A networked mobile robot event-triggered data-driven control method and system

Abstract

The application discloses a networked mobile robot event-triggered data-driven control method and system, and the control method comprises the following steps: constructing a networked mobile robot kinematic model, and establishing a corresponding networked mobile robot discrete-time error model according to the networked mobile robot kinematic model; introducing a disturbance term, constructing a general nonlinear system, and constructing a data model with input expectation; designing a disturbance approximation mechanism based on a radial basis neural network; designing an event-triggered mechanism based on a tracking error norm square and a dynamic threshold variable; obtaining actual control input controllers by minimizing a control input criterion function, constructing a parameter estimator and a parameter resetter; constructing an event-triggered data-driven trajectory tracking control strategy, and the networked mobile robot obtains a control scheme according to the event-triggered data-driven trajectory tracking control strategy. The application realizes high-precision trajectory tracking control of the networked mobile robot in a complex environment, saves communication resources, and enhances environmental adaptability and practicability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mobile robot control, and particularly relates to a networked mobile robot event-triggered data-driven control method and system. BACKGROUND

[0002] In intelligent manufacturing, networked mobile robot systems (NMRSs) are gradually replacing fixed-position robots due to their outstanding flexibility and scalability. These networked mobile robot systems (NMRSs) can be equipped with manipulators, 3D cameras, 3D scanners, and other devices to perform manufacturing tasks in large areas and different scenarios.

[0003] Operators need to control networked mobile robot systems (NMRSs) using control methods, but existing control methods have the following shortcomings:

[0004] 1. Traditional model-based trajectory tracking control methods rely on system dynamics models. In actual systems, due to factors such as friction, structural errors, and external disturbances, it is often difficult to obtain complete and accurate system dynamics models. Inaccurate models will directly affect the performance of the controller and may even cause system instability. For complex systems (such as multi-degree-of-freedom robots or strongly nonlinear systems), the modeling process usually involves complex physical mechanism analysis, mathematical derivation, and experimental identification, which not only requires high professional requirements for the modeler, but also takes a long time and has high development costs. In addition, such model-based control methods lack good portability and are difficult to quickly adapt to changes in system structure or working environment.

[0005] 2. Existing data-driven control methods usually only establish data models based on historical system input and output data without fully considering the influence of desired signals of control inputs on system behavior.

[0006] 3. Most existing data-driven methods focus on path tracking problems and do not fully consider time-dependent target trajectories.

[0007] 4. Current research has used data-driven methods for trajectory tracking, but has not considered the problem of limited network communication. SUMMARY

[0008] The present application provides a networked mobile robot event-triggered data-driven control method and system to solve the technical problems in the prior art.

[0009] To achieve the above purpose, the technical solution of the present application is as follows:

[0010] The application provides a networked mobile robot event-triggered data-driven control method, comprising the following steps:

[0011] S1, a networked mobile robot kinematic model is constructed, and a corresponding networked mobile robot discrete-time error model is established according to the networked mobile robot kinematic model;

[0012] S2, an additional disturbance term is introduced based on the networked mobile robot discrete-time error model, a general nonlinear system is constructed, and a data model with input expectation is constructed according to the general nonlinear system;

[0013] S3, a disturbance approximation mechanism based on a radial basis neural network is designed for the uncertain disturbance term in the data model with input expectation, then the disturbance approximation mechanism is used to estimate the disturbance term, and a final data model with input expectation is obtained;

[0014] S4, an event-triggered mechanism based on a tracking error norm square and a dynamic threshold variable is designed considering the network resource limitation problem;

[0015] S5, a control input criterion function containing a tracking error, a control input increment and a control input error is designed, an actual control input controller is obtained by minimizing the control input criterion function according to the final data model with input expectation, and a parameter estimator and a parameter resetter are constructed according to a least square method;

[0016] S6, a signal keeper is designed according to the event-triggered mechanism in S4, and an event-triggered data-driven trajectory tracking control strategy is constructed by combining the disturbance approximation mechanism, the event-triggered mechanism, the actual control input controller, the parameter estimator and the parameter resetter, so that the networked mobile robot can obtain a control scheme according to the event-triggered data-driven trajectory tracking control strategy to cope with external disturbances.

[0017] Further, the S1 specifically comprises the following steps:

[0018] S11, a tracking trajectory of the networked mobile robot is set as a spiral line, and expected heading angles and expected control inputs of the networked mobile robot are obtained through geometric relations and differential operation, wherein the expected control inputs include expected linear velocities, expected angular velocities and expected lateral velocities;

[0019] S12, then a networked mobile robot kinematic model is constructed according to actual linear velocities, lateral velocities and heading angular velocities of the networked mobile robot on a reference trajectory;

[0020] S13, then a networked mobile robot continuous-time error model is constructed according to the networked mobile robot kinematic model;

[0021] S14, collate the continuous-time error model of the networked mobile robot to obtain a discrete-time error model of the networked mobile robot.

[0022] Further, the kinematic model of the networked mobile robot is specifically as follows:

[0023] ;

[0024] wherein, represents the current pose of the networked mobile robot; and are the current horizontal coordinate and vertical coordinate of the networked mobile robot respectively, is the current heading angle of the networked mobile robot; , , represent the linear velocity, lateral velocity and heading angle velocity respectively; the symbol represents the derivative;

[0025] The continuous-time error model of the networked mobile robot in S13 is specifically as follows:

[0026] ;

[0027] wherein, , , represent the horizontal coordinate error, vertical coordinate error and heading angle error of the networked mobile robot respectively; , , represent the expected value of the horizontal coordinate, vertical coordinate and heading angle of the networked mobile robot respectively;

[0028] The discrete-time error model of the networked mobile robot is specifically as follows:

[0029] ;

[0030] wherein, represents the discrete sampling interval, represents the discrete time, represents the final time in the finite time range; , , represent the expected value of the linear velocity, lateral velocity and heading angle velocity of the networked mobile robot respectively.

[0031] Further, S2 specifically comprises the following steps:

[0032] S21. Based on the discrete-time error model of the networked mobile robot, an additional perturbation term is introduced, and then combined with the discrete-time error model of the networked mobile robot, an unknown general nonlinear system with perturbation is constructed.

[0033] S22. Given two assumptions: Assumption 1 is that the partial derivatives of all variables in the discrete-time error model of the networked mobile robot are continuous; Assumption 2 is that the general nonlinear system obtained in S21 satisfies the generalized Lipschitz conditions, which are as follows:

[0034] ;

[0035] in, This represents the discrete-time error model of a networked mobile robot. It is a constant of a generalized Lipschitz condition; and They represent the first and The total control input signal at time k is composed of the actual control input and the desired input signal at the same time, i.e., the total control input signal at time k. , and They represent the first k The actual control input and the desired input signal at any given time; Indicates transpose; , These represent two different moments in time; Represents the 2-norm;

[0036] S23. Based on satisfying two assumptions, and in accordance with the general nonlinear system in S21, construct a data model with input expectations.

[0037] Furthermore, the general nonlinear system is specifically as follows:

[0038] ;

[0039] in, This represents the expected pose of a networked mobile robot. It is an unknown but bounded disturbance term, that is, an additional disturbance term introduced;

[0040] The data model with input expectations (i.e., the IR-DL data model) is as follows:

[0041] ;

[0042] in, ,and , denotes the real set; sub-block matrix , ; each vector in can be written as ; denotes the difference between the total control input signal composed of actual control input and desired input at the kth time instant and the (k-1)th time instant, i.e. ; denotes the disturbance function, i.e. the difference between the disturbance term at the kth time instant and the (k-1)th time instant.

[0043] where the IR-DL data model can be obtained by input reference dynamic linearization (i.e. IR-DL) technique, which is as follows:

[0044] For a general nonlinear system at the kth time instant and the (k-1)th time instant, the following relationship is satisfied:

[0045] (1)

[0046] By subtracting the formula in the formula (1), the following relationship can be obtained:

[0047] (2)

[0048] In order to further process, the equivalent transformation of formula (2) is carried out to obtain formula (3):

[0049] (3)

[0050] In order to simplify formula (3), the first custom parameter is set, and the first custom parameter satisfies the following relationship:

[0051] (4)

[0052] Since the first custom parameter is only related to the historical input and output (I / O) data, it can be written as a term related to , that is:

[0053] (5)

[0054] When , there is at least one solution that makes formula (5) true.

[0055] According to the Cauchy mean value theorem, we have: ​​

[0056] (6)

[0057] wherein, , , and ;

[0058] Thus, the second custom parameter is set

[0059] (7)

[0060] So far, the IR-DL data model has been obtained by using the input reference type dynamic linearization (IR-DL) technology.

[0061] Further, the S3 specifically comprises the following steps:

[0062] S31, to solve the interference function This uncertain interference term, the interference function The estimated value , and the estimated value is used to approximate the interference function , wherein the calculation formula of the estimated value

[0063] ;

[0064] wherein, is the weight matrix to be trained, wherein is the number of nodes in the radial basis neural network RBF-NNs, is the dimension of the interference function ; denotes the radial basis function, i.e. the activation function within the radial basis neural network RBF-NNs, and the calculation formula of the radial basis function

[0065] ;

[0066] wherein, is the reference output signal of the networked mobile robot at the moment ; and are the center matrix and bandwidth vector of the radial basis neural network RBF-NNs respectively; e represents the natural constant;

[0067] S32, determine the update rule of the weight matrix , so far, the disturbance approximation mechanism is obtained, and the disturbance term is estimated by using the disturbance approximation mechanism, wherein the update rule is specifically as follows:

[0068] ​​ ;

[0069] in, It is the learning rate;

[0070] S33. Update to obtain the final data model with input expectations.

[0071] Furthermore, the event triggering mechanism in S4 is as follows:

[0072] ;

[0073] in, This represents the event triggering function. and These are two predefined positive integers; It is the trajectory tracking error triggered by the event; Represents a dynamic variable, and the dynamic variable The formula for calculation is:

[0074] ;

[0075] in, It is a constant;

[0076] The update rules for the event triggering mechanism are expressed by a formula, as follows:

[0077] ;

[0078] in, Indicates the event triggering function In the set of nonnegative integers The infimum of the upper boundary; This represents the difference between the current time and the t-th trigger time, i.e. ; and These represent the t-th and t+1-th trigger times, respectively.

[0079] Furthermore, step S5 specifically includes the following steps:

[0080] S51. Without considering the event triggering mechanism, design the control input criterion function of the data-driven control scheme based on the final data model with input expectations. The specific control input criterion function is as follows:

[0081] ;

[0082] in, This represents the function that controls the input criteria. and These are two penalty factors that are positive numbers;

[0083] S52, Minimize the control input criterion function, i.e. Then the control input needs to satisfy the following relationship:

[0084] ;

[0085] in, It is the identity matrix. In the input reference type pseudo-Jacobian matrix The estimated value;

[0086] S53. To avoid the inversion operation, the relation in S52 is rewritten to obtain the actual control input controller, as follows:

[0087] ;

[0088] Among them, two scalars and They are respectively represented as and ;matrix Then it is written as , Represented as the step size factor, and , yes The Subvectors, that is, as well as ; Indicates the first Time and the The difference between the actual control inputs at two different time points; Indicates the first Time and the The difference between the expected values ​​of the control input at two different time intervals;

[0089] S54. Design a parameter estimator, and then use the parameter estimator to solve for the estimated value. The parameter estimator is as follows:

[0090] ;

[0091] in, and They are two positive numbers; This represents the estimated value of the input reference pseudo-Jacobian matrix;

[0092] S55. To ensure that the final controller remains effective even when faced with time-varying parameters and external disturbances, a parameter resetter is designed, as follows:

[0093] ;

[0094] wherein, is a negation operation; , and are three normal quantities; denotes a sign function.

[0095] Further, the S6 specifically comprises the following steps:

[0096] S61, in order not to violate the causality of signal transmission, rewriting the data model with input expectation, obtaining a signal holder, and the relationship obtained by rewriting is specifically as follows:

[0097] ;

[0098] wherein, is an event-triggered , denotes the first and the difference between the total control input signal composed of the actual control input and the expected input at the second two adjacent time points; and are the signal holders at the k+1 and k time points, respectively, wherein, , used for maintaining the latest updated networked mobile robot state information when the network communication transmission is not triggered;

[0099] S62, combining the signal holder, the disturbance approximation mechanism, the event-triggered mechanism, the data-driven trajectory tracking controller, the parameter estimator and the parameter resetter to construct an event-triggered data-driven trajectory tracking control strategy; the event-triggered data-driven trajectory tracking control strategy is specifically as follows:

[0100] ;

[0101] S63, the networked mobile robot obtains a control scheme according to the event-triggered data-driven trajectory tracking control strategy to realize data compensation when coping with external interference.

[0102] Another aspect of the present application also provides a networked omnidirectional mobile composite robot system, comprising a networked mobile robot, and the networked mobile robot is configured or executes the networked mobile robot event-triggered data-driven control method described above.

[0103] The present application has the following advantages:

[0104] 1. Compared with the traditional model-based trajectory tracking control method relying on the system dynamics model, the application adopts a data-driven method, only uses input-output (I / O) data for controller design, and reduces the requirement for accurate modeling.

[0105] 2. In view of the fact that the existing data-driven control method is usually based only on the historical I / O data of the system when establishing a data model, the influence of the control input expected signal on the behavior of the networked mobile robot is not fully considered, the application introduces the reference signal of the control input into the data model, the reference signal is the expected value related information, including the expected trajectory and the expected control input (namely: expected linear velocity, expected lateral velocity, and expected heading angle velocity), so that a more flexible and adjustable data model with input expectation is constructed, which is helpful to improve the equivalence of the model to the dynamic characteristics of the complex system and the control performance of the event-triggered data-driven trajectory tracking control strategy.

[0106] 3. In view of the fact that most of the existing data-driven methods focus on path tracking problems and do not fully consider the time-dependent target trajectory, the application directly faces the trajectory tracking control task, which is more in line with the timing accuracy requirements of actual production applications (such as multi-robot cooperative handling).

[0107] 4. In view of the fact that although the current research has used data-driven methods for trajectory tracking, it does not consider the problem of limited network communication; the application introduces an event-triggering mechanism into the control framework, effectively reduces the network bandwidth occupation, and improves the real-time performance and communication efficiency of the networked mobile robot. The event-triggering mechanism for MIMO systems proposed in the application is based on the norm design of multi-dimensional tracking error, and is more general and practical.

[0108] 5. The application realizes high-precision trajectory tracking control of the networked mobile robot in a complex environment, saves communication resources, and enhances environmental adaptability and practicality. BRIEF DESCRIPTION OF DRAWINGS

[0109] Figure 1 It is a schematic diagram of the geometric relationship between the reference trajectory and each variable of the networked mobile robot on the reference trajectory in the embodiment of the application.

[0110] Figure 2 It is a labeling diagram of each parameter of the networked mobile robot.

[0111] Figure 3 It is a schematic diagram of the position difference between the event-triggered data-driven trajectory tracking control strategy (ET-DDTTC) provided by the application and the MFAC For MIMO method in the embodiment of the application.

[0112] Figure 4The schematic diagram of the heading angle difference between the event-triggered data-driven trajectory tracking control strategy (ET-DDTTC) and the MFAC For MIMO method provided by the application in the embodiment of the application;

[0113] Figure 5 The perturbation curve diagram in the embodiment of the application;

[0114] Figure 6 The comparison diagram of the mean square error between the event-triggered data-driven trajectory tracking control strategy (ET-DDTTC) and the MFAC For MIMO method provided by the application in the embodiment of the application;

[0115] Figure 7 The event-triggered interval schematic diagram in the embodiment of the application. DETAILED DESCRIPTION

[0116] In order to facilitate the understanding of the application, the application will be described more fully below with reference to the accompanying drawings. The preferred embodiments of the application are shown in the drawings. However, the application can be realized in many other different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the application more thorough and comprehensive.

[0117] The embodiment discloses a networked mobile robot event-triggered data-driven control method, comprising the following steps:

[0118] S1, a networked mobile robot kinematics model is constructed, and a corresponding networked mobile robot discrete-time error model is established according to the networked mobile robot kinematics model;

[0119] S2, an additional disturbance term is introduced on the basis of the networked mobile robot discrete-time error model, a general nonlinear system is constructed, and then a data model with input expectation is constructed according to the general nonlinear system;

[0120] S3, a disturbance approximation mechanism based on a radial basis neural network is designed for the uncertain disturbance term in the data model with input expectation, and then the disturbance approximation mechanism is used to estimate the disturbance term, so that the final data model with input expectation is obtained; and the control performance and robustness of the mobile robot are improved;

[0121] S4, since multiple sensors are connected to an actual network (such as a local area network ROS2 LAN), but the total bandwidth is limited, the network resource limited problem is considered, and an event-triggered mechanism based on the norm square of the tracking error and a dynamic threshold variable is designed; the event-triggered mechanism is compatible with static and decaying threshold mechanisms, and can be flexibly set according to actual task requirements, so as to reduce the network communication frequency and save network communication resources;

[0122] S5, designing a control input criterion function containing tracking error, control input increment and control input error, obtaining an actual control input controller according to a final data model with input expectation and by minimizing the control input criterion function, and constructing a parameter estimator and a parameter resetter according to a least square method;

[0123] S6, designing a signal keeper according to the event-triggered mechanism in S4, and constructing an event-triggered data-driven trajectory tracking control strategy (ET-DDTTC) combining the disturbance approximation mechanism, the event-triggered mechanism, the actual control input controller, the parameter estimator and the parameter resetter, so that the networked mobile robot obtains a control scheme according to the event-triggered data-driven trajectory tracking control strategy (ET-DDTTC) to cope with external disturbances.

[0124] In some embodiments, S1 specifically includes the following steps:

[0125] S11, setting a tracking trajectory of the networked mobile robot as a spiral line, and obtaining an expected heading angle and an expected control input of the networked mobile robot through geometric relationship and differential operation, the expected control input including an expected linear velocity, an expected angular velocity and an expected lateral velocity;

[0126] S12, then constructing a kinematic model of the networked mobile robot according to actual linear velocity, lateral velocity and heading angular velocity of the networked mobile robot on the reference trajectory;

[0127] S13, then constructing a continuous-time error model of the networked mobile robot according to the kinematic model of the networked mobile robot;

[0128] S14, arranging the continuous-time error model of the networked mobile robot to obtain a discrete-time error model of the networked mobile robot.

[0129] In some embodiments, the kinematic model of the networked mobile robot is specifically as follows:

[0130] ;

[0131] wherein, represents a current pose of the networked mobile robot; and are a current lateral coordinate and a current longitudinal coordinate of the networked mobile robot, respectively, is a current heading angle of the networked mobile robot; 、 、 represent linear velocity, lateral velocity and heading angular velocity, respectively; symbol represents derivative;

[0132] The networked mobile robot continuous-time error model in S13 is specifically as follows:

[0133] ;

[0134] wherein, , , respectively represent the lateral coordinate error, the longitudinal coordinate error and the heading angle error of the networked mobile robot; , , respectively represent the lateral coordinate expected value, the longitudinal coordinate expected value and the heading angle expected value of the networked mobile robot;

[0135] The networked mobile robot discrete-time error model is specifically as follows:

[0136] ;

[0137] wherein, represents a discrete sampling interval, represents a discrete time, represents a final time in a finite time range; , , respectively represent the linear velocity expected value, the lateral velocity expected value and the heading angle velocity expected value of the networked mobile robot. The control input signal is defined as . The above discretization method is not limited to the Euler method. The networked mobile robot discrete-time error model is only used to provide input-output (I / O) data.

[0138] In some embodiments, S2 specifically comprises the following steps:

[0139] S21, based on the networked mobile robot discrete-time error model, an additional disturbance term is introduced, and then a disturbed unknown general nonlinear system is constructed in combination with the networked mobile robot discrete-time error model;

[0140] S22, two assumption conditions are given, assumption condition one is that the networked mobile robot discrete-time error model is partially derivable with respect to all variable components and the partial derivative is continuous; assumption condition two is that the general nonlinear system obtained in S21 satisfies the generalized Lipschitz condition, and the generalized Lipschitz condition is specifically as follows:

[0141] ;

[0142] wherein, represents the networked mobile robot discrete-time error model, is a constant of a generalized Lipschitz condition; and denote the total control input signal at the kth and (k-1)th moment, respectively, which is composed of the actual control input and the desired input signal at the same moment, i.e., the total control input signal at the kth moment , denotes the actual control input and the desired input signal at the kth and (k-1)th moment, respectively; , and denote the actual control input and the desired input signal at the kth and (k-1)th moment, respectively; k denotes the transpose; , denote two different moments, respectively; denotes the 2-norm;

[0143] S23, based on satisfying two hypothesis conditions, and according to the general nonlinear system in S21, a data model with input expectation is constructed.

[0144] In some embodiments, the general nonlinear system is specifically as follows:

[0145] ;

[0146] wherein, denotes the pose expectation value of the networked mobile robot; is an unknown but bounded disturbance term, i.e., an additional disturbance term introduced; the disturbance term illustrates that in the actual operation process of the networked mobile robot system NMRSs, there is a disturbance similar to the road roughness and the workpiece vibration transmitted by the clamping system. The disturbance term enhances the universality of the system, and the corresponding disturbance term added in simulation is wherein , which will be described in detail below. Figure 5 .

[0147] The data model with input expectation (i.e., the IR-DL data model) is specifically as follows:

[0148] ;

[0149] wherein, , and , denotes the real number set; the sub-block matrix , ; Each vector in ; denotes the difference between the total control input signal composed of the actual control input and the desired input at the kth moment and the total control input signal composed of the actual control input and the desired input at the (k-1)th moment, i.e.,​ ; represents the difference of the interference terms between the kth time instant and the (k-1)th time instant.

[0150] where the IR-DL data model can be obtained by an input reference type dynamic linearization (i.e. IR-DL) technique, as follows:

[0151] For the kth time instant of the general nonlinear system, the following relationship is satisfied: and the (k-1)th time instant of the general nonlinear system, the following relationship is satisfied:

[0152] (1)

[0153] By subtracting the equation in the formula (1), the following relationship can be obtained:

[0154] (2)

[0155] In order to further process, the equivalent transformation is performed on the formula (2), and the formula (3) is obtained:

[0156] (3)

[0157] In order to simplify the formula (3), the first custom parameter is set, and the first custom parameter satisfies the following relationship:

[0158] (4)

[0159] Since the first custom parameter is only related to the historical input and output (I / O) data, it can be written as a term related to , that is:

[0160] (5)

[0161] When , there is at least one solution that makes the formula (5) true.

[0162] According to the Cauchy mean value theorem, the following relationship is obtained:

[0163] (6)

[0164] where , , and ;

[0165] The second custom parameter is set, and the following relationship can be obtained: ​

[0166] (7)

[0167] So far, the IR-DL data model has been obtained by using the input reference type dynamic linearization (IR-DL) technology.

[0168] In some embodiments, the S3 specifically comprises the following steps:

[0169] S31, since the IR-DL data model contains an uncertain disturbance term, in order to solve the disturbance function This uncertain disturbance term, the estimated value of the disturbance function is calculated Since the disturbance function is approximated by RBF-NNs, the estimated value can be used to approximate the disturbance function , where the calculation formula of the estimated value is:

[0170] ;

[0171] Where, is the weight matrix to be trained, where is the number of nodes in the radial basis neural network RBF-NNs, is the dimension of the disturbance function ; Indicates a radial basis function, that is, an activation function within the radial basis neural network RBF-NNs, and the calculation formula of the radial basis function is:

[0172] ;

[0173] Where, is the reference output signal of the networked mobile robot at time ; and are the center matrix and bandwidth vector of the radial basis neural network RBF-NNs, respectively; e represents the natural constant;

[0174] S32, determine the update rule of the weight matrix , so far, the disturbance approximation mechanism is obtained, and the disturbance term is estimated by using the disturbance approximation mechanism, where the update rule is specifically expressed by the formula as follows:

[0175] ;

[0176] Where, is the learning rate;

[0177] S33, update to obtain the final data model with input expectations.

[0178] In some embodiments, the event-triggering mechanism in S4 is specified as follows:

[0179] ;

[0180] wherein, is an event-triggering function, and are two preset normal numbers; is the trajectory tracking error of event triggering; denotes a dynamic variable, and the dynamic variable is calculated as:

[0181] ;

[0182] wherein, is a constant;

[0183] The updating rule of the event-triggering mechanism is expressed by a formula, which is specified as follows:

[0184] ;

[0185] wherein, is an event-triggering function is the lower bound on the set of non-negative integers ; denotes the difference between the current time and the tth triggering time, i.e. ; and denote the tth and (t+1)th triggering times, respectively; the triggering time interval generated by the event-triggering mechanism in the simulation experiment is shown in Figure 7 It can be obviously seen that the number of data transmission in the network is significantly reduced after the processing by the event-triggering mechanism, thereby reducing the network communication pressure.

[0186] In some embodiments, S5 specifically comprises the following steps:

[0187] S51. Without considering the event-triggering mechanism, a data-driven control scheme control input criterion function is designed according to the final data model with input expectation, and the control input criterion function is specified as follows:

[0188] ;

[0189] wherein, denotes the control input criterion function; and are two normal punishment factors; wherein is adjusted by adjusting a penalty factor to ensure the smoothness of the control input symbols; and the penalty factor is designed to adjust the error term of the control input more flexibly ;

[0190] S52, minimizing the control input criterion function, i.e. , the control input needs to satisfy the following relationship:

[0191] ;

[0192] wherein, is a unit matrix, is an estimated value of in the input reference type pseudo Jacobian matrix;

[0193] S53, to avoid the inverse operation, the relationship in S52 is rewritten to obtain the actual control input controller, which is as follows:

[0194] ;

[0195] wherein, two scalars and are respectively represented as = and ; the matrix is written as , is represented as a step factor, and , the step factor is used to make the control law more flexible, is the th sub-vector of , i.e. , and ; represents the difference between the actual control input at the kth time period and the actual control input at the (k-1)th time period; represents the difference between the expected value of the control input at the kth time period and the expected value of the control input at the (k-1)th time period;

[0196] S54, since the input reference type pseudo Jacobian matrix on which the update of the control signal depends is currently unknown, a parameter estimator needs to be designed, and then the estimated value is obtained by using the parameter estimator; the parameter estimator is as follows:

[0197] ;

[0198] wherein, and are two normal numbers; represents an estimated value of an input reference type pseudo Jacobian matrix;

[0199] S55, to ensure that the final event-triggered data-driven trajectory tracking control strategy can remain effective even in the face of time-varying parameters and external disturbances, a parameter resetter is designed, which is specifically as follows:

[0200] ;

[0201] ;

[0202] wherein, is an inverse operation; , and are three normal quantities, any infinitesimal normal quantity can guarantee that the main diagonal elements of are non-zero in ; the remaining two normal quantities and are used to ensure the upper bound of ; another condition can guarantee that the sign of is unchanged relative to the initial setting ; represents a sign function;

[0203] In some embodiments, the S51 specifically comprises the following steps:

[0204] S511, without considering the event-triggering mechanism, an initial control input criterion function of the data-driven control scheme is designed, which is specifically as follows:

[0205] ;

[0206] S512, the data model with input expectation obtained in S2 is substituted into the initial control input criterion function, the initial control input criterion function can be rewritten, and a final control input criterion function can be obtained, which is specifically as follows:

[0207] .

[0208] In some embodiments, the S6 specifically comprises the following steps:

[0209] S61, to not violate the causality of signal transmission, the data model with input expectation is rewritten to obtain a signal maintainer, and the rewritten relationship is specifically as follows:

[0210] ;

[0211] wherein, is the event-triggered , denotes the and the difference of the total control input signal composed of the actual control input and the desired input between the two adjacent time instants; and are the signal holders at the k+1 and k time instants, respectively, wherein, , for holding the latest updated networked mobile robot state information when the network communication transmission is not triggered;

[0212] S62, combining the signal holder, the disturbance approximation mechanism, the event-triggered mechanism, the actual control input controller, the parameter estimator and the parameter resetter to construct an event-triggered data-driven trajectory tracking control strategy; the event-triggered data-driven trajectory tracking control strategy is specifically as follows:

[0213] ;

[0214] wherein, all the variables related to and are replaced by and respectively. The ET trajectory tracking error is written as . In addition, are replaced by and respectively, so as to form a vector . The tracking performance of the control method is seen from Figure 3 , 4 , 6, and is compared with the method of MFAC For MIMO, and the method of the application has a smaller trajectory tracking error.

[0215] S63, the networked mobile robot obtains a control scheme according to the event-triggered data-driven trajectory tracking control strategy to realize data compensation when coping with external interference.

[0216] As can be seen from the event-triggered data-driven trajectory tracking control strategy, the application only uses the input and output I / O data of the system at the previous time instant, does not violate the causality law, and does not involve any explicit NMRSs model (i.e. a series of models based on physical, chemical and other properties, such as the dynamics and kinematics of the networked mobile robot). The triggering time is determined by the event-triggered mechanism, thereby saving the communication resources. The disturbance approximation mechanism constructed by the radial basis function neural network RBF-NNs generates an estimated value of the interference function, which can compensate for external interference such as uneven terrain and workpiece vibration.

[0217] Furthermore, when the normal number is set as

[0218] Currently, parameters such as , , , and are mainly selected by trial and error. The usual practice is to initially set these parameters to 1 before determining the penalty factor , and then adjust them according to the performance of the networked mobile robot system (NMRS). The penalty factor is used to limit the rate of change of the control input. Generally speaking, the larger the penalty factor , the slower the system response and the smaller the overshoot; conversely, the response is fast but may result in a larger overshoot. The specific selection of the penalty factor should be combined with the application scenario and system characteristics.

[0219] The present application proposes an input reference driven dynamic linearization (IR-DL) data model. Based on the traditional dynamic linearization method, the incremental variable of the control reference input is further introduced, thereby significantly improving the degree of freedom and flexibility of system modeling, adapting to various types of nonlinear and under-actuated mobile robot systems. This model can directly construct a controller based on input-output (I / O) data without the need for an explicit system model, and has good generalization ability and realizability.

[0220] In view of the uncertain external disturbances such as workpiece vibration and uneven ground commonly encountered by mobile robots in actual handling tasks, the present application designs a disturbance approximation mechanism based on a radial basis function neural network (RBF-NN), which can estimate and compensate unknown disturbance terms online, ensuring control accuracy and system stability, thereby improving the trajectory tracking ability of the robot in complex uncertain environments.

[0221] Considering the problem of limited network resources, the present application proposes an event-triggered mechanism based on the norm square of the tracking error and a dynamic threshold variable. The event-triggering condition is adjustable, compatible with static and decaying threshold mechanisms, and can be flexibly set according to actual task requirements. At the same time, the event-triggered mechanism supports multiple-input multiple-output (MIMO) systems and can be widely applied to multi-degree-of-freedom robot platforms, reducing network communication frequency while ensuring system performance.

[0222] The second aspect of the present application also provides an omnidirectional mobile composite robot system, which includes a networked omnidirectional mobile robot configured or executing the networked mobile robot event-triggered data-driven control method described above. ​

[0223] The above merely provides a specific implementation of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application. Furthermore, the technical solutions of each embodiment of the present application can be combined with each other, but it must be based on the realization of the ordinary skilled in the art, when the combination of the technical solutions appears contradictory or unachievable, it should be considered that the combination of the technical solutions does not exist, nor within the protection scope required by the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A networked mobile robot event-triggered data-driven control method, characterized by, The method comprises the following steps: S1, a kinematic model of the networked mobile robot is constructed, and a corresponding discrete-time error model of the networked mobile robot is established according to the kinematic model; S2, an additional disturbance term is introduced based on the discrete-time error model of the networked mobile robot, a general nonlinear system is constructed, and a data model with input expectation is constructed according to the general nonlinear system; S3, a disturbance approximation mechanism based on a radial basis neural network is designed for the uncertain disturbance term in the data model with input expectation, the disturbance term is estimated by using the disturbance approximation mechanism, and a final data model with input expectation is obtained; S4, an event-triggered mechanism based on a tracking error norm square and a dynamic threshold variable is designed considering the network resource limitation problem; S5, a control input criterion function including a tracking error, a control input increment and a control input error is designed, an actual control input controller is obtained by minimizing the control input criterion function according to the final data model with input expectation, and a parameter estimator and a parameter resetter are constructed according to a least square method; S6, a signal keeper is designed according to the event-triggered mechanism in S4, and an event-triggered data-driven trajectory tracking control strategy is constructed by combining the disturbance approximation mechanism, the event-triggered mechanism, the actual control input controller, the parameter estimator and the parameter resetter, so that the networked mobile robot can obtain a control scheme according to the event-triggered data-driven trajectory tracking control strategy to cope with external disturbances; The general nonlinear system is as follows: ； wherein, represents the desired pose value of the networked mobile robot; is an unknown but bounded disturbance term, i.e. an additional perturbation term introduced; represents the discrete time instants, represents the final time instant of the finite time horizon; represents the discrete time error model of the networked mobile robot, and respectively represent the actual and desired input signals at the k time instant. The data model with input expectation is as follows: ； in, ,and , Represents the set of real numbers; sub-matrix , ; Each vector in All can be written as ; Indicates the first With the The difference between the total control input signal, consisting of the actual control input and the desired input, at two adjacent moments, i.e. ; Represents the interference function, i.e., the th With the The difference between the interference terms at two adjacent time points.

2. The networked mobile robot event-triggered data-driven control method of claim 1, wherein, S1 specifically comprises the following steps: S11, the tracking trajectory of the networked mobile robot is set as a spiral line, and the expected heading angle and the expected control input of the networked mobile robot are obtained through geometric relationship and differential operation, wherein the expected control input includes an expected linear velocity, an expected angular velocity and an expected lateral velocity; S12, a kinematic model of the networked mobile robot is constructed according to the actual linear velocity, the lateral velocity and the heading angular velocity of the networked mobile robot on the reference trajectory; S13, a continuous-time error model of the networked mobile robot is constructed according to the kinematic model of the networked mobile robot; S14, the continuous-time error model of the networked mobile robot is arranged to obtain a discrete-time error model of the networked mobile robot.

3. The networked mobile robot event-triggered data-driven control method of claim 2, wherein, The kinematic model of the networked mobile robot is as follows: ； wherein, represents the current pose of the networked mobile robot; and are the current lateral and longitudinal coordinates of the networked mobile robot, respectively, is the current heading angle of the networked mobile robot; , , represent the linear, lateral and heading velocities, respectively; the symbol denotes the derivative; The continuous-time error model of the networked mobile robot in S13 is as follows: ； wherein, , , respectively represent the lateral coordinate error, the longitudinal coordinate error and the heading angle error of the networked mobile robot; , , respectively represent the lateral coordinate expected value, the longitudinal coordinate expected value and the heading angle expected value of the networked mobile robot; The discrete-time error model of the networked mobile robot is as follows: ； wherein, denotes a discrete sampling interval, , , denote a linear velocity desired value, a lateral velocity desired value, and a yaw rate desired value of the networked mobile robot, respectively.

4. The networked mobile robot event-triggered data-driven control method of claim 3, wherein, S2 specifically comprises the following steps: S21, an additional disturbance term is introduced based on the discrete-time error model of the networked mobile robot, and an unknown general nonlinear system with disturbance is constructed by combining the discrete-time error model of the networked mobile robot; S22, given two assumptions, assumption one is that the partial derivative of all variables in the component of the discrete-time error model of the networked mobile robot is continuous; assumption two is that the general nonlinear system obtained in S21 satisfies the generalized Lipschitz condition, which is as follows: ； in, It is a constant of a generalized Lipschitz condition; and They represent the first and The total control input signal at time k is composed of the actual control input and the desired input signal at the same time, i.e., the total control input signal at time k. , Indicates transpose; , These represent two different moments in time; Represents the 2-norm; S23, based on the two assumptions and according to the general nonlinear system in S21, a data model with input expectation is constructed.

5. The networked mobile robot event-triggered data-driven control method of claim 4, wherein, The S3 specifically includes the following steps: S31、for solving the interference function This uncertain interference term, the estimate value of the interference function And use the estimate value To approximate the interference function Where the calculation formula of the estimate value Is​ ； wherein, is the weight matrix to be trained, wherein is the number of nodes in the radial basis function neural network, RBF-NNs, is the interference function is the dimension of the input vector; denotes the radial basis function, i.e. the activation function within the radial basis function neural network, RBF-NNs, the radial basis function is calculated as: ； wherein, is the reference output signal of the networked mobile robot at time instant and are the center matrix and the bandwidth vector of the radial basis function neural network (RBF-NN), respectively; denotes the natural constant; S32, determining an update rule of the weight matrix The update rule is expressed by the following formula: ； wherein, is the learning rate; S33, update the final data model with input expectation.

6. The networked mobile robot event-triggered data-driven control method of claim 5, wherein, The event trigger mechanism in S4 is as follows: ； wherein, represents an event-triggering function, and are two preset normal numbers; is an event-triggering trajectory tracking error; represents a dynamic variable, and the dynamic variable is calculated as follows: ； wherein is a constant; The update rule of the event trigger mechanism is expressed by a formula, which is as follows: ； wherein, represents an event trigger function represents the lower bound on the set of non-negative integers ; represents the difference between the current time and the tth trigger time, i.e. ; and represent the tth and t+1th trigger times, respectively.

7. The networked mobile robot event-triggered data-driven control method of claim 6, wherein, The S5 specifically includes the following steps: S51, without considering the event trigger mechanism, the control input criterion function of the data-driven control scheme is designed according to the final data model with input expectation, and the control input criterion function is as follows: ； wherein represents a control input criterion function; and are two positive constant penalty factors; S52, minimize the control input criterion function, i.e. The control input needs to satisfy the following relation: ； wherein, is the identity matrix, is an estimate of the input reference type pseudo Jacobian matrix in the input reference type. S53, in order to avoid the inverse operation, the relationship in S52 is rewritten to obtain the actual control input controller, which is as follows: ； where two scalars and are represented as and respectively; the matrix is written as , is represented as a step factor, and , is the th sub-vector of , i.e., and ; represents the difference between the actual control input in the time period from the th time instant to the th time instant; represents the difference between the expected value of the control input in the time period from the th time instant to the th time instant; S54, a parameter estimator is designed, and then the parameter estimator is used to solve to obtain an estimated value ; the parameter estimator is specifically as follows: ； wherein, and are two normal numbers; denotes an estimated value of the input reference-type pseudo Jacobian matrix; S55, in order to ensure that the final obtained controller can remain effective even in the face of time-varying parameters and external disturbances, a parameter resetter is designed, and the parameter resetter is as follows: ； wherein is the negation operation; , and are three normal quantities; denotes the sign function.

8. The networked mobile robot event-triggered data-driven control method of claim 7, wherein, The S6 specifically includes the following steps: S61, in order to not violate the causality of signal transmission, the data model with input expectation is rewritten to obtain a signal keeper, and the relationship obtained by rewriting is as follows: ； wherein, is the event triggered , denotes the and the difference of the total control input signal composed of the actual control input and the desired input between two adjacent time instants; and are the signal holders at the k+1 and k time instants, respectively, wherein, , for holding the most recently updated networked mobile robot state information when the network communication transmission is not triggered. S62, combined with the signal keeper, the disturbance approximation mechanism, the event trigger mechanism, the actual control input controller, the parameter estimator and the parameter resetter, an event-triggered data-driven trajectory tracking control strategy is constructed, and the event-triggered data-driven trajectory tracking control strategy is as follows: ； S63, the networked mobile robot obtains the control scheme according to the event-triggered data-driven trajectory tracking control strategy to realize data compensation in the face of external disturbances.

9. An omnidirectional mobile robotic system, comprising: The networked mobile robot is configured or executes the networked mobile robot event-triggered data-driven control method of any one of claims 1 to 8.

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