CN113885316B - Seven-degree-of-freedom collaborative robot stiffness modeling and identification method - Google Patents
Seven-degree-of-freedom collaborative robot stiffness modeling and identification method Download PDFInfo
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Abstract
The invention relates to the field of cooperative robots, in particular to a seven-degree-of-freedom cooperative robot stiffness modeling and identification method, which comprises the following steps: step one: performing kinematic modeling on the robot to define robot joint parameters; step two: carrying out rigidity modeling on the robot; step three: selecting a reverse condition number
As the observability index of the optimal method, solving the inverse condition number of each joint pair
And according to the individual influence of each joint on the inverse condition number
Is to obtain a well-identified region within the joint space; step four: joint stiffness is calculated. According to the invention, the seven-degree-of-freedom robot rigidity identification pose selection is studied, the good identification region with higher flexibility of the robot is determined by taking the inverse condition number as an observation index, the identification precision of a rigidity model is improved, and the optimal configuration selection can be effectively performed.
Description
Technical Field
The invention relates to the field of cooperative robots, in particular to a seven-degree-of-freedom cooperative robot stiffness modeling and identification method.
Background
Along with the continuous promotion of the industrial process of China, the demand of the market for industrial robots is also continuously changed, wherein the cooperative demand of robots and people has prompted the development of the cooperative robots.
The cooperative robot is a robot capable of directly interacting with people in a designated cooperative area, has the characteristics of man-machine fusion, safety, easiness in use, sensitivity, accuracy, flexibility and universality, is suitable for small-batch, multi-variety and user-customized flexible manufacturing requirements in the industrial field, has potential application prospects in the fields of dealing with aging social services, rehabilitation medical treatment and the like, and has become an important direction for guiding the development of future robots. The design concept of the cooperative robot with light weight and high load-to-weight ratio requires the integration of the joints of the robot, the compact structure and the light weight of the arm lever, so that a large number of flexible factors are introduced into the cooperative robot, the influence of structural members such as connecting rods and supporting pieces on the rigidity of the whole robot is not negligible, the improvement of the rigidity of the whole robot is difficult, and the dynamic performance and the precision of the robot are influenced. The virtual joint method is a common method for modeling the rigidity of the robot, but the modeling workload is large, and the problem to be solved is how to reduce the modeling workload and ensure the modeling accuracy for the cooperative robot.
Disclosure of Invention
The invention aims to provide a seven-degree-of-freedom collaborative robot stiffness modeling and identification method, which is used for researching seven-degree-of-freedom robot stiffness identification pose selection, and determining a good identification area with high flexibility of a robot by taking the reverse condition number as an observation index, so that the identification precision of a stiffness model is improved, and the optimal configuration selection can be effectively carried out.
The aim of the invention is realized by the following technical scheme:
a seven-degree-of-freedom collaborative robot stiffness modeling and identification method comprises the following steps:
step one: performing kinematic modeling on the robot to define robot joint parameters;
step two: carrying out rigidity modeling on the robot;
step three: selecting a reverse condition number
As the observability index of the optimal method, solving the counter condition number of each joint>
And according to the individual influence of the joints on the adverse condition number->
Is to obtain a well-identified region within the joint space;
step four: joint stiffness is calculated.
In step one, each two adjacent links are described as follows with modified DH parameters:
wherein the method comprises the steps of
Is the homogeneous transformation matrix of the ith connecting rod-1, and represents the transformation from the ith connecting rod coordinate system to the ith connecting rod-1 coordinate system;
the seven-degree-of-freedom robot kinematic equation is deduced as:
in the second step, the rigidity model K of the redundant robot X The simplification is as follows:
K X ＝(J) T K Θ J (6)；
in the above formula (6), J represents the Jacobian matrix, K of the robot Θ Representing a joint stiffness matrix.
In the second step, the rigidity model K of the redundant robot X The simplification process is as follows:
the rigidity performance of the robot at the end point is defined by a rigidity matrix, and specifically comprises the following steps:
F＝K X Δt (3)；
in the above formula (3), F is an external force and moment vector applied to the robot end point, and Δt represents the elastic deformation of the robot end point in cartesian space;
stiffness model K of redundant robot X Expressed as:
K X ＝(J) T (K Θ -K C ) J (4)；
in the above formulas (4) and (5), J represents the Jacobian matrix of the robot, K C Is the complementary stiffness matrix of the stiffness model, K Θ Representing a matrix of joint stiffness,
is a joint displacement vector;
for redundant robotic arms, the jacobian J is irreversible and it is assumed that the jacobian J of the robot does not change with end load, i.e., the complementary stiffness matrix K C The influence on the rigidity model is negligible, and the rigidity model is simplified into:
K X ＝(J) T K Θ J (6)。
in step three, the reverse condition number is defined as follows:
in the above formula (7), κ is F Representing the condition number of a jacobian matrix based on the Frobenius (Luo Beini us) norm, tr (g) representing the trace of the matrix;
the jacobian matrix J of the robot is normalized through the characteristic length L, and the jacobian matrix J with uniform dimension N The relationship with the unnormalized jacobian matrix J is expressed as:
in step three, the characteristic length L of the robot is derived as follows:
a max ＝max{a i }，
d max ＝max{d i }(i＝1，2，…7)，
M＝max{a max ,d max }，
wherein a is i Is the length of a connecting rod of the robot, d i The connecting rod offset distance is;
by making a jacobian matrix J N Minimum condition number is minimum
To find the feature length L, put all design variables into the new design vector, i.e.: />
Solving for vector value x may translate into solving an optimization problem:
in the third step, solving the counter condition number of each joint
The process of obtaining a well-identified region is as follows:
will be
Expressed as:
by influencing factor x i Individual effects of (2)
When x is expressed as i The condition number average value obtained by changing other m-1 influence factors is unchanged, namely:
by making each influencing factor x i Within the allowable variation range [ a ] i ,b i ]Internal dispersion into s i Among cells, an equal division point is defined as a discrete node (s i +1), then:
in the above formula (13), p j Numbering discrete points, x j (p j ) Indicating that the jth influencing factor is at p j Values at discrete points;
by influencing factor x i And each influencing factor x i Is constructed of Orthogonal Arrays (OA) shown in the following formula (14):
wherein, lambda j,i Is the serial number of the discrete point of the ith influence factor in the jth experimental unit;
the individual utility f (x) is solved by the following formula (16) i ) Is to be added to the following:
wherein x is m (Λ j,m ) Represented at lambda j,m Influence factor x of discrete points m Is a value of (2);
determination of influencing factor x by performing analysis of variance i Whether to counter condition number
The number has great influence according to each influence factorx i For the counter condition number->
Is to acquire a well-identified region in joint space.
In step three, the influence factor x is determined by performing analysis of variance i Whether or not to reverse the condition
The number has a significant impact due to the following hypothesis test:
influence factor x i The total average value mu (x i ) The deduction is as follows:
influence factor x i Sum of squares of errors S E (x i ) The following steps are obtained:
influence factor x i Sum of squares S A (x i ) The following steps are obtained:
thus, test statistics T i F distribution test statistics of (c):
ignoring the reverse condition number by analysis of variance
Without significant influencing factors and simplifying the inverse condition number +.>
Mathematical model by comparing T i Deriving each influencing factor x i For the counter condition number->
T i The greater the i-th factor is +.>
The greater the impact of (c).
In the third step, according to each influencing factor x i Against condition number
And drawing a joint profile, and calculating the inverse condition numbers of the global area, the well-identified area and other areas respectively, wherein the average inverse condition number, the maximum inverse condition number and the minimum inverse condition number of the well-identified area are all larger than those of the global area and other areas.
And step four, calculating the joint stiffness value by a least square method.
The invention has the advantages and positive effects that:
1. according to the method, the seven-degree-of-freedom robot stiffness identification pose selection is studied, the good identification region with high robot flexibility is determined by using the most observed indexes of the inverse condition number, and a plurality of groups of measurement poses are selected in the region for stiffness identification, so that the error sensitivity of the least square solution is reduced, and the identification precision of the stiffness model is improved.
2. According to the invention, the individual influence of the joints on the inverse condition number is separated by adopting an Influence Factor Separation Method (IFSM) based on an Orthogonal Design Experiment (ODE), the change rule of each joint is found out according to the inverse condition number, and the joints with obvious influence on the index can be found out through analysis of variance (ANOVA) of experimental results, so that a good identification area of the robot in the joint space is obtained, and the modeling workload is reduced.
Drawings
FIG. 1 is a flow chart of a design method of the present invention;
FIG. 2 is a schematic diagram of a seven degree-of-freedom redundant robot of the present invention;
FIG. 3 is a schematic diagram of a virtual joint of the seven-degree-of-freedom redundant robot of FIG. 2;
FIG. 4 is a graph of the inverse condition number versus influencing factors for an embodiment of the present invention;
FIG. 5 is a joint profile view of a well-identified region determined in accordance with an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
As shown in fig. 1 to 5, the present invention includes the steps of:
step one: and performing kinematic modeling on the robot to define robot joint parameters.
As shown in fig. 2-3, the seven-degree-of-freedom redundant robot can be regarded as consisting of eight connecting rods and seven joints, and the DHm parametric modeling method can be realized through the connecting rod rotation angle alpha i-1 Length of connecting rod a i-1 Offset distance d of connecting rod i Angle of articulation theta i Four parameters describe the motion characteristics of the connecting rod, wherein α i-1 、a i-1 Describing the motion characteristics of the connecting rod i-1 itself, d i 、θ i The coupling relationship between the link i-1 and the link i is described.
Coordinate system O i -x i y i z i Relative to the coordinate system O i-1 -x i-1 y i-1 z i-1 The general formula of the connecting rod transformation is as follows:
cθ in the above formula (1) i ＝cosθ i ，sθ i ＝sinθ i ，cα i-1 ＝cosα i-1 ，sα i-1 ＝sinα i-1 。
Every two adjacent connecting rods can be described by the improved DH parameter (namely formula (1)), the pose of the tail end of the robot can be obtained by the continuous multiplication of the homogeneous transformation matrix of the connecting rods, and the seven-degree-of-freedom robot kinematics equation can be deduced as follows:
in the above-mentioned (2),
representing the pose matrix and the position matrix, respectively.
The robot joint displacement vector can be obtained by the robot kinematics equation of the above (2)
θ i Indicating the displacement angle of the ith joint.
Step two: the robot is subjected to rigidity modeling by using a Virtual Joint Method (VJM), specifically:
(2.1) defining the rigidity performance of the robot at the end point through a rigidity matrix, specifically:
F＝K X Δt (3)；
in the above formula (3), F is an external force and moment vector applied to the robot end point, and Δt represents the elastic deformation of the robot end point in the cartesian space.
(2.2) modeling the stiffness of the redundant robot K X Expressed as:
K X ＝(J)T(K Θ -K C )J (4)；
in the above formulas (4) and (5), J represents the Jacobian matrix of the robot, K C Is the complementary stiffness matrix of the stiffness model, K Θ Representing a matrix of joint stiffness,
the joint displacement vector is obtained by a robot kinematics equation in the first step.
For redundant robots, the jacobian J is irreversible, so the Moore-Penrose inverse (molar-Peng Resi inverse) is used, and it is assumed that the jacobian J of the robot does not change with end load, i.e. the complementary stiffness matrix K C The influence on the rigidity model is negligible, and the rigidity model can be simplified into:
K X ＝(J) T K Θ J (6)；
step three: selecting observable indexes, solving the influence degree of each joint on the observable indexes, and solving a better identification area in a joint space, wherein the method specifically comprises the following steps:
(3.1) selecting the reverse condition number
The observability index as the optimal method is specifically:
(3.1.1) the inverse condition number of Jacobian matrix based on Frobenius (Luo Beini us) norm is defined as follows:
in the above formula (7), κ is F Representing the condition number of a Jacobian matrix based on the Frobenius (Luo Beini Uss) norm, tr (g) representing the trace of the matrix, the inverse condition number
The closer to 1, the better the flexibility of the robot configuration, when +.>
The configuration of the robot is called isotropic and this configuration is most flexible, while +.>
The smaller the robot configuration, the closer to the singularity.
Due to the reverse condition number
The result of the stiffness recognition is highly sensitive and therefore is used as a criterion for selecting the optimal robot configuration and should be as close to 1 as possible.
(3.1.2) normalizing the Jacobian matrix J of the robot by the characteristic length L, wherein the Jacobian matrix J is used for the Jacobian matrix with uniform dimension N The relationship between it and the unnormalized jacobian J can be expressed as:
in the above formula (8), L represents the characteristic length of the obtained robot.
The derivation of L is as follows:
a max ＝max{a i }，
d max ＝max{d i }(i＝1，2，…7)，
M＝max{a max ,d max }，
wherein a is i Is the length of a connecting rod of the robot, d i Is the offset distance of the connecting rod.
Thus, it is possible to obtain a matrix of jacobian J N Minimum condition number is minimum
To find the feature length L, put all design variables into the new design vector, i.e.:
solving for vector value x may translate into solving an optimization problem:
(3.2) obtaining individual effects of each Joint and the Joint against the condition number by IFSM
Specifically:
(3.2.1) separation of Joint vs. adverse condition number Using an Orthogonal Design Experiment (ODE) based Influence Factor Separation Method (IFSM)
And according to the inverse condition number +.>
The change rule of each joint is found out, and the joint with obvious influence on the index can be found out through analysis of variance (ANOVA) of experimental results, so that a good identification area of the robot in the joint space is obtained.
Will be
Expressed as:
by joint influencing factor x i Individual effects of (2)
When x is expressed as i The condition number average value obtained by changing other m-1 influence factors is unchanged, namely:
obviously, it is very difficult to integrate the weights of the above formula, and is practically impossible. However, in the analysis of a robot condition number model, it is generally only necessary to know the condition number κ F Displacement angle theta of each joint of robot i Rather than an exact profile. Thus, complex mathematical derivation of multiple integrals can be converted into a series summation problem, i.e., each joint influencing factor x i In its allowable variation range [ a ] i ,b i ]Internal dispersion into s i Among cells, an equal division point is defined as a discrete node (s i +1)。
Then:
in the above formula (13), p j Numbering discrete points, x j (p j ) Indicating that the jth influencing factor is at p j Values at discrete points.
(3.2.2) obtaining the influence of each factor with a small calculation amount by using a factor-influence separation method which can rapidly separate each factor x from the inverse condition number mathematical model of the above formula (11) i Is a function of (a) and (b).
Let each influencing factor x i The number of discrete points is the same, i.e. s i S, according to influencing factor x i And the number of discrete points thereof, by influencing factor x i And each influencing factor x i Is to construct an Orthogonal Array (OA) L shown in the following equation (14) c (s m ). Each column of the Orthogonal Array (OA) represents an influencing factor x i While each row represents one experimental unit at a different discrete point combination of factors, the total number of experiments is c=s 2 。
In the above formula (15), Λ j,i Is the serial number of the discrete point of the ith influencing factor in the jth experimental unit.
The individual utility f (x) is solved by the following equation (16) i ) Is to be added to the following:
wherein x is m (Λ j,m ) Represented at lambda j,m Influence factor x of discrete points m Is a value of (2).
(3.2.3) determination of Joint influencing factor x by performing analysis of variance i Whether or not to reverse the condition
The number has a significant impact and this problem can be attributed to the following hypothesis test:
influence factor x i The total average value mu (x i ) Can be deduced as:
influence factor x i Sum of squares of errors S E (x i ) It can be derived that:
influence factor x i Sum of squares S A (x i ) It can be derived that:
thus, test statistics T i F distribution test statistics of (c):
let lambda be the significance level, typically 0.01, if it is the test statistic T i ≤F λ (s-1,s 2 S), then it is indicated that 99% certainty is acceptable for H 0 I.e. influencing factor x i Against condition number
Has no significant effect, but is the contrary when T i >F λ (s-1,s 2 -s) representing that H is to be rejected 0 At a certainty of 99%, i.e. influencing factor x i Has a significant impact on the reverse condition number. Therefore, the counter condition number can be neglected by analysis of variance (ANOVA)>
Without significant influencing factors and simplifying the inverse condition number +.>
Mathematical model by comparing T i Can obtain each factor x i For the counter condition number->
Order of influence from primary to secondary, T i The greater the i-th factor is +.>
The greater the impact of (c).
For a seven degree of freedom collaborative robot as shown in FIGS. 2-3, the displacement of the first and last joints does not affect the reverse condition number of the robot
It can be set to any value during the analysis, in this embodiment the joint 1 displacement is set to θ 1 =0°, the last joint 7 displacement is set to θ 7 =0°, the other five joints are influencing factors x i 。
In the present embodiment, the working range of each robot joint is equally divided into 60 intervals, and thus the Orthogonal Array (OA) of the above formula (14) is composed of 5 factors, each factor containing 61 levels.
FIG. 4 shows the five joints described above in terms of the reverse condition number
As can be seen from FIG. 4, the effect curve per joint pair against condition number +.>
The degree of influence of the joints 4, 5 and 6 on the reverse condition number is unequal compared to joints 2 and 3>
Is more effective.
Each influencing factor x is calculated according to step (3.2.3) above i Test statistic T of (1) i Among the five joints, joint 4 test statistic T i Maximum, indicate against condition number
The greatest effect of (2) is followed by joint 6, while joint 3 is +_against the condition number +_against>
With a 99% confidence that joint 3 is judged to be ++against the condition number, based on the above-described step (3.2.3) analysis of variance>
No significant effect was observed.
(3.3) acquisition in joint spaceSeveral good recognition areas (areas with higher robot flexibility) and selecting a group with a larger reverse condition number in these areas
To achieve good convergence of stiffness identification.
Optimizing joints 4, 5 and 6, dividing the working space of the joint 5 into 10 equal intervals, drawing a joint outline diagram at the interval points of the joint 5, and respectively calculating the inverse condition numbers of a global area, a good recognition area and other areas by a Monte Carlo method as shown in fig. 5
Since the joint space is symmetrical, only half of the joint space is used for analysis and computation, using two million sampling points per computation. The calculation verifies that the average inverse condition number, the maximum inverse condition number and the minimum inverse condition number of the well-identified region are all larger than those of the global region and other regions, and the effectiveness of an Influence Factor Separation Method (IFSM) based on an Orthogonal Design Experiment (ODE) is proved. The monte carlo process is well known in the art.
In several well-identified regions in the acquired joint space, selecting a set of measurement poses with a large inverse condition number in these regions achieves good convergence of stiffness identification.
Step four: according to the rigidity model in the second step and the good recognition area of rigidity recognition selected in the third step, calculating a joint rigidity value by a least square method, wherein the joint rigidity value is specifically:
according to the good recognition area (the area with higher robot flexibility) of the rigidity recognition selected in the third step, selecting a plurality of groups of measurement poses in the area for rigidity recognition to be substituted into the rigidity model in the second step, and using a least square method to minimize the sum of squares of residual errors, wherein the sum of squares is as shown in the following formula:
in the above formulas (22) and (23), F i Is the i-th component of the force vector F applied to the robot end point and c is the joint stiffness vector.
Each experiment yielded a 6 x 1 force vector, a 6 x 1 elastic displacement vector, and a 6 x 6A matrix. Thus, the size of the matrix is changed from 6×7 to 6nq×7, based on the generalized inverse of a, the value c of c min The euclidean norm delta of the approximation error is minimized.
c min ＝(A T A) -1 A T Δt (24)；
The least squares calculation described above is well known in the art.
In this embodiment, the operations and drawings of each step may be implemented by commercial software such as matlab.
Claims (8)
1. A seven-degree-of-freedom collaborative robot stiffness modeling and identification method is characterized in that: the method comprises the following steps:
step one: performing kinematic modeling on the robot to define robot joint parameters;
step two: carrying out rigidity modeling on the robot;
step three: selecting a reverse condition number
As the observability index of the optimal method, solving the counter condition number of each joint>
And according to the individual influence of the joints on the adverse condition number->
Is to obtain a well-identified region within the joint space;
solving the counter condition number of each joint
The process of obtaining a well-identified region is as follows:
will be
Expressed as:
by influencing factor x i Individual effects of (2)
When x is expressed as i The condition number average value obtained by changing other m-1 influence factors is unchanged, namely:
by making each influencing factor x i Within the allowable variation range [ a ] i ,b i ]Internal dispersion into s i Among cells, an equal division point is defined as a discrete node (s i +1), then:
in the above formula (13), p j Numbering discrete points, x j (p j ) Indicating that the jth influencing factor is at p j Values at discrete points;
by influencing factor x i And each influencing factor x i Is constructed of Orthogonal Arrays (OA) shown in the following formula (14):
wherein, lambda j,i Is the serial number of the discrete point of the ith influence factor in the jth experimental unit;
the individual utility f (x) is solved by the following formula (16) i ) Is to be added to the following:
wherein x is m (Λ j,m ) Represented at lambda j,m Influence factor x of discrete points m Is a value of (2);
determination of influencing factor x by performing analysis of variance i Whether to counter condition number
The number has great influence according to each influence factor x i For the counter condition number->
Is used to obtain a well-identified region in joint space;
determination of influencing factor x by performing analysis of variance i Whether or not to reverse the condition
The number has a significant impact due to the following hypothesis test:
H 0 :f(x i (1))＝f(x i (2))＝…＝f(x i (s))
H 1 :f(x i (1))，f(x i (2))，…，f(x i (s))Not all equal (17)；
influence factor x i The total average value mu (x i ) The deduction is as follows:
influence factor x i Sum of squares of errors S E (x i ) The following steps are obtained:
influence factor x i Sum of squares S A (x i ) The following steps are obtained:
thus, test statistics T i F distribution test statistics of (c):
ignoring the reverse condition number by analysis of variance
Without significant influencing factors and simplifying the inverse condition number +.>
Mathematical model by comparing T i Deriving each influencing factor x i For the counter condition number->
T i The greater the i-th factor is +.>
The greater the effect of (a) is,
step four: joint stiffness is calculated.
2. The seven-degree-of-freedom collaborative robot stiffness modeling and recognition method of claim 1, wherein:
in step one, each two adjacent links are described as follows with modified DH parameters:
wherein the method comprises the steps of
Is the homogeneous transformation matrix of the ith connecting rod-1, and represents the transformation from the ith connecting rod coordinate system to the ith connecting rod-1 coordinate system;
the seven-degree-of-freedom robot kinematic equation is deduced as:
3. the seven-degree-of-freedom collaborative robot stiffness modeling and recognition method of claim 1, wherein:
in the second step, the rigidity model K of the redundant robot X The simplification is as follows:
K X ＝(J) T K Θ J (6)；
in the above formula (6), J represents the Jacobian matrix, K of the robot Q Representing a joint stiffness matrix.
4. The seven-degree-of-freedom collaborative robot stiffness modeling and recognition method of claim 3, wherein:
in the second step, the rigidity model K of the redundant robot X The simplification process is as follows:
the rigidity performance of the robot at the end point is defined by a rigidity matrix, and specifically comprises the following steps:
F＝K X Δt (3)；
in the above formula (3), F is an external force and moment vector applied to the robot end point, and Δt represents the elastic deformation of the robot end point in cartesian space;
stiffness model K of redundant robot X Expressed as:
K X ＝(J) T (K Θ -K C )J (4)；
in the above formulas (4) and (5), J represents the Jacobian matrix of the robot, K C Is the complementary stiffness matrix of the stiffness model, K Q Representing a matrix of joint stiffness,
is a joint displacement vector;
for redundant robotic arms, the jacobian J is irreversible and it is assumed that the jacobian J of the robot does not change with end load, i.e., the complementary stiffness matrix K C The influence on the rigidity model is negligible, and the rigidity model is simplified into:
K X ＝(J) T K Θ J (6)。
5. the seven-degree-of-freedom collaborative robot stiffness modeling and recognition method of claim 1, wherein:
in step three, the reverse condition number is defined as follows:
in the above formula (7), k F Representing the condition number of a jacobian matrix based on the Frobenius (Luo Beini us) norm, tr (g) representing the trace of the matrix;
the jacobian matrix J of the robot is normalized through the characteristic length L, and the jacobian matrix J with uniform dimension N The relationship with the unnormalized jacobian matrix J is expressed as:
6. the seven-degree-of-freedom collaborative robot stiffness modeling and recognition method of claim 5, wherein:
in step three, the characteristic length L of the robot is derived as follows:
a max ＝max{a i }，
d max ＝max{d i }(i＝1，2，…7)，
M＝max{a max ,d max }，
wherein a is i Is the length of a connecting rod of the robot, d i The connecting rod offset distance is;
by making a jacobian matrix J N Minimum condition number is minimum
To find the feature length L, put all design variables into the new design vector, i.e.:
solving for vector value x may translate into solving an optimization problem:
7. the seven-degree-of-freedom collaborative robot stiffness modeling and recognition method of claim 1, wherein: in the third step, according to each influencing factor x i Against condition number
And drawing a joint profile, and calculating the inverse condition numbers of the global area, the well-identified area and other areas respectively, wherein the average inverse condition number, the maximum inverse condition number and the minimum inverse condition number of the well-identified area are all larger than those of the global area and other areas.
8. The seven-degree-of-freedom collaborative robot stiffness modeling and recognition method of claim 1, wherein: and step four, calculating the joint stiffness value by a least square method.
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