A robot dynamics parameter identification method and system

Abstract

The present invention provides a robot dynamic parameter identification method and system, including: establishing a mapping relationship between a minimum parameter set and a standard parameter set when a rigid body dynamic model is linearized; establishing a symmetric positive definite matrix manifold, and calculating relevant formulas based on the differential geometry structure of the manifold; establishing a geometric excitation optimization criterion and generating an optimal excitation trajectory with a traditional observation matrix condition number; establishing a parameter identification optimization objective function, and constructing a geometric convex approximate upper bound constraint suitable for iteration as a regularization term; iteratively identifying a minimum parameter set and nonlinear friction parameters. The present invention combines the geometric excitation trajectory optimization criterion with the traditional observation matrix condition number to stimulate the robot system characteristics, constructs a convex approximate upper bound constraint suitable for iterative optimization as a regularization term of the parameter identification optimization function, and iteratively identifies it with a nonlinear friction model to obtain inertia parameters that are more in line with the robot structure, ensuring the physical rationality of the parameters while improving the identification accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of robot dynamics parameter identification, and in particular to a robot dynamics parameter identification method and system. Background Art

[0002] Robot dynamics parameter identification is of great significance in robot control and dynamic analysis. Accurate parameters help improve control accuracy, execution efficiency and stability of dynamic response.

[0003] In a multi-DOF robot system, the identification parameters usually include the inertia matrix, the center of mass position, nonlinear friction parameters, etc. The accuracy of these parameters directly affects the accuracy of the robot's dynamic model, and thus affects the performance of the controller. At present, the dynamic parameter identification methods are all based on the linearized equations of inverse dynamics. Traditional parameter identification methods are generally based on the least squares method or maximum likelihood estimation, which minimizes the error between the model prediction value and the actual measurement value by adjusting the inertia parameters.

[0004] There are certain problems with the current identification methods: 1. When using semi-positive definite programming to solve semi-definite linear matrix inequality constraints, the physical consistency of the parameters imposed by the rigid constraints will cause the final estimated parameters to be on the edge of the physical consistency, that is, the mass and inertia tensor are abnormally close to zero. 2. When considering regularization for problem 1, the parameter distribution in the dynamic model often has complex non-Euclidean geometric characteristics, and the traditional Euclidean space regularization method is difficult to effectively express the intrinsic geometric relationship between parameters. 3. In view of the high-dimensional and high-degree-of-freedom system characteristics of robots, the existing excitation trajectory optimization criteria based on the condition number of the observation matrix are difficult to fully stimulate the characteristics of high-dimensional systems. Summary of the invention

[0005] In order to solve the deficiencies of the prior art, the present invention provides a robot dynamics parameter identification method and system;

[0006] On the one hand, a method for identifying robot dynamic parameters is provided, comprising:

[0007] Establish a rigid body dynamics model for the robot, and establish a mapping operator between the minimum parameter set and the standard parameter set based on the linearization process of the rigid body dynamics model for the robot; establish a symmetric positive definite matrix manifold, and calculate the metric tensor based on the differential geometry structure-related formula of the symmetric positive definite matrix manifold;

[0008] According to the mapping operator and the metric tensor, the geometric excitation trajectory optimization criterion is established; the excitation trajectory of the robot is generated by combining the geometric excitation trajectory optimization criterion with the traditional observation matrix condition number; the excitation trajectory of the robot is run on the robot to obtain the actual data collected by the robot;

[0009] Based on the actual data collected by the robot, the geodesic distance of the symmetric positive definite matrix manifold is used to establish the parameter identification optimization objective function, and the geometric convex approximate upper bound constraint suitable for iterative optimization is constructed. The geometric convex approximate upper bound constraint is used as the regularization term of the parameter identification optimization objective function.

[0010] The parameter identification optimization objective function containing the regularization term of the geometric convex approximation upper bound constraint is solved to obtain the identified minimum parameter set; based on the identified minimum parameter set, the optimization objective function of the nonlinear friction model is solved to obtain the identified friction parameters;

[0011] Based on the identified minimum parameter set and the identified friction parameters, the weights are calculated, and according to the weight values, it is determined whether to return to the solution step of the parameter identification optimization objective function containing the regularization term of the geometric convex approximation upper bound constraint, and finally the identified minimum parameter set and friction parameters are output.

[0012] On the other hand, a robot dynamics parameter identification system is provided, comprising:

[0013] A model building module is configured to: establish a robot rigid body dynamics model, establish a mapping operator between a minimum parameter set and a standard parameter set based on a linearization process of the robot rigid body dynamics model; establish a symmetric positive definite matrix manifold, and calculate a metric tensor according to a differential geometry structure-related formula of the symmetric positive definite matrix manifold;

[0014] The criterion establishment module is configured to: establish a geometric excitation trajectory optimization criterion according to the mapping operator and the metric tensor; combine the geometric excitation trajectory optimization criterion with the traditional observation matrix condition number to generate the robot's excitation trajectory; run the robot's excitation trajectory on the robot to obtain the robot's actual collection data;

[0015] The function establishment module is configured as follows: based on the actual data collected by the robot, the geodesic distance of the symmetric positive definite matrix manifold is adopted to establish the parameter identification optimization objective function, a geometric convex approximate upper bound constraint suitable for iterative optimization is constructed, and the geometric convex approximate upper bound constraint is used as the regularization term of the parameter identification optimization objective function;

[0016] A solution module is configured to: solve a parameter identification optimization objective function containing a geometric convex approximation upper bound constraint regularization term to obtain an identified minimum parameter set; based on the identified minimum parameter set, solve an optimization objective function of a nonlinear friction model to obtain identified friction parameters;

[0017] A calculation module is configured to: calculate weights based on the identified minimum parameter set and the identified friction parameters, determine whether to return to the solution step of the parameter identification optimization objective function containing the regularization term of the geometric convex approximation upper bound constraint according to the weight value, and finally output the identified minimum parameter set and friction parameters.

[0018] On the other hand, there is also provided an electronic device, comprising:

[0019] a memory for non-transitory storage of computer-readable instructions; and

[0020] a processor for executing the computer readable instructions,

[0021] When the computer-readable instructions are executed by the processor, the method described in the first aspect is executed.

[0022] On the other hand, a storage medium is provided, which non-temporarily stores computer-readable instructions, wherein when the non-temporary computer-readable instructions are executed by a computer, the method described in the first aspect is executed.

[0023] On the other hand, a computer program product is provided, comprising a computer program, wherein the computer program is used to implement the method described in the first aspect when running on one or more processors.

[0024] The above technical solution has the following advantages or beneficial effects:

[0025] The present invention adds the differential geometric structure of the symmetric positive definite matrix manifold of the robot inertial parameter space into the Fisher information matrix, which helps to minimize the variance in the geometric direction and enhance the distinguishability between parameters, so that it can better stimulate dynamic characteristics such as joint inertia and friction, thereby achieving the goal of improving recognition accuracy.

[0026] The present invention introduces the geodesic distance based on the symmetric positive definite matrix manifold, considers the geometric distance in the inertial parameter space, characterizes the constraint relationship between the robot joint and connecting rod parameters, and prefers the physically reasonable parameter region in the optimization to avoid solutions that do not conform to the physical meaning.

[0027] The present invention constructs a geometric convex approximation upper bound constraint as a regularization term, which reasonably expresses the intrinsic correlation of parameters in geometry while improving the recognition accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0029] Figure 1 It is a calculation flow chart of the present invention;

[0030] Figure 2(a) to Figure 2(c) The optimal excitation trajectory generated on a 7-DOF collaborative robot according to the method provided by the present invention;

[0031] Figure 3(a) to Figure 3(g) Comparison between the predicted joint torque diagram obtained after identification on a collaborative robot according to the method provided by the present invention and the actual measured torque;

[0032] Figure 4(a) and Figure 4(b) are the visual comparison results after parameter identification under different regularization methods. DETAILED DESCRIPTION

[0033] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0034] Embodiment 1

[0035] This embodiment provides a method for identifying robot dynamic parameters;

[0036] like Figure 1 As shown, a robot dynamics parameter identification method includes:

[0037] S1: Establish a rigid body dynamics model of the robot, and establish a mapping operator between the minimum parameter set and the standard parameter set based on the linearization process of the rigid body dynamics model of the robot;

[0038] S2: Establish a symmetric positive definite matrix manifold and calculate the metric tensor according to the differential geometry structure related formula of the symmetric positive definite matrix manifold;

[0039] S3: According to the mapping operator and the metric tensor, a geometric excitation trajectory optimization criterion is established; the excitation trajectory of the robot is generated by combining the geometric excitation trajectory optimization criterion with the traditional observation matrix condition number; the excitation trajectory of the robot is run on the robot to obtain the actual collected data of the robot;

[0040] S4: Based on the actual data collected by the robot, the geodesic distance of the symmetric positive definite matrix manifold is used to establish the parameter identification optimization objective function, and the geometric convex approximate upper bound constraint suitable for iterative optimization is constructed. The geometric convex approximate upper bound constraint is used as the regularization term of the parameter identification optimization objective function;

[0041] S5: Solve the parameter identification optimization objective function containing the geometric convex approximation upper bound constraint regularization term to obtain the identified minimum parameter set;

[0042] S6: Based on the identified minimum parameter set, the optimization objective function of the nonlinear friction model is solved to obtain the identified friction parameters;

[0043] S7: Based on the identified minimum parameter set and the identified friction parameters, the weight is calculated, and it is determined whether to return to S5 according to the weight value, and finally the identified minimum parameter set and friction parameters are output.

[0044] The present invention provides a method and system for identifying robot dynamic parameters, the method comprising: establishing a robot rigid body dynamics model based on the recursive Newton-Euler method, establishing a mapping relationship between a minimum parameter set and a standard parameter set when the model is linearized; establishing a symmetric positive definite matrix manifold, and calculating relevant formulas according to the differential geometry structure of the manifold; establishing a geometric excitation optimization criterion and generating the robot's optimal excitation trajectory with the traditional observation matrix condition number; establishing a target optimization function suitable for iterative optimization based on the symmetric matrix manifold related formula, and combining the nonlinear friction model with the convex optimization technology for iterative identification optimization. The present invention combines the geometric excitation trajectory optimization criterion with the traditional observation matrix condition number to stimulate the high degree of freedom and high-dimensional system characteristics of the robot system, and then constructs a convex approximate upper bound constraint suitable for iterative optimization as the regularization of the optimization function and the nonlinear friction force for iterative identification, so as to obtain inertia parameters that are more in line with the robot structure, and improve the identification accuracy while ensuring the physical rationality of the parameters.

[0045] Furthermore, the actual observation data of the robot includes: joint angles, joint velocities, joint accelerations and joint torques.

[0046] Furthermore, the S1: establishing a rigid body dynamics model of the robot, and establishing a mapping operator between a minimum parameter set and a standard parameter set based on a linearization process of the rigid body dynamics model of the robot, includes:

[0047] For the n-link multi-body dynamics system, the inverse dynamics model for calculating the joint torque is written as:

[0048]

[0049] Where M(q)∈R n×n represents the inertia force matrix, Represents the centrifugal Coriolis force matrix, g(q)∈R n×1 is the robot link gravity matrix, τ∈R n×1 represents the robot joint torque;

[0050] On the basis of the obtained dynamic model, it is linearized into the multiplication form of the observation matrix and the standard parameter set:

[0051]

[0052] in, is the observation matrix under the standard parameter set, χ∈R n×p is the standard parameter set, which can be written as the matrix expression of the n-link inertia parameter set:

[0053] χ=[π1,π2,...,π i ,...,π n];

[0054] Among them, π i =[I xx i ,I xy i ,I xz i ,I yy i ,I yz i ,I zz i ,m i x i ,m i y i ,m i z i ,m i ] is the inertia parameter set of the i-th connecting rod.

[0055] Since the matrix W χ The structure of makes it not full rank, so the solutions of the inertia parameters are not independent of each other. Based on the numerical decomposition method, The observation matrix of is decomposed with the standard parameter set, specifically:

[0056]

[0057] Among them, W ind is the observation matrix W χ Linearly independent columns of W are also called full-rank observation matrices; d is the observation matrix W χ The linear correlation column, W d It can also be written as ind The linear combination form is:

[0058] W d =W ind Q d ;

[0059] Among them, Q d is a constant matrix. So, the linearly independent column indices U ind Linearly related column index U d The following formula is composed:

[0060]

[0061] According to the linearly independent column index U ind Linearly related column index U d , linearly independent parameters and linearly dependent parameters are expressed as:

[0062]

[0063] Among them, χ ind are the independent inertia parameters corresponding to the linearly independent column indices, χ d is the non-independent inertial parameter corresponding to the linearly related column index. On this basis, the minimum linear combination of the standard parameter set is expressed as the minimum parameter set, specifically:

[0064] β=χ ind +Q d χ d =Kχ;

[0065] Among them, β is the minimum parameter set, K is the mapping operator from the standard parameter set to the minimum parameter set, and the specific form is:

[0066]

[0067] Finally, the full-rank observation matrix W is obtained ind The joint torque expression composed of the minimum parameter set β is:

[0068]

[0069] Furthermore, the S2: establishing a symmetric positive definite matrix manifold, and calculating the metric tensor according to the differential geometry structure related formula of the symmetric positive definite matrix manifold, includes:

[0070] Let the space of all n×n real symmetric matrices be S(n), and define an open set subset of symmetric positive definite matrices in S(n) Define the physically consistent symmetric positive definite matrix in the robot:

[0071]

[0072] in, For R 1×p →R 4×4 The mapping of P i is the symmetric positive definite matrix of the i-th link, tr(·) is the trace operator, I∈R 3×3 The identity matrix, I i is the inertia tensor of the rigid body, m is the mass of the rigid body, and c is the center of mass of the rigid body.

[0073] When the matrix When the robot's physical consistency is satisfied, P i On the fourth-order symmetric positive definite matrix manifold On the manifold is considered to be embedded in S(n).

[0074] From the above, we can see that the set is a symmetric positive definite matrix manifold Its tangent space at any point P is the space Then the infinitesimal arc length is defined as:

[0075] ds=(tr(P -1 dP) 2 ) 1 / 2 =‖P -1 / 2 dPP -1 / 2 ‖ F ;

[0076] Where dP represents the infinitesimal change of the symmetric positive definite matrix P. ds reflects the geometric distance between two points on the manifold.

[0077] Expanding the infinitesimal arc length ds using the definition of trace metric, first consider the quadratic distance ds between two points on the following manifold 2 To simplify for convenience:

[0078]

[0079] If P is the parameter π i Function, π i is the inertia parameter set of the i-th connecting rod, that is, P = P(π i ), which can be written in differential form as Substituting this into the infinitesimal arc length formula yields:

[0080]

[0081] According to the affine invariant Riemann metric formula:

[0082] ds 2 =dπ T m(π)dπ;

[0083] Among them, m, as a metric tensor, indirectly represents the distance and angle between two points in the manifold space by calculating the inner product in the tangent space;

[0084] At this time, each element m in the metric tensor m(π) ij (π) is expressed as:

[0085]

[0086] Where j, k = 1, 2, ..., p represents the inertia parameter set π of the i-th connecting rod i p components in , by calculating each element m jk (π) to obtain the final metric tensor m(π)∈R p×p The analytical expression of .

[0087] Further, S3: according to the mapping operator and the metric tensor, a geometric excitation trajectory optimization criterion is established, including:

[0088] According to the metric tensor m(π)∈R p×p The metric tensor of the n-link multibody dynamics system is defined as a diagonal block matrix composed of the metric tensors of the inertia parameters of the n links:

[0089] M(π)=diag(m(π1),m(π2),...,m(π n ))∈R np×np ;

[0090] Where M(π) is the metric tensor of the n-link multibody dynamics system, diag is expressed as a diagonal operator, and m(π n ) is the metric tensor of the nth link. Assume that the nominal value of the standard parameter set of the n-link multibody dynamics system is χ0, and the constant metric tensor under the nominal value χ0 is for:

[0091]

[0092] Combined with the mapping operator K, the metric tensor M is calculated from the standard parameter set space to the minimum parameter set space. β :

[0093]

[0094] In order to reduce the geometric uncertainty of the worst direction of the excitation trajectory, the metric tensor in the minimum parameter set space is added to the Fisher information matrix as geometric normalization information to obtain the geometric excitation trajectory optimization criterion:

[0095] λ max ((W ind T ∑ -1 W ind ) -1 M β );

[0096] Among them, λ max (·) is the solution to minimize the maximum eigenvalue of the Fisher information matrix, and ∑ is Gaussian additive noise.

[0097] Furthermore, the S3: combining the geometric excitation trajectory optimization criterion with the traditional observation matrix condition number to generate the robot's excitation trajectory; running the robot's excitation trajectory on the robot to obtain the robot's actual collection data, including:

[0098] The geometric excitation trajectory optimization criterion and the traditional measurement matrix condition number are used as the optimization objectives of the excitation trajectory:

[0099] J = γ1cond(W ind )+γ2λ max ((Wind T ∑ -1 W ind ) -1 M β );

[0100] Among them, γ1, γ2 represent the penalty adjustment coefficients of the optimization target, and cond(·) represents the operation of the condition number of the observation matrix.

[0101] The finite Fourier series is used as the robot's excitation trajectory, specifically:

[0102]

[0103] Among them, q i (t), are the robot joint angle, joint velocity, and joint acceleration at time t, respectively, i0 is the starting position of the robot joint, a l,i ,b l,i is the hyperparameter of the finite Fourier series, ω f is the basic frequency of the excitation trajectory, and N is the order of the finite Fourier series. At the same time, the optimization condition that the excitation trajectory should meet is:

[0104]

[0105] Among them, q i,max , are the position, velocity, and acceleration limits of joint i, which are given by the robot manufacturer; t0, t f The starting and ending time of the trajectory respectively.

[0106] The finite Fourier series is given by a l,i ,b l,i Indicates that the incentive trajectory optimization problem is described as:

[0107] min J=γ1cond(W ind )+γ2λ max ((W ind T ∑ -1 W ind ) -1 M β );

[0108]

[0109] Run the excitation trajectory on the robot and measure the robot joint angle q m , Joint speed Joint acceleration Torque τ real, and zero-phase filtering is used to reduce the acquisition noise information.

[0110] Further, S4: based on the actual data collected by the robot, the geodesic distance of the symmetric positive definite matrix manifold is used to establish the parameter identification optimization objective function, and the geometric convex approximate upper bound constraint suitable for iterative optimization is constructed, and the geometric convex approximate upper bound constraint is used as the regularization term of the parameter identification optimization objective function, including:

[0111] In the face of positive definite matrix manifolds There are two points Then the geodesic distance d between the two points is R (P,Q) is expressed as:

[0112]

[0113] in,‖·‖ F is the F-norm calculation, log(·) is the matrix logarithm calculation, and λ(·) is the eigenvalue calculation. For an n-link multi-body dynamic system, the total distance of its geodesic is expressed as the sum of the geodesic distances:

[0114]

[0115] Among them, χ1 and χ0 are the standard parameter set identification value and the standard parameter set nominal value of the n-link multi-body dynamics system, respectively, i ,x i 0 are the inertia parameter identification value and the inertia parameter nominal value of the i-th connecting rod, For R 1×p →R 4×4 , and λ(·) is the eigenvalue calculation.

[0116] The total geodesic distance of the symmetric positive definite matrix manifold of the n-link multi-body dynamics system is taken as the regularization term of the optimization objective function, and its expression is written as follows:

[0117]

[0118] Among them, W (k) Optimize the weights for the kth iteration, with the initial element being 1; is the observation matrix of the minimum parameter set, and the filtered q m , Substituting into the calculation, we can get; β (k) is the minimum parameter set identification value for the kth iteration; τ f is the friction torque, the initial element is 0; τ real is the measurement of the actual joint torque; γ3 is the penalty coefficient of the regularization term; for Total geodesic distance on the manifold; χ1 (k)Identify the value of the standard parameter set for the kth iteration.

[0119] Because the total distance of the geodesic is non-convex, the solution set is prone to fall into the local optimal solution, so a geodesic convex approximation upper bound constraint is constructed as a regularization term to reflect the geometric deviation between the current estimated parameter value and the nominal value in the manifold space.

[0120] First, consider another geodesic distance logarithmic Euclidean metric for symmetric positive definite matrix manifolds, specifically:

[0121]

[0122] Among them, log(·) is the matrix logarithm calculation, For R 1×p →R 4×4 This function is about the parameter to be identified π i is a concave function. Based on convexity analysis and Taylor expansion of the matrix, Written as the following convex approximate upper bound constraint:

[0123]

[0124] in, is the inertia parameter of the i-th connecting rod identified in the k-th iteration i π0 (k) The calculated iterative change reference point (symmetric positive definite matrix), the optimization target distance of the i-th link is:

[0125]

[0126] For an n-link multibody dynamic system, the total geodesic distance based on the log-Euclidean metric is expressed as the sum of the log-Euclidean metric:

[0127]

[0128] Among them, χ1 and χ0 are the standard parameter set identification value and the standard parameter set nominal value of the n-link multi-body dynamics system, respectively, i ,x i 0 are the inertia parameter identification value and the nominal value of the inertia parameter of the i-th connecting rod respectively.

[0129] Furthermore, the S5: solving the parameter identification optimization objective function containing the geometric convex approximation upper bound constraint regularization term to obtain the identified minimum parameter set includes:

[0130] Constrain the regularization term based on the geometric convex approximation upper bound Add it to the optimization objective function suitable for iterative calculation:

[0131]

[0132] Combined with physically consistent symmetric matrix The physical consistency of the n-link multibody dynamics system is expressed as a linear matrix inequality constraint form, specifically:

[0133] D(χ)=diag(P1,P2,...,P n )>0;

[0134] Where diag(·) represents a diagonal block matrix operation.

[0135] Finally, the optimization problem of parameter identification is described as:

[0136]

[0137] Among them, m i is the mass of each link, and M is the total mass of the robot.

[0138] Further, S6: based on the identified minimum parameter set, solving the optimization objective function of the nonlinear friction model to obtain the identified friction parameters, including:

[0139] The actual measured torque τ real and the minimum parameter set β for the kth iteration (k) The residual of the estimated torque is calculated as the actual friction torque, specifically:

[0140]

[0141] Where Δτ is the moment residual, To estimate the torque.

[0142] The nonlinear friction model under no-load conditions is expressed as:

[0143]

[0144] Among them, α 1,j ,α 2,j ,α 3,j ,α 4,j ,α 5,j is the nonlinear friction parameter of the jth connecting rod, τ f (t) is the joint friction torque at sampling time t, is the joint angular velocity at sampling time t.

[0145] In the formula, describes the Stribeck friction effect, Describe the phenomenon of viscous friction. Describe the phenomenon of Coulomb friction;

[0146] The friction parameters are identified using a global nonlinear optimization algorithm. The nonlinear friction model optimization problem of the n-link multi-body dynamics system is expressed as follows:

[0147]

[0148] Further, S7: based on the identified minimum parameter set and the identified friction parameters, a weight is calculated, and it is determined whether to return to S5 according to the weight value, and finally the identified minimum parameter set and friction parameters are output.

[0149] Based on the identified estimated torque and nonlinear friction torque obtained in S5 and S6 respectively, the residual torque residual is calculated from the actual measured torque. Specifically:

[0150] ξ=τ real -W ind β (k) -τ f ;

[0151] Where ξ is the residual moment residual.

[0152] The residual moment residual includes noise and unknown moment components. The residual moment is used as the main basis for updating the next generation of weights. The weights are expressed using Lorentz functions to suppress noise and unknown moment components. Specifically:

[0153]

[0154] Among them, W is the weight, ξ is the residual moment residual, and c controls the weight decay speed;

[0155] Based on the latest weights, iterative calculations are performed in the order of S5, S6, and S7 to continuously update W (k) ,β (k) , i π0 (k) ,t f Repeat the above process until the weight matrix reaches the following standard and stops the iteration:

[0156]

[0157] Among them, ε is the tolerance of the weight matrix change.

[0158] The robot of this embodiment is a 7-DOF collaborative robot, and all of its seven joints are rotational joints.

[0159] like Figure 2(a) to Figure 2(c) The figure shows that the geometric excitation trajectory optimization criterion and the traditional observation matrix condition number are used as optimization targets to generate the optimal excitation trajectory of the robot. The trajectory is a periodic trajectory with a period of 20s, a sampling rate of 1kHz, and a trajectory base frequency of 0.471.

[0160] As shown in Table 2, the method of the present invention is used to identify the dynamic parameters of the robot. The problem that the physical consistency imposed by the rigid constraints causes the final estimated parameters to be located on the edge of the semi-positive definite matrix is ​​significantly improved, while the occurrence of unreasonable physical data is reduced, such as the mass of the connecting rod 3 in Table 1.

[0161] Table 1 Comparison of robot part link parameter identification results

[0162]

[0163] like Figure 1 As shown, an embodiment of the present invention provides a robot dynamics parameter identification method and system, the system specifically comprising:

[0164] The dynamic parameter linearization module establishes the rigid body dynamics model of the robot based on the recursive Newton-Euler method, converts the linearized model into the form of a full-rank observation matrix and a minimum parameter set, and on this basis establishes a mapping relationship between the minimum parameter set and the standard parameter set.

[0165] The excitation trajectory generation module establishes a symmetric positive definite matrix manifold and calculates the metric tensor according to the differential geometry structure related formula of the symmetric positive definite matrix set; it is connected with the dynamic parameter linearization module, and the geometric excitation trajectory optimization criterion is established in combination with the mapping relationship, and is used together with the traditional observation matrix condition number as the optimization target of the optimal excitation trajectory.

[0166] Parameter identification geometric optimization objective function module: connected with the excitation trajectory generation module, the optimization objective function of parameter identification is established with the geodesic distance of the symmetric positive definite matrix manifold, and a geometric convex approximate upper bound constraint suitable for iterative optimization is created as a regularization term.

[0167] Iteration module: connected with the parameter identification geometry optimization objective function module to solve the parameter identification geometry optimization objective function of the module; optimize and solve the nonlinear friction model based on the identified minimum parameter set; update the weights after obtaining the predicted torque and friction torque; finally, iteratively solve the parameter identification objective function containing the geometric convex approximation regularization term and the nonlinear friction model objective function and weights to achieve the optimal value.

[0168] like Figure 2(a) to Figure 2(c) As shown, the excitation trajectory of the 7-DOF Franka robot is actually generated by the geometric excitation trajectory optimization criterion adopted by the present invention.

[0169] like Figure 3(a) to Figure 3(g)As shown in FIG. 1 , a schematic diagram of the prediction of the joints of the manipulator generated by iterative identification using geometric optimization excitation trajectory and geometric convex approximation regularization term in an example of the present invention is shown. The root mean square error of the joint torque prediction obtained is within 0.25 Nm, and the obtained joint torque prediction model has a high accuracy.

[0170] As shown in Figure 4(a) and Figure 4(b), the examples of the present invention respectively consider the traditional Euclidean distance as a regularization term and the geometric convex approximation regularization term for iterative identification. From the visualization results, it can be seen that after the traditional Euclidean distance is used as a regularization term to complete the identification, the robot inertia tensor, center of mass distance, and mass cannot maintain a normal robot configuration, that is, a geometric deviation occurs; and after the geometric convex approximation regularization term is used to complete the identification, the robot inertia tensor, center of mass distance, and mass can better form a normal configuration of the robot, indicating that the geometric convex approximation regularization term proposed by the present invention can better reflect the intrinsic geometric relationship of the parameters in the dynamic model during the identification process.

[0171] As shown in Table 2, the example of the present invention optimizes and identifies three excitation trajectories respectively, and predicts the same excitation trajectory. From the results in the table, it can be seen that the geometric excitation optimization criterion proposed in the present invention can improve the robot torque prediction accuracy. Compared with the trajectory without using the geometric excitation optimization criterion, the torque prediction accuracy is improved by 12% and 16% respectively, indicating that the method proposed in the present invention has a better effect.

[0172] Table 2 shows the comparison results of torque prediction error after parameter identification under different excitation trajectory optimization objectives.

[0173]

[0174] Embodiment 2

[0175] This embodiment provides a robot dynamics parameter identification system, including:

[0176] A model building module is configured to: establish a robot rigid body dynamics model, establish a mapping operator between a minimum parameter set and a standard parameter set based on a linearization process of the robot rigid body dynamics model; establish a symmetric positive definite matrix manifold, and calculate a metric tensor according to a differential geometry structure-related formula of the symmetric positive definite matrix manifold;

[0177] The criterion establishment module is configured to: establish a geometric excitation trajectory optimization criterion according to the mapping operator and the metric tensor; combine the geometric excitation trajectory optimization criterion with the traditional observation matrix condition number to generate the robot's excitation trajectory; run the robot's excitation trajectory on the robot to obtain the robot's actual collection data;

[0178] The function establishment module is configured as follows: based on the actual data collected by the robot, the geodesic distance of the symmetric positive definite matrix manifold is adopted to establish the parameter identification optimization objective function, a geometric convex approximate upper bound constraint suitable for iterative optimization is constructed, and the geometric convex approximate upper bound constraint is used as the regularization term of the parameter identification optimization objective function;

[0179] A solution module is configured to: solve a parameter identification optimization objective function containing a geometric convex approximation upper bound constraint regularization term to obtain an identified minimum parameter set; based on the identified minimum parameter set, solve an optimization objective function of a nonlinear friction model to obtain identified friction parameters;

[0180] A calculation module is configured to: calculate weights based on the identified minimum parameter set and the identified friction parameters, determine whether to return to the solution step of the parameter identification optimization objective function containing the regularization term of the geometric convex approximation upper bound constraint according to the weight value, and finally output the identified minimum parameter set and friction parameters.

[0181] It should be noted that the above modules correspond to the steps in Embodiment 1, and the examples and application scenarios implemented by the above modules and the corresponding steps are the same, but are not limited to the contents disclosed in the above Embodiment 1. It should be noted that the above modules, as part of the system, can be executed in a computer system such as a set of computer executable instructions.

[0182] The description of each embodiment in the above embodiments has different emphases. For parts not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0183] The proposed system can be implemented in other ways. For example, the system embodiment described above is only illustrative, and the division of the modules is only a logical function division. In actual implementation, there may be other division methods, such as multiple modules can be combined or integrated into another system, or some features can be ignored or not executed.

[0184] Embodiment 3

[0185] This embodiment also provides an electronic device, including: one or more processors, one or more memories, and one or more computer programs; wherein the processor is connected to the memory, and the one or more computer programs are stored in the memory. When the electronic device is running, the processor executes the one or more computer programs stored in the memory so that the electronic device executes the method described in the above embodiment one.

[0186] It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate arrays FPGA or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0187] The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0188] In the implementation process, each step of the above method can be completed by an integrated logic circuit of hardware in a processor or an instruction in the form of software.

[0189] The method in the first embodiment can be directly embodied as a hardware processor, or a combination of hardware and software modules in the processor. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware. To avoid repetition, it will not be described in detail here.

[0190] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with this embodiment can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0191] Embodiment 4

[0192] This embodiment further provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the method described in the first embodiment is completed.

[0193] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for identifying robot dynamic parameters, characterized in that: include: Establish a rigid body dynamics model of the robot, and establish a mapping operator between the minimum parameter set and the standard parameter set based on the linearization process of the rigid body dynamics model of the robot; Establish a symmetric positive definite matrix manifold and calculate the metric tensor based on the differential geometry structure formula of the symmetric positive definite matrix manifold; According to the mapping operator and the metric tensor, the optimization criterion of the geometric excitation trajectory is established; The robot's excitation trajectory is generated by combining the geometric excitation trajectory optimization criterion with the traditional observation matrix condition number; the robot's excitation trajectory is run on the robot to obtain the robot's actual collection data; Based on the actual data collected by the robot, the geodesic distance of the symmetric positive definite matrix manifold is used to establish the parameter identification optimization objective function, and the geometric convex approximate upper bound constraint suitable for iterative optimization is constructed. The geometric convex approximate upper bound constraint is used as the regularization term of the parameter identification optimization objective function. Solve the parameter identification optimization objective function containing the regularization term of the geometric convex approximation upper bound constraint to obtain the identified minimum parameter set; Based on the identified minimum parameter set, the optimization objective function of the nonlinear friction model is solved to obtain the identified friction parameters; Based on the identified minimum parameter set and the identified friction parameters, the weights are calculated, and according to the weight values, it is determined whether to return to the solution step of the parameter identification optimization objective function containing the regularization term of the geometric convex approximation upper bound constraint, and finally the identified minimum parameter set and friction parameters are output.

2. A robot dynamics parameter identification method as claimed in claim 1, characterized in that: Establish a rigid body dynamics model of the robot, and establish a mapping operator between the minimum parameter set and the standard parameter set based on the linearization process of the rigid body dynamics model of the robot, including: For the n-link multi-body dynamics system, the inverse dynamics model for calculating the joint torque is written as: Where M(q)∈R n×n represents the inertia force matrix, Represents the centrifugal Coriolis force matrix, g(q)∈R n×1 is the robot link gravity matrix, τ∈R n×1 represents the robot joint torque; On the basis of the obtained dynamic model, it is linearized into the multiplication form of the observation matrix and the standard parameter set: in, is the observation matrix under the standard parameter set, χ∈R n×p is the standard parameter set, which can be written as the matrix expression of the n-link inertia parameter set: x=[π1,π2,...,π i ,...,p n ]; Among them, π i =[I xx i ,I xy i ,I xz i ,I yy i ,I yz i ,I zz i ,m i x i ,m i y i ,m i z i ,m i ] is the inertia parameter set of the i-th connecting rod; Based on the numerical decomposition method, The observation matrix of is decomposed with the standard parameter set, specifically: Among them, W ind is the observation matrix W χ Linearly independent columns of W are also called full-rank observation matrices; d is the observation matrix W χ The linear correlation column, W d It can also be written as ind The linear combination form is: W d =W ind Q d ; Among them, Q d is a constant matrix with linearly independent column indices U ind Linearly related column index U d The following formula is composed: According to the linearly independent column index U ind Linearly related column index U d , linearly independent parameters and linearly dependent parameters are expressed as: Among them, χ ind are the independent inertia parameters corresponding to the linearly independent column indices, χ d are the non-independent inertial parameters corresponding to the linearly dependent column indices; the minimum linear combination of the standard parameter set is expressed as the minimum parameter set, specifically: β=x ind +Q d x d =Kx; Among them, β is the minimum parameter set, K is the mapping operator from the standard parameter set to the minimum parameter set, and the specific form is: Finally, the full-rank observation matrix W is obtained ind The joint torque expression composed of the minimum parameter set β is:

3. A robot dynamics parameter identification method as claimed in claim 1, characterized in that: Establish a symmetric positive definite matrix manifold and calculate the metric tensor according to the differential geometry structure related formulas of the symmetric positive definite matrix manifold, including: Let the space of all n×n real symmetric matrices be S(n), and define an open set subset of symmetric positive definite matrices in S(n) Define the physically consistent symmetric positive definite matrix in the robot: in, For R 1×p →R 4×4 The mapping of P i is the symmetric positive definite matrix of the i-th link, tr(·) is the trace operator, I∈R 3×3 The identity matrix, I i is the inertia tensor of the rigid body, m is the mass of the rigid body, and c is the center of mass of the rigid body; When the matrix When the robot's physical consistency is satisfied, P i On the fourth-order symmetric positive definite matrix manifold On the manifold Considered as embedded in S(n); From the above, we can see that the set is a symmetric positive definite matrix manifold Its tangent space at any point P is the space Then the infinitesimal arc length is defined as: ds=(tr(P -1 dP) 2 ) 1 / 2 =‖P -1 / 2 dPP -1 / 2 ‖ F ; Among them, dP represents the infinitesimal change of the symmetric positive definite matrix P, and ds reflects the geometric distance between two points on the manifold; Expanding the infinitesimal arc length ds using the definition of trace metric, first consider the quadratic distance ds between two points on the following manifold 2 To simplify for convenience: If P is the parameter π i Function, π i is the inertia parameter set of the i-th connecting rod, that is, P = P(π i ), which can be written in differential form as Substituting this into the infinitesimal arc length formula yields: According to the affine invariant Riemann metric formula: ds 2 =dπ T m(π)dπ; Among them, m, as a metric tensor, indirectly represents the distance and angle between two points in the manifold space by calculating the inner product in the tangent space; At this time, each element m in the metric tensor m(π) ij (π) is expressed as: Where j, k = 1, 2, ..., p represents the inertia parameter set π of the i-th connecting rod i p components in , by calculating each element m jk (π) to obtain the final metric tensor m(π)∈R p×p The analytical expression of .

4. A robot dynamics parameter identification method as claimed in claim 1, characterized in that: According to the mapping operator and the metric tensor, the geometric excitation trajectory optimization criteria are established, including: According to the metric tensor m(π)∈R p×p The metric tensor of the n-link multibody dynamics system is defined as a diagonal block matrix composed of the metric tensors of the inertia parameters of the n links: M(π)=diag(m(π1),m(π2),...,m(π n ))∈R np×np ; Where M(π) is the metric tensor of the n-link multibody dynamics system, diag is expressed as a diagonal operator, and m(π n ) is the metric tensor of the nth link; let the nominal value of the standard parameter set of the n-link multibody dynamics system be χ0, the constant metric tensor under the nominal value χ0 for: Combined with the mapping operator K, the metric tensor M is calculated from the standard parameter set space to the minimum parameter set space. β : In order to reduce the geometric uncertainty of the worst direction of the excitation trajectory, the metric tensor in the minimum parameter set space is added to the Fisher information matrix as geometric normalization information to obtain the geometric excitation trajectory optimization criterion: λ max ((W ind T ∑ -1 W ind ) -1 M β ); Among them, λ max (·) is to solve the problem of minimizing the maximum eigenvalue of the Fisher information matrix, ∑ is Gaussian additive noise; The robot's excitation trajectory is generated by combining the geometric excitation trajectory optimization criterion with the traditional observation matrix condition number. The robot's excitation trajectory is run on the robot to obtain the robot's actual collection data, including: The geometric excitation trajectory optimization criterion and the traditional measurement matrix condition number are used as the optimization objectives of the excitation trajectory: J=γ1cond(W ind )+γ2λ max ((W ind T ∑ -1 W ind ) -1 M β ); Among them, γ1,γ2 represent the optimization target penalty adjustment coefficients, and cond(·) represents the operation of the observation matrix condition number; The finite Fourier series is used as the robot's excitation trajectory, specifically: Among them, q i (t), are the robot joint angle, joint velocity, and joint acceleration at time t, respectively, i0 is the starting position of the robot joint, a l,i ,b l,i is the hyperparameter of the finite Fourier series, ω f is the basic frequency of the excitation trajectory, and N is the order of the finite Fourier series. At the same time, the optimization condition that the excitation trajectory should satisfy is: Among them, q i,max , are the position, velocity, and acceleration limits of joint i, which are given by the robot manufacturer; t0, t f The starting and ending time of the trajectory respectively; The finite Fourier series is given by a l,i ,b l,i Indicates that the incentive trajectory optimization problem is described as: min J=γ1cond(W ind )+γ2λ max ((W ind T ∑ -1 W ind ) -1 M β ); Run the excitation trajectory on the robot and measure the robot joint angle q m , Joint speed Joint acceleration Torque τ real , and zero-phase filtering is used to reduce the acquisition noise information.

5. A robot dynamics parameter identification method as claimed in claim 1, characterized in that: Based on the actual data collected by the robot, the geodesic distance of the symmetric positive definite matrix manifold is used to establish the parameter identification optimization objective function, and the geometric convex approximate upper bound constraint suitable for iterative optimization is constructed. The geometric convex approximate upper bound constraint is used as the regularization term of the parameter identification optimization objective function, including: In the face of positive definite matrix manifolds There are two points Then the geodesic distance d between the two points is R (P,Q) is expressed as: in,‖·‖ F is the F-norm calculation, log(·) is the matrix logarithm calculation, and λ(·) is the eigenvalue calculation; for the n-link multi-body dynamics system, the total distance of its geodesic is expressed as the sum of the geodesic distances: Among them, χ1, χ0 are the standard parameter set identification value and the standard parameter set nominal value of the n-link multi-body dynamics system, respectively, π i ,x i 0 are the inertia parameter identification value and the inertia parameter nominal value of the i-th connecting rod, For R 1×p →R 4×4 The mapping of , λ(·) is the eigenvalue calculation; The total geodesic distance of the symmetric positive definite matrix manifold of the n-link multi-body dynamics system is taken as the regularization term of the optimization objective function, and its expression is written as follows: Among them, W (k) Optimize the weights for the kth iteration, with the initial element being 1; is the observation matrix of the minimum parameter set, and the filtered q m , Substituting into the calculation, we can get; β (k) is the minimum parameter set identification value for the kth iteration; τ f is the friction torque, the initial element is 0; τ real is the measurement of the actual joint torque; γ3 is the penalty coefficient of the regularization term; for Total geodesic distance on the manifold; χ1 (k) Identify the value of the standard parameter set for the kth iteration; First, consider another geodesic distance logarithmic Euclidean metric for symmetric positive definite matrix manifolds, specifically: Where log(·) is the matrix logarithm calculation, For R 1×p →R 4×4 Mapping; based on convexity analysis and Taylor expansion of the matrix, Written as the following convex approximate upper bound constraint: in, is the inertia parameter of the i-th connecting rod identified in the k-th iteration i π0 (k) The calculated iterative change reference point and the optimized target distance of the i-th link are: For an n-link multibody dynamic system, the total geodesic distance based on the log-Euclidean metric is expressed as the sum of the log-Euclidean metric: Among them, χ1, χ0 are the standard parameter set identification value and the standard parameter set nominal value of the n-link multi-body dynamics system, respectively, π i ,x i 0 are the inertia parameter identification value and the nominal value of the inertia parameter of the i-th connecting rod respectively.

6. A robot dynamics parameter identification method as claimed in claim 1, characterized in that: The parameter identification optimization objective function containing the regularization term of the geometric convex approximation upper bound constraint is solved to obtain the minimum identified parameter set, including: Constrain the regularization term based on the geometric convex approximation upper bound Add it to the optimization objective function suitable for iterative calculation: Combined with physically consistent symmetric matrix The physical consistency of the n-link multibody dynamics system is expressed as a linear matrix inequality constraint form, specifically: D(χ) diag(P1,P2,...,P n )00 Where diag(·) represents the diagonal block matrix operation; Finally, the optimization problem of parameter identification is described as: Among them, m i is the mass of each link, and M is the total mass of the robot.

7. A robot dynamics parameter identification method as claimed in claim 1, characterized in that: Based on the identified minimum parameter set, the optimization objective function of the nonlinear friction model is solved to obtain the identified friction parameters, including: The actual measured torque τ real and the minimum parameter set β for the kth iteration (k) The residual of the estimated torque is calculated as the actual friction torque, specifically: Where Δτ is the moment residual, is the estimated moment; The nonlinear friction model under no-load conditions is expressed as: Among them, α 1,j ,α 2,j ,α 3,j ,α 4,j ,α 5,j is the nonlinear friction parameter of the jth connecting rod, τ f (t) is the joint friction torque at sampling time t, is the joint angular velocity at sampling time t; describes the Stribeck friction effect, Describe the phenomenon of viscous friction. Describe the phenomenon of Coulomb friction; The friction parameters are identified using a global nonlinear optimization algorithm. The nonlinear friction model optimization problem of the n-link multi-body dynamics system is expressed as follows: Based on the identified minimum parameter set and the identified friction parameter, the weight is calculated, and according to the weight value, it is determined whether to return to solve the parameter identification optimization objective function containing the geometric convex approximation upper bound constraint regularization term, and finally the identified minimum parameter set and friction parameter are output; Based on the identified estimated torque and nonlinear friction torque, the residual torque residual is calculated from the actual measured torque. Specifically: ξ=τ real -W ind b (k) -t f ; Among them, ξ is the residual moment residual; The residual moment residual includes noise and unknown moment components. The residual moment is used as the main basis for updating the next generation of weights. The weights are expressed using Lorentz functions to suppress noise and unknown moment components. Specifically: Among them, W is the weight, ξ is the residual moment residual, and c controls the weight decay speed; Based on the latest weights calculated, iterative calculations are performed to continuously update W (k) ,β (k) , i π0 (k) ,t f Repeat the above process until the weight matrix reaches the following standard and stops the iteration: Among them, ε is the tolerance of the weight matrix change.

8. A robot dynamic parameter identification system, characterized in that: include: A model building module is configured to: establish a robot rigid body dynamics model, establish a mapping operator between a minimum parameter set and a standard parameter set based on a linearization process of the robot rigid body dynamics model; establish a symmetric positive definite matrix manifold, and calculate a metric tensor according to a differential geometry structure-related formula of the symmetric positive definite matrix manifold; A criterion establishment module is configured to: establish a geometric excitation trajectory optimization criterion according to a mapping operator and a metric tensor; The robot's excitation trajectory is generated by combining the geometric excitation trajectory optimization criterion with the traditional observation matrix condition number; the robot's excitation trajectory is run on the robot to obtain the robot's actual collection data; The function establishment module is configured as follows: based on the actual data collected by the robot, the geodesic distance of the symmetric positive definite matrix manifold is adopted to establish the parameter identification optimization objective function, a geometric convex approximate upper bound constraint suitable for iterative optimization is constructed, and the geometric convex approximate upper bound constraint is used as the regularization term of the parameter identification optimization objective function; A solution module is configured to: solve a parameter identification optimization objective function containing a geometric convex approximation upper bound constraint regularization term to obtain an identified minimum parameter set; Based on the identified minimum parameter set, the optimization objective function of the nonlinear friction model is solved to obtain the identified friction parameters; A calculation module is configured to: calculate weights based on the identified minimum parameter set and the identified friction parameters, determine whether to return to the solution step of the parameter identification optimization objective function containing the regularization term of the geometric convex approximation upper bound constraint according to the weight value, and finally output the identified minimum parameter set and friction parameters.

9. An electronic device, comprising: a memory for non-transitory storage of computer readable instructions; as well as a processor for executing the computer readable instructions, When the computer-readable instructions are executed by the processor, the method described in any one of claims 1 to 7 is executed.

10. A storage medium, characterized in that: The computer-readable instructions are non-transitory stored, wherein when the non-transitory computer-readable instructions are executed by a computer, the method according to any one of claims 1 to 7 is performed.

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