribution of the motion trajectory curve of the industrial robot obtained by the method proposed by the invention in the cartesian three-dimensional space is shown in fig. 6.
TABLE 1
TABLE 2
TABLE 3 Table 3
TABLE 4 Table 4
TABLE 5
Based on the same inventive concept, the embodiment of the invention also provides an industrial robot motion track planning and evaluating device 700, as shown in fig. 7, comprising an industrial robot ginseng model construction unit 710, a control point set generation unit 720, a track curve generation unit 730 and a track scoring unit 740;
the industrial robot parameter model construction unit 710 is configured to obtain a relative transformation matrix from a base to an end rod according to a relative pose transformation matrix of a front link to a rear link of the industrial robot in a joint angle space, and obtain an industrial robot parameter model in a cartesian space according to the relative transformation matrix;
the control point set generating unit 720 is used for setting motion trail planning parameters to obtain a motion trail set, and generating a motion trail control point set containing a plurality of control points in a joint angle space by adopting a random control point binary tree model according to the start-stop joint angles and the motion trail set of the industrial robot;
the track curve generating unit 730 is configured to perform interpolation operation on the motion track control point set by using a B-spline interpolation model to obtain a smooth curve in the joint angle space, and perform coordinate transformation on the smooth curve according to the industrial machine ginseng number model to obtain a three-dimensional track curve in the cartesian space;
the track scoring unit 740 is configured to repeat the industrial robot ginseng number model construction unit 710, the control point set generation unit 720, and the track curve generation unit 730, and input the three-dimensional track curve generated in batch into the track evaluation model to perform quality scoring including energy, curvature, and flexibility, so as to obtain an optimal motion track for guiding the motion of the industrial robot.
Based on the same inventive concept, the embodiment also provides an industrial robot motion trail planning and evaluating device, which comprises a memory and a processor, wherein the memory is used for storing a computer program, and the processor is used for realizing the industrial robot motion trail planning and evaluating method when executing the computer program.
It should be noted that, the apparatus and the apparatus for planning and evaluating a motion trajectory of an industrial robot provided in the foregoing embodiments all belong to the same concept as the embodiment of the method for planning and evaluating a motion trajectory of an industrial robot, and detailed implementation processes of the apparatus and the apparatus are described in the embodiment of the method for planning and evaluating a motion trajectory of an industrial robot, which are not described herein again.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the foregoing detailed description of the invention has been provided, it will be apparent to those skilled in the art that modifications may be made to the embodiments described in the foregoing examples, and that certain features may be substituted for those illustrated and described herein. Modifications, equivalents, and alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (10)
1. The industrial robot motion track planning and evaluating method is characterized by comprising the following steps:
step 1: under the joint angle space, a relative transformation matrix from a base to an end rod is obtained according to a relative pose transformation matrix of a front connecting rod to a rear connecting rod of the industrial robot, and an industrial robot ginseng number model in Cartesian space is obtained according to the relative transformation matrix;
step 2: setting motion trail planning parameters to obtain a motion trail set, and generating a motion trail control point set containing a plurality of control points in a joint angle space by adopting a random control point binary tree model according to the start-stop joint angles and the motion trail set of the industrial robot;
step 3: performing interpolation operation on the motion track control point set by adopting a B spline interpolation model to obtain a smooth curve in a joint angle space, and performing coordinate transformation on the smooth curve according to an industrial machine ginseng number model to obtain a three-dimensional track curve in a Cartesian space;
step 4: and (3) repeating the steps 1-3, inputting the three-dimensional track curve generated in batch into a track evaluation model to perform quality scoring comprising energy, curvature and flexibility rate, and obtaining an optimal movement track for guiding the movement of the industrial robot.
2. The method for planning and evaluating a motion trajectory of an industrial robot according to claim 1, wherein in step 1, the industrial robot ginseng number model is expressed as:
，
wherein,representing Cartesian homogeneous coordinate vectors, +.>Representing the first joint angle spaceiA transformation relationship of individual joint space angles to corresponding coordinates in cartesian three-dimensional space, 1 for ensuring consistency in homogeneous coordinate transformation of three-dimensional space points, said transformation relationshipIs used for describing a ginseng number model of an industrial machine,mindicating the degree of freedom of the joints of the industrial robot, +.>Representing the relative transformation matrix of the industrial robot from the base to the end bar,q i,j representing the first of the relative transformation matricesiFirst joint space pointjThe angle value of each joint is calculated,xyzVrepresenting the base coordinate offset vector, ">。
3. The method for planning and evaluating motion trajectories of industrial robots according to claim 2, wherein in step 2, the motion trajectory set comprises:
aggregate sizeMThe method is used for representing the number of the generated motion tracks;
control point binary tree layer numbern，The binary tree model is used for limiting the random control points to generate a plurality of random control points;
track curve point numberT，The interpolation points are used for representing the B spline interpolation model;
evaluation of Curve parametersβ，The method is used for participating in a track evaluation model and scoring the generated plurality of motion tracks.
4. The method for planning and evaluating a motion trajectory of an industrial robot according to claim 3, wherein in step 2, the motion trajectory control point set including a plurality of control points in a joint angle space is generated by adopting a random control point binary tree model according to a start-stop joint angle and a motion trajectory set of the industrial robot, and the method comprises the following steps:
according to the control point binary tree layer number in the motion trail setnThe total number of control points generated by the binary tree model of the random control points is obtained asNExpressed by the formula:
，
creation ofN×mJoint angle control point matrixThArrAccording to the initial joint angleAnd termination joint angle->Obtaining a joint angle control point matrixThArrStarting point in (a)ThArr(0)=Th 0 And end pointThArr(N-1)=Th e ；
Will start the pointThArr(0)=Th 0 And end pointThArr(N-1)=Th e Inputting the random control point binary tree model, traversing through a stack structure according to initialization parameters s and e of the random control point binary tree model, and controlling a point matrix by joint angles in the traversing processThArrIntermediate state of (2)ThArr(k) Expressed by the formula:
，
wherein,λe (0, 1) is a randomly generated number,ThArr(k)represent the firstk+1 row joint angle;
after the traversing is completed, a motion trail control point set containing a plurality of control points is generated.
5. The method for planning and evaluating a motion trajectory of an industrial robot according to claim 4, wherein in step 3, the interpolation operation is performed on the motion trajectory control point set by using a B-spline interpolation model to obtain a smooth curve under a joint angle space, and the method comprises the following steps:
solving tri-diagonal matrix equations using chase methodA Coefficient matrix of B-spline interpolation model in (a)pvThe first of (3)jIndividual elementspv j Wherein, the method comprises the steps of, wherein,Afor a pre-set tri-diagonal matrix,bn j for vectors constructed from a set of motion trajectory control points, a coefficient matrixpvExpressed by the formula:
，
obtaining an interpolation result matrix after the B spline interpolation model performs integrated interpolation on the motion track control points according to the coefficient matrixQvConnecting the interpolation result matrixQvThe nodes in the matrix obtain a smooth curve and an interpolation result matrixQvExpressed by the formula:
，
wherein,representing the first of the interpolation result matricesiLine 1jOne node of the column,/>、/>，/>Representation ofkA single-row matrix of the order polynomial,QCV j representation ofmDegree of freedomkSub-index position transformation matrixQCVThe first of (3)jThe column elements are arranged in a row,Brepresentation ofkThe coefficient matrix of the secondary polynomial is expressed as:
，
wherein,，/>and->。
6. The method for planning and evaluating a motion trajectory of an industrial robot according to claim 5, wherein in step 3, the coordinate transformation is performed on the smooth curve according to the industrial robot parameter model to obtain a three-dimensional trajectory curve in cartesian space, and the method comprises the following steps:
according to the industrial machine ginseng number model in Cartesian space, the interpolation result matrixQvPerforming space conversion to obtain a three-dimensional track curve in Cartesian space, wherein a three-dimensional coordinate matrix corresponding to the three-dimensional track curve is expressed as follows by a formula:
，
wherein,ip3Dthe three-dimensional coordinate matrix is corresponding to the three-dimensional track curve.
7. The method for planning and evaluating a motion trajectory of an industrial robot according to claim 6, wherein in the trajectory evaluation model, a three-dimensional coordinate matrix corresponding to a three-dimensional trajectory curve is usedip3DThe energy vector, curvature vector and deflection rate vector of the track curve are obtained by the step change of the track curve, and the method specifically comprises the following steps:
separately calculateip3DIs the first order derivative of (2)ip3Dd1. Second derivativeip3Dd2 and third order guidesip3Dd3；
According toip3Dd1 mould lengthip3DnsCalculating the energy vector of the trajectory curvep3DEnergy，p3DEnergyExpressed by the formula:
，
wherein,eg i =ns i ，ns i representing the length of the mouldip3DnsThe first of (3)iAn element;
calculating a first order derivativeip3Dd1 and second derivativeip3DdCross product of 2ip3DvsIs longer than the die length of (2)ip3DncAccording toip3DncAndip3Dns，calculating curvature vector of motion trail curvep3DCurvity，p3DCurvityExpressed by the formula:
，
wherein the method comprises the steps ofcv i =nc i /(ns i ) 3 ，nc i Representing the length of the mouldip3DncThe first of (3)iAn element;
calculating third order guidesip3Dd3 andip3Dvsdot product of (2)ip3DesAccording toip3DesAndip3Dnscalculating the deflection rate vector of the motion trail curvep3DTorsion：
,
Wherein,tv i =de i /(ns i ) 2 ，de i representation ofip3DesThe first of (3)iThe number of elements to be added to the composition,。
8. the method of claim 7, further calculating a quality score based on the energy vector, the curvature vector, and the flex rate vector of the three-dimensional trajectory, comprising:
calculating track energy according to the energy vector, curvature vector and deflection rate vector of the three-dimensional track curvetrackEnergyTrack curvaturetrackCurvityFlexibility of tracktrackTorsionExpressed by the formula:
，/>，/>，
respectively giving track energytrackEnergyTrack curvaturetrackCurvityFlexibility of tracktrackTorsionWeighting is given、/>、/>Obtaining an evaluation indexestIndexExpressed by the formula:
，
outputting final quality scores according to the evaluation indexes by the track evaluation modelestScoreExpressed by the formula:
，
wherein,βthe evaluation curve parameters are shown.
9. The industrial robot motion track planning and evaluating device is characterized by comprising an industrial robot ginseng number model building unit, a control point set generating unit, a track curve generating unit and a track scoring unit;
the industrial robot ginseng model construction unit is used for obtaining a relative transformation matrix from a base to a tail end rod according to a relative pose transformation matrix of a front connecting rod to a rear connecting rod of the industrial robot under the joint angle space, and obtaining an industrial robot ginseng model in Cartesian space according to the relative transformation matrix;
the control point set generating unit is used for setting motion trail planning parameters to obtain a motion trail set, and generating a motion trail control point set containing a plurality of control points in a joint angle space by adopting a random control point binary tree model according to the start-stop joint angles of the industrial robot and the motion trail set;
the track curve generating unit is used for carrying out interpolation operation on the motion track control point set by adopting a B spline interpolation model to obtain a smooth curve in a joint angle space, and carrying out coordinate transformation on the smooth curve according to an industrial machine ginseng number model to obtain a three-dimensional track curve in a Cartesian space;
the track scoring unit is used for repeating the industrial robot ginseng number model construction unit, the control point integration generation unit and the track curve generation unit, inputting the three-dimensional track curve generated in batch into the track evaluation model to perform quality scoring comprising energy, curvature and flexibility rate, and obtaining an optimal motion track for guiding the motion of the industrial robot.
10. An industrial robot motion trajectory planning and evaluation device comprising a memory for storing a computer program and a processor, characterized in that the processor is adapted to implement the industrial robot motion trajectory planning and evaluation method according to any one of claims 1-8 when executing the computer program.
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