CN108656116A - Serial manipulator kinematic calibration method based on dimensionality reduction MCPC models - Google Patents
Serial manipulator kinematic calibration method based on dimensionality reduction MCPC models Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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- B25J9/00—Programme-controlled 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 invention discloses a kind of serial manipulator kinematic calibration methods based on dimensionality reduction MCPC models, including step：(1) kinematics model based on dimensionality reduction MCPC models is established；(2) kinematic error model based on dimensionality reduction MCPC models is established；(3) kinematic calibration based on the LM algorithms using trusted zones skill.The present invention can carry out dimensionality reduction to kinematic error model, to achieve the purpose that simplified operation, under the basis for having established error model, the calibration to Mechanical transmission test parameter be completed, to improve the kinematic accuracy of mechanical arm.
Description
Technical Field
The invention belongs to the technical field of calibration, and particularly relates to a serial robot kinematic parameter calibration method based on a dimension reduction MCPC model.
Background
Due to the influence of errors of machining, assembly and the like, errors exist between actual kinematic parameters and nominal kinematic parameters of the series robot, so that the positioning precision of the tail end of the series robot is reduced, and the robot is greatly limited from working in high-precision machining. Therefore, it is important to calibrate the kinematic parameters of the tandem robot by using a proper joint parameter calibration method.
The most commonly used robot kinematic model is a D-H model, which is proposed by Denavit and Hartenbe in 1955, but because the model can cause singular problems in model parameter calibration when processing adjacent parallel joint modeling problems, Hayati proposes an MDH model by introducing a rotation angle β around a y axis at a parallel axis, Stone proposes a six-parameter S model on the basis of a standard D-H model, and Zhuang and Schroer and the like propose a CPC model and an MCPC model.
When a kinematics model is selected, the MCPC model can model serial robots with various structures and can avoid singular behaviors, but the kinematics parameters introduced by the modeling are too many, so that the process of modeling kinematics errors is complex, and the later calibration work is not facilitated.
After the kinematic parameters of the mechanical arm are calibrated, the error compensation is also important research work. The most common parameter identification method at present is a least square method, the iteration process of the method is simple, the convergence rate is high, disturbance factors are not required to be considered, and the calculation amount of the method is relatively large. The Levemberg-Marquardt method is an improved algorithm for the least square method, and the method is high in convergence speed and strong in robustness, but the memory required by the operation of the method is large. Other algorithms include extended kalman filter algorithms, genetic algorithms, simulated annealing algorithms, and the like.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems, the invention provides a serial robot kinematic parameter calibration method based on a dimension reduction MCPC model.
The technical scheme is as follows: in order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: a serial robot kinematic parameter calibration method based on a dimension reduction MCPC model comprises the following steps:
(1) establishing a kinematics model based on a dimension reduction MCPC model;
(2) establishing a kinematic error model based on a dimension reduction MCPC model;
(3) kinematic parameter calibration based on LM algorithm using confidence domain techniques.
Further, the step (1) specifically includes:
(1.1) establishing a coordinate system of each connecting rod of the serial robot from an inertial coordinate system;
(1.2) deriving a transformation matrix between the coordinate systems of the middle connecting rods and a transformation matrix from the coordinate system of the tail end connecting rod to the coordinate system of the tool;
(1.3) deriving a transformation matrix from the inertial frame to the tool frame, i.e. a kinematic model.
Further, the step (2) is specifically to judge the error influence condition of the change of each joint kinematic parameter on the terminal pose; and eliminating the kinematic parameters with small influence from the error influence condition data, and deriving a kinematic error model based on the dimension-reduced MCPC model.
Further, the step (2) specifically includes:
(2.1) deriving an intermediate link parameter error model:
(2.2) deriving a parameter error model of the tail end connecting rod:
(2.3) establishing representation delta of the pose error of the tail end of the mechanical arm in a tool coordinate system according to the pose errors of the middle connecting rod and the tail end connecting rodE：
ΔE＝JE·Ω
Wherein, JEThe method is characterized in that the method is a mapping matrix of the pose error of the tail end of the mechanical arm and the kinematic parameter error, and omega is a kinematic parameter error vector of the mechanical arm.
Further, derivation of intermediate link parameter error model:
(a) intermediate link transformation matrix differential dTiA linear form;
wherein, Delta αi,Δβi,Δxi,ΔyiIs the parameter error of the connecting rod i;
(b) solving a pose error matrix T corresponding to each connecting rod parameter according to the accepting or rejecting condition of the kinematic parameters of the middle connecting rod of the dimension-reducing MCPC modelα,Tβ,Tx,Ty；
(c) Solving a pose error matrix delta T of a connecting rod coordinate system i +1 relative to a connecting rod coordinate system ii；
(d) Solving the position error d of the connecting rod coordinate system i +1 relative to the connecting rod coordinate system iiAnd attitude error deltai。
Further, derivation of the parameter error model of the end link:
(a) end link transformation matrix differential dTnLinear form:
wherein, Delta αn,Δβn,Δxn,Δyn,Δγn,ΔznIs the parameter error of the end connecting rod;
(b) according to the end links of the dimension-reducing MCPC modelSolving the position and pose error matrix T corresponding to each connecting rod parameter according to the accepting or rejecting condition of the kinematic parametersα,Tβ,Tx,Ty,Tγ,Tz；
(c) Pose error matrix delta T for solving parameters of tail end connecting rodn；
(d) Solving the position error d of the terminal connecting rod coordinate systemnAnd attitude error deltan。
Further, the step (3) specifically includes:
(3.1) sampling the actual terminal pose vector of the mechanical arm, solving a corresponding nominal terminal pose vector according to the kinematics model, wherein the terminal pose error is the difference between the two terminal pose vectors;
(3.2) acquiring a plurality of groups of data, and solving a kinematic parameter error vector omega of the mechanical arm by adopting a Levenberg-Marquardt method utilizing confidence domain skills;
wherein,αkcorrecting by using a trust domain;
and (3.3) carrying out finite iterations according to the LM algorithm until the kinematic parameters meet the precision requirement.
Has the advantages that: the invention can reduce the dimension of the kinematic error model so as to achieve the purpose of simplifying the operation, and completes the calibration of the kinematic parameters of the mechanical arm on the basis of establishing the error model so as to improve the motion precision of the mechanical arm.
Drawings
FIG. 1 is a block diagram of the design flow of the present invention;
FIG. 2 is a diagram of an S-R-S seven-degree-of-freedom robot arm model;
FIG. 3 is a diagram of the system establishment of each joint of the S-R-S seven-degree-of-freedom mechanical arm;
FIG. 4 is a kinematic parameter diagram of an S-R-S seven degree-of-freedom robotic arm;
FIG. 5 is a distribution diagram of the effect of the kinematic parameters of the joints 1-4 on the end pose;
FIG. 6 is a distribution diagram of the effect of joint 5-7 kinematic parameters on end pose;
fig. 7 is a diagram of an end pose experimental data acquisition scheme.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Calculating the terminal pose information of the mechanical arm by using MATLAB through a plurality of groups of input angles, extracting a position and a pose vector from the pose information to form a nominal terminal pose vector TN(ii) a Reading pose information in an actual state through a high-precision measuring instrument such as a laser tracker to form an actual terminal pose vector TA(ii) a Mapping matrix J of tail end pose error and kinematic parameter error of mechanical armESolving through a kinematic error model; and finally, calculating the error condition of the kinematic parameters by an LM algorithm based on confidence domain skills, thereby completing the calibration work of the kinematic parameters of the mechanical arm.
As shown in fig. 1, the method for calibrating kinematic parameters of a tandem robot based on a dimension-reduced MCPC model of the present invention includes the steps of:
(1) performing kinematic modeling based on a dimension reduction MCPC model;
(1.1) establishing a coordinate system of each connecting rod of the serial robot from an inertial coordinate system according to a system establishing rule of the MCPC model;
(1.2) obtaining a transformation matrix between the middle connecting rod coordinate systems and a transformation matrix from the tail end connecting rod coordinate system to the tool coordinate system according to the established connecting rod coordinate systems;
the MCPC model describes the transformation relationship between the inner link coordinate systems using 4 parameters α, x, y, from which an intermediate link coordinate system transformation matrix is derived as:
Ti＝QiRot(c,αi)Rot(y,βi)Trans(xi,yi,0)i＝0,1,2,…,n-1
wherein
Adding two parameters gamma in the transformation from the end connecting rod coordinate system to the tool coordinate systemn,znThe angle of rotation of the tool coordinate system around the z-axis of the end link coordinate system and the distance of translation along the z-axis are respectively represented, so that a transformation matrix from the end link coordinate system to the tool coordinate system is obtained as follows:
Tn＝QnRot(x,αn)Rot(y,βn)Rot(z,γn)Trans(xn,yn,zn)
wherein,representing a homogeneous transformation matrix corresponding to a rotation of theta around the a axis, representing a homogeneous transformation matrix corresponding to X, Y, Z translation along X, Y, Z axes.
As shown in fig. 2, in order to build an S-R-S model diagram of a seven-degree-of-freedom robot arm, four joint rotation axes of the robot arm, 1,3,5, and 7, are perpendicular to the ground; the rotation axes of the 2,4,6 joints are then parallel to the ground. FIG. 3 is a diagram of the system establishment situation of each joint of the S-R-S seven-degree-of-freedom mechanical arm, and initial kinematic parameters are obtained under the system establishment situation; FIG. 4 is a kinematic parameter diagram of an S-R-S seven-degree-of-freedom mechanical arm, and the nominal end pose information of the mechanical arm at different input angles can be calculated through original kinematic parameters.
(1.3) deducing a transformation matrix from an inertial coordinate system to a tool coordinate system, namely a mechanical arm kinematic model;
T＝T0·T1…Tn-1Tn
(1.4) according to the established initial kinematics model of the tandem robot, judging the error influence condition of the change of the kinematics parameters of each joint on the terminal pose by a Monte Carlo method;
(1.5) eliminating kinematic parameters with small influence from the error influence condition data to obtain a kinematic error model based on the dimension-reduced MCPC model;
as shown in fig. 5 and 6, all parameters of the joint 1 are retained, all parameters alfa2 of the joint 2 are removed, all parameters of the joint 3 are retained, all parameters alfa4 of the joint 4 are removed, all parameters of the joint 5 are retained, all parameters alfa6, x6 and y6 of the joint 6 are removed, and all parameters alfa7, beta7, y7 and gamma7 of the joint 7 are removed.
And (4) establishing a kinematic error model according to the parameters reserved by the result.
(2) Establishing a kinematic error model based on a dimension reduction MCPC model:
(2.1) intermediate Link transformation matrix differential dTiAnd link parameter αi,βi,xi,yiIs related to the error of (1), will dTiWriting in linear form;
wherein, Delta αi,Δβi,Δxi,ΔyiIs the parameter error of the connecting rod i.
(2.2) solving a pose error matrix T corresponding to each connecting rod parameter according to the linear form and the accepting or rejecting condition of the intermediate connecting rod kinematic parameter of the dimension-reducing MCPC modelα,Tβ,Tx,Ty；
Wherein, Ti NAnd a nominal transformation matrix representing the link coordinate system i +1 relative to i can be obtained according to the establishment process of the kinematic model:
wherein, c βi,sβiRepresents cos (β)i) And sin (β)i)。
Four pose error matrices T for joints 1,3,5α,Tβ,Tx,TyAll require a solution for joint 2,4, TαInstead of solving, only T needs to be solved for the joint 6β。
(2.3) differentiating dT according to the transformation matrixiSolving a pose error matrix delta T of a connecting rod coordinate system i +1 relative to a connecting rod coordinate system ii；
The differential expression pattern differs for different joints, and for joints 1,3, 5:
dTi＝Ti N(TαΔαi+TβΔβi+TxΔxi+TyΔyi)
δTi＝(TαΔαi+TβΔβi+TxΔxi+TyΔyi)
the differential expression pattern is different for different joints, and for joints 2, 4:
dTi＝Ti N(TβΔβi+TxΔxi+TyΔyi)
δTi＝(TβΔβi+TxΔxi+TyΔyi)
the differential expression pattern differs for different joints, for joint 6:
dTi＝Ti N·TβΔβi
δTi＝TβΔβi
(2.4) according to the position error matrix delta TiSolving the position error d of the connecting rod coordinate system i +1 relative to the connecting rod coordinate system iiAnd attitude error deltai；
Substituting the above calculation results into δ T for joints 1,3,5iIt is possible to obtain:
according to the above equation, the position error and the attitude error of the link coordinate system i +1 with respect to i can be expressed as:
at this time, let
For joints 2,4, the attitude error expression can be derived by the same calculation:
at this time, let
For the joint 6, it is possible to obtain:
at this time, let
The position error d between the intermediate links can be correctediAnd attitude error deltaiThe formula is simplified as follows:
and the derivation of the intermediate connecting rod parameter error model is completed.
(2.5) terminal Link transformation matrix differential dTnBy introducing a parameter gamman,znWill dTnWriting in linear form;
wherein, Delta αn,Δβn,Δxn,Δyn,Δγn,ΔznIs the parameter error of the end link.
(2.6) solving a pose error matrix T corresponding to each connecting rod parameter according to the linear form and the accepting or rejecting condition of the kinematic parameter of the tail end connecting rod of the dimension-reducing MCPC modelα,Tβ,Tx,Ty,Tγ,Tz；
Because the tail end connecting rod only considers the parameters x7 and z7, only the pose error matrix T needs to be solvedx,Tz。
(2.7) differentiating dT according to the transformation matrixnThe position and attitude error matrix delta T of the parameters of the tail end connecting rod is solvedn；
(2.8) according to the position and pose error matrix delta TnSolving the position error d of the terminal connecting rod coordinate systemnAnd attitude error deltan；
Similar to the calculation steps of steps 2.1 to 2.4, the position error d of the end link coordinate system is calculatednAnd attitude error deltan：
δn＝[0,0,0]T
Order to
The position error d of the end link can be correctednAnd attitude error deltanThe reduction is the following equation:
and the derivation of the parameter error model of the tail end connecting rod is completed.
(2.9) establishing representation delta of the pose error of the tail end of the mechanical arm in a tool coordinate system according to the pose errors of the middle connecting rod and the tail end connecting rodE：
ΔE＝JE·Ω
Wherein, JEThe method is characterized in that the method is a mapping matrix of the pose error of the tail end of the mechanical arm and the kinematic parameter error, and omega is a kinematic parameter error vector of the mechanical arm.
And deducing from an inertial coordinate system to a tool coordinate system, namely the situation of the kinematic error model of the mechanical arm, according to the deduction situation of the intermediate connecting rod parameter error model and the tail end connecting rod parameter error model. Let dT be the matrix differential transformation from the inertial coordinate system of the robot to the end coordinate system, one can deduce:
order:
in the above formula, ni,oi,aiRepresents a rotation matrix RiThree column vectors of (1), piRepresenting the position vector, dT is further reduced to:
according to the above formula, can further simplify:
in conclusion, the pose error vector of the robot can be obtained as follows:
the formula is arranged to obtain:
wherein, let ΔE＝[ΔαT,ΔβT,ΔxT,ΔyT,Δγn,Δzn]T，ΔEAn error vector representing kinematic parameters of the robot, wherein Δ α, Δ β, Δ x, Δ y may be expressed as follows:
Δα＝[Δα0,Δα1…Δαn]T
Δβ＝[Δβ0,Δβ1…Δβn]T
Δx＝[Δx0,Δx1…Δxn]T
Δy＝[Δy0,Δy1…Δyn]T
the above equation
Wherein A is1,A2,A3,A4,A5,A6Is a matrix of 3 (n +1),wherein each column vector is represented in turn asWhich in turn corresponds to the above formula.
Combining the above derivation, the kinematic error model of the robot can be simplified into the following form:
ΔE＝JE·Ω
(3) calibrating the kinematic parameters based on an LM algorithm utilizing confidence domain skills;
(3.1) sampling the actual terminal pose vector of the mechanical arm by using a laser tracker, and solving a corresponding nominal terminal pose vector according to a kinematics model, wherein a terminal pose error is the difference between the actual terminal pose vector and the nominal terminal pose vector;
as shown in fig. 7, it is a scheme diagram for acquiring experimental data of end pose, measuring actual pose data of the end by inputting multiple sets of joint angles, and calculating nominal pose data output by the current angle, where the difference between the two is ΔE。
(3.2) acquiring a plurality of groups of data to ensure the solving reliability, and solving a kinematic parameter error vector omega of the mechanical arm by adopting a Levenberg-Marquardt method utilizing confidence domain skills;
wherein,αkthe correction is performed using the trust domain.
(3.3) carrying out finite iteration according to the LM algorithm until the kinematic parameters meet the precision requirement;
on the premise of establishing a kinematics model and a kinematics error model based on an MCPC model, the method selects an LM algorithm to compensate kinematics parameter errors, and improves the motion precision of the tail end.
The specific implementation steps are as follows:
(a) initial MCPC kinematic parameters, let:
k＝1,ε＝10-7,p0＝0.25,p1＝0.5,p2＝0.75,α1＝0.01,m＝0.001
(b) if it isThe calculation is stopped and solved for:
(c) for ΔEDefining function E (x) | | | Δ E | | non-conducting phosphor2And calculating:
AreΩk＝||ΔEk||2-||E(xk+Ωk)||2
(d) order:
making k equal to k +1, turning to step (b),through a limited number of iterations, thereby ensuringThe calibration of the kinematic parameters of the mechanical arm is achieved.
Claims (7)
1. A serial robot kinematic parameter calibration method based on a dimension reduction MCPC model is characterized by comprising the following steps: the method comprises the following steps:
(1) establishing a kinematics model based on a dimension reduction MCPC model;
(2) establishing a kinematic error model based on a dimension reduction MCPC model;
(3) kinematic parameter calibration based on LM algorithm using confidence domain techniques.
2. The method for calibrating kinematic parameters of a tandem robot based on a dimension-reducing MCPC model according to claim 1, wherein the method comprises the following steps: the step (1) specifically comprises:
(1.1) establishing a coordinate system of each connecting rod of the serial robot from an inertial coordinate system;
(1.2) deriving a transformation matrix between the coordinate systems of the middle connecting rods and a transformation matrix from the coordinate system of the tail end connecting rod to the coordinate system of the tool;
(1.3) deriving a transformation matrix from the inertial frame to the tool frame, i.e. a kinematic model.
3. The method for calibrating kinematic parameters of a tandem robot based on a dimension-reducing MCPC model according to claim 1, wherein the method comprises the following steps: specifically, the step (2) is to judge the error influence condition of the change of the kinematic parameters of each joint on the pose of the tail end; and eliminating the kinematic parameters with small influence from the error influence condition data, and deriving a kinematic error model based on the dimension-reduced MCPC model.
4. The method for calibrating kinematic parameters of a tandem robot based on a dimension-reducing MCPC model according to claim 3, wherein the method comprises the following steps: the step (2) specifically comprises:
(2.1) deriving an intermediate link parameter error model:
(2.2) deriving a parameter error model of the tail end connecting rod:
(2.3) establishing representation delta of the pose error of the tail end of the mechanical arm in a tool coordinate system according to the pose errors of the middle connecting rod and the tail end connecting rodE：
ΔE＝JE·Ω
Wherein, JEThe method is characterized in that the method is a mapping matrix of the pose error of the tail end of the mechanical arm and the kinematic parameter error, and omega is a kinematic parameter error vector of the mechanical arm.
5. The method for calibrating kinematic parameters of a tandem robot based on a dimension-reducing MCPC model according to claim 4, wherein the method comprises the following steps: and (3) derivation of a parameter error model of the intermediate connecting rod:
(a) intermediate link transformation matrix differentialdTiA linear form;
wherein, Delta αi,Δβi,Δxi,ΔyiIs the parameter error of the connecting rod i;
(b) solving a pose error matrix T corresponding to each connecting rod parameter according to the accepting or rejecting condition of the kinematic parameters of the middle connecting rod of the dimension-reducing MCPC modelα,Tβ,Tx,Ty；
(c) Solving a pose error matrix delta T of a connecting rod coordinate system i +1 relative to a connecting rod coordinate system ii；
(d) Solving the position error d of the connecting rod coordinate system i +1 relative to the connecting rod coordinate system iiAnd attitude error deltai。
6. The method for calibrating kinematic parameters of a tandem robot based on a dimension-reducing MCPC model according to claim 4, wherein the method comprises the following steps: derivation of a parameter error model of the tail end connecting rod:
(a) end link transformation matrix differential dTnLinear form:
wherein, Delta αn,Δβn,Δxn,Δyn,Δγn,ΔznIs the parameter error of the end connecting rod;
(b) solving a pose error matrix T corresponding to each connecting rod parameter according to the accepting or rejecting condition of the kinematic parameters of the tail end connecting rod of the dimension-reducing MCPC modelα,Tβ,Tx,Ty,Tγ,Tz；
(c) Pose error matrix delta T for solving parameters of tail end connecting rodn；
(d) Solving the position error d of the terminal connecting rod coordinate systemnAnd attitude error deltan。
7. The method for calibrating kinematic parameters of a tandem robot based on a dimension-reducing MCPC model according to claim 1, wherein the method comprises the following steps: the step (3) specifically comprises:
(3.1) sampling the actual terminal pose vector of the mechanical arm, solving a corresponding nominal terminal pose vector according to the kinematics model, wherein the terminal pose error is the difference between the two terminal pose vectors;
(3.2) acquiring a plurality of groups of data, and solving a kinematic parameter error vector omega of the mechanical arm by adopting a Levenberg-Marquardt method utilizing confidence domain skills;
wherein,αkcorrecting by using a trust domain;
and (3.3) carrying out finite iterations according to the LM algorithm until the kinematic parameters meet the precision requirement.
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