CN111366392B - Method for measuring and calculating minimum positioning time of industrial robot - Google Patents

Method for measuring and calculating minimum positioning time of industrial robot Download PDF

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CN111366392B
CN111366392B CN202010251642.4A CN202010251642A CN111366392B CN 111366392 B CN111366392 B CN 111366392B CN 202010251642 A CN202010251642 A CN 202010251642A CN 111366392 B CN111366392 B CN 111366392B
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尹荣造
田坤淼
周文
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Borunte Robot Co Ltd
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Abstract

The invention relates to the field of minimum positioning time of robots, in particular to a method for measuring and calculating the minimum positioning time of an industrial robot, which comprises the steps of selecting five points P1-P5 in a working space of the robot, enabling a rectangular inclined plane formed by P2-P5 in the clockwise direction to occupy the working space of the robot to the maximum extent, enabling the P1 to be in the central position of a rectangular area surrounded by P2-P5, recording instruction coordinates and measurement coordinates, constructing a space coordinate transformation relation, enabling the robot to drive the robot to traverse at 100% rated speed/optimal speed, and recording space point location information of the tail end of the robot by sampling frequency; recording point location information of the tail end of the robot according to a sampling period, arranging the point location information in sequence according to time, and forming a space coordinate sequence after coordinate change; the product of the total number of the time sequence elements in the motion process and the sampling period is the minimum positioning time, and the average value of the minimum positioning time of 3 times of circulation is calculated; the method is used for measuring and calculating the minimum positioning time of the robot and has clear principle.

Description

Method for measuring and calculating minimum positioning time of industrial robot
Technical Field
The invention relates to the technical field of minimum positioning time of robots, in particular to a method for measuring and calculating the minimum positioning time of an industrial robot.
Background
Industrial robots have many characteristics such as universality, high flexibility and high precision, and are vigorously developed under the promotion of the intelligent trend of the global manufacturing industry. Currently, most industrial robots are controlled in an open loop mode, and in order to ensure the end precision of the robot, calibration and calibration are required before leaving a factory or after the robot is used for a period of time. The minimum time required for the robot to complete the full per-command execution is measured in terms of the minimum positioning time. The minimum positioning time is the time that the robot moves a preset distance from a rest state and/or swings a certain angle to reach a stable state in a point position control mode and the actual distance of the robot. To obtain the minimum positioning time, the speed used for the experiment was chosen to be 100% of the nominal speed, and the test should be performed at the optimum speed for each part of the cycle. The national standard gives stability definition and requirements, but does not have detailed explanatory documents and steps, and the existing measuring system is assisted by a high-precision measuring instrument, but the internal principle of measurement and the data processing mechanism are unclear.
Disclosure of Invention
The present invention aims to provide a method for measuring and calculating the minimum positioning time of an industrial robot, so as to solve the problems in the background technology.
In order to achieve the purpose, the invention provides the following technical scheme:
a method for measuring and calculating the minimum positioning time of an industrial robot comprises the following steps:
step 1, selecting five points P1, P2, P3, P4 and P5 in a working space of the robot, enabling a rectangular inclined plane formed by P2-P5 in a clockwise direction to occupy the working space of the robot to the maximum extent, recording instruction coordinates and measurement coordinates in the central position of a rectangular area surrounded by P2-P5 by P1, and constructing a space coordinate conversion relation;
step 2, selecting points on a diagonal line P2-P4 of the inscribed cuboid of the robot: P-P1+1—P1+2—P1+3—P1+4—P1+5—P1+6—P1+7；
Step 3, the robot drives the robot to traverse the P-P at 100% rated speed/optimal speed1+1—P1+2—P1+3—P1+4—P1+5—P1+6—P1+7Recording space point location information of the tail end of the robot by using a laser tracker at a set sampling frequency;
step 4, reaching P1+7Staying for 5 seconds, returning to the point P, staying for 5 seconds, and repeating the step 1 for two times;
step 5, recording point location information of the tail end of the robot according to a sampling period, arranging the point location information in sequence according to time, and forming a space coordinate sequence after coordinate change;
step 6, solving a first-order difference of the distance between adjacent points to form a time sequence of the speed, setting a threshold, comparing the size of the threshold and the time sequence, counting, and dividing the time sequence, the space coordinate sequence and the speed sequence corresponding to the robot in the 3-segment circulation process according to the counting value;
and 7, the product of the total number of the time sequence elements in the motion process and the sampling period is the minimum positioning time, and the average value of the minimum positioning time of 3 times of circulation is calculated.
Further, the coordinate system conversion method is as follows:
any point PiMatrix representation of coordinates:
the robot terminal instruction coordinate point set is as follows:
Figure GDA0003236730230000021
formed by points corresponding to points measured by the measuring apparatusPoint set:
Figure GDA0003236730230000022
further, the coordinate system conversion method is as follows:
(1) separately computing a set of points Pr、PtThe barycenter of (1), i.e. the average of the coordinates of all points included in the point set, is:
Figure GDA0003236730230000023
(2) aligning and superposing the centers of gravity of the two point sets, and respectively calculating the relative coordinates of the point sets relative to the center of gravity to form a new point set
Figure GDA0003236730230000024
Recording:
Figure GDA0003236730230000025
comprises the following steps:
Figure GDA0003236730230000026
Figure GDA0003236730230000031
recording:
Figure GDA0003236730230000032
comprises the following steps:
Figure GDA0003236730230000033
(3) set of points
Figure GDA0003236730230000034
Constructing co-matrices
Figure GDA0003236730230000035
Carrying out SVD on the co-matrix:
Figure GDA0003236730230000036
(4) the rotation matrix is R3×3＝VUTTranslation matrix is T3×1＝μr-Rμt，
When n is more than or equal to 3, the R matrix can be obtained, and each column of R is a unit vector with the length of 3 and is mutually vertical in pairs.
Further, the minimum positioning time is calculated as:
sampled by the measuring instrument and having a spatial coordinate sequence of Pt＝{Pt i|(xt i,yt i,zt i) 1,2,3, N, and transforming the spatial coordinate sequence of the measuring instrument into a spatial sequence under a robot coordinate system through a space transformation method
Figure GDA0003236730230000037
Further, the minimum positioning time is calculated as:
(1) speed sequence
The product of the first difference of the distance between two adjacent points in the position sequence and the sampling frequency Fs is the speed sequence
Vi＝Si·Fs，i＝1,2,3...,N-1
In the formula: si＝cond(△Pi)2
△Pi＝Pi+1-Pi＝(xi+1,yi+1,zi+1)-(xi,yi,zi)＝(dxi,dyi,dzi)；
(2)ViRecording the speed sequence of the whole testing process, wherein the speed sequence stays for a short time in each section of the circulating process, the number of times of round trip is judged according to the speed, and then the time sequence of each circulating moving process is judged, and the difference between the number of the speed sequence elements and the number of the time sequence elements is 1, so that the time of the telecontrol section can be converted into the number of the speed sequence elements of each moving section;
(3) traverse the whole velocity sequence ViJudging 10 continuous elements of the speed sequence, wherein the first 5 elements are less than the threshold value, and the last 5 elements are all greater than the threshold value, recording the continuous elements as the index [ k ] of the moving point subscript]I +5, whereas if the first 5 occurrences are all greater than the threshold and the last 5 occurrences are less than the threshold, then record as the stationary index [ p ]]＝i+5；
(4) The number of test points of the minimum positioning time is c, the number of elements of each motion segment is L (n) ═ ind [ p + c ] -ind [ p ] +1, p ═ 1, c +2, 2c +2,. once, and n is the cycle number;
(5) the time of each motion segment is: time (n) ═ Fs · (l (n) +1) n is the cycle number, and the minimum positioning time is:
Figure GDA0003236730230000041
the user can adjust the number of cycles based on the method according to specific needs.
Compared with the prior art, the invention has the beneficial effects that:
the invention aims to provide a measuring and calculating method for the minimum positioning time of a robot. Firstly, converting data obtained by a measuring instrument into a robot coordinate system through coordinate conversion, solving a speed sequence according to a coordinate sequence, counting and distinguishing the number of sequence elements of each telecontrol segment by using the speed sequence, wherein the speed sequence is in one-to-one correspondence with a time sequence, the former is 1 less than the latter, the quotient of the number of the elements of the speed sequence of each motion segment plus 1 and the sampling frequency is the time of each motion segment, and the average value of the time of all the motion segments is the minimum positioning time. The sampled spatial point location data are discrete data, and the time precision of the method depends on the sampling frequency of a measuring instrument.
Drawings
Fig. 1 is a schematic diagram of a calculation process of the minimum positioning time according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it should be noted that the terms "upper/lower end", "inner", "outer", "front end", "rear end", "both ends", "one end", "the other end", and the like indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be configured in a specific orientation, and operate, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "disposed/sleeved," "connected," and the like are to be construed broadly, e.g., "connected," which may be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Referring to fig. 1, the present invention provides a technical solution:
the measuring method comprises the following steps:
(1) in the working space of the robot, five points P1\ P2\ P3\ P4\ P5 are selected, a rectangular inclined plane formed by P2-P5 in the clockwise direction can occupy the working space of the robot to the maximum extent, and the central position of a rectangular area surrounded by P2-P5 of P1 is recorded with instruction coordinates and measurement coordinates, so that a space coordinate conversion relation is constructed.
TABLE 1 Experimental pose and distance of minimum positioning time
Figure GDA0003236730230000051
TABLE 2 Experimental conditions for minimum positioning time
Figure GDA0003236730230000052
Figure GDA0003236730230000061
(2) Selecting points on a diagonal (P2-P4) of the inscribed cuboid of the robot: P-P1+1—P1+2—P1+3—P1+4—P1+5—P1+6—P1+7；
(3) Robot driven robot traversal P-P with 100% nominal/optimal speed1+1—P1+2—P1+3—P1+4—P1+5—P1+6—P1+7Recording space point location information of the tail end of the robot by using a laser tracker at a set sampling frequency;
(4) to reach P1+7Staying for 5 seconds, returning to the point P, staying for 5 seconds, and repeating the step (1) for 2 times;
(5) recording point location information of the tail end of the robot according to a sampling period, arranging the point location information in sequence according to time, and forming a space coordinate sequence after coordinate change;
(6) solving a first-order difference of the distance between adjacent points to form a time sequence of the speed, setting a threshold, comparing the size of the threshold and the time sequence, counting, and dividing the time sequence, the space coordinate sequence and the speed sequence corresponding to the robot in the 3-stage circulation process according to the counting value;
(7) the product of the total number of the time sequence elements in the motion process and the sampling period is the minimum positioning time, and the average value of the minimum positioning time of 3 times of circulation is calculated;
secondly, a coordinate system conversion method:
any point PiMatrix representation of coordinates:
the robot terminal instruction coordinate point set is as follows:
Figure GDA0003236730230000062
instructing a point set consisting of points corresponding to the points measured by the measuring instrument:
Figure GDA0003236730230000063
(1) separately computing a set of points Pr、PtThe barycenter of (1), i.e. the average of the coordinates of all points included in the point set, is:
Figure GDA0003236730230000064
(2) aligning and superposing the centers of gravity of the two point sets, and respectively calculating the relative coordinates of the point sets relative to the center of gravity to form a new point set
Figure GDA0003236730230000071
Recording:
Figure GDA0003236730230000072
comprises the following steps:
Figure GDA0003236730230000073
Figure GDA0003236730230000074
recording:
Figure GDA0003236730230000075
comprises the following steps:
Figure GDA0003236730230000076
(3) set of points
Figure GDA0003236730230000077
Constructing co-matrices
Figure GDA0003236730230000078
Carrying out SVD on the co-matrix:
Figure GDA0003236730230000079
(4) the rotation matrix is R3×3＝VUTTranslation matrix is T3×1＝μr-Rμt，
When n is more than or equal to 3, the R matrix can be obtained, and each column of R is a unit vector with the length of 3 and is mutually vertical in pairs. To ensure goodness of fit, n is taken to be 5. The number of points may be increased as necessary.
And thirdly, calculating the minimum positioning time:
sampled by the measuring instrument and having a spatial coordinate sequence of Pt＝{Pt i|(xt i,yt i,zt i) 1,2,3, N, and transforming the spatial coordinate sequence of the measuring instrument into a spatial sequence under a robot coordinate system through a space transformation method
Figure GDA00032367302300000710
(1) Speed sequence
The product of the first difference of the distance between two adjacent points in the position sequence and the sampling frequency Fs is the speed sequence
Vi＝Si·Fs，i＝1,2,3...,N-1
In the formula: si＝cond(△Pi)2
△Pi＝Pi+1-Pi＝(xi+1,yi+1,zi+1)-(xi,yi,zi)＝(dxi,dyi,dzi)
(2)ViThe recorded speed sequence of the whole testing process has short stay in each section of the circulating process, the number of times of round trip is judged according to the speed, and the time sequence of the moving process of each circulation is further judged, because the difference between the number of the speed sequence elements and the number of the time sequence elements is 1, the time sequence is obtainedThe time of the telecontrol segment can be converted into the number of the speed sequence elements of each motion segment. The calculation flow chart is shown in the attached drawing.
(3) Traverse the whole velocity sequence ViJudging 10 continuous elements of the speed sequence, wherein the first 5 elements are less than the threshold value, and the last 5 elements are all greater than the threshold value, recording the continuous elements as the index [ k ] of the moving point subscript]I +5, whereas if the first 5 occurrences are all greater than the threshold and the last 5 occurrences are less than the threshold, then record as the stationary index [ p ]]＝i+5；
(4) The number of test points of the minimum positioning time is c, the number of elements of each motion segment is l (n) ═ ind [ p + c ] -ind [ p ] +1, p ═ 1, c +2, 2c + 2.
(5) The time of each motion segment is: time (n) ═ Fs · (l (n) +1) n is the cycle number, and the minimum positioning time is:
Figure GDA0003236730230000081
the user can adjust the number of cycles according to the specific requirements based on the method.
The invention aims to provide a measuring and calculating method for the minimum positioning time of a robot. The method comprises the steps of firstly converting data obtained by a measuring instrument into a robot coordinate system through coordinate conversion, solving a speed sequence according to a coordinate sequence, counting and distinguishing the number of sequence elements of each telecontrol segment by using the speed sequence, wherein the speed sequence is in one-to-one correspondence with a time sequence, the speed sequence is 1 less than the time sequence, the quotient of the sampling frequency and the number of the elements of the speed sequence of each motion segment after adding 1 is the time of each motion segment, and the average value of the time of all the motion segments is the minimum positioning time. The sampled spatial point location data are discrete data, and the time precision of the method depends on the sampling frequency of a measuring instrument.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (5)

1. A method for measuring and calculating the minimum positioning time of an industrial robot is characterized by comprising the following steps:
step 1, selecting five points P1, P2, P3, P4 and P5 in a working space of the robot, enabling a rectangular inclined plane formed by P2-P5 in a clockwise direction to occupy the working space of the robot to the maximum extent, recording instruction coordinates and measurement coordinates in the central position of a rectangular area surrounded by P2-P5 by P1, and constructing a space coordinate conversion relation;
step 2, selecting points on a diagonal line P2-P4 of the inscribed cuboid of the robot: P-P1+1—P1+2—P1+3—P1+4—P1+5—P1+6—P1+7；
Step 3, the robot drives the robot to traverse the P-P at 100% rated speed/optimal speed1+1—P1+2—P1+3—P1+4—P1+5—P1+6—P1+7Recording space point location information of the tail end of the robot by using a laser tracker at a set sampling frequency;
step 4, reaching P1+7Staying for 5 seconds, returning to the point P, staying for 5 seconds, and repeating the step 1 for two times;
step 5, recording point location information of the tail end of the robot according to a sampling period, arranging the point location information in sequence according to time, and forming a space coordinate sequence after coordinate change;
step 6, solving a first-order difference of the distance between adjacent points to form a time sequence of the speed, setting a threshold, comparing the size of the threshold and the time sequence, counting, and dividing the time sequence, the space coordinate sequence and the speed sequence corresponding to the robot in the 3-segment circulation process according to the counting value;
and 7, the product of the total number of the time sequence elements in the motion process and the sampling period is the minimum positioning time, and the average value of the minimum positioning time of 3 times of circulation is calculated.
2. Method for measuring and calculating a minimum positioning time of an industrial robot according to claim 1, characterized in that the coordinate system transformation method is as follows:
any point PiMatrix representation of coordinates:
the robot terminal instruction coordinate point set is as follows:
Figure FDA0003236730220000011
instructing a point set consisting of points corresponding to the points measured by the measuring instrument:
Figure FDA0003236730220000012
3. a method for measuring and calculating a minimum positioning time of an industrial robot according to claim 2, characterized in that the coordinate system transformation method is as follows:
(1) separately computing a set of points Pr、PtThe barycenter of (1), i.e. the average of the coordinates of all points included in the point set, is:
Figure FDA0003236730220000021
(2) aligning and superposing the centers of gravity of the two point sets, and respectively calculating the relative coordinates of the point sets relative to the center of gravity to form a new point set
Figure FDA0003236730220000022
Recording:
Figure FDA0003236730220000023
comprises the following steps:
Figure FDA0003236730220000024
Figure FDA0003236730220000025
recording:
Figure FDA0003236730220000026
comprises the following steps:
Figure FDA0003236730220000027
(3) set of points
Figure FDA0003236730220000028
Constructing co-matrices
Figure FDA0003236730220000029
Carrying out SVD on the co-matrix:
Figure FDA00032367302200000210
(4) the rotation matrix is R3×3＝VUTTranslation matrix is T3×1＝μr-Rμt，
When n is more than or equal to 3, the R matrix can be obtained, and each column of R is a unit vector with the length of 3 and is mutually vertical in pairs.
4. A method for measuring and calculating a minimum positioning time of an industrial robot according to claim 1, characterized in that the minimum positioning time is calculated as:
sampled by the measuring instrument and having a spatial coordinate sequence of Pt＝{Pt i|(xt i,yt i,zt i) 1,2,3, N, and the spatial sequence of the measuring instrument spatial coordinate sequence after spatial transformation to the robot coordinate system is P { (x)i,yi,zi)Pr i＝R·Pi t+T}。
5. Method for measuring and calculating a minimum positioning time of an industrial robot according to claim 4, characterized in that the minimum positioning time is calculated as:
(1) speed sequence
The product of the first difference of the distance between two adjacent points in the position sequence and the sampling frequency Fs is the speed sequence
Vi＝Si·Fs，i＝1,2,3...,N-1
In the formula: si＝cond(△Pi)2
△Pi＝Pi+1-Pi＝(xi+1,yi+1,zi+1)-(xi,yi,zi)＝(dxi,dyi,dzi)；
(2)ViRecording the speed sequence of the whole testing process, wherein the speed sequence stays for a short time in each section of the circulating process, the number of times of round trip is judged according to the speed, and then the time sequence of each circulating moving process is judged, and the difference between the number of the speed sequence elements and the number of the time sequence elements is 1, so that the time of the telecontrol section can be converted into the number of the speed sequence elements of each moving section;
(3) traverse the whole velocity sequence ViJudging 10 continuous elements of the speed sequence, wherein the first 5 elements are less than the threshold value, and the last 5 elements are all greater than the threshold value, recording the continuous elements as the index [ k ] of the moving point subscript]I +5, whereas if the first 5 occurrences are all greater than the threshold and the last 5 occurrences are less than the threshold, then record as the stationary index [ p ]]＝i+5；
(4) The number of test points of the minimum positioning time is c, the number of elements of each motion segment is L (n) ═ ind [ p + c ] -ind [ p ] +1, p ═ 1, c +2, 2c +2,. once, and n is the cycle number;
(5) the time of each motion segment is: time (n) ═ Fs · (l (n) +1) n is the cycle number, and the minimum positioning time is:
Figure FDA0003236730220000031
the user can adjust the number of cycles based on the method according to specific needs.
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