CN112549019B - Industrial robot track accuracy analysis method based on continuous dynamic time warping - Google Patents
Industrial robot track accuracy analysis method based on continuous dynamic time warping Download PDFInfo
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Abstract
The invention discloses an industrial robot trajectory accuracy analysis method based on continuous dynamic time warping, which is based on the idea of dynamic programming and searches for the best matching point in two sequences step by step. Defining the accumulated distance matrix D as the similarity metric of the two track sequences. And interpolating the two sequences, wherein the regular path meets a certain optimal strategy to minimize the cumulative distance, and the backtracking method searches from back to front to minimize the cumulative distance of the two sequences. The invention adopts the CDTW algorithm, analyzes the mapping between the track points, and solves the problem that the mapping error between the instruction track and the actual track point is caused to cause larger track measuring error due to the influence of the movement speed and the movement deviation of the robot, the sampling frequency of a measuring system and the measuring error when the plane is constructed by a nonlinear track method. By measuring and analyzing the track accuracy of the industrial robot, the problem of mapping errors in a standard method can be effectively avoided, and the track accuracy is improved.
Description
Technical Field
The invention relates to the field of performance testing of industrial robots, in particular to a method for measuring and evaluating track accuracy.
Background
Industrial robots are one of the key devices for intelligent manufacturing, and with the increasing application of industrial robots in high-precision fields such as precision manufacturing, aerospace, precision measurement and the like, the requirements on the motion performance of the robots are higher and higher. The robot track accuracy is one of the most critical indexes for measuring the performance of the robot, so that the measurement and evaluation of the robot track accuracy are particularly important.
At present, the track performance test of the robot mainly refers to international standard ISO 9283: "operating industrial robot-performance standard and related test method", national standard GB/T12642-.
In the ISO9283 and GB/T12642 standards, a plane perpendicular to an instruction track needs to be constructed, and the track accuracy is calculated by intersecting with an actual track, but the position of the normal plane construction is not specified. ANSI/RIA specifies that the equidistant construction method on the command trajectory intersects the actual trajectory in a plane. For a non-linear track, under the influence of motion deviation and running speed of the robot, sampling frequency of a measuring system and measuring errors, normals of all points on the track are constantly changed, and constructed normal planes may intersect, so that wrong mapping is generated between an instruction track and an actual track point, and a large measuring error is caused.
Disclosure of Invention
The invention provides an industrial robot track accuracy analysis method based on a continuous dynamic time warping algorithm (CDTW) aiming at the problems in the existing robot track accuracy test method, the method solves the problem of mapping error at a complex track in the existing standard method, effectively avoids the problem of time sequence staggering of a theoretical track and an actual track, and improves the accuracy of track accuracy evaluation.
In order to achieve the purpose, the technical scheme adopted by the invention is an industrial robot trajectory analysis method based on continuous dynamic time warping, which comprises the following steps:
1) based on the idea of dynamic programming, searching the best matching points in the two sequences step by step; defining a theoretical trajectory P { (X) of an industrial robot1,Y1),…(Xi,Yi),…(Xm,Ym) And the actual trajectory p { (x {)1,y1),…(xj,yj),…(xn,yn) Definition d (i, j) denotes PiAnd pjThe distance formula of every two data points between the theoretical track and the actual track of the industrial robot is obtained by the distance between the two points as follows:
2) the cumulative distance matrix D for defining the track of the industrial robot is a similarity measure value of two track sequences, namely the cumulative distance between two sequence points, and the smaller the distance is, the more similar the two points are, and the higher the matching degree is. Firstly, defining a first row and a first column of a matrix, secondly, defining internal elements of the matrix, and obtaining a complete accumulative distance matrix in a recursion mode:
D(1,1)＝d(1,1)
D(m,1)＝d(m,1)+D(m-1,1)
D(1,n)＝d(1,n)+D(1,n-1)
D(m,n)＝d(m,n)+min{D(m-1,n),D(m-1,n-1),D(m,n-1)}
3) inserting two sequences of a robotValue, for two trajectory curves C to be mapped1And C2The linear interpolation model is described by the arc length parameterization, and the interpolation points on the curve respectively correspond to r1And r2，r1Is curve C1Upper point (x)1(i-1),y1(i-1)) and a point (x)1(i),y1(i) Interpolation points between r)2Is curve C2Upper point (x)2(i-1),y2(i-1)) and a point (x)2(i),y2(i) Interpolation points between). Curve C1And C2The point coordinate equation of (a) is:
wherein:
4) define regular path ω ═ w1,···wt,···wT]TWherein w ist＝[i j]，ωtIs the t-th element on the regular path ω, representing the point PiAnd pjAnd establishing a corresponding relation. The regular path meets a certain optimization strategy, and the back and forth searching is carried out through a backtracking method, so that the cumulative distance between the two sequences is minimum. The preferred strategy for defining the regular path ω is:
boundary property: the regular path ω is found starting from the last point D (m, n) and ending at the first point D (1, 1).
Monotonic continuity: the regular path ω looks for the element point with the smallest cumulative distance D from D (m, n) to the interpolation point direction between the lines below, to the left, or below.
A regular path with the minimum accumulated distance along the path can be found through the constraint conditions, and the optimal matching between two sequence track points of the robot is realized.
(5) Calculating the maximum Euclidean distance AT between the mapping points of the P sequence and the P sequence AT the momentpFor trajectory accuracy:
at this time, i and j represent the theoretical track point and the actual track point of the robot with the mapping relation established in the regular path.
Compared with the prior art, the invention has the following beneficial effects: by adopting the CDTW algorithm and analyzing the mapping of the track of the industrial robot, the problem of large track measurement error caused by mapping error between an instruction track and an actual track point due to the influence of the motion speed and the motion deviation of the robot, the sampling frequency of a measurement system and the measurement error during the plane construction by a nonlinear track method is solved. By measuring and analyzing the accuracy of the track of the industrial robot and comparing the accuracy with the evaluation method in the international standard ISO9283, the problem of mapping errors in the standard method can be effectively solved, and the accuracy of the track is improved.
Drawings
FIG. 1 is a schematic diagram of a robot trajectory measuring method
FIG. 2 is a diagram of theoretical movement locus of robot
FIG. 3 is a diagram of the actual movement locus of the robot
FIG. 4 is a warping path diagram
FIG. 5 is a diagram of a CDTW algorithm trajectory mapping method
FIG. 6 is a diagram of ISO method trajectory mapping method
FIG. 7 is a graph comparing the results of trajectory accuracy
Detailed Description
The invention is further described with reference to the following figures and detailed description.
The track of the industrial robot is measured by a laser tracker, and a measuring system is shown in figure 1. The system comprises 1-an industrial robot, 2-a laser tracker, 3-a target ball and 4-an upper computer.
A test trajectory is compiled from an alternative test trajectory data set specified in the ISO standard, the trajectory lying in a standard test plane of the industrial robot workspace range and comprising a combination of linear, circular and corner motions. The robot first executes a straight track with coordinates (400, -50,750) at the starting point P1 and coordinates (450, -50,750) at the arrival point P2. Then, a round corner of a circular arc type is performed, and the corner is set to be 5 mm. Finally, a straight line trajectory is executed, and the end point P3 is (450,0, 750).
Communication with the robot system is established through the upper computer, and a theoretical motion track of the robot is obtained in real time, wherein the theoretical motion track x (t) is shown in fig. 2. The actual movement track of the robot is obtained by the laser tracker, and the actual track data x (t) is shown in fig. 3. The sampling frequency of the upper computer and the laser tracker is set to be fn＝50Hz。
Take 50 pairs of data points at the corner locus for analysis. And projecting the actual track and the theoretical track into a two-dimensional coordinate system, wherein the coordinate values of the actual track are marked on the horizontal axis, the coordinate values of the theoretical track are marked on the vertical axis, and each intersection point (i, j) represents the relationship between the ith point on the actual track and the jth point on the theoretical track in a grid formed by the intersection line of the horizontal axis and the vertical axis.
Defining the number of data points of the two tracks as M and N respectively, and calculating the distance between the two track points:
constructing an M multiplied by N cumulative distance matrix D, each item coefficient D in the matrixi,jFor the cumulative distance of the mapping between the actual track point i and the theoretical track point j, the smaller the distance is, the higher the similarity of the mapping between the two points is. The elements in definition D are as follows:
Di,jthe starting points of (1) are:
D1,1＝d(1,1)
the elements of the first row are defined as:
D1,j＝d(1,j)+D1,j-1
the elements of the first column are defined as:
Di,1＝d(i,1)+Di-1,1
the other parts are defined as:
Di,j＝d(i,j)+min{Di-1,j,Di-1,j-1,Di,j-1}
and finding the corresponding relation between the actual track point and the theoretical track point according to a backtracking method, namely, regulating the path. Regular path ω ═ w1,···wt,···wT]TWherein w ist＝[i j]，ωtThe t-th element on the regular path omega represents the mapping established by the two track points. For matrix D, from the last element DM,NAt the beginning, along DM-1,M，DM,N-1，DM-1,N-1The node with the minimum value is searched for the next optimal point in the direction until D1,1The point ends. The warping path ω can be plotted on the grid points established in step 4, with the result shown in fig. 4.
Partial points on the theoretical track and the actual track of the robot do not meet one-to-one mapping, and a situation of mapping one point at multiple points occurs, as shown in table 1, so that the similarity metric value between the two tracks is increased, and the track accuracy is reduced.
TABLE 1 Multi-Point mapping between Trace points
Interpolating between the many-to-one mapped data points by a linear interpolation model:
it is composed of
The coordinate of the interpolation point can be determined by defining the size of the parameter delta, and the invention ensures that
The interpolated point is made to be the midpoint of the two points.
Interpolating points (x) according to the mapping situationδ,yδ,zδ) Inserting the data into the original data of the actual track or the theoretical track, recalculating the distance D (i, j) between the two tracks, calculating to obtain an accumulated distance matrix D, and searching the regular path omega through a backtracking method in an optimizing way until all points meet the one-to-one mapping. The mapping relationship between the command track and the actual track mapped by the CDTW algorithm is shown in fig. 5.
And calculating the track accuracy. Trajectory accuracy ATPThe maximum value of the distance between the corresponding points, the results are shown in table 2.
TABLE 2 trajectory accuracy results of the CDTW algorithm
And (4) performing track accuracy calculation comparison analysis by adopting an ISO method. In the standard, s points are selected along an instruction track and a normal plane of the instruction track is calculated, and the maximum value AT of the distance between the average value of intersection point coordinates of r actual measurement tracks and the normal plane and the instruction trackPPosition trajectory accuracy. Constructing tangent line vector e (i) ═ e between actual track pointsx(i),ey(i),ez(i)]Wherein e isx(i)＝x(i+1)-x(i)，ey(i)＝y(i+1)-y(i)，ez(i) Z (i +1) -z (i). Constructing the normal plane equation D (i) ═ e perpendicular to the tangentx(i)x(i)+ey(i)y(i)+ez(i) z (i), calculating the intersection point (x) of the law plane and the theoretical trajectory0(i),y0(i),z0(i) ). The actual track point and the intersection point are connected to obtain a mapping relation as shown in fig. 6, the track accuracy result is shown in table 3, and the track accuracy result pair after the ISO standard method and the CDTW algorithm are mapped is shown in fig. 7.
TABLE 3 Trace accuracy results for ISO method
The CDTW algorithm adopted in the invention in FIG. 5 not only can not generate the mapping error problem, but also can map the actual track point of the robot to the non-reference point of the theoretical track due to the existence of the interpolation point, and the situation of mapping a plurality of points at one point can not occur. As can be seen in fig. 6, when the robot executes a corner track, the shape of the actual track differs from the shape of the command track to some extent due to the influence of the robot movement speed and the robot movement deviation, and the ISO track mapping method has distortion of the time sequence, which causes mapping errors.
The measurement errors at points 20-30 in FIG. 7 are due to mapping errors of the ISO method, resulting in larger trajectory errors. The CDTW algorithm solves this problem by interpolating points, and the error curve is smoother. From tables 2 and 3, it can be calculated that the accuracy of the trajectory after the CDTW algorithm mapping is improved by 73% and the standard deviation is reduced by 86%. The CDTW algorithm solves the problem of track mapping errors, improves the track accuracy and obviously reduces the overall fluctuation range of errors.
In summary, the above is only a preferred embodiment of the present invention, and is not limited to the protection scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (2)
1. An industrial robot trajectory analysis method based on continuous dynamic time warping is characterized in that: the method comprises the following steps:
1) based on the idea of dynamic programming, searching matched points in the two sequences step by step; defining a theoretical trajectory P { (X) of an industrial robot1,Y1),…(Xi,Yi),…(Xm,Ym) And the actual trajectory p { (x {)1,y1),…(xj,yj),…(xn,yn) H, define the sum of d (i,j) represents PiAnd pjAnd (3) solving a distance formula between every two data points between the theoretical track and the actual track of the industrial robot according to the distance between the two points as follows:
2) defining an accumulated distance matrix D of the industrial robot track as a similarity metric value of two track sequences, namely the accumulated distance between two sequence points, wherein the smaller the distance is, the more similar the two points are, and the higher the matching degree is; firstly, defining a first row and a first column of a matrix, secondly, defining internal elements of the matrix, and obtaining a complete accumulative distance matrix in a recursion mode:
D(1,1)＝d(1,1)
D(m,1)＝d(m,1)+D(m-1,1)
D(1,n)＝d(1,n)+D(1,n-1)
D(m,n)＝d(m,n)+min{D(m-1,n),D(m-1,n-1),D(m,n-1)}
3) interpolating two sequences of the robot, and for two track curves C to be mapped1And C2The linear interpolation model is described by the arc length parameterization, and the interpolation points on the curve respectively correspond to r1And r2，r1Is curve C1Upper point (x)1(i-1),y1(i-1)) and a point (x)1(i),y1(i) Interpolation points between r)2Is curve C2Upper point (x)2(i-1),y2(i-1)) and a point (x)2(i),y2(i) Interpolation points between); curve C1And C2The point coordinate equation of (a) is:
Ck:
wherein:
4) define regular path ω ═ w1,…wt,…wT]TWherein w ist＝[i j]，ωtIs the t-th element on the regular path ω, representing the point PiAnd pjEstablishing a corresponding relation; the regular path omega meets the optimal strategy, and the back and forth searching is carried out through a backtracking method, so that the cumulative distance between the two sequences is minimum;
5) calculating the maximum Euclidean distance AT between the mapping points of the P sequence and the P sequence AT the momentpFor trajectory accuracy:
at this time, i and j represent the theoretical track point and the actual track point of the robot with the mapping relation established in the regular path.
2. The method for analyzing the trajectory of the industrial robot based on the continuous dynamic time warping as claimed in claim 1, wherein: the preferred strategy for the warping path ω in step 4) is as follows:
boundary property: the regular path omega is searched from the last point D (m, n) to the initial point D (1, 1);
monotonic continuity: the regular path omega searches an element point with the minimum accumulated distance D from D (m, n) to the direction of interpolation points between lines at the lower left, the left or the lower left;
and finding a regular path with the minimum accumulated distance along the path to realize the optimal matching between the two sequence track points of the robot.
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