CN110722562B - Space Jacobian matrix construction method for machine ginseng number identification - Google Patents

Abstract

The invention discloses a method for constructing a space Jacobian matrix for robot parameter identification. S300: Assuming that a certain joint coordinate system undergoes differential motion, establish a virtual coordinate system corresponding to the joint on this basis, and construct a transformation matrix between the two, and then calculate the relative position of the robot end relative to the base. The actual pose of the coordinate system is compared with the original theoretical pose, and the pose error of the robot end relative to the base coordinate system caused by the motion error of the joint coordinate system is obtained, and the spatial Jacobian matrix of the robot is constructed. The method of the present invention, based on the differential transformation principle and the virtual coordinate system method, has lower time consumption and can quickly construct the robot's spatial Jacobian matrix.

Description

A Construction Method of Spatial Jacobian Matrix for Robot Parameter Identification

technical field

The invention belongs to the technical field of robot calibration, and more particularly relates to a spatial Jacobian matrix construction method for robot parameter identification.

Background technique

The motion accuracy of an industrial robot plays a crucial role in its application reliability in production. The geometric parameter error of each connecting rod of the robot is the most important link that causes the positioning error of the robot.

Identifying the geometric parameter errors of each link of the robot is an important means to improve the motion accuracy of the robot. The main task of parameter identification is to construct the transformation relationship between the robot parameter error and the robot end error. It is divided into two steps. First, the robot parameter error direction is constructed. The transformation relationship G _i of the joint coordinate system error, and then the transformation relationship _Ji (ie, the space Jacobian matrix or the object Jacobian matrix) of the robot joint coordinate system error to the terminal error is constructed. After obtaining the transformation relationship between the robot parameter error and the terminal error, the parameter error value of the robot can be solved by the least square method. In the existing method of constructing the robot space Jacobian matrix, generally the object Jacobian matrix of the robot is first constructed, and then the spatial Jacobian matrix is constructed by using the transformation relationship between the two. The time consumption of the parameter identification algorithm is relatively long, and it is difficult to adapt. Technical requirements for robot calibration.

SUMMARY OF THE INVENTION

Aiming at the above defects or improvement needs of the prior art, the present invention provides a method for constructing a space Jacobian matrix for robot parameter identification, and a method for constructing a robot space Jacobian matrix based on the differential transformation principle and the virtual coordinate system method, which is more than the traditional method. It has lower time consumption and can quickly construct the spatial Jacobian matrix of the robot, which provides favorable conditions for realizing the parameter identification of the robot.

In order to achieve the above object, the present invention provides a method for constructing a spatial Jacobian matrix for robot parameter identification, comprising the following steps:

S100: Analyze the influence of rod length, torsion angle, offset distance and joint angle in the robot D-H model on the relationship between the robot links and joints, use translation and rotation operators to calculate the homogeneous transformation matrix of the robot's adjacent joints, and construct the robot kinematic model;

S200: based on the robot kinematics model, analyze the differential motion characteristics of the robot joints, and establish a homogeneous transformation matrix between coordinate systems under the differential motion;

S300: Assuming that a certain joint coordinate system undergoes a differential motion, on this basis, a virtual coordinate system corresponding to the joint is established, and a transformation matrix between the two is constructed, and then the actual pose of the robot end relative to the base coordinate system is calculated, Compared with the original theoretical pose, the pose error of the robot end relative to the base coordinate system caused by the motion error of the joint coordinate system is obtained, and the spatial Jacobian matrix of the robot is constructed.

Further, in step S200, the establishment of the homogeneous transformation matrix includes the following specific steps:

S201: The magnitude of translation and rotation in the differential motion is small, so the angle operation of the robot is approximated in the differential transformation. When the joint angle is small, sinθ≈θ, cosθ≈1;

S202: The robot joint i-1 to the joint i performs a differential rotational motion δ=[δ _x δ _y δ _z ] ^T and a translational motion d=[d _x d _y d _z ] ^T , the differential rotational motion δ=[δ _x The transformation matrix of δ _y δ _z ] ^T is:

Wherein, k=[k _x k _y k _z ] ^T ,δ _x =k _x δθ,δ _y =k _y δθ,δz=k _z δθ;

The transformation matrix corresponding to the translational motion d=[d _x d _y d _z ] ^T is:

Further, through the differential rotational motion and translational motion, the total transformation matrix of the differential motion between the robot joint coordinate systems is constructed as:

Further, step S200 also includes:

S203: Introduce an antisymmetric matrix [δ]:

Further, S300 includes the following specific steps:

S301: Analyze the error form of the robot joint coordinate system, and introduce a virtual coordinate system to indicate the pose error of the joint coordinate system;

S302: Using the basic principle of the differential change method, obtain the homogeneous transformation relationship between the virtual coordinate system and the original joint coordinate system;

S303: Obtain the pose relationship of the robot end coordinate system relative to the base coordinate system after the virtual coordinate system is introduced, and compare it with the original pose relationship to obtain the pose deviation of the robot end coordinate system;

S304: Constructing a space Jacobian matrix of the robot according to the pose deviation of the coordinate system at the end of the robot.

Further, the spatial Jacobian matrix J(q) of the robot described in S304 is:

In the formula: J _li and J _ai represent the translation and rotation of the end effector caused by the unit joint motion of joint i, respectively.

Further, in S301, the transformation matrix of the robot end joint n relative to the base coordinate system is denoted as

分别表示坐标系n、i、n相对于坐标系0、0、i的变换矩阵；

分别表示

中的旋转矩阵；⁰P_i0、ⁱP_n0、⁰P_n0分别表示

中的位置向量。where:

Represent the transformation matrices of coordinate systems n, i, and n relative to coordinate systems 0, 0, and i, respectively;

Respectively

The rotation matrix in ; ⁰ P _i0 , ⁱ P _n0 , ⁰ P _n0 represent

The position vector in .

Further, in S302, it is assumed that the coordinate system i reaches the virtual coordinate system i' after the differential motion occurs, then the coordinate system n moves to the n' place, and the transformation matrix of the coordinate system n' relative to the base coordinate system is:

分别表示坐标系i、i′、n′相对于坐标系o、i、i′的变换矩阵；

分别表示

中的旋转矩阵；⁰P_i0、ⁱP_i′0、^i′P_n′0分别表示

中的位置向量。where:

respectively represent the transformation matrices of coordinate systems i, i', n' relative to coordinate systems o, i, i';

Respectively

The rotation matrix in ; ⁰ P _i0 , ⁱ P _i′0 , ^i′ P _n′0 represent

The position vector in .

Further, in S303, the pose deviation of the robot end coordinate system is:

⁰ D _ni =[ ⁰ d _ni ^{T 0} δ _ni ^T ] ^T

表示

的旋转矩阵。Among them, ⁰ d _ni is the position deviation, which is equal to the position ⁰ P _no ' of the origin of the coordinate system n in the final state under the base coordinate system minus the position ⁰ P _no ' of the origin of the coordinate system n in the initial state under the base coordinate system ; ⁰ δ _ni is the attitude deviation,

express

the rotation matrix.

Further, in S100, the robot kinematics model is the transformation matrix of the robot connecting rod coordinate system i relative to the connecting rod coordinate system i-1:

Where: a _i-1 is the length of the connecting rod i-1; α _i-1 is the torsion angle of the connecting rod i-1; d _i is the offset distance of the connecting rod i relative to the connecting rod i-1; θ _i is the connecting rod The rotation angle of i relative to the connecting rod i-1 around the axis i; Rot(x,α _i-1 ) represents the homogeneous transformation matrix corresponding to the rotation angle α _i-1 around the x-axis of the coordinate system, specifically:

Trans(x,a _i-1 ) represents the homogeneous transformation matrix corresponding to the translation distance a _i-1 around the x-axis of the coordinate system, specifically:

Rot(z, θ _i ) represents the homogeneous transformation matrix corresponding to the rotation angle θ _i around the z-axis of the coordinate system, which is specifically

Trans(z, d _i ) represents the homogeneous transformation matrix corresponding to the translation distance d _i around the z-axis of the coordinate system, specifically:

In general, compared with the prior art, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

1. The space Jacobian matrix construction method of the present invention, the robot space Jacobian matrix construction method based on the differential transformation principle and the virtual coordinate system method, has lower time consumption than the traditional method, and can quickly construct the space Jacobian of the robot. The matrix provides favorable conditions for realizing the parameter identification of the robot.

2. The spatial Jacobian matrix construction method of the present invention uses the basic principle of differential transformation to analyze the characteristics of differential motion of robot joints, establishes a homogeneous transformation matrix between coordinate systems under differential motion, and interprets the generation of errors as coordinate system differentials The result of the motion, the mathematical description method of the coordinate system error is conveniently established, which lays a foundation for solving the end pose error.

3. The space Jacobian matrix construction method of the present invention establishes a virtual coordinate system corresponding to the joint, and derives the transformation matrix between the two, and then calculates the actual pose of the robot end relative to the base coordinate system, which is different from the original theoretical pose. For comparison, the spatial Jacobian matrix of the robot is constructed.

Description of drawings

1 is a flowchart of a method for constructing a spatial Jacobian matrix for robot parameter identification according to an embodiment of the present invention;

Fig. 2 is the description schematic diagram of the robot connecting rod in the embodiment of the present invention;

3 is a schematic diagram illustrating the connection mode between the connecting rods in the embodiment of the present invention;

FIG. 4 is a schematic diagram of the description of the coordinate system of the robot connecting rod in the embodiment of the present invention;

5 is a flowchart of solving a homogeneous transformation matrix based on a differential transformation method in an embodiment of the present invention;

6 is a schematic diagram of a differential transformation process in an embodiment of the present invention;

7 is a schematic diagram of the differential motion of the joint coordinate system and the virtual coordinate system in the embodiment of the present invention;

FIG. 8 is a flowchart of constructing a spatial Jacobian matrix based on a virtual coordinate system method in an embodiment of the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

As shown in FIG. 1 , an embodiment of the present invention provides a method for constructing a spatial Jacobian matrix for robot parameter identification, including the following steps:

S100: Establish a kinematic model of the robot based on the D-H method. Analyze the influence of rod length a, torsion angle α, offset distance d and joint angle θ in the D-H model on the relationship between the robot's links and joints; use the translation and rotation operators to calculate the homogeneous transformation matrix of the robot's adjacent joints, so that Get the kinematics model of the robot;

S200: Using the basic principle of differential transformation, deduce the homogeneous transformation matrix between coordinate systems in the case of differential motion. Analyze the characteristics of the differential motion of the robot joints, and establish the homogeneous transformation matrix between the coordinate systems under the differential motion;

S300: Use the virtual coordinate system method to derive the Jacobian matrix formula of the robot space. Assuming that a certain joint coordinate system undergoes differential motion, on this basis, a virtual coordinate system corresponding to the joint is established, and the transformation matrix between the two is deduced, and then the actual pose of the robot end relative to the base coordinate system is calculated. The theoretical poses are compared, and the spatial Jacobian matrix of the robot is finally constructed.

Specifically, it includes the following steps:

(1) The kinematics model of the robot is established based on the D-H method.

As shown in FIG. 2 , the link i-1 is determined by the joint axis i-1 and the common normal length a _i-1 of the joint axis i and the included angle α _i-1 between the two axes. a _i-1 is called the length of the link i-1, and its direction is defined as the direction from the joint i-1 to the joint i; α _i-1 is called the torsion angle of the link i-1, and its direction is defined as from the axis i- 1 Go around the common normal to a parallel to axis i.

As shown in Figure 3, there is a joint axis between adjacent connecting rods. Correspondingly, each joint axis has two common normal lines perpendicular to it. The distance between these two common normal lines (connecting rods) is called the The offset distance, recorded as d _i , represents the offset distance of connecting rod i relative to connecting rod i-1; the angle between these two common normals (links) is called the joint angle, marked as θ _i , which represents the connecting rod i The rotation angle of the relative link i-1 around the axis i.

As shown in Figure 4, in order to determine the relative motion and pose relationship between the links of the robot, a coordinate system is fixed on each link. The one fixed to the base (link 0) is called the base coordinate system, and the one fixed to the link i is called the coordinate system i.

For the intermediate coordinate system i, it is stipulated that its z _i axis is collinear with the joint axis i, and points to any point; its x _i axis is collinear with a _i , and points to i+1 from joint i, when a _i =0, take x _i = ±z _i+1 ×z _i ; its y _i axis is determined according to the right-hand rule; the origin o _i of the coordinate system is taken at the intersection of _xi and zi , when zi ₊₁ and _zi intersect, _{o i is} taken at At the intersection, when zi ₊₁ and _zi are parallel, o _i is taken at a place where d _i+1 =0.

For the head and end link coordinate systems, it is generally specified that the z-axis of the coordinate system 0 is along the direction of the joint axis 1. When the joint variable 1 is zero, the coordinate systems 0 and 1 coincide. The specification of the coordinate system of the end link is similar to that of the coordinate system 0. For the rotating joint n, x _{n is} selected so that when θ _n =0, x _n and x _n-1 coincide, and the origin of the coordinate system n is selected so that d _n =0; For the moving joint n, the coordinate system n is specified so that θ _n =0, and when dn =0, x _n and x _{n -1} coincide.

Based on the above method of establishing the link coordinate system of the robot, it can be seen that the link coordinate system i can be regarded as the link coordinate system i-1 obtained by the following transformation:

(a) rotate α _i-1 angle around x _i-1 axis; (b) move a _i-1 along x _i-1 axis; (c) rotate θ _i angle around _zi axis; (d) along _zi axis Move d _i .

According to the principle of robot kinematics, the transformation matrix of the robot link coordinate system i relative to the link coordinate system i-1 can be obtained by the following formula:

Where: a _i-1 is the length of the connecting rod i-1; α _i-1 is the torsion angle of the connecting rod i-1; d _i is the offset distance of the connecting rod i relative to the connecting rod i-1; θ _i is the connecting rod The rotation angle of i relative to the connecting rod i-1 around the axis i; Rot(x,α _i-1 ) represents the homogeneous transformation matrix corresponding to the rotation angle α _i-1 around the x-axis of the coordinate system, specifically:

Trans(x,a _i-1 ) represents the homogeneous transformation matrix corresponding to the translation distance a _i-1 around the x-axis of the coordinate system, specifically:

Rot(z, θ _i ) represents the homogeneous transformation matrix corresponding to the rotation angle θ _i around the z-axis of the coordinate system, which is specifically

Trans(z, d _i ) represents the homogeneous transformation matrix corresponding to the translation distance d _i around the z-axis of the coordinate system, specifically:

Specifically:

This modeling method is used to establish the kinematics model of the robot.

(2) The basic principle of differential transformation

The basic principle of the differential transformation method is shown in Figure 5. Since the magnitude of translation and rotation is small in differential motion, the angle operation is approximated in the differential transformation, that is, sinθ≈θ, cosθ≈1. After this approximation process , the homogeneous transformation matrix between the coordinate systems before and after the differential motion can be further deduced. By observing the composition of the homogeneous transformation matrix, we can see that the rotation matrix is the antisymmetric matrix corresponding to the differential rotation, so the antisymmetric matrix is introduced to simplify the homogeneous transformation. A representation of the secondary transformation matrix. The basic principle of the differential transformation method is described in detail below with reference to the diagrams.

As shown in Fig. 6, it is assumed that the coordinate system B initially coincides with the coordinate system A, and then the differential rotational motion δ=[δ _x δ _y δ _z ] ^T and translational motion d=[d _x d _y d of B relative to A occur in sequence _z ] ^T reaches B'. According to the principle of robot kinematics, the rotation transformation matrix around the x-axis, y-axis and z-axis by θ angle is as follows:

When θ is small, the following formula can be approximated:

sinθ=θ, cosθ=1 (10)

Then for the differential rotational motion of B relative to A, δ=[δ _x δ _y δ _z ] ^T , the differential rotation around each single axis can be transformed into:

The total transformation of the differential rotational motion can be regarded as the compound action of the above three transformations, as shown in formula (11). Among them, the equivalent rotation axis k=[k _x k _y k _z ] ^T , and the relationship between the equivalent differential rotation angle δθ and δ _x , δ _y , δ _z is:

δ _x = k _x δθ, δ _y = k _y δθ, δ _z = k _z δθ (14)

The multiplication of differential rotation transformation matrices conforms to the commutative law, that is, the order of operators Rot( _x ,δx), Rot(y, _δy ), Rot( _z ,δz) can be arbitrarily exchanged.

In order to facilitate subsequent calculations, the differential rotation transformation matrix is expanded to a homogeneous transformation matrix of order 4 as follows:

When B has differential rotational motion relative to A, and then has translational motion d=[d _x d _y d _z ] ^T relative to A, the transformation matrix corresponding to the translational motion is:

Because B always performs differential motion relative to A (reference frame), the left multiplication rule is adopted when calculating the total transformation matrix, then the total transformation matrix corresponding to the differential motion [d ^T δ ^T ] ^T is:

In actual calculation, we often denote the antisymmetric matrix of δ=[δ _x δ _y δ _z ] ^T as [δ], which can be expressed as:

可表示为：but

can be expressed as:

In the formula: δ=[δ _x δ _y δ _z ] ^T , d=[d _x d _y d _z ] ^T , and E is a third-order unit matrix.

(3) Using the virtual coordinate system method to derive the Jacobian matrix formula of the robot space

The embodiment of the present invention constructs the space Jacobian matrix of the robot based on the virtual coordinate system method. As shown in FIG. 8 , the error form (position error and attitude error) of the robot joint coordinate system is first analyzed, and the generation of the error is understood as the robot joint coordinate The result of the differential motion is obtained, and a virtual coordinate system is introduced to indicate the pose error of the joint coordinate system. Then use the basic principle of the differential change method to solve the homogeneous transformation relationship between the virtual coordinate system and the original joint coordinate system (error-free, theoretical coordinate system), and then deduce that the robot end coordinate system is relative to the virtual coordinate system after the introduction of the virtual coordinate system. The pose relationship of the base coordinate system is compared with the original pose relationship (error-free, theoretical pose relationship), and the pose deviation of the robot end coordinate system is obtained. Observe the composition of the pose deviation, which can be constructed. Robot's spatial Jacobian matrix. The basic principle of constructing the Jacobian matrix of robot space based on the virtual coordinate system method is described in detail below with reference to the accompanying drawings.

到操作速度矢量

的线性映射。由于速度可以看作是单位时间内的微分运动，因此，速度雅可比矩阵可以看成是关节空间的微分运动dq向操作空间的微分运动D之间的转换矩阵。机器人的物体雅克比矩阵是指关节运动量误差向末端相对于其理论位姿的运动量误差(相对于末端工具坐标系表示)的转换矩阵；空间雅克比矩阵则是指关节运动量误差向末端相对于基坐标系的运动量误差(相对于基坐标系表示)的转换矩阵。机器人的物体雅克比矩阵与空间雅克比矩阵可相互转化。即It is specified in robot kinematics that the robot's velocity Jacobian matrix J(q) is expressed from the joint velocity vector

to the operating velocity vector

Linear mapping of . Since the velocity can be regarded as the differential motion in unit time, the velocity Jacobian matrix can be regarded as the transformation matrix between the differential motion dq in the joint space and the differential motion D in the operation space. The object Jacobian matrix of the robot refers to the transformation matrix of the joint motion error to the motion error of the end relative to its theoretical pose (represented by the end tool coordinate system); the space Jacobian matrix refers to the joint motion error to the end relative to the base. The transformation matrix of the motion amount error of the coordinate system (represented relative to the base coordinate system). The object Jacobian matrix and the space Jacobian matrix of the robot can be transformed into each other. which is

D=J(q)dq (21)

Further, J(q) can be expressed in blocks as

In the formula: J _li and J _ai represent the translation and rotation of the end effector caused by the unit joint motion of joint i, respectively. When the terminal differential motion amount D=[d ^T δ ^T ] ^T is expressed in the end tool coordinate system, the corresponding Jacobian matrix is denoted as ^T J(q), which is called the object Jacobian matrix; D=[d ^T δ ^T ] ^T When expressed in the base coordinate system, the corresponding Jacobian matrix is denoted as J(q), which is called the spatial Jacobian matrix.

Here, it is assumed that the DH parameters a _i-1 , α _i-1 , d _i and θ i corresponding to the joint coordinate system _i produce small changes Δa _i-1 , Δα _i-1 , Δd _i and Δθ _i , resulting in the coordinate System i has differential rotation δ _i and differential translation d _i relative to its theoretical pose, that is, differential motion D _i =[d _i ^T δ _i ^T ] ^T , which will lead to the occurrence of robot end coordinate system n Differential motion, so that the pose of the coordinate system n relative to the base coordinate system (coordinate system 0) changes.

根据机器人运动学原理，有下述关系：As shown in Figure 7, in the initial state, the transformation matrix of the robot end joint n relative to the base coordinate system is recorded as

According to the principle of robot kinematics, there are the following relationships:

分别表示坐标系n、i、n相对于坐标系o、o、i的变换矩阵；

分别表示

中的旋转矩阵；⁰P_i0、ⁱP_n0、⁰P_n0分别表示

中的位置向量。where:

Represent the transformation matrices of coordinate systems n, i, and n relative to coordinate systems o, o, and i, respectively;

Respectively

The rotation matrix in ; ⁰ P _i0 , ⁱ P _n0 , ⁰ P _n0 represent

The position vector in .

则：It is assumed that the coordinate system i reaches the position of the coordinate system i' (virtual coordinate system) after the differential motion occurs, and accordingly, the coordinate system n moves to the position n'. At this time, the transformation matrix of the coordinate system n' relative to the base coordinate system is recorded as

but:

Because in this process, the pose of the coordinate system n relative to the coordinate system i remains unchanged, so

Substitute equation (25) into equation (24) to get:

可由微分变换求得，已知微分运动量为D_i＝[d_i ^T δ_i ^T]^T，则：According to the foregoing content, it can be known that the transformation matrix of coordinate system i' relative to coordinate system i

It can be obtained by differential transformation, and the known differential motion is D _i =[d _i ^T δ _i ^T ] ^T , then:

Substitute equation (27) into (25) to get:

及⁰P_io与式(23)中的相应元素一致。In particular, in the formula:

and ⁰ P _io are consistent with the corresponding elements in Eq. (23).

记作Will

Referred to as

From the corresponding equations (28) and (29), it can be obtained:

与式(23)中的

比较，即可得到关节坐标系i的微分运动D_i＝[d_i ^T δ_i ^T]^T导致末端坐标系n相对于基坐标系产生的位姿偏差⁰D_ni＝[⁰d_ni ^{T 0}δ_ni ^T]^T，其中⁰d_ni为位置偏差，⁰δ_ni为姿态偏差。So far, we only need to convert the equation (28) into

and in formula (23)

By comparison, it can be obtained that the differential motion of the joint coordinate system i D _i =[d _i ^T δ _i ^T ] ^T causes the pose deviation of the end coordinate system n relative to the base coordinate system ⁰ D _ni =[ ⁰ d _ni ^{T 0} δ _ni ^T ] ^T , where ⁰ d _ni is the position deviation and ⁰ δ _ni is the attitude deviation.

For the calculation of the position deviation ⁰ d _ni , we only need to use the position ⁰ P _no ' of the origin of the coordinate system n in the final state under the base coordinate system minus the position 0 of the origin of the coordinate system n under the base coordinate system in the initial state ⁰ P _no is enough, and it can be obtained from formula (31):

由

左乘

得到，这说明末端坐标系n在初始姿态的基础上又相对于基坐标系发生了微分转动，再结合公式(20)可知，该微分转动量⁰δ_ni为：For the calculation of the attitude deviation ⁰ δ _ni , the analysis formula (30) shows that,

Depend on

left multiply

It is obtained, which shows that the end coordinate system n has undergone a differential rotation relative to the base coordinate system on the basis of the initial attitude. Combined with formula (20), it can be known that the differential rotation ⁰ δ _ni is:

Arranging formulas (32) and (33) into matrix form can be obtained:

Compared with formula (22), it can be known that:

According to the formula (22), the space Jacobian matrix of the robot can be obtained. It is worth noting that ⁰ D _ni is described in the base coordinate system of the robot, so the space Jacobian matrix of the robot is obtained according to formula (22).

Those skilled in the art can easily understand that the above are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, etc., All should be included within the protection scope of the present invention.

Claims (9)

1. A space Jacobian matrix construction method for machine parameter identification is characterized by comprising the following steps:

s100, analyzing the influence of the rod length, the torsion angle, the offset and the joint angle in the D-H model of the robot on the relationship between the connecting rod and the joint of the robot, calculating a homogeneous transformation matrix of the adjacent joints of the robot by using translation and rotation operators, and constructing a robot kinematics model;

s200, analyzing differential motion characteristics of the robot joint based on a robot kinematic model, and establishing a homogeneous transformation matrix between coordinate systems under the condition of differential motion;

s300, assuming that a certain joint coordinate system generates differential motion, establishing a virtual coordinate system corresponding to the joint on the basis, establishing a transformation matrix between the two, further calculating the actual pose of the tail end of the robot relative to a base coordinate system, comparing the actual pose with a theory pose, obtaining the pose error of the tail end of the robot relative to the base coordinate system caused by the motion amount error of the joint coordinate system, and constructing a space Jacobian matrix of the robot;

s300 comprises the following specific steps:

s301: analyzing the error form of the robot joint coordinate system, and introducing a virtual coordinate system to indicate the pose error of the joint coordinate system;

s302: solving a homogeneous transformation relation between the virtual coordinate system and the original joint coordinate system by utilizing a basic principle of a differential variation method;

s303: solving the pose relation of the robot tail end coordinate system relative to the base coordinate system after the virtual coordinate system is introduced, and comparing the pose relation with the in-situ pose relation to obtain the pose deviation of the robot tail end coordinate system;

s304: and constructing a space Jacobian matrix of the robot according to the pose deviation of the terminal coordinate system of the robot.

2. The method for constructing space Jacobian matrix for machine-generated numerical identification as claimed in claim 1, wherein in step S200, the establishment of the homogeneous transformation matrix comprises the following specific steps:

s201: the amplitude of translation and rotation in differential motion is small, so that the angular operation of the robot is approximately processed in differential transformation, when the joint angle is small, sin theta is approximately equal to theta, and cos theta is approximately equal to 1;

s202: differential rotation motion delta from joint i-1 to joint i of robot_x δ_y δ_z]^TAnd translational motiond＝[d_x d_y d_z]^TThe differential rotational movement δ ═ δ_x δ_y δ_z]^TThe transformation matrix of (a) is:

wherein, the equivalent rotation axis k ═ k_x k_y k_z]^T,δ_x＝k_xδθ,δ_y＝k_yδθ,δz＝k_zδθ；

The translational movement d ═ d_x d_y d_z]^TThe corresponding transformation matrix is:

3. the method for constructing a spatial Jacobian matrix for robot parameter identification according to claim 2, wherein a total transformation matrix of differential motion between robot joint coordinate systems is constructed by differentiating rotational motion and translational motion as follows:

4. the method of claim 2, wherein the step S200 further comprises:

s203: introduction of an antisymmetric matrix [ δ ]:

5. the method of claim 4, wherein the space Jacobian matrix J (q) of the robot in S304 is:

in the formula: j. the design is a square_liAnd J_aiRespectively representing the translation and rotation of the end effector, dq, due to the unit joint motion amount of the joint i_iRepresenting the spatial differential motion of joint i.

6. The method as claimed in claim 4, wherein in S301, the transformation matrix of the robot end joint n with respect to the base coordinate system is recorded as

In the formula:

respectively representing transformation matrixes of the coordinate systems n, i and n relative to the coordinate systems 0, 0 and i;

respectively represent

The rotation matrix of (1);⁰P_i0、ⁱP_n0、⁰P_n0respectively represent

Position vector of。

7. The method of claim 4, wherein in step S302, if the coordinate system i reaches the virtual coordinate system i ' after differential motion, the coordinate system n moves to n ', and the transformation matrix of the coordinate system n ' relative to the base coordinate system is the same as the transformation matrix of the base coordinate system

In the formula:

respectively representing transformation matrices of the coordinate systems i, i ', n ' relative to the coordinate systems o, i ';

respectively represent

The rotation matrix of (1);⁰P_i0、ⁱP_i′0、^i′P_n′0respectively represent

Is determined.

8. The method of constructing a spatial Jacobian matrix for machine parameter identification as claimed in claim 4, wherein in S303, the pose deviation of the robot end coordinate system is:

⁰D_ni＝[⁰d_ni ^T0δ_ni ^T]^T

wherein,⁰d_niis a positional deviation equal to the position of the origin of the coordinate system n in the final state under the base coordinate system⁰P_no' subtracting the position of the origin of the coordinate system n in the initial state under the base coordinate system⁰P_no；⁰δ_niIn order to be the attitude deviation,

to represent

The rotation matrix of (2).

9. The method of claim 1, wherein in S100, the robot kinematics model is a transformation matrix of a robot link coordinate system i relative to a link coordinate system i-1:

wherein: a is_i-1Is the length of the connecting rod i-1; alpha is alpha_i-1Is the torsion angle of the connecting rod i-1; d_iThe offset distance of the connecting rod i relative to the connecting rod i-1 is shown; theta_iThe rotation angle of the connecting rod i relative to the connecting rod i-1 around the axis i; rot (x, alpha)_i-1) Representing the rotation angle alpha around the x-axis of the coordinate system_i-1The corresponding homogeneous transformation matrix is specifically as follows:

Trans(x,a_i-1) Representing the x-axis translation distance a around the coordinate system_i-1The corresponding homogeneous transformation matrix is specifically as follows:

Rot(z,θ_i) Representing the angle of rotation theta around the z-axis of the coordinate system_iThe corresponding homogeneous transformation matrix is specifically

Trans(z,d_i) Representing a translation distance d around the z-axis of the coordinate system_iThe corresponding homogeneous transformation matrix is specifically as follows:

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