CN117124336A - Two-step absolute positioning error compensation method and system for serial robots - Google Patents
Two-step absolute positioning error compensation method and system for serial robots Download PDFInfo
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- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
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Abstract
The application discloses a two-step absolute positioning error compensation method and a system for serial robots, wherein the method comprises the following steps: acquiring positioning error coordinates of a robot, randomly sampling and selecting a plurality of groups of point positions, taking relative coordinates of the point positions relative to the initial position of the tail end of the robot as input quantity, solving a required joint rotation angle by using a serial robot inverse kinematics model on the premise of restraining joint gestures, driving the robot by using the solved joint rotation angle, updating the gesture joint rotation angle, driving the robot, acquiring the positioning error coordinates of the serial robot after the first compensation, constructing a serial robot positioning error prediction model after the first compensation, and acquiring the positioning coordinates of the serial robot after the second compensation. The application can simultaneously compensate the absolute positioning error caused by the geometrical parameter error of the serial robot and the time-varying joint clearance. The method and the system for compensating the absolute positioning error of the serial robots in two steps can be widely applied to the technical field of robot positioning.
Description
Technical Field
The application relates to the technical field of robot positioning, in particular to a two-step absolute positioning error compensation method and system for serial robots.
Background
In recent years, with the rapid development of the robot industry, robots are being applied in mass to the industrial fields of assembly, palletizing, loading and unloading, parts processing, and the like. The serial robots have large working space and high flexibility and are most widely applied in the industrial field; at present, the repeated positioning precision of the serial robots is high, namely about +/-0.02 mm, the absolute positioning precision is low, namely about +/-1-2 mm, and the requirement of fine assembly with high positioning precision is difficult to meet; therefore, there is a need to improve the absolute positioning accuracy of tandem robots;
the error compensation method generates new errors through artificial means and counteracts the original errors of robots, is a main method for improving the absolute positioning accuracy of serial robots, and is currently commonly used as a kinematic calibration method.
Disclosure of Invention
In order to solve the technical problems, the application aims to provide the two-step absolute positioning error compensation method and system for the serial robots, which do not need to accurately model the time-varying joint gaps, and realize the absolute positioning error caused by compensating the geometric parameter error of the robots and the time-varying joint gaps, thereby improving the absolute positioning accuracy of the serial robots.
The first technical scheme adopted by the application is as follows: the two-step absolute positioning error compensation method for the serial robots comprises the following steps:
determining a working space of the serial robots and acquiring positioning error coordinates of the serial robots;
constructing an error jacobian matrix according to the positioning error coordinates of the serial robots, and performing decomposition identification processing to obtain error identification results of the lengths of the connecting rods of the serial robots;
acquiring an updated pose joint corner according to the error identification result of the length of each connecting rod of the serial robots and driving the serial robots to move to obtain a first serial robot positioning error coordinate compensation result;
based on the first serial robot positioning error coordinate compensation result, acquiring serial robot positioning error coordinates after the first compensation;
carrying out vector decomposition on the positioning error coordinates of the serial robots after the first compensation to obtain a space coordinate system error vector of the serial robots;
constructing a serial robot positioning error prediction model after serial first compensation based on a spatial coordinate system error vector of the serial robot;
and acquiring the serial robot positioning coordinates after the second compensation based on the serial robot positioning error prediction model after the first compensation, and guiding the serial robots to move according to the serial robot positioning coordinates after the second compensation.
Further, the step of determining the working space of the tandem robot specifically includes:
constructing a space rectangular coordinate system of the serial robots according to the space positions of the serial robots;
determining the corner range of each joint of the serial robots according to the space rectangular coordinate system of the serial robots;
according to the rotation angle range of each joint of the serial robots, solving the pose of each joint of the serial robots by a DH method to construct a positive kinematic model of the serial robots;
sampling by pseudo-random numbers according to the rotation angle range of each joint of the serial robots, and arranging and combining sampling results to obtain a joint space of random sampling of the serial robots;
and determining the working space of the serial robots by combining the positive kinematic model of the serial robots and the joint space randomly sampled by the serial robots.
Further, the step of obtaining the positioning error coordinates of the serial robots specifically includes:
based on the working space of the serial robots, acquiring information of the tail ends of all joints of the serial robots through a laser tracker to obtain initial coordinates of the tail ends of all joints of the serial robots;
constructing position and posture constraint conditions of joints of the serial robots based on the working space of the serial robots;
establishing an inverse kinematics model of the serial robots, and performing inverse kinematics solution on the serial robots according to the constraint conditions of the joint poses of the serial robots to obtain first pose joint corners corresponding to the joint poses of the serial robots;
driving the serial robots to move according to the first pose joint corners, and acquiring information of the tail ends of all joints of the serial robots through a laser tracker to obtain actual coordinates of the tail ends of all joints of the serial robots;
and performing difference calculation on the actual coordinates of the tail ends of the joints of the serial robots and the initial coordinates of the tail ends of the joints of the serial robots to obtain the positioning error coordinates of the serial robots.
Further, the step of constructing an error jacobian matrix according to the positioning error coordinates of the serial robots and performing decomposition identification processing to obtain an error identification result of the length of each connecting rod of the serial robots specifically comprises the following steps:
based on a differential transmission principle of the positioning errors of the serial robots, an error jacobian matrix of the serial robots is constructed, wherein the error jacobian matrix represents a partial differential relation between the positioning error coordinates of the serial robots and the errors of the lengths of all connecting rods of the serial robots;
performing orthogonal triangular decomposition on the error jacobian matrix of the serial robots to obtain decomposed error jacobian matrix parameters;
eliminating error Jacobian matrix parameters smaller than a preset threshold value to obtain error Jacobian matrix with redundant parameters removed;
combining the error Jacobian matrix for removing redundant parameters and the positioning error coordinates of the serial robots, and identifying by a least square method to obtain the errors of the lengths of the connecting rods of the serial robots;
and obtaining the theoretical errors of the lengths of the connecting rods of the serial robots and adding the theoretical errors with the errors of the lengths of the connecting rods of the serial robots to obtain the error identification result of the lengths of the connecting rods of the serial robots.
Further, the step of obtaining an updated pose joint angle according to the error identification result of the length of each connecting rod of the serial robots and driving the serial robots to move to obtain a first serial robot positioning error coordinate compensation result specifically comprises the following steps:
substituting the error identification result of the length of each connecting rod of the serial robot into the serial robot positive kinematics model to obtain an updated pose joint corner;
driving the serial robots to move according to the updated pose joint corners, and acquiring information of the tail ends of all joints of the serial robots through a laser tracker to obtain coordinates of the tail ends of all joints of the serial robots after the first correction;
and performing difference processing on the coordinates of the tail ends of the joints of the first corrected serial robots and the actual coordinates of the tail ends of the joints of the serial robots to obtain a first serial robot positioning error coordinate compensation result.
Further, the step of obtaining the first compensated positioning error coordinates of the serial robots based on the first serial robot positioning error coordinates compensation result specifically includes:
defining a traveling included angle of the serial robots based on the first serial robot positioning error coordinate compensation result, wherein the traveling included angle of the serial robots represents an included angle between a vertical plane and a XoZ plane;
driving the serial robots to perform linear motion according to the traveling included angles of the serial robots to obtain displacement coordinates of the tail ends of all joints of the serial robots;
the serial robots are subjected to inverse kinematics solution according to the error identification result of the lengths of the connecting rods of the serial robots and the displacement coordinates of the tail ends of the joints of the serial robots, so that the second pose joint corners of the serial robots are obtained;
substituting the second pose joint rotation angle into a serial robot positive kinematics model to obtain theoretical coordinates of the tail ends of all joints of the serial robots;
driving the serial robots to move according to the second pose joint corners of the serial robots, and acquiring the actual coordinates of the tail ends of all joints of the serial robots through a laser tracker;
and carrying out difference processing on the theoretical coordinates of the tail ends of all joints of the serial robots and the actual coordinates of the tail ends of all joints of the serial robots to obtain the positioning error coordinates of the serial robots after the first compensation.
Further, the step of performing vector decomposition on the positioning error coordinates of the serial robots after the first compensation to obtain a spatial coordinate system error vector of the serial robots specifically includes:
carrying out vector decomposition on the positioning error coordinates of the serial robots after the first compensation to obtain horizontal plane error vectors of the serial robots and Z-axis direction error vectors of the serial robots;
performing vector decomposition on the horizontal plane error vectors of the serial robots to obtain an x-axis direction error vector of the serial robots and a Y-axis direction error vector of the serial robots;
and integrating the X-axis direction error vector of the serial robots, the Y-axis direction error vector of the serial robots and the Z-axis direction error vector of the serial robots to obtain a space coordinate system error vector of the serial robots.
Further, the step of constructing a serial robot positioning error prediction model after serial first compensation based on the spatial coordinate system error vector of the serial robot specifically comprises the following steps:
performing numerical fitting treatment on the space coordinate system error vectors of the serial robots through polynomial functions to obtain a numerical fitting relation, wherein the numerical fitting relation represents a fitting relation between coefficients of the polynomial functions, a traveling included angle of the serial robots and a vertical plane;
substituting the numerical fitting relation into a polynomial function to construct a serial robot positioning error prediction model after serial first compensation.
Further, the step of obtaining the positioning coordinates of the serial robot after the second compensation based on the serial robot positioning error prediction model after the first compensation specifically includes:
predicting the positioning error of the first compensated serial robot according to the serial robot positioning error prediction model after the first compensation serial;
the series robot feedforward compensation quantity is constructed by combining the series robot inverse kinematics model and the error identification result of the length of each connecting rod of the series robot;
performing secondary compensation processing on the serial robot positioning error after the first compensation according to the feedforward compensation quantity of the serial robot to obtain serial robot positioning coordinates after the second compensation
The second technical scheme adopted by the application is as follows: an absolute positioning error two-step compensation system for a tandem robot, comprising:
the determining module is used for determining the working space of the serial robots and acquiring the positioning error coordinates of the serial robots;
the identification module is used for constructing an error jacobian matrix according to the positioning error coordinates of the serial robots and performing decomposition identification processing to obtain error identification results of the lengths of the connecting rods of the serial robots;
the driving module is used for acquiring an updated pose joint corner according to the error identification result of the length of each connecting rod of the serial robots and driving the serial robots to move so as to obtain a first serial robot positioning error coordinate compensation result;
the primary compensation module is used for acquiring the positioning error coordinates of the serial robots after the primary compensation based on the positioning error coordinate compensation results of the serial robots;
the decomposing module is used for carrying out vector decomposition on the positioning error coordinates of the serial robots after the first compensation to obtain a space coordinate system error vector of the serial robots;
the construction module is used for constructing a series robot positioning error prediction model after series first compensation based on the spatial coordinate system error vector of the series robot;
the secondary compensation module is used for acquiring the serial robot positioning coordinates after the secondary compensation based on the serial robot positioning error prediction model after the first compensation and guiding the serial robots to move according to the serial robot positioning coordinates after the second compensation.
The method and the system have the beneficial effects that: according to the application, the working space of the serial robots is determined, the positioning error coordinates of the serial robots are obtained, a plurality of groups of points are selected through random sampling in the space range, the relative coordinates of the points relative to the initial position of the tail end of the robot are used as input quantity, the serial robots are utilized to solve the required joint rotation angle under the premise of restraining the joint posture, the robot is driven by the solved joint rotation angle, the error identification result of each connecting rod length of the serial robots is utilized, the pose joint rotation angle is updated to drive the serial robots, the positioning error coordinates of the serial robots after the first compensation are obtained, the vector decomposition is further carried out on the positioning error coordinates of the serial robots after the first compensation, the positioning error prediction model of the serial robots after the first compensation is constructed, and the positioning coordinates of the serial robots after the second compensation are obtained, namely, the absolute positioning error caused by the geometric parameter errors of the serial robots and the time-varying joint clearance can be compensated simultaneously under the condition that accurate modeling is not needed.
Drawings
FIG. 1 is a flow chart of the steps of a two-step method for compensating absolute positioning errors of serial robots according to an embodiment of the present application;
FIG. 2 is a block diagram of a two-step absolute positioning error compensation system for a tandem robot according to an embodiment of the present application;
FIG. 3 is a device diagram of an experimental platform for measuring the positioning error of the tail ends of serial robots by a laser tracker according to an embodiment of the application;
FIG. 4 is a flow chart of identifying the length of each link of a robot according to the differential transmission principle of the robot positioning error in accordance with an embodiment of the present application;
FIG. 5 is a diagram showing the compensation effect of the first step of positioning error compensation according to the embodiment of the present application;
FIG. 6 shows an embodiment of the application with a difference in XoY planeA discrete point schematic diagram of theoretical linear motion away from a point o in a different height plane with a specific linear feed amount;
FIG. 7 is a schematic diagram of vector decomposition of the positioning error after the first compensation according to an embodiment of the present application;
FIG. 8 is a graph of the result of numerical fitting of a positioning error in the X direction and a corresponding linear feed according to a polynomial function by a MATLAB fitting tool box in accordance with an embodiment of the present application;
FIG. 9 is a graph of the results of numerical fitting of a positioning error in the Y direction and a corresponding linear feed according to a polynomial function by a MATLAB fitting tool box in accordance with an embodiment of the present application;
FIG. 10 is a graph of the results of numerical fitting of a positioning error in the Z direction and a corresponding linear feed according to a polynomial function by a MATLAB fitting tool box in accordance with an embodiment of the present application;
FIG. 11 is a diagram showing the effect of the second compensation of positioning errors according to an embodiment of the present application;
reference numerals: 1. a serial robot base; 2. the joints of the robots are connected in series; 3. connecting the connecting rods of the robots in series; 4. a serial robot; 5. a serial robot tip; 6. a target ball; 7. a laser tracker.
Detailed Description
The application will now be described in further detail with reference to the drawings and to specific examples. The step numbers in the following embodiments are set for convenience of illustration only, and the order between the steps is not limited in any way, and the execution order of the steps in the embodiments may be adaptively adjusted according to the understanding of those skilled in the art.
The application builds an experimental platform for measuring the positioning error of the tail end 5 of the serial robot by using a laser tracker, and provides a two-step compensation method for the absolute positioning error of the serial robot based on the experimental platform, wherein a rod piece and a kinematic pair (joint) of an operation machine (also called an arm) of the serial robot are connected in a serial mode (open chain type).
Referring to fig. 1, the present application provides a two-step compensation method of absolute positioning errors of serial robots, the method comprising the steps of:
s1, determining a working space of the serial robots and acquiring positioning error coordinates of the serial robots;
specifically, an experimental platform for measuring the positioning error of the tail end of the serial robot by using a laser tracker is built, and the positioning error is acquired for random sampling points in the serial robot working space;
in this embodiment, as shown in fig. 3, a serial robot base 1 is used as a coordinate origin, a space rectangular coordinate system XYZ is defined, wherein the Z axis corresponds to the height direction, and a positive kinematic model of the serial robot, that is, a mathematical model for obtaining the pose of the tail end of the serial robot by knowing the rotation angle of each joint, is further established, and can be established by using conventional methods such as DH;
then, each joint 2 of the tandem robot is sampled by a pseudo random number within the allowable joint rotation angle range, and each joint sampling rotation angle is further arranged and combined to form a randomly sampled joint space. Determining the working space of the serial robot by using the positive kinematic model and the randomly sampled joint space;
the laser tracker is placed in front of the working space of the serial robots, the height of the laser tracker 7 should be moderately higher than that of the serial robots, the placement position should be such that the measuring range of the laser tracker is larger than that of the working space of the serial robots, and information acquisition is performed by installing the target ball 6 on the tail end of the serial robots. Further, a plurality of groups of points are selected by random sampling within the working space. And on the premise of randomly constraining joint postures, solving a mathematical model of each joint corner by using a serial robot inverse kinematics model, namely the terminal posture of the known serial robot, by taking relative coordinates of the point positions relative to the initial position of the tail end of the robot as input quantity, solving the required joint corner, and driving the robot by using the solved joint corner. The actual coordinates of the tail end positions of the robots are acquired by using a laser tracker, the actual relative coordinates are calculated, the actual relative coordinates and the input quantity are correspondingly differed, and the positioning errors of the serial robots 4 at different points are obtained.
S2, constructing an error jacobian matrix according to the positioning error coordinates of the serial robots, and performing decomposition identification processing to obtain error identification results of the lengths of the connecting rods 3 of the serial robots;
specifically, according to the differential transmission principle of the robot positioning error, an error jacobian matrix reflecting the partial differential relation between the positioning error of the serial robot and the errors of the lengths of all the connecting rods of the robot is constructed, parameters of the error jacobian matrix are screened through orthogonal triangular decomposition and near-zero detection, parameters with small influence on the tail end position of the robot are removed, and the positioning error data obtained in the step S1 are combined, so that the lengths of all the connecting rods of the serial robot are subjected to parameter identification by using a least square method;
in the embodiment, an error jacobian matrix reflecting the partial differential relation between the positioning error of the serial robot and the error of the length of each connecting rod of the robot is constructed according to the differential transmission principle of the positioning error of the robot, parameters of the error jacobian matrix are screened through orthogonal triangular decomposition and near-zero detection, parameters with small influence on the tail end position of the robot are removed, and the length of each connecting rod of the serial robot is identified by utilizing a least square method in combination with the positioning error data obtained in the step S1;
specifically, by using the differential transmission principle of the robot positioning error, the following can be obtained:
;
in the above-mentioned method, the step of,a combination vector representing the column vectors of the positioning errors of the robot tip at each random sampling point,representing the links of the robotA length error column vector;
error jacobian matrixThe method comprises the following steps:
;
in the above-mentioned method, the step of,indicate->The length of the individual links>Representing the number of robot links in series, +.> For robot end at +.>Sample point edge->Displacement in axial direction>Representing the total number of the groups of point positions selected in the working space range in the step S1 through random sampling;
performing orthogonal triangular decomposition on the error jacobian matrix, wherein elements on the diagonal line of the upper triangular matrix are marked as characteristic values of corresponding columns of the error jacobian matrix, the smaller the characteristic values are, the smaller the influence of the parameters of the columns corresponding to the characteristic values on the tail end position of the robot is, so that the parameters corresponding to the columns with the characteristic values of 0 or the characteristic values very close to 0 are ignored, and the error jacobian matrix with redundant parameters removed is formed;
and (3) combining the positioning error data obtained in the step (S1) with an error Jacobian matrix for removing redundant parameters, and identifying the length error of each connecting rod of the robot by using a least square method. Then, the length error of each link of the robot is added to the theoretical length of each link of the robot to form the result of recognition of the length of each link of the robot, as shown in fig. 4.
S3, acquiring an updated pose joint corner according to the error identification result of the length of each connecting rod of the serial robots and driving the serial robots to move to obtain a first serial robot positioning error coordinate compensation result;
specifically, the length of each connecting rod of the robot identified in the step S2 is combined with the positive kinematic model of the robot, so that the first-step positioning error compensation is realized;
in this embodiment, the length of each link of the robot identified in step S2 is substituted into the quasi-kinematic model of the robot, so that the required joint rotation angle can be updated. The updated joint rotation angle is utilized to drive the serial robots, so that the actual pose of the tail end of the robot is closer to the target pose of the tail end of the robot. Measuring the actual pose of the tail end of the robot by using a laser tracker, and observing the compensation effect of the robot, wherein the specific compensation effect is shown in fig. 5;
specifically, referring to fig. 5, the compensation effect of the first step positioning error compensation is shown in fig. 5 for a certain point in the working space where the robot moves, which is different from the random sampling point in step S1.
S4, based on the first serial robot positioning error coordinate compensation result, acquiring serial robot positioning error coordinates after the first compensation;
specifically, on the basis of completing the first positioning error compensation, each connecting rod bundle of the robot is arranged on the same vertical plane, and the included angle between the vertical plane and the XoZ plane is defined as. Then, with different +.>The different height planes of the robot tail end and the specific linear feeding amount of the robot tail end in the direction away from the point o at one height plane are used as target input amountsAnd solving displacement relative coordinates of the tail end of the robot by using a geometric relationship. And (2) leading the solved relative coordinates into a robot inverse kinematics model, and solving the joint rotation angle required for reaching the target input quantity by combining the length of the connecting rod identified in the step (S2). Further, driving the tandem robots with the resolved joint angles makes the robot ends at different +.>And (3) carrying out theoretical linear motion away from the point o in different height planes with specific linear feed, and simultaneously, guiding the calculated joint rotation angle into a robot positive kinematics model to obtain the theoretical predicted displacement relative coordinates of the tail end of the robot. The actual coordinates of the discrete points on the retraction movement are acquired by using the coordinate acquisition method in the step S1. The relative coordinates of the theoretical predicted displacement and the corresponding actual coordinates are differenced, so that the positioning error of the robot after the first compensation is calculated, and referring to FIG. 6, the relative coordinates of the theoretical predicted displacement and the corresponding actual coordinates are different on a plane parallel to the XoY planeDiscrete points of theoretical linear motion away from point o with a particular amount of linear feed are shown in fig. 6 (only the discrete points of the first quadrant are shown in fig. 6 of the present application, and so on for other quadrants).
S5, carrying out vector decomposition on the positioning error coordinates of the serial robots after the first compensation to obtain a space coordinate system error vector of the serial robots;
specifically, the positioning error vector after the first compensation is subjected to orthogonal decomposition and is divided into an error vector on a horizontal plane and an error vector in the Z-axis direction;
in the present embodiment, referring to fig. 7, the formula is as followsProceeding, wherein->For the first compensated positioning error, +.>For the first compensation +.>Positioning error in axial direction, +.>For compensating for positioning errors in the horizontal plane after the first time, < >>An included angle between the positioning error vector after the first compensation and the oZ axis;
further carrying out vector decomposition on the positioning error on the horizontal plane, and decomposing the positioning error into the positioning error in the X direction and the positioning error in the Y direction;
specifically, referring to FIG. 7, the formula is followedIs carried out in the formulaFor the first compensation +.>Positioning error in axial direction, +.>For the first compensation +.>Positioning error in axial direction, +.>Is the angle between the positioning error vector on the horizontal plane and the oY axis.
S6, constructing a serial robot positioning error prediction model after serial first compensation based on a spatial coordinate system error vector of the serial robot;
specifically, for different a and height planes, performing numerical fitting on the positioning error in the X-axis direction after the first compensation and the corresponding linear feed according to a polynomial function with the same order.The same numerical fitting method is also used for positioning errors in the Y-axis direction and the Z-axis direction after the first compensation. Analyzing the polynomial function coefficientsFitting relation between the height plane positions, and further substituting the fitting relation into a corresponding polynomial function to form a prediction model of the positioning error of the robot tail end after the first compensation;
in this embodiment, after the first compensation is completed, the laser tracker is used to perform the compensation at different positionsAnd collecting the actual coordinates of the tail end of the robot at discrete points on the linear motion of different height planes far away from the o point, and then calculating the positioning error in the X, Y, Z axial direction after the first compensation according to the steps S4-S5. According to the calculated positioning error, using a fitting tool box of MATLAB, performing numerical fitting on the positioning error in the X-axis direction after the first compensation and the corresponding linear feeding amount according to a polynomial function with the same order, and keeping the square sum of residuals to be larger than 0.8, as shown in FIG. 8. The same numerical fitting method is also employed for the positioning errors in the Y-axis direction and the Z-axis direction after the first compensation, as shown in fig. 9 and 10.
S7, based on the serial robot positioning error prediction model after the first compensation, the serial robot positioning coordinates after the second compensation are obtained, and the serial robots are guided to move according to the serial robot positioning coordinates after the second compensation.
Specifically, according to the prediction model of the positioning error after the first compensation established in the step S5, the positioning error of the tail end of the robot moving from the initial position to any target position after the first compensation is predicted, and the feedforward compensation quantity of the joint space of the robot is obtained by combining the inverse kinematics model of the robot and the length of the identified connecting rod, so that the second compensation of the positioning error is realized;
in the present embodiment, referring to fig. 11, the feedforward compensation amount for each joint of the robot is added to the joint driving angle calculated by using each link length identified in step S2 and the inverse kinematics model of the robot, and the result of the addition is used as a secondary update value of the joint driving angle. By driving the serial robots by using the updated joint rotation angles, the actual pose of the tail end of the robot can be further close to the target pose of the tail end of the robot, and the positioning error is secondarily compensated, and the compensation effect is shown in fig. 11.
Referring to fig. 2, an absolute positioning error two-step compensation system of a tandem robot includes:
the determining module is used for determining the working space of the serial robots and acquiring the positioning error coordinates of the serial robots;
the identification module is used for constructing an error jacobian matrix according to the positioning error coordinates of the serial robots and performing decomposition identification processing to obtain error identification results of the lengths of the connecting rods of the serial robots;
the driving module is used for acquiring an updated pose joint corner according to the error identification result of the length of each connecting rod of the serial robots and driving the serial robots to move so as to obtain a first serial robot positioning error coordinate compensation result;
the primary compensation module is used for acquiring the positioning error coordinates of the serial robots after the primary compensation based on the positioning error coordinate compensation results of the serial robots;
the decomposing module is used for carrying out vector decomposition on the positioning error coordinates of the serial robots after the first compensation to obtain a space coordinate system error vector of the serial robots;
the construction module is used for constructing a series robot positioning error prediction model after series first compensation based on the spatial coordinate system error vector of the series robot;
the secondary compensation module is used for acquiring the serial robot positioning coordinates after the secondary compensation based on the serial robot positioning error prediction model after the first compensation and guiding the serial robots to move according to the serial robot positioning coordinates after the second compensation.
The content in the method embodiment is applicable to the system embodiment, the functions specifically realized by the system embodiment are the same as those of the method embodiment, and the achieved beneficial effects are the same as those of the method embodiment.
While the preferred embodiment of the present application has been described in detail, the application is not limited to the embodiment, and various equivalent modifications and substitutions can be made by those skilled in the art without departing from the spirit of the application, and these equivalent modifications and substitutions are intended to be included in the scope of the present application as defined in the appended claims.
Claims (10)
1. The two-step absolute positioning error compensation method for the serial robots is characterized by comprising the following steps of:
determining a working space of the serial robots and acquiring positioning error coordinates of the serial robots;
constructing an error jacobian matrix according to the positioning error coordinates of the serial robots, and performing decomposition identification processing to obtain error identification results of the lengths of the connecting rods of the serial robots;
acquiring an updated pose joint corner according to the error identification result of the length of each connecting rod of the serial robots and driving the serial robots to move to obtain a first serial robot positioning error coordinate compensation result;
based on the first serial robot positioning error coordinate compensation result, acquiring serial robot positioning error coordinates after the first compensation;
carrying out vector decomposition on the positioning error coordinates of the serial robots after the first compensation to obtain a space coordinate system error vector of the serial robots;
constructing a serial robot positioning error prediction model after serial first compensation based on a spatial coordinate system error vector of the serial robot;
and acquiring the serial robot positioning coordinates after the second compensation based on the serial robot positioning error prediction model after the first compensation, and guiding the serial robots to move according to the serial robot positioning coordinates after the second compensation.
2. The method for two-step compensation of absolute positioning errors of serial robots according to claim 1, wherein said step of determining the working space of serial robots comprises:
constructing a space rectangular coordinate system of the serial robots according to the space positions of the serial robots;
determining the corner range of each joint of the serial robots according to the space rectangular coordinate system of the serial robots;
according to the rotation angle range of each joint of the serial robots, solving the pose of each joint of the serial robots by a DH method to construct a positive kinematic model of the serial robots;
sampling by pseudo-random numbers according to the rotation angle range of each joint of the serial robots, and arranging and combining sampling results to obtain a joint space of random sampling of the serial robots;
and determining the working space of the serial robots by combining the positive kinematic model of the serial robots and the joint space randomly sampled by the serial robots.
3. The method for two-step compensation of absolute positioning errors of serial robots according to claim 2, wherein said step of obtaining the positioning error coordinates of serial robots comprises:
based on the working space of the serial robots, acquiring information of the tail ends of all joints of the serial robots through a laser tracker to obtain initial coordinates of the tail ends of all joints of the serial robots;
constructing position and posture constraint conditions of joints of the serial robots based on the working space of the serial robots;
establishing an inverse kinematics model of the serial robots, and performing inverse kinematics solution on the serial robots according to the constraint conditions of the joint poses of the serial robots to obtain first pose joint corners corresponding to the joint poses of the serial robots;
driving the serial robots to move according to the first pose joint corners, and acquiring information of the tail ends of all joints of the serial robots through a laser tracker to obtain actual coordinates of the tail ends of all joints of the serial robots;
and performing difference calculation on the actual coordinates of the tail ends of the joints of the serial robots and the initial coordinates of the tail ends of the joints of the serial robots to obtain the positioning error coordinates of the serial robots.
4. The method for compensating absolute positioning errors of serial robots according to claim 3, wherein the steps of constructing an error jacobian matrix according to the positioning error coordinates of the serial robots and performing decomposition identification processing to obtain an error identification result of each connecting rod length of the serial robots comprise:
based on a differential transmission principle of the positioning errors of the serial robots, an error jacobian matrix of the serial robots is constructed, wherein the error jacobian matrix represents a partial differential relation between the positioning error coordinates of the serial robots and the errors of the lengths of all connecting rods of the serial robots;
performing orthogonal triangular decomposition on the error jacobian matrix of the serial robots to obtain decomposed error jacobian matrix parameters;
eliminating error Jacobian matrix parameters smaller than a preset threshold value to obtain error Jacobian matrix with redundant parameters removed;
combining the error Jacobian matrix for removing redundant parameters and the positioning error coordinates of the serial robots, and identifying by a least square method to obtain the errors of the lengths of the connecting rods of the serial robots;
and obtaining the theoretical errors of the lengths of the connecting rods of the serial robots and adding the theoretical errors with the errors of the lengths of the connecting rods of the serial robots to obtain the error identification result of the lengths of the connecting rods of the serial robots.
5. The method for compensating absolute positioning errors of serial robots according to claim 4, wherein the step of obtaining the updated pose joint angle according to the error identification result of the length of each connecting rod of the serial robots and driving the serial robots to move to obtain the first serial robot positioning error coordinate compensation result comprises the following steps:
substituting the error identification result of the length of each connecting rod of the serial robot into the serial robot positive kinematics model to obtain an updated pose joint corner;
driving the serial robots to move according to the updated pose joint corners, and acquiring information of the tail ends of all joints of the serial robots through a laser tracker to obtain coordinates of the tail ends of all joints of the serial robots after the first correction;
and performing difference processing on the coordinates of the tail ends of the joints of the first corrected serial robots and the actual coordinates of the tail ends of the joints of the serial robots to obtain a first serial robot positioning error coordinate compensation result.
6. The method for compensating absolute positioning errors of serial robots according to claim 5, wherein the step of obtaining the first compensated serial robot positioning error coordinates based on the first serial robot positioning error coordinate compensation result specifically comprises:
defining a traveling included angle of the serial robots based on the first serial robot positioning error coordinate compensation result, wherein the traveling included angle of the serial robots represents an included angle between a vertical plane and a XoZ plane;
driving the serial robots to perform linear motion according to the traveling included angles of the serial robots to obtain displacement coordinates of the tail ends of all joints of the serial robots;
the serial robots are subjected to inverse kinematics solution according to the error identification result of the lengths of the connecting rods of the serial robots and the displacement coordinates of the tail ends of the joints of the serial robots, so that the second pose joint corners of the serial robots are obtained;
substituting the second pose joint rotation angle into a serial robot positive kinematics model to obtain theoretical coordinates of the tail ends of all joints of the serial robots;
driving the serial robots to move according to the second pose joint corners of the serial robots, and acquiring the actual coordinates of the tail ends of all joints of the serial robots through a laser tracker;
and carrying out difference processing on the theoretical coordinates of the tail ends of all joints of the serial robots and the actual coordinates of the tail ends of all joints of the serial robots to obtain the positioning error coordinates of the serial robots after the first compensation.
7. The method for compensating the absolute positioning error of the serial robots according to claim 6, wherein the step of performing vector decomposition on the positioning error coordinates of the serial robots after the first compensation to obtain the spatial coordinate system error vector of the serial robots comprises the following steps:
carrying out vector decomposition on the positioning error coordinates of the serial robots after the first compensation to obtain horizontal plane error vectors of the serial robots and Z-axis direction error vectors of the serial robots;
performing vector decomposition on the horizontal plane error vectors of the serial robots to obtain an x-axis direction error vector of the serial robots and a Y-axis direction error vector of the serial robots;
and integrating the X-axis direction error vector of the serial robots, the Y-axis direction error vector of the serial robots and the Z-axis direction error vector of the serial robots to obtain a space coordinate system error vector of the serial robots.
8. The method for compensating absolute positioning errors of serial robots according to claim 7, wherein said step of constructing a serial robot positioning error prediction model after serial first compensation based on a spatial coordinate system error vector of serial robots comprises:
performing numerical fitting treatment on the space coordinate system error vectors of the serial robots through polynomial functions to obtain a numerical fitting relation, wherein the numerical fitting relation represents a fitting relation between coefficients of the polynomial functions, a traveling included angle of the serial robots and a vertical plane;
substituting the numerical fitting relation into a polynomial function to construct a serial robot positioning error prediction model after serial first compensation.
9. The method for compensating the absolute positioning error of the tandem robots according to claim 8, wherein the step of obtaining the positioning coordinates of the tandem robots after the second compensation based on the prediction model of the positioning error of the tandem robots after the first compensation in the tandem comprises the following steps:
predicting the positioning error of the first compensated serial robot according to the serial robot positioning error prediction model after the first compensation serial;
the series robot feedforward compensation quantity is constructed by combining the series robot inverse kinematics model and the error identification result of the length of each connecting rod of the series robot;
and carrying out secondary compensation treatment on the positioning error of the serial robot after the first compensation according to the feedforward compensation quantity of the serial robot to obtain the positioning coordinate of the serial robot after the second compensation.
10. The absolute positioning error two-step compensation system of the serial robot is characterized by comprising the following modules:
the determining module is used for determining the working space of the serial robots and acquiring the positioning error coordinates of the serial robots;
the identification module is used for constructing an error jacobian matrix according to the positioning error coordinates of the serial robots and performing decomposition identification processing to obtain error identification results of the lengths of the connecting rods of the serial robots;
the driving module is used for acquiring an updated pose joint corner according to the error identification result of the length of each connecting rod of the serial robots and driving the serial robots to move so as to obtain a first serial robot positioning error coordinate compensation result;
the primary compensation module is used for acquiring the positioning error coordinates of the serial robots after the primary compensation based on the positioning error coordinate compensation results of the serial robots;
the decomposing module is used for carrying out vector decomposition on the positioning error coordinates of the serial robots after the first compensation to obtain a space coordinate system error vector of the serial robots;
the construction module is used for constructing a series robot positioning error prediction model after series first compensation based on the spatial coordinate system error vector of the series robot;
the secondary compensation module is used for acquiring the serial robot positioning coordinates after the secondary compensation based on the serial robot positioning error prediction model after the first compensation and guiding the serial robots to move according to the serial robot positioning coordinates after the second compensation.
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