CN109483555B - Method for identifying parameters of statics model of serial rotary joint industrial robot - Google Patents
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Abstract
The invention discloses a method for identifying parameters of a statics model of a serial rotary joint industrial robot, which relates to the fields of industrial robots, model identification and the like and is completed by a least square method. The method can identify the parameters of the static model of the robot in an off-line manner, so that the static model of the robot can be applied to the fields of feedforward control, dragging teaching and the like.
Description
Technical Field
The invention relates to a method for identifying parameters of a static model of a serial rotary joint industrial robot.
Background
The identification problem of the static model of the robot is a sub-problem of the dynamic identification problem of the robot, namely when the speed and the acceleration of the robot are zero, the dynamic model is degraded into the static model. However, although the problem of robot dynamics model identification has been solved academically, its application in the industry is limited due to the complexity of the specific operations of the identification algorithm and the non-real-time nature of the specific implementation of the dynamics model. In many applications, such as feedforward compensation controllers, drag teaching, and wearable devices, the compensation gravity and stiction have met performance requirements; meanwhile, the static model is much simpler than the dynamic model, so that the static model can meet the real-time requirement in the specific implementation aspect. Therefore, the identification of the static model has great industrial value.
Further, it was found through search that, in the document "Gravity compensation of an upper extremity wearable device", Moubarak et al calculates the Gravity parameter by a specific position, but this method requires a specific analysis of the kinematic configuration of the robot, and the amount of data is relatively small, and the stability of the identified parameter is relatively poor.
It was found through the search that Palpacelli et al in the document "Experimental identification of the static model of the hpkm three induced robot static model" identifies the static model parameters by deriving the static model and finding a regression matrix, but this method needs to find the regression matrix by a numerical method, and at the same time, this method is difficult to express the regression matrix by a symbol expression, which means that this method is difficult to satisfy the real-time requirement in practical application.
Disclosure of Invention
The invention aims to provide a method for identifying parameters of a static model of a serial rotary joint industrial robot, which aims to solve the problems in the background technology.
In order to achieve the purpose, the invention provides the following technical scheme:
a method for identifying parameters of a static model of a serial rotary joint industrial robot comprises the following steps:
s1, establishing a robot kinematic model according to a DH method, and generating a regression matrix Y of the robot according to the kinematic model;
s2, removing the linear related column vectors in the regression matrix Y to obtain the maximum linear independent group in the regression matrix Y to form Y*；
S3, controlling the robot to make each joint of the robot track a sine signal with a period more than 50S, obtaining a feedback position, a current and a torque command of each joint, and controlling each joint to be converted to a connecting rod side;
s4, selecting a sinusoidal signal with a complete cycle from the data obtained in the step S3, dividing the sinusoidal signal into a positive section and a negative section according to the motion direction, and filtering the intercepted current command by using a low-pass zero-phase-shift filter;
s5, randomly selecting N data from the positive direction segment and the negative direction segment, and calculating and arranging the data according to the following modes:
s6, using least square method to form the formula pi*＝(YT·Y)-1·YTT to calculate the static model parameter values.
As a further scheme of the invention: the calculation method of the regression matrix Y in step S1 is:
firstly, the driving moment of each joint of the robot is obtained according to a kinematic model:
wherein i represents the ith link, Z0Is a constant vector [001]T，mjMass of the j-th connecting rod, Pi-1，jIs a vector pointing from the origin of the coordinate system to the origin of the j-th link coordinate system under the i-1 st link coordinate system,
is a rotation matrix from the jth link coordinate system to the i-1 th link coordinate system, rjIs the connecting rod centroid coordinate under the jth connecting rod coordinate system, g is the gravity acceleration vector under the world coordinate system, fiThe Coulomb friction of the proximal joint of the connecting rod, sgn (-) is the symbol operator,
the ith joint speed is obtained, and n is the number of joints of the robot;
order to
Wherein,
(g is an acceleration constant), nf＝[f1…fi…fn]TThen the above formula can be expressed as τ ═ Y · π;
in the formula,
namely the regression matrix, is used for determining the regression matrix,
wherein S (-) is a cross product operator, YgIs a matrix of (n × 4n), YfIs a diagonal matrix of (n × n), ZgIs a unit vector pointing to the same as g.
As a still further scheme of the invention: the period of the sinusoidal signal is more than 50s, and the amplitude of the sinusoidal signal needs to be selected to ensure that all joints do not interfere with each other and cover the whole working space.
As a still further scheme of the invention: the method for eliminating the linearly related column vectors in the regression matrix Y in step S2 is:
considering the j-1 th rotary joint, the j-th connecting rod mass mjThe corresponding row is removed, and if the joint axes at the two ends of the connecting rod are parallel to each other, the connecting rod is parallel to the joint axis mjrjyThe corresponding column is removed, otherwise, m is equal tojrjyRemoving corresponding columns; if the 0 th joint axis is parallel to the gravity acceleration vector g, then m1、m1r1x、m1r1y、m1r1zRemoving the corresponding column; therefore, YgIs a matrix of (n × 2n) or (n × (2 n-2)).
As a still further scheme of the invention: the filter is a second order zero phase shift butterworth filter with a cutoff frequency of 1 Hz.
Compared with the prior art, the invention has the beneficial effects that: the method comprises the steps of firstly establishing a statics model of the robot, expressing the model as a linear form of a body parameter, then finding out a maximum linear independent group of regression matrix column vectors, and finally calculating the model parameter by a least square method through collecting experimental data.
Drawings
FIG. 1 is a static parameter identification flow chart of the present invention;
FIG. 2 is a diagram of a DH model of a robot in accordance with a preferred embodiment of the present invention;
FIG. 3 is a diagram of a second joint feedback position and current command signal for a preferred embodiment of the present invention;
FIG. 4 is a static model parameter verification diagram according to a preferred embodiment of 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.
Referring to fig. 1-4, in an embodiment of the present invention, a method for identifying parameters of a static model of a tandem rotary joint industrial robot,
taking Fuji kang A-05-2 series rotary joint industrial robot as an example, FIG. 2 is a kinematic model established by the robot according to DH method, the DH parameter table is shown in Table 1 (robot DH parameter table),
in the table: in the table, alpha is a connecting rod parameter and represents an included angle between two joint shafts on the connecting rod, a is a connecting rod parameter and represents the length of a common perpendicular line between the two joint shafts on the connecting rod, d is a joint parameter and represents the distance between the x axis and the z axis of the adjacent coordinate systems, and theta is a joint parameter and represents an included angle between the x axes of the adjacent coordinate systems.
And the drive torque of each joint can be expressed as:
wherein i represents the ith link, Z0Is a constant vector [001]T，mjMass of the j-th connecting rod, Pi-1，jIs a vector pointing from the origin of the coordinate system to the origin of the j-th link coordinate system under the i-1 st link coordinate system,
is a rotation matrix from the jth link coordinate system to the i-1 th link coordinate system, rjIs the connecting rod centroid coordinate under the jth connecting rod coordinate system, g is the gravity acceleration vector under the world coordinate system, fiThe Coulomb friction of the proximal joint of the connecting rod, sgn (-) is the symbol operator,
the ith joint speed is obtained, and n is the number of joints of the robot;
order to
Wherein,
(g is an acceleration constant), nf＝[f1…fi…fn]TThe above formula can be expressed as τ ═ Y · π, where,πgis a gravity-related parameter that is a collection of first-order mass moments mr and masses m of the respective connecting rods; pifA set of coulomb friction forces f for each joint;
in the formula,
namely the regression matrix, is used for determining the regression matrix,
wherein S (-) is a cross product operator, YgIs a matrix of (n × 4n), YfIs a diagonal matrix of (n × n), ZgIs a unit vector pointing to the same direction as g, wherein,
is z0Transpose of (z)0Is [001 ]]T3 x 1 column vectors of, so here
Is [001 ]]TThe line vectors of (a) are,
is a rotation matrix from the world coordinate system to the (n-1) th connecting rod coordinate system.
The regression matrix Y (6x30) of the robot can be obtained from the formula (2),
the column vectors of the regression matrix Y are linearly related and before applying the least squares method, the largest linearly independent set thereof needs to be found, and it is now provided to remove the linearly related column vectors in the regression matrix in the following way:
considering now the 5 th revolute joint, the 6 th link mass m6The corresponding row can be removed, and if the joint axes at the two ends of the connecting rod are parallel to each other, the connecting rod is parallel to the joint axis m6r6zThe corresponding column may be removed, otherwise corresponding to m6r6yThe corresponding column can be removed, in particular if the 0 th joint axis is parallel to the gravitational acceleration vector g, then m1、m1r1x、m1r1y、m1r1zRemoving the corresponding column; therefore, YgA matrix of (n × 2n) or (n × (2 n-2));
according to the above rule, it can be concluded that the 1 st, 2 nd, 3 rd, 4 th, 7 th, 8 th, 10 th, 12 th, 14 th, 16 th, 18 th, 20 th, 23 th and 24 th columns in Y can be removed, thereby obtaining Y*(6×16)；
In this example, we control the robot with the MicroLabBox of dSPACE; in the experimental process, each joint of the robot tracks a sinusoidal signal with a period of 400s, and the amplitude of the sinusoidal signal is pi, 0.4 pi, 0.3 pi, pi and pi sequentially from the first axis to the sixth axis; and simultaneously, the feedback position and the current/torque command of each joint are recorded and converted to the connecting rod side, so that the feedback position and the current/torque command can be identified by using a static model of the robot, and fig. 3 shows a position feedback signal and a current command signal of a second joint after conversion.
In this embodiment, we filter the current command by using a second-order zero-phase shift Butterworth filter with a cut-off frequency of 1Hz, then randomly extract 500 data points from the positive and negative data respectively, and calculate Y respectively*Then, the T, Y corresponding to each point*Arranged in the following form:
And finally, calculating the parameter value of the static model according to the following formula by a least square method:
π*＝(YT·Y)-1·YT·T (3)
calculating a static model parameter pi*(see table 2);
TABLE 2 statics model parameter π*
To verify whether the identified parameters of the static model are correct or not, the formula tau is equal to Y*·π*Carry the experimental data of a complete cycle into Y*In the method, a set of torque values predicted by a static model is calculated and compared with a recorded current command (on a connecting rod side), and the result is shown in fig. 4, and it can be seen from fig. 4 that the predicted current command and the collected current command almost coincide, which shows that the identified model parameters are accurate and reliable.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.
Claims (3)
1. A method for identifying parameters of a static model of a serial rotary joint industrial robot is characterized by comprising the following steps:
s1, establishing a robot kinematic model according to a DH method, and generating a regression matrix Y of the robot according to the kinematic model;
s2, removing the linear related column vectors in the regression matrix Y to obtain the maximum linear independent group in the regression matrix Y to form Y*；
S3, controlling the robot to make each joint of the robot track a sine signal with a period more than 50S, obtaining a feedback position, a current and a torque command of each joint, and controlling each joint to be converted to a connecting rod side;
s4, selecting a sinusoidal signal with a complete cycle from the data obtained in the step S3, dividing the sinusoidal signal into a positive section and a negative section according to the motion direction, and filtering the intercepted current command by using a low-pass zero-phase-shift filter;
s5, randomly selecting N data from the positive direction segment and the negative direction segment, and calculating and arranging the data according to the following mode
s6, using least square method to form the formula pi*＝(YT·Y)-1·YTT to calculate the static model parameter values;
the method for eliminating the linearly related column vectors in the regression matrix Y in step S2 is: considering the j-1 th rotary joint, the j-th connecting rod mass mjThe corresponding row is removed, and if the joint axes at the two ends of the connecting rod are parallel to each other, the connecting rod is parallel to the joint axis mjrjyThe corresponding column is removed, otherwise, m is equal tojrjyCorresponding column removal, mr is a 3 x 1 vector representing the first moment of inertia of the connecting rod, i.e. the product of the mass of the connecting rod and the vector of the centroid of the connecting rod, mjrjyDenotes a j linkThe y-axis component of the order moment of inertia in the connecting rod coordinate system is a scalar;
if the 0 th joint axis is parallel to the gravity acceleration vector g, then m1、m1r1x、m1r1y、m1r1zRemoving the corresponding column; therefore, YgIs (n × 2n) or (n × (2 n-2));
the calculation method of the regression matrix Y in step S1 is:
firstly, the driving moment of each joint of the robot is obtained according to a kinematic model:
wherein i represents the ith link, Z0Is a constant vector [001]T，mjMass of the j-th connecting rod, Pi-1，jIs a vector pointing from the origin of the coordinate system to the origin of the j-th link coordinate system under the i-1 st link coordinate system,
is a rotation matrix from the jth link coordinate system to the i-1 th link coordinate system, rjIs the connecting rod centroid coordinate under the jth connecting rod coordinate system, g is the gravity acceleration vector under the world coordinate system, fiThe Coulomb friction of the proximal joint of the connecting rod, sgn (-) is the symbol operator,
the ith joint speed is obtained, and n is the number of joints of the robot;
let τ be [ τ ]1…τi…τn]T，
Wherein,
πf＝[f1…fi…fn]Tthen the above formula can be expressed as τ ═ Y · π; in the formula, pigIs a gravity-related parameter that is a collection of first-order mass moments mr and masses m of the respective connecting rods; pifA set of coulomb friction forces f for each joint;
in the formula,
namely the regression matrix, is used for determining the regression matrix,
wherein S (-) is a cross product operator, YgIs a matrix of (n × 4n), YfIs a diagonal matrix of (n × n), ZgIs a unit vector pointing to the same direction as g, wherein,
is z0Transpose of (z)0Is [001 ]]T3 x 1 column vectors of, so here
Is [001 ]]TThe line vectors of (a) are,
is a rotation matrix from the world coordinate system to the (n-1) th connecting rod coordinate system.
2. The method for identifying the parameters of the statics model of the serial rotary joint industrial robot as claimed in claim 1, wherein the period of the sinusoidal signal is greater than 50s, and the amplitude of the sinusoidal signal is selected to ensure that the joints do not interfere with each other and cover the whole working space.
3. The method for identifying parameters of a statics model of a serial revolute joint industrial robot according to claim 1, wherein the filter is a second order zero phase shift butterworth filter with a cut-off frequency of 1 Hz.
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