An online identification method for spherical robot system based on Koopman operator

Abstract

The present invention proposes an online identification method for a spherical robot system based on the Koopman operator, comprising the following steps: firstly, determining the Koopman operator dimensionality-raising function according to the system theoretical model, then collecting a section of operation data to initialize the identification model and the online update algorithm, and finally switching to the online operation stage to update the identification model according to the algorithm. The method uses the Koopman operator to establish an accurate approximate linear model for a highly nonlinear robot model, which is convenient for iterative prediction and beneficial for subsequent use. In the online update link, observation errors are introduced, and real-time error estimation is performed, and a targeted update method for online identification parameters is given, so that the algorithm can accurately and stably update the robot identification model in any environment, any working condition, and any instruction. The present invention helps to improve the overall performance of the robot system.

Description

Technical Field

[0001] The invention relates to the field of spherical robot system identification, and in particular to an online identification method of a spherical robot system based on a Koopman operator. Background Art

[0002] The spherical robot is a new type of spherical robot that relies on its internal two-degree-of-freedom weight to achieve flexible movement on a plane. It has the advantages of high movement efficiency, good resistance to confrontation, and strong environmental adaptability. It has great application potential in the fields of security, field exploration, and patrol protection. However, the strong nonlinearity, incompleteness, and under-actuation of the spherical robot have created challenges for the robot's perception, planning, and control modules.

[0003] Model-based control methods have been proven to be a powerful solution to these problems, but they require an accurate robot model. Robot models built based on theory are often too complex to be used for real-time calculations, and many of the coefficients related to the environment and friction dissipation are difficult to obtain accurately, so model identification is required to obtain an accurate model. For the identification of nonlinear systems, there are still two difficulties that have not been well solved in current methods: first, nonlinear systems are difficult to describe concisely, and the use of nonlinear models to identify the system often requires complex offline identification experiments, and parameter convergence is difficult; then, the established nonlinear model is difficult to predict, infer, and optimize, and it is difficult to build a real-time application algorithm. Therefore, seeking a model that can concisely describe nonlinear systems is the top priority of system identification work.

[0004] At present, the parameter identification of robots is mostly carried out offline, including direct measurement method, parameter identification method, etc. There are few studies on online identification algorithms. The few existing studies did not consider the influence of noise in the process, and the identification results fluctuated violently in high-noise scenes, and even the iteration deteriorated, making them unable to be put into practical use. However, robots are highly time-varying systems, and changes in robot load and operating environment will cause changes in the system model. Modifications to the underlying control algorithm will also cause changes in the system model, requiring corresponding adjustments to the upper-level algorithm. These characteristics make it difficult to meet control requirements using fixed models and control algorithms during operation. There is an urgent need for an online identification method that can stably give a real-time model of the system so that the subsequent control system can implement model reference adaptive control.

[0005] The nonlinear characteristics will make the model more sensitive to noise, further increasing the difficulty of online identification parameter convergence. It is necessary to improve the robustness of online identification to cope with the challenges brought by the combination of the above problems. Summary of the invention

[0006] The present invention mainly solves the technical problems existing in the prior art, such as the model is too complex, difficult to calculate in real time, and insufficiently resistant to noise, and provides an accurate, stable and robust online identification method for a spherical robot system based on the Koopman operator. It can establish an accurate approximate linear model for a highly nonlinear theoretical model, avoid conducting special identification experiments, and can accurately and stably update the robot identification model in any environment, any working condition, and any instruction.

[0007] The present invention aims to solve the above technical problems mainly through the following technical solutions: a spherical robot system online identification method based on Koopman operator, comprising the following steps:

[0008] S1. Determine the discrete dynamic model of the spherical robot and express it using the multidimensional mapping dictionary function group ξ as follows:

[0009] ,

[0010] ,

[0011] ,

[0012] Where d is the system dimension, x=[ψ,α,β,η] T is the system state vector, n x represents the dimension of the system state; ψ is the pitch angle of the robot, η is the roll angle of the robot, α and β are the rotation angles of the main axis motor and the secondary axis motor respectively, and u[k] is [(k-1)T s ,kT s The average system input in the time range of ], T s is the system sampling interval, n u represents the dimension of vector u;

[0013] S2, collect the real-time system state vector x[k] and system input vector u[k] of the spherical robot, filter out high-frequency noise through a low-pass filter, and then concatenate the historical state vectors (x[k-1] to x[kd], etc.) and historical input vectors (u[k-1] to u[kd], etc.) to form X[k] and U[k], and map the system state according to the mapping dictionary function group ξ(X[k], U[k]) in step S1 to obtain the mapped observation vector f[k];

[0014] S3. According to the online identification recursive algorithm based on Kalman filtering, the model coefficients and the online identification related parameter matrix are updated to obtain the real-time posterior coefficient matrix θ[k+1|k+1]. The posterior coefficient matrix θ[k+1|k+1] can be used for robot control system prediction and control.

[0015] The updated online identification model is used for subsequent robot state prediction, navigation control, etc.

[0016] Preferably, the step S3 is specifically as follows:

[0017] The robot discrete model established using Koopman theory is represented by N observables f as follows: f[k]=θ T f[k-1],

[0018] ,

[0019] ,

[0020] Among them, θ is the model parameter vector that needs to be obtained, which is used as the observation of the Kalman filter. Based on the slowly changing characteristics of the robot's model parameters, the prediction equation is simplified to:

[0021] θ[k]=θ[k-1],

[0022] In the process of updating the model parameters using Kalman filtering, each observable f i The corresponding parameter vector θ i =[θ 1i θ 2i … θ Ni ] T The update is performed independently; when the system state value at a new moment is obtained, the observation value f[k] is obtained by dimensioning according to the dictionary function. For each observation value f i [k] Update θ according to the following formula i :

[0023] θ i [k|k-1]=θ i [k-1|k-1],

[0024] P i [k|k-1]=P i [k-1|k-1],

[0025] ,

[0026] K i [k]=P i [k|k-1]f[k-1](f T [k-1]P i [k|k-1]f[k-1]+R i [k]),

[0027] ,

[0028] P i[k|k]=(IK i [k]f T [k-1])P i [k|k-1],

[0029] Among them, P i [k|k-1] is the i-th parameter vector θ i The prior confidence matrix at time k, P i [k|k] is the posterior confidence matrix after Kalman filter update, R i [k] is the i-th observation f i The variance of the observation noise corresponding to time k, K i [k] is θ i The required gain matrix is ​​updated at time k, and I is the unit matrix of the corresponding dimension.

[0030] Compared with the standard Kalman filter algorithm, the method proposed in this invention increases the noise R i Real-time estimation: Use a sliding array to store the observations f over the past period of time, and use the parameter vector θ obtained in real time i The prediction is made on the array. The fitting error can be regarded as the observation error that meets the white noise condition, and then an approximate estimate of the noise variance is obtained, n w is the window length, and the parameter vector θ is updated each time i Update the noise variance R i and window array. Experiments show that using this method to estimate the noise variance can obtain accurate real-time estimates.

[0031] Preferably, the initialization steps of the online identification algorithm in step S3 are as follows:

[0032] S31, collecting a robot state trajectory and input trajectory information for a period of 5-10 seconds, and performing filtering preprocessing according to the above method, and finally obtaining the states at n moments;

[0033] S32, after the state information at each moment is dimensioned according to the mapping dictionary function group ξ proposed above, it is spliced ​​into a state matrix according to the following rules:

[0034] ,

[0035] The least squares method is used to obtain the initial identification result matrix:

[0036] θ init =(Ω T Ω) -1 Ω T F,

[0037] S33, use the identification results to calculate the variance R of the initial observation noise one by one i_init :

[0038] ,

[0039] S34, determine the series confidence matrix P according to the dimension of the Koopman operator and the dimension of the discrete model i And the gain matrix K i Dimension, each P i All are initialized to P i_init =γI, the two matrices are gradually updated by sliding according to the following rules using the collected trajectory information until the nth state, thereby completing parameter initialization and entering the online operation stage:

[0040] K i_init [j]=P i_init [j-1]f[j-1](f T [j-1]P i_init [j-1]f[j-1]+R i_init ),

[0041] P i_init [j]=(IK i_init [j]f T [j-1])P i_init [j-1],

[0042] γ is a sufficiently large positive number, for example, greater than or equal to 10000.

[0043] Preferably, the step S1 is specifically as follows:

[0044] The discrete dynamics model of the spherical robot is expressed as:

[0045] x[k+1]=F(x[k],x[k-1],…,x[kd],u[k],u[k-1],…,u[kd]),

[0046] x=[ψ,α,β,η] T is the system state vector, d is the system dimension, n x represents the dimension of vector x; u[k] is [(k-1)T s ,kT s The average system input in the time range of ], T s is the system sampling interval, n u Represents the dimension of vector u; transfer the state to manifold Φ T_s It is expressed as follows:

[0047] Φ T_s :X×U→X×U,

[0048] Φ T_s (X[0],U[0])=(X[1],U[0]),

[0049] ,

[0050] ,

[0051] The Koopman operator is introduced to establish the identification model, and the discrete system model of the spherical robot is expressed as:

[0052] K Φ f=Φ°f,

[0053] Among them, K Φ represents the Koopman operator, f∈F Φ For the new space F Φ The observed quantity in F Φ It is an infinite-dimensional space spanned by all square-integrable real-valued functions of the robot state vector and the input vector; the observation vector f is given by the corresponding dictionary function family ξ ,ξ i is the observed quantity f i The corresponding mapping function, N represents the total number of observations f, which is also the width of the vector; Koopman operator K Φ :F→F Φ Represent the system in the new state space; ° represents the function combination of the response, so that the forward prediction of the system is expressed as:

[0054] K Φ (X[k],U[k])=Φ°ξ(X[k],U[k])=ξ(X[k+1],U[k+1]),

[0055] Finite-dimensional dictionary functions are used to approximate infinite-dimensional space. After analyzing the theoretical model and considering the coupling effects between robot orders and variables, the N-dimensional mapping dictionary function group ξ specifically for spherical robots is finally determined:

[0056] .

[0057] Preferably, in step S2, data collection is performed by using the sensors and controller of the robot itself, according to the sampling period T s Sampling: The spherical robot is divided into three parts: the axis body, the weight pendulum and the spherical shell according to the mechanical connection relationship. Sensors (such as inertial sensor IMU, motor encoder, etc.) are used to obtain the real-time status information of the robot, including pitch angle, roll angle, main axis motor rotation angle and secondary axis motor rotation angle information; for the input vector of the system, the motor command torque is directly recorded.

[0058] As a preferred embodiment, after a preset time T K Finally, the identification model is tested and verified: a section of the robot's actual running trajectory is selected, and the online updated model is used to obtain the robot's predicted trajectory according to the input sequence. The weighted root mean square error between the predicted trajectory and the actual trajectory is calculated, and the weighting coefficient is determined by the design goal; if the error is less than the warning limit, the online identification algorithm continues to run; if it exceeds the warning limit, the system model and algorithm parameters of the last test verification moment are read from the database, and the state of the last moment is restored to restart the online identification, and the warning information is reported.

[0059] The substantial effect brought by the present invention is: the present invention introduces the Koopman theory to establish an approximate linear model for a nonlinear spherical robot, which can fit the nonlinear characteristics to a great extent, and meet the accuracy requirements while achieving high-speed prediction and reasoning. The online identification method proposed by the present invention introduces real-time noise estimation into the algorithm, which can complete stable and robust parameter updates in high-noise scenes, so that the robot can adapt to the impact of changes in the ground, load, etc. Experiments have proved that the stability of the parameter update method proposed by the present invention is far better than that of traditional algorithms, and can meet the application of robots in various field scenes. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 This is a flow chart of an online identification method for a spherical robot system based on a Koopman operator of the present invention. DETAILED DESCRIPTION

[0061] The technical solution of the present invention is further specifically described below through embodiments and in conjunction with the accompanying drawings.

[0062] Embodiment: The flowchart of the online identification algorithm proposed by the present invention is as follows Figure 1 The spherical robot theoretical model applicable to the present invention is as follows:

[0063] ,

[0064] ,

[0065] ,

[0066] ,

[0067] ,

[0068] ,

[0069] Among them, M and m pare the masses of the whole ball and the heavy pendulum respectively; I pl ,I fl and I sl is the moment of inertia of the pendulum, frame and spherical shell about the principal axis, I ps ,I fs and I ss is the moment of inertia of the weight pendulum, frame and spherical shell around the secondary axis; r is the radius of the spherical shell; l is the distance from the center of mass of the weight pendulum to the center of the sphere; g is the acceleration of gravity; ψ is the pitch angle of the robot, θ is the roll angle of the robot; α and β are the rotation angles of the main axis motor and the secondary axis motor, α can be calculated by the formula Converted to the robot's forward speed; τ l and τ s is the output torque of the main shaft motor and the secondary shaft motor; F fx and F fy is the friction between the sphere and the ground in the major and minor axis directions; ζ is the Rayleigh dissipation coefficient.

[0070] A spherical robot system online identification method based on Koopman operator comprises the following steps:

[0071] S1. Determine the discrete dynamic model of the spherical robot and express it using the multidimensional mapping dictionary function group ξ as follows:

[0072] ,

[0073] ,

[0074] ,

[0075] Where d is the system dimension, x=[ψ,α,β,η] T is the system state vector, n x represents the dimension of the system state; ψ is the pitch angle of the robot, η is the roll angle of the robot, α and β are the rotation angles of the main axis motor and the secondary axis motor respectively, and u[k] is [(k-1)T s ,kT s The average system input in the time range of ], T s is the system sampling interval, n u represents the dimension of vector u;

[0076] S2, collect the real-time system state vector x[k] and system input vector u[k] of the spherical robot, filter out high-frequency noise through a low-pass filter, and then concatenate the historical state vectors (x[k-1] to x[kd], etc.) and historical input vectors (u[k-1] to u[kd], etc.) to form X[k] and U[k], and map the system state according to the mapping dictionary function group ξ(X[k], U[k]) in step S1 to obtain the mapped observation vector f[k];

[0077] S3. According to the online identification recursive algorithm based on Kalman filtering, the model coefficients and the online identification related parameter matrix are updated to obtain the real-time posterior coefficient matrix θ[k+1|k+1].

[0078] The step S1 is specifically as follows:

[0079] The discrete dynamics model of the spherical robot is expressed as:

[0080] x[k+1]=F(x[k],x[k-1],…,x[kd],u[k],u[k-1],…,u[kd]),

[0081] x=[ψ,α,β,η] T is the system state vector, d is the system dimension, n x represents the dimension of vector x; u[k] is [(k-1)T s ,kT s The average system input in the time range of ], T s is the system sampling interval, n u Represents the dimension of vector u; transfer the state to manifold Φ T_s It is expressed as follows:

[0082] Φ T_s :X×U→X×U,

[0083] Φ T_s (X[0],U[0])=(X[1],U[0]),

[0084] ,

[0085] ,

[0086] The Koopman operator is introduced to establish the identification model, and the discrete system model of the spherical robot is expressed as:

[0087] K Φ f=Φ°f,

[0088] Among them, K Φ represents the Koopman operator, f∈F ΦFor the new space F Φ The observed quantity in F Φ It is an infinite-dimensional space spanned by all square-integrable real-valued functions of the robot state vector and the input vector; the observation vector f is given by the corresponding dictionary function family ξ ,ξ i is the observed quantity f i The corresponding mapping function, N represents the total number of observations f, which is also the width of the vector; Koopman operator K Φ :F→F Φ Represent the system in the new state space; ° represents the function combination of the response, so that the forward prediction of the system is expressed as:

[0089] K Φ (X[k],U[k])=Φ°ξ(X[k],U[k])=ξ(X[k+1],U[k+1]),

[0090] Finite-dimensional dictionary functions are used to approximate infinite-dimensional space. After analyzing the theoretical model and considering the coupling effects between robot orders and variables, the N-dimensional mapping dictionary function group ξ specifically for spherical robots is finally determined:

[0091] .

[0092] The step S3 is specifically as follows:

[0093] The robot discrete model established using Koopman theory is represented by N observables f as follows: f[k]=θ T f[k-1],

[0094] ,

[0095] ,

[0096] Among them, θ is the model parameter vector to be obtained, which is the observation quantity of the Kalman filter. Based on the slowly changing characteristics of the robot's model parameters, the prediction equation is simplified to:

[0097] θ[k]=θ[k-1],

[0098] In the process of updating the model parameters using Kalman filtering, each observable f i The corresponding parameter vector θ i =[θ 1i θ 2i … θ Ni ] T The update is performed independently; when the system state value at a new moment is obtained, the observation value f[k] is obtained by dimensioning according to the dictionary function. For each observation value f i[k] Update θ according to the following formula i :

[0099] θ i [k|k-1]=θ i [k-1|k-1],

[0100] P i [k|k-1]=P i [k-1|k-1],

[0101] ,

[0102] K i [k]=P i [k|k-1]f[k-1](f T [k-1]P i [k|k-1]f[k-1]+R i [k]),

[0103] ,

[0104] P i [k|k]=(IK i [k]f T [k-1])P i [k|k-1],

[0105] Among them, P i [k|k-1] is the i-th parameter vector θ i The prior confidence matrix at time k, P i [k|k] is the posterior confidence matrix after Kalman filter update, R i [k] is the i-th observation f i The variance of the observation noise corresponding to time k, K i [k] is θ i The required gain matrix is ​​updated at time k, and I is the unit matrix of the corresponding dimension.

[0106] Compared with the standard Kalman filter algorithm, the method proposed in this invention increases the noise R i Real-time estimation: Use a sliding array to store the observations f over the past period of time, and use the parameter vector θ obtained in real time i The prediction is made on the array. The fitting error can be regarded as the observation error that meets the white noise condition, and then an approximate estimate of the noise variance is obtained, n w is the window length, and the parameter vector θ is updated each time i Update the noise variance R i and window array. Experiments show that using this method to estimate the noise variance can obtain accurate real-time estimates.

[0107] The initialization steps of the online identification algorithm in step S3 are as follows:

[0108] S31, collecting a robot state trajectory and input trajectory information for a period of 5-10 seconds, and performing filtering preprocessing according to the above method, and finally obtaining the states at n moments;

[0109] S32, after the state information at each moment is dimensioned according to the mapping dictionary function group ξ proposed above, it is spliced ​​into a state matrix according to the following rules:

[0110] ,

[0111] The least squares method is used to obtain the initial identification result matrix:

[0112] θ init =(Ω T Ω) -1 Ω T F,

[0113] S33, use the identification results to calculate the variance R of the initial observation noise one by one i_init :

[0114] ,

[0115] S34, determine the series confidence matrix P according to the dimension of the Koopman operator and the dimension of the discrete model i And the gain matrix K i Dimension, each P i All are initialized to P i_init =γI (γ is a sufficiently large positive number), the two matrices are gradually updated by sliding according to the following rules using the collected trajectory information until the nth state, thereby completing parameter initialization and entering the online operation stage:

[0116] K i_init [j]=P i_init [j-1]f[j-1](f T [j-1]P i_init [j-1]f[j-1]+R i_init ),

[0117] P i_init [j]=(IK i_init [j]f T [j-1])P i_init [j-1].

[0118] In step S2, data collection is specifically performed by using the robot's own sensors and controllers according to the sampling period T sSampling: The spherical robot is divided into three parts: the axis body, the weight pendulum and the spherical shell according to the mechanical connection relationship. Sensors (such as inertial sensor IMU, motor encoder, etc.) are used to obtain the real-time status information of the robot, including pitch angle, roll angle, main axis motor rotation angle and secondary axis motor rotation angle information; for the input vector of the system, the motor command torque is directly recorded.

[0119] After a preset time T K Finally, the identification model is tested and verified: a section of the robot's actual running trajectory is selected, and the online updated model is used to obtain the robot's predicted trajectory according to the input sequence. The weighted root mean square error between the predicted trajectory and the actual trajectory is calculated, and the weighting coefficient is determined by the design goal; if the error is less than the warning limit, the online identification algorithm continues to run; if it exceeds the warning limit, the system model and algorithm parameters of the last test verification moment are read from the database, and the state of the last moment is restored to restart the online identification, and the warning information is reported.

[0120] The verified online identification model is used for subsequent robot state prediction, navigation control, etc.

[0121] The specific embodiments described herein are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in similar ways, but they will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

[0122] Although the terms such as dynamic model, system state vector, average system input, etc. are used more frequently in this article, the possibility of using other terms is not excluded. These terms are used only to more conveniently describe and explain the essence of the present invention; interpreting them as any additional restrictions is contrary to the spirit of the present invention.

Claims

1. A spherical robot system online identification method based on Koopman operator, characterized in that: The steps include: S1. Determine the discrete dynamic model of the spherical robot and express it using the multidimensional mapping dictionary function group ξ as follows: ， ， ， Where d is the system dimension, x=[ψ,α,β,η] T is the system state vector, n x represents the dimension of the system state vector x; ψ is the pitch angle of the robot, η is the roll angle of the robot, α and β are the rotation angles of the main axis motor and the secondary axis motor respectively, and u[k] is [(k-1)T s ,kT s The average system input in the time range of ], T s is the system sampling interval, n u represents the dimension of vector u; S2, collect the real-time system state vector x[k] and system input vector u[k] of the spherical robot, filter out high-frequency noise through a low-pass filter, and concatenate the historical state vector and historical input vector to form X[k] and U[k], map the system state according to the mapping dictionary function group ξ(X[k], U[k]) in step S1, and obtain the mapped observation vector f[k]; S3, according to the online identification recursive algorithm based on Kalman filtering, the model coefficients and the online identification related parameter matrix are updated to obtain the real-time posterior coefficient matrix θ[k+1|k+1]; The step S3 is specifically as follows: The robot discrete model established using Koopman theory is represented by N observables f as follows: f[k]=θ T f[k-1], ， ， Among them, θ is the model parameter vector that needs to be obtained, which is used as the observation of the Kalman filter. Based on the slowly changing characteristics of the robot's model parameters, the prediction equation is simplified to: θ[k]=θ[k-1], In the process of updating the model parameters using Kalman filtering, each observable f i The corresponding parameter vector θ i =[θ 1i θ 2i … θ Ni ] T The update is performed independently; when the system state value at a new moment is obtained, the observation value f[k] is obtained by dimensioning according to the dictionary function. For each observation value f i [k] Update θ according to the following formula i : i i [k|k-1]=θ i [k-1|k-1], P i [k|k-1]=P i [k-1|k-1], ， K i [k]=P i [k|k-1]f[k-1](f T [k-1]P i [k|k-1]f[k-1]+R i [k]), ， P i [k|k]=(I-K i [k]f T [k-1])P i [k|k-1], Among them, P i [k|k-1] is the i-th parameter vector θ i The prior confidence matrix at time k, P i [k|k] is the posterior confidence matrix after Kalman filter update, R i [k] is the i-th observation f i The variance of the observation noise corresponding to time k, K i [k] is θ i The required gain matrix is ​​updated at time k, and I is the unit matrix of the corresponding dimension.

2. The method for online identification of a spherical robot system based on Koopman operator according to claim 1, characterized in that: The initialization steps of the online identification algorithm in step S3 are as follows: S31, collecting a robot state trajectory and input trajectory information for a period of 5-10 seconds, and performing filtering preprocessing according to the above method, and finally obtaining the states at n moments; S32, after the state information at each moment is dimensioned according to the mapping dictionary function group ξ proposed above, it is spliced ​​into a state matrix according to the following rules: ， The least squares method is used to obtain the initial identification result matrix: i init =(Oh T Oh) -1 Oh T F, S33, use the identification results to calculate the variance R of the initial observation noise one by one i_init : ， S34, determine the series confidence matrix P according to the dimension of the Koopman operator and the dimension of the discrete model i And the gain matrix K i Dimension, each P i All are initialized to P i_init =γI, the two matrices are gradually updated by sliding according to the following rules using the collected trajectory information until the nth state, thereby completing parameter initialization and entering the online operation stage: K i_init [j]=P i_init [j-1]f[j-1](f T [j-1]P i_init [j-1]f[j-1]+R i_init ), P i_init [j]=(I-K i_init [j]f T [j-1])P i_init [j-1], γ is a sufficiently large positive number.

3. The method for online identification of a spherical robot system based on Koopman operator according to claim 1, characterized in that: The step S1 is specifically as follows: The discrete dynamics model of the spherical robot is expressed as: x[k+1]=F(x[k],x[k-1],…,x[kd],u[k],u[k-1],…,u[kd]), Transition state manifold Φ T_s It is expressed as follows: F T_s :X×U→X×U, Φ T_s (X[0],U[0])=(X[1],U[0]), The Koopman operator is introduced to establish the identification model, and the discrete system model of the spherical robot is expressed as: K Φ f=Φ°f, Among them, K Φ represents the Koopman operator, f∈F Φ For the new space F Φ The observed quantity in F Φ It is an infinite-dimensional space spanned by all square-integrable real-valued functions of the robot state vector and the input vector; the observation vector f is given by the corresponding dictionary function family ξ ,ξ i is the observed quantity f i The corresponding mapping function, N represents the total number of observations f, which is also the width of the vector; Koopman operator K Φ :F→F Φ Represent the system in the new state space; ° represents the function combination of the response, so that the forward prediction of the system is expressed as: K Φ (X[k],U[k])=Φ°ξ(X[k],U[k])=ξ(X[k+1],U[k+1]), Use finite-dimensional dictionary functions to approximate infinite-dimensional space; finally determine the N-dimensional mapping dictionary function group ξ that is unique to spherical robots: 。 4. The method for online identification of a spherical robot system based on Koopman operator according to claim 1, characterized in that: In step S2, data collection is specifically performed by using the robot's own sensors and controllers according to the sampling period T s Sampling: The spherical robot is divided into three parts: the axis body, the weight pendulum and the spherical shell according to the mechanical connection relationship. The real-time status information of the robot is obtained by using sensors, including the pitch angle, roll angle, main axis motor rotation angle and secondary axis motor rotation angle information. For the input vector of the system, the motor command torque is directly recorded.

5. A spherical robot system online identification method based on Koopman operator according to any one of claims 1 to 4, characterized in that: After a preset time T K Finally, the identification model is tested and verified: a section of the robot's actual running trajectory is selected, and the robot's predicted trajectory is obtained using the online updated model according to the input sequence. The weighted root mean square error between the predicted trajectory and the actual trajectory is calculated, and the weight coefficient is determined by the design goal; If the error is less than the warning limit, the online identification algorithm continues to run; If the warning limit is exceeded, the system model and algorithm parameters of the last test verification moment are read from the database, the state at the last moment is restored to restart online identification, and the warning information is reported.

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