Compound robot dynamics full parameter identification method based on maximum likelihood estimation

Abstract

The application belongs to the field of robot model identification, and relates to a composite robot dynamics full parameter identification method based on maximum likelihood estimation, comprising the following steps: step one: constructing a full parameter linearized dynamics model of the composite robot based on Lagrange equation; step two: designing a maximum likelihood estimation algorithm of the full parameter of the composite robot dynamics based on periodic Fourier series excitation trajectory and measurement noise distribution characteristics; step three: designing a parameter optimization model of the excitation trajectory of the composite robot by using a Fisher information matrix of the covariance of the maximum likelihood estimation algorithm, obtaining the optimal excitation trajectory of the composite robot by minimizing the asymptotic convergence domain of the covariance matrix, and realizing high-precision dynamics full parameter identification of the composite robot. The method can improve the accuracy and robustness of the composite robot dynamics model identification.

Description

Technical Field

[0001] This invention belongs to the field of robot model identification and relates to a method for identifying all parameters of composite robot dynamics based on maximum likelihood estimation. Background Technology

[0002] Hybrid robots, composed of mobile platforms and manipulators, can perform complex tasks such as material handling, human-robot collaboration, and exploration and grasping in large spaces. In recent years, they have been increasingly applied in popular fields such as industrial production, smart warehousing, wilderness exploration, and public services, and possess promising market prospects. However, mature products and application technologies that simultaneously possess high reliability, high autonomy, and high interactivity are currently rare. The main reason for this is that the planning and control capabilities of hybrid robots are still insufficient to cope with the dynamic changes in complex environments. The development and implementation effectiveness of advanced control algorithms for hybrid robots directly depend on the accuracy of their dynamic models. However, in practical engineering, it is difficult to effectively obtain the parameters of dynamic models. Therefore, research on their identification methods has significant engineering implications and practical value.

[0003] The dynamics model of a composite robot depends on both kinematic geometry parameters and mass inertia parameters. Existing methods for identifying robot dynamics models often identify mass inertia parameters based on known kinematic parameters, without considering the adverse effects of kinematic parameter uncertainties on the accuracy of dynamics model identification. In reality, errors in kinematic geometry parameters can cause mass inertia parameter identification errors several times greater, ultimately reducing the accuracy of composite robot dynamics model identification. Current methods for solving linearized robot dynamics models, such as least squares, Kalman filtering, genetic algorithms, and gradient descent, rarely consider the measurement noise of motion trajectories and driving torques. They often assume that "noise from robot joint angle measurements is negligible" or "noise from joint driving torque measurements has variance consistency" to optimize the solution of dynamic parameters. Furthermore, most methods obtain joint angular velocities and angular accelerations through numerical differentiation. However, high-frequency noise at this point also significantly affects the accuracy of velocity and acceleration values, ultimately leading to low accuracy in the dynamics parameter solution. Furthermore, existing methods for designing robot excitation trajectories often use the condition number of the observation matrix of the linearized dynamic model as the optimization index, without effectively considering the measurement noise of the input and output data and the uncertainty of the dynamic parameter estimation during the experiment. This makes it difficult to achieve high-precision identification of the dynamic model of the composite robot in practical engineering. Summary of the Invention

[0004] To address the aforementioned technical problems in existing technologies, this invention proposes a method for identifying the full parameters of a composite robot's dynamics based on maximum likelihood estimation. First, a fully parameterized linearized model of the composite robot's dynamics is constructed using the Lagrange equation. Then, a maximum likelihood estimation method for the full dynamic parameters is designed to effectively suppress the adverse effects of measurement noise. Finally, an optimal periodic excitation trajectory is designed based on the Fischer information matrix, ultimately achieving full parameter identification of a high-precision dynamic model of the composite robot. The specific technical solution is as follows:

[0005] A method for identifying all dynamic parameters of a composite robot based on maximum likelihood estimation includes the following steps:

[0006] Step 1: Construct a fully parameterized linearized dynamic model of the composite robot based on the Lagrange equation;

[0007] Step 2: Design a maximum likelihood estimation algorithm for the full dynamic parameters of the composite robot based on the periodic Fourier series excitation trajectory and measurement noise distribution characteristics;

[0008] Step 3: Using the Fischer information matrix of the covariance from the maximum likelihood estimation algorithm, design a parameter optimization model for the excitation trajectory of the composite robot. By minimizing the asymptotic convergence region of the covariance matrix, the optimal excitation trajectory of the composite robot is obtained, thus realizing the full parameter identification of the composite robot's dynamics.

[0009] Furthermore, step one includes the following sub-steps:

[0010] Step 1.1: Construct the Lagrange equations for the dynamics of the composite robot, specifically expressed as follows:

[0011]

[0012] In formula (1) These are the generalized joint space coordinates of the composite robot, where θ1,…,θ n This indicates the rotation angles of each joint of the manipulator. This indicates the position and rotation angle of the mobile platform within the world coordinate system; Let represent the homogeneous transformation matrix of the manipulator joint coordinate system {i} relative to the world coordinate system {W}. and m i Let represent the pseudo-inertia matrix and mass of link i of the manipulator arm, respectively. Represents the gravitational acceleration vector. And r i =[r ix ,r iy ,r iz ] T This represents the position of the center of gravity of the manipulator link i relative to its joint coordinate system {i}; m O and IO These represent the mass and moment of inertia of the mobile platform, respectively; Tr(·) represents the trace operator of the matrix; in It is the joint coordinate x O ,y O ,φ O ,θ1,…,θ i The function matrix, It is the kinematic parameter a O ,b O ,d O ,a1,α1,d1,…,a i ,α i ,d i The constant coefficient matrix, a O ,b O ,d O a represents the position parameter of the mobile platform coordinate system {O} relative to its drive wheel coordinate system. i ,α i ,d i The length, torsion angle, and joint offset of the manipulator link i are given, thus yielding the full parameter terms of the composite robot dynamics model. m O I O That is, a combination of kinematic geometric parameters and mass inertia parameters;

[0013] Step 1.2: Based on the constructed Lagrange equations, the fully parameterized linearized dynamic model of the composite robot is derived. The specific process is as follows:

[0014] The expression for formula (1) is derived as follows:

[0015]

[0016] In formula (2) The function represents the number of terms related to the Lagrange linearized equation and the link i of the manipulator. The mass inertia parameter representing the link i of the manipulator arm is given by: The moment of inertia vector representing link i; Represents kinematic geometric parameters, a combination of all parameters.

[0017] Define function vectors Define the dynamic full parameter combination vector The fully parameterized linearized dynamic model of the composite robot is constructed as follows:

[0018]

[0019] In formula (3) The driving torques of the composite robot are represented by τ1,…,τ. n This represents the driving torque of each joint of the manipulator. The mobile platform represents the translation along the x-axis of the world coordinate system. O y O Directional driving force and rotation axis z O Directional driving torque; observation vector of joint i Full dynamic parameters of link i Where I ai ,F vi ,F ci These are the rotational inertia, viscous friction, and Coulomb friction coefficient of joint i; It is the dynamic observation matrix of the mobile platform. Represents the dynamic parameters of the mobile platform, where F vx ,F vy ,F vz ,F cx ,F cy ,F cz These are along the translation axis x O y O and rotation axis z O Viscous friction and Coulomb friction coefficient in the directional direction;

[0020] in, It is the observation matrix of the fully parameterized linearized dynamic model of the composite robot. These are its unknown parameters that need to be identified;

[0021] Step 1.3: Eliminate unidentifiable dynamic parameters from the dynamic model and complete the modeling of the dynamic basis parameters. The specific process is as follows:

[0022] Through random sampling Calculate the dynamic regression matrix and remove its zero-element column to obtain Where p is the number of random samples and satisfies (n+3)p≥c.

[0023] Singular value decomposition in and These represent the orthogonal right singular matrix, the left singular matrix, and the singular value matrix, respectively. Only the main diagonal has non-zero elements and the diagonal matrix Representation matrix S c The rank is b, and the diagonal elements And the constant ε=∈p(n+3)∑ 11 ,∈>0; submatrix Easy to know The zero-element column corresponds to unidentifiable kinetic parameters. The zero-element column corresponds to the kinetic parameters that can be identified independently, while the remaining ones are the parameters that can only be identified by combination.

[0024] Select regular matrices from matrix V2 in reverse order. and its corresponding combinatorial identification parameter set Design a permutation matrix satisfy By S c PP T V2 = S c1 V 21 +S c2 V 22 =0 (n+3)p×(c-b) Get S c2 =-S c1 V 21 V 22 -1 Then the final model is:

[0025]

[0026] In formula (4) It is the basis parameter set of the dynamic model. It is its corresponding dynamic observation matrix; and They are respectively from S and S c1 S c2 The submatrix formed by the corresponding columns.

[0027] Furthermore, step two specifically involves:

[0028] The excitation trajectories of each joint of the composite robot are designed using periodic Fourier series, and the specific expressions are as follows:

[0029]

[0030] In formula (5) ω f Let N and N represent the fundamental frequency and order of the Fourier series, respectively. Define the excitation trajectory parameters δ = [δ1, ..., δ]. n+3 ] T and Where q i0 Let S represent the initial position offset of joint i; let S be the number of cycles of the excitation trajectory of the composite robot, and M be the number of sampling points in each cycle, then the mean of the measurement data is... in and These represent the position and torque value of joint i of the composite robot at sampling time k during the j-th excitation cycle; then the measurement noise variance is calculated.

[0031] The maximum likelihood estimation algorithm for all dynamic parameters of a composite robot is designed as follows:

[0032]

[0033] In formula (6) The mean value of the sampled joint angle data of the composite robot. The mean value of the sampled data of the joint driving torque; The measurement error of the joint angle is represented by q. i (δ,k) is the joint angle calculated by parameter δ and formula (5); The measurement error representing the driving torque of each joint of the composite robot, where The joint torque is calculated using the full-parameter model formula (4) of the dynamics. The i-th element, These are the joint angle, velocity, and acceleration calculated by parameter δ and formula (5), respectively, thus avoiding the adverse effects of high-frequency noise introduced when solving the joint velocity by numerical differentiation of the joint angle; It is the cost function of the maximum likelihood estimation of the total dynamic parameters; the Gauss-Newton iteration method is used to solve formula (6) to obtain the total dynamic parameters. and sampling trajectory parameter δ * The maximum likelihood estimate.

[0034] Furthermore, step three specifically involves:

[0035] The maximum likelihood estimates of the total dynamic parameters of the composite robot are obtained from formula (6). The covariance matrix will asymptotically converge to F -1 ,in It is the Fisher information matrix and represents the signal-to-noise ratio of the measured data relative to the estimated parameters, where and

[0036] Initialize all dynamic parameters of the composite robot Based on formula (5), a parameter optimization model for the dynamic excitation trajectory is designed, and the specific expression is as follows:

[0037]

[0038]

[0039] In formula (7), det(·) represents the determinant of the matrix, and q imax q imin , and These represent the maximum angle limit, minimum angle limit, maximum velocity limit, and maximum acceleration limit of joint i of the composite robot, respectively. The equality constraint terms are used to limit the initial position, velocity, and acceleration of the excitation trajectory of each joint of the composite robot to zero, while the inequality constraint terms satisfy the physical constraints during the motion process.

[0040] Beneficial effects: The method of the present invention can realize the combined full-parameter linear dynamic modeling of kinematic geometric parameters and mass inertial parameters. At the same time, it can achieve high-precision maximum likelihood estimation of the full dynamic parameters based on the measurement noise distribution of periodic excitation trajectory and the minimization of parameter estimation variance, thereby improving the accuracy and robustness of the identification of the dynamic model of the composite robot. Attached Figure Description

[0041] Figure 1 This is a flowchart of the method for identifying all dynamic parameters of a composite robot based on maximum likelihood estimation according to the present invention.

[0042] Figure 2 This is a flowchart of the application of the composite robot dynamics full parameter identification method according to an embodiment of the present invention;

[0043] Figure 3 This is a schematic diagram of the periodic average joint angles of the composite robot after it runs the optimal excitation trajectory according to the present invention;

[0044] Figure 4 This is a schematic diagram of the periodic average joint driving torque measured after the composite robot of the present invention runs the optimal excitation trajectory;

[0045] Figure 5 This is a schematic diagram illustrating the test results of the maximum likelihood estimation of all parameters of the composite robot dynamics according to the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and technical effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0047] like Figure 1 As shown, the present invention provides a method for identifying the full parameters of the dynamics of a composite robot based on maximum likelihood estimation, which specifically includes the following steps:

[0048] Step 1: Design a fully parameterized linearized dynamic model of the composite robot based on the Lagrange equations, obtain the combined influence of kinematic geometry parameters and mass inertia parameters on the dynamics, and obtain the basis parameter set and observation matrix of the dynamic model through singular value decomposition, thus realizing the fully parameterized modeling of the composite robot's dynamics. Specifically, this includes:

[0049] Step 1.1: Construct the Lagrange equations for the dynamics of the composite robot, as shown in the following expression:

[0050]

[0051] In formula (1) These are the generalized joint space coordinates of the composite robot, where θ1,…,θ n This indicates the rotation angles of each joint of the manipulator. This indicates the position and rotation angle of the mobile platform within the world coordinate system; Let represent the homogeneous transformation matrix of the manipulator joint coordinate system {i} relative to the world coordinate system {W}. and m i Let represent the pseudo-inertia matrix and mass of link i of the manipulator arm, respectively. Represents the gravitational acceleration vector. And r i =[r ix ,r iy ,r iz ] T This represents the position of the center of gravity of the manipulator link i relative to its joint coordinate system {i}; m O and I O These represent the mass and moment of inertia of the mobile platform, respectively; Tr(·) represents the trace operator of the matrix; in It is the joint coordinate x O ,y O ,φ O ,θ1,…,θ i The function matrix, It is the kinematic parameter a O ,b O ,d O ,a1,α1,d1,…,a i ,α i ,d i The constant coefficient matrix, a O ,b O ,d O a represents the position parameter of the mobile platform coordinate system {O} relative to its drive wheel coordinate system. i ,α i ,d iThe length, torsion angle, and joint offset of the manipulator link i are given, thus yielding the full parameter terms of the composite robot dynamics model. m O I O This refers to a combination of kinematic geometric parameters and mass inertia parameters.

[0052] Step 1.2: Based on the constructed Lagrange equations, the fully parameterized linearized dynamic model of the composite robot is derived. Specifically, the fully parameterized linearized dynamic model of the composite robot based on the Lagrange equations is derived from formula (1) as follows:

[0053] The expression for formula (1) is derived as follows:

[0054]

[0055] In formula (2) The function represents the number of terms related to the Lagrange linearized equation and the link i of the manipulator. The mass inertia parameter representing the link i of the manipulator arm is given by: The moment of inertia vector representing link i; Represents kinematic geometric parameters, a combination of all parameters.

[0056] Define function vectors Define the dynamic full parameter combination vector The fully parameterized linearized dynamic model of the composite robot is constructed as follows:

[0057]

[0058] In formula (3) Indicates the driving torque of the composite robot. This represents the driving torque of each joint of the manipulator. The mobile platform represents the translation along the x-axis of the world coordinate system. O y O Directional driving force and rotation axis z O Directional driving torque; observation vector of joint i Full dynamic parameters of link i Where I ai ,F vi ,F ci These are the rotational inertia, viscous friction, and Coulomb friction coefficient of joint i; It is the dynamic observation matrix of the mobile platform. Represents the dynamic parameters of the mobile platform, where F vx ,F vy ,F vz ,F cx ,F cy ,F cz These are along the translation axis x O y O and rotation axis z O Viscous friction and Coulomb friction coefficient in the directional direction;

[0059] in, It is the observation matrix of the fully parameterized linearized dynamic model of the composite robot. These are its unknown parameters that need to be identified;

[0060] Step 1.3: Eliminate unidentifiable dynamic parameters in the dynamic model to achieve modeling of the dynamic basis parameters of the composite robot;

[0061] To address the incomplete rank problem of the observation matrix S, random sampling is employed. Calculate the dynamic regression matrix and remove its zero-element column to obtain Where p is a random sample number and satisfies This eliminates unidentifiable dynamic parameters;

[0062] Singular value decomposition in and These represent the orthogonal right singular matrix, the left singular matrix, and the singular value matrix, respectively. Only the main diagonal has non-zero elements and the diagonal matrix Representation matrix S c The rank is b, and the diagonal elements And the constant ε=∈p(n+3)∑ 11 ,∈>0; submatrix Easy to know The zero-element column corresponds to unidentifiable kinetic parameters. The zero-element column corresponds to the kinetic parameters that can be identified independently, while the remaining ones are parameters that can only be identified by combination.

[0063] Select regular matrices from matrix V2 in reverse order. and its corresponding combinatorial identification parameter set Design a permutation matrix satisfy By S c PP T V2 = S c1 V 21 +S c2 V 22 =0(n+3)p×(c-b) Get S c2 =-S c1 V 21 V 22 -1 Then the final model is:

[0064]

[0065] In formula (4) It is the basis parameter set of the dynamic model. It is its corresponding dynamic observation matrix; and They are respectively from S and S c1 S c2 The submatrix formed by the corresponding columns;

[0066] This enables fully parameterized linear modeling of the dynamics of the composite robot.

[0067] Step 2: Based on the periodic Fourier series excitation trajectory and measurement noise distribution characteristics, a maximum likelihood estimation algorithm for the full dynamic parameters of the composite robot is designed. The velocity and acceleration values ​​of each joint of the composite robot are solved through the parameterized equations of the excitation trajectory, effectively avoiding the influence of high-frequency noise and ensuring the accuracy of the dynamic model solution. Specifically, this includes:

[0068] To determine the distribution characteristics of measurement noise and improve the signal-to-noise ratio of experimental data during dynamic identification, periodic Fourier series are used to design the excitation trajectories of each joint of the composite robot, as follows:

[0069]

[0070] In formula (5) ω f Let N and δ represent the fundamental frequency and order of the Fourier series, respectively. Define the excitation trajectory parameters v = [δ1, ..., δ1]. n+3 ] T and Where q i0 Let S represent the initial position offset of joint i; let S be the number of cycles of the excitation trajectory of the composite robot, and M be the number of sampling points in each cycle, then the mean of the measurement data is... in and These represent the position and torque value of joint i of the composite robot at sampling time k during the j-th excitation cycle; then the measurement noise variance is calculated. Based on this design, a maximum likelihood estimation algorithm for the full parameters of the composite robot's dynamics is as follows:

[0071]

[0072] In formula (6) The mean value of the sampled joint angle data of the composite robot. The mean value of the sampled data of the joint driving torque; The measurement error of the joint angle is represented by q. i (δ,k) is the joint angle calculated by parameter δ and formula (5); The measurement error representing the driving torque of each joint of the composite robot, where The joint torque is calculated using the full-parameter model formula (4) of the dynamics. The i-th element, These are the joint angle, velocity, and acceleration calculated by parameter δ and formula (5), respectively, thus avoiding the adverse effects of high-frequency noise introduced when solving the joint velocity by numerical differentiation of the joint angle; The cost function for the maximum likelihood estimation of the total dynamic parameters is obtained by solving formula (6) using the Gauss-Newton iterative method. and sampling trajectory parameter δ * The maximum likelihood estimate.

[0073] Step 3: Based on the Fisher information matrix of the covariance of the maximum likelihood estimation algorithm, design a parameter optimization model for the excitation trajectory of the composite robot. The optimal excitation trajectory is obtained by minimizing the asymptotic convergence region of the covariance of the maximum likelihood estimation algorithm, achieving high-precision full-parameter identification of the composite robot's dynamics. Specifically, this includes:

[0074] The maximum likelihood estimates of the total dynamic parameters of the composite robot are obtained from formula (6). The covariance matrix will asymptotically converge to F -1 ,in It is the Fisher information matrix and represents the signal-to-noise ratio of the measured data relative to the estimated parameters, where and It is evident that improving the signal-to-noise ratio of the measurement data can reduce the uncertainty of the parameter estimates. Based on this, the full set of dynamic parameters of the composite robot is initialized. Based on formula (5), design the parameter optimization model for the dynamic excitation trajectory as follows:

[0075]

[0076]

[0077] In formula (7), det(·) represents the determinant of the matrix, and q imax q imin , and These represent the maximum angle limit, minimum angle limit, maximum velocity limit, and maximum acceleration limit of joint i of the composite robot, respectively. The equality constraints ensure that the initial position, velocity, and acceleration of the excitation trajectory of each joint of the composite robot are all zero, while the inequality constraints satisfy the physical constraints during motion. Solving the above optimization problem, the optimal excitation trajectory parameters are obtained by minimizing the asymptotic convergence region of the covariance matrix of the maximum likelihood estimation algorithm for all dynamic parameters. This leads to high-precision identification of all dynamic parameters of the composite robot, and finally, a test trajectory is designed to verify the effectiveness of the identification results.

[0078] Example:

[0079] The method for identifying the full parameters of composite robot dynamics based on maximum likelihood estimation, as proposed in this invention, is applied to a composite robot consisting of a Mecanum wheeled omnidirectional mobile platform and a six-degree-of-freedom robotic arm. Figure 2 As shown, it includes the following steps:

[0080] Step S101: Initially obtain the nominal dynamic parameters of the composite robot using CAD 3D software or traditional identification methods, and initialize the total dynamic parameters.

[0081] Step S102, let the fundamental frequency ω of the periodic Fourier series in formula (5) be... f =0.1π and order N=5, the motion position constraints q of each joint of the composite robot in formula (7) 1min =q 4min =q 5min =q 6min = -3.14 rad, q 1max =q 4max =q 5max =q 6max =3.14 rad, q 2min =q 3min = -1.57 rad, q 2max =1.57 rad, q 3max =3.84 rad, q 7min =q 8min =-2m, q 7max =q 8max =2m, q 9min = -6.28 rad, q 9max = 6.28 rad, velocity constraint Acceleration constraints

[0082] Based on this optimization model of solving formula (7), the optimal parameters of the dynamic excitation trajectory of the composite robot are obtained.

[0083] In step S103, during the actual machine experiment, each joint of the composite robot is equipped with a 48V brushless DC servo motor. The joint motion position is measured by a 17-bit encoder. A self-developed controller based on EtherCAT real-time bus communication and supporting a 1000Hz control frequency is used to complete the excitation trajectory distribution and execution for S=50 cycles. The number of sampling points in each cycle is M=200, and the angle values ​​of each joint of the composite robot are collected in real time. and torque value The joint degrees of freedom are numbered i = 1, ..., 9, the sampling period numbers are j = 1, ..., 50, and the sampling point numbers within each period are k = 1, ..., 200. Furthermore, the joint torques collected by the omnidirectional moving platform are the driving torques of the Mecanum wheelsets, which need to be converted into the translational torques of the moving platform along the translation axis x. O y O The driving force in the direction and along the rotation axis z O The driving torque in the direction is used to obtain the required torque data.

[0084] Step S104: Calculate the average motion angle of each joint based on the measurement data. and the average driving torque The excitation trajectory and joint torques used for identifying the dynamic parameters of the composite robot are obtained, such as... Figure 3 and Figure 4 As shown, the noise variance of joint angle measurements was calculated. Torque measurement noise variance

[0085] Step S105: The Gauss-Newton iterative algorithm is used to solve formula (6). During the iterative solution process, the velocity and acceleration of each joint are directly calculated from the excitation trajectory parameter δ and formula (5), effectively avoiding the influence of high-frequency noise caused by numerical differentiation. Finally, the full dynamic parameters of the composite robot are obtained. and sampling trajectory parameter δ * The maximum likelihood estimate.

[0086] Step S106: Based on the maximum likelihood estimate of the total parameters of the composite robot's dynamics. Further, the optimization model formula (6) of the excitation trajectory parameters is resolved to obtain the test trajectory parameters used to verify the dynamic full parameter identification results; then, the test trajectory is run on the composite robot, and the motion angle and driving torque data of each joint are collected in real time. The joint angles are then substituted into the dynamic full parameter linearization model formula (4) to calculate the theoretical value of the driving torque of each joint. The tracking accuracy is compared with the actual torque measurement data to complete the dynamic full parameter estimation. The test results are as follows: Figure 5As shown, the calculated torque of each joint of the composite robot can track the actual measured driving torque well, which verifies the effectiveness of the dynamic full parameter identification results and realizes the high-precision dynamic model identification of the composite robot.

[0087] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Although the implementation process of the present invention has been described in detail above, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for identifying all dynamic parameters of a composite robot based on maximum likelihood estimation, characterized in that, Includes the following steps: Step 1: Construct a fully parameterized linearized dynamic model of the composite robot based on the Lagrange equation; Step 2: Design a maximum likelihood estimation algorithm for the full dynamic parameters of the composite robot based on the periodic Fourier series excitation trajectory and measurement noise distribution characteristics; Step 3: Using the Fisher information matrix of the covariance from the maximum likelihood estimation algorithm, design a parameter optimization model for the excitation trajectory of the composite robot. By minimizing the asymptotic convergence region of the covariance matrix, the optimal excitation trajectory of the composite robot is obtained, thus realizing the identification of all dynamic parameters of the composite robot. Step one includes the following sub-steps: Step 1.1: Construct the Lagrange equations for the dynamics of the composite robot, specifically expressed as follows: ， In formula (1) These are the generalized joint space coordinates of a composite robot, where This indicates the rotation angles of each joint of the manipulator. This indicates the position and rotation angle of the mobile platform within the world coordinate system; Represents the operator arm joint coordinate system Relative to the world coordinate system The homogeneous transformation matrix, and These represent the operating arm linkages. The pseudo-inertia matrix and mass, Represents the gravitational acceleration vector. and Indicates the operating arm linkage Relative to its joint coordinate system The position of the center of gravity; and These represent the mass and moment of inertia of the mobile platform, respectively. The trace operator represents a matrix; ,in Joint coordinates The function matrix, Kinematic parameters The constant coefficient matrix, Represents the coordinate system of the mobile platform Position parameters relative to its drive wheel coordinate system Indicates the operating arm linkage The length, twist angle, and joint offset are used to obtain the full parameter terms of the composite robot dynamics model. , , , That is, a combination of kinematic geometric parameters and mass inertia parameters; Step 1.2: Based on the constructed Lagrange equations, the fully parameterized linearized dynamic model of the composite robot is derived. The specific process is as follows: The following expression is obtained by deriving formula (1): ， In formula (2) , Representing the Lagrange linearized equations and the manipulator linkage Number of related terms, function ; Represents the operating arm linkage The mass inertia parameter, where Representative link The moment of inertia vector; Represents kinematic geometric parameters, a combination of all parameters. ; , ; Define function vectors Define the dynamic full parameter combination vector The fully parameterized linearized dynamic model of the composite robot is constructed as follows: ， In formula (3) Indicates the driving torque of the composite robot. This represents the driving torque of each joint of the manipulator. Represents the translation axis of the mobile platform along the world coordinate system. , Directional driving force and rotation axis Directional driving torque; joint observation vector ,link Full dynamic parameters ,in It is a joint The moment of inertia, viscous friction, and Coulomb friction coefficient; It is the dynamic observation matrix of the mobile platform. ; Represents the dynamic parameters of the mobile platform, where They are along the translation axis , and rotating axis Viscous friction and Coulomb friction coefficient in the directional direction; in, It is the observation matrix of the fully parameterized linearized dynamic model of the composite robot. These are its unknown parameters that need to be identified; Step 1.3: Eliminate unidentifiable dynamic parameters from the dynamic model and complete the modeling of the dynamic basis parameters. The specific process is as follows: Through random sampling Calculate the dynamic regression matrix and remove its zero-element column to obtain , ,in It is a random sample number and satisfies , ; Singular value decomposition ,in and These represent the orthogonal right singular matrix, the left singular matrix, and the singular value matrix, respectively. Only the main diagonal has non-zero elements and the diagonal matrix Representation matrix The rank is diagonal elements and constant Submatrix , It is easy to know The zero-element column corresponds to unidentifiable kinetic parameters. The zero-element column corresponds to the kinetic parameters that can be identified independently, while the remaining ones are parameters that can only be identified by combination. From the matrix Selecting regular matrices by reverse order and its corresponding combinatorial identification parameter set Design the permutation matrix satisfy , ,Depend on get Then the final model is: ， In formula (4) It is the basis parameter set of the dynamic model. It is its corresponding dynamic observation matrix; and They are respectively by Zhongyu , The submatrix formed by the corresponding columns.

2. The method for identifying all dynamic parameters of a composite robot based on maximum likelihood estimation as described in claim 1, characterized in that, Step two specifically involves: The excitation trajectories of each joint of the composite robot are designed using periodic Fourier series, and the specific expressions are as follows: ， In formula (5) and Representing the fundamental frequency and order of the Fourier series respectively, the excitation trajectory parameters are defined. and ,in Represents joint The initial position offset; Let the number of cycles of the excitation trajectory of the composite robot be The number of sampling points in each period is The mean of the measured data , ,in and These represent the joints of a composite robot. In the Sampling time within each excitation cycle The position and torque values ​​are then used to calculate the measurement noise variance. , ; The maximum likelihood estimation algorithm for the full dynamic parameters of the designed composite robot is as follows: ， In formula (6) The mean value of the sampled joint angle data of the composite robot. The mean value of the sampled data of the joint driving torque; The measurement error representing the joint angle, where It is determined by parameters The joint angle calculated using formula (5); The measurement error representing the driving torque of each joint of the composite robot, where The joint torque is calculated using the full-parameter model formula (4) of the dynamics. The One element, They are respectively composed of parameters The joint angle, velocity, and acceleration are calculated using formula (5); It is the cost function of the maximum likelihood estimation of the total dynamic parameters; the Gauss-Newton iterative method is used to solve formula (6) to obtain the total dynamic parameters. and sampling trajectory parameters The maximum likelihood estimate.

3. The method for identifying all dynamic parameters of a composite robot based on maximum likelihood estimation as described in claim 2, characterized in that, Step three specifically involves: The maximum likelihood estimates of the total dynamic parameters of the composite robot are obtained from formula (6). The covariance matrix will asymptotically converge to ,in It is the Fisher information matrix and represents the signal-to-noise ratio of the measured data relative to the estimated parameters, where and ; Initialize all dynamic parameters of the composite robot Based on formula (5), a parameter optimization model for the dynamic excitation trajectory is designed, and the specific expression is as follows: ， ， In formula (7) Represents the determinant of a matrix. , , and These represent the joints of a composite robot. Maximum angle limit, minimum angle limit, maximum speed limit and maximum acceleration limit; equality constraint terms are used to limit the initial position, velocity and acceleration of the excitation trajectory of each joint of the composite robot to zero, and inequality constraint terms satisfy the physical constraints during the motion process.

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