A trajectory tracking autonomous control method fusing bayesian optimization and radial basis neural network

Abstract

The application discloses a trajectory tracking autonomous control method fusing Bayesian optimization and a radial basis neural network, and relates to the field of automatic control; the method steps are as follows: the Bayesian optimization method is used to realize efficient adaptive setting of controller parameters, and a multi-objective optimization function is constructed to balance tracking accuracy and control energy; a large amount of simulation is carried out by using the Bayesian optimization, parameter samples under various working conditions are obtained, and a double radial basis neural network is constructed and trained; based on the double radial basis neural network, autonomous adjustment of the control parameters is realized, and meanwhile, the optimal control performance of the control system can be guaranteed. The control strategy designed in the application can make the controller have the parameter autonomous adjustment capability, maintain the optimal performance, and overcome the limitations of artificial parameter adjustment.

Description

Technical Field

[0001] This invention relates to the field of automatic control, specifically to a trajectory tracking autonomous control method that integrates Bayesian optimization and radial basis neural networks. Background Technology

[0002] Currently, most existing trajectory tracking control systems employ fixed-parameter controllers, relying on pre-tuned parameters to complete the entire control process. However, actual operating conditions are complex and varied; the operating state of the controlled object, external disturbances, and the tracking task all undergo dynamic changes. Pre-setting fixed parameters is difficult to adapt to various scenarios and differentiated tasks, and cannot guarantee that the control system always operates in the optimal state. Consequently, problems such as decreased tracking accuracy, lag in dynamic response, and insufficient anti-interference capability often occur.

[0003] To improve controller parameter tuning, some studies have introduced intelligent optimization algorithms. Among them, Bayesian optimization utilizes surrogate models and acquisition functions to search for optimal control parameters with fewer simulations, making it suitable for scenarios with nonlinear parameter spaces, difficult-to-analyze objective functions, and high single-evaluation costs. However, Bayesian optimization requires multiple iterations, making the computation process relatively complex. Directly applying it to online trajectory tracking fails to meet the stringent real-time requirements of control systems. Therefore, although Bayesian optimization is highly effective in offline optimization, its use alone is insufficient for rapid online autonomous parameter tuning.

[0004] On the other hand, neural networks possess powerful nonlinear mapping capabilities and fast online inference speeds, and have been used for controller parameter estimation and adaptive tuning. However, their control performance is highly dependent on the quality of the training samples. If the controller parameter samples mainly originate from human experience or random parameters, the mapping relationships learned by the neural network are difficult to reflect the optimal global control performance, resulting in insufficient accuracy, limited generalization ability, or unstable control effects in the online output parameters. Therefore, while neural networks can guarantee good real-time performance, without the support of high-quality optimal parameter samples, their online parameter tuning results cannot guarantee superior control performance.

[0005] In summary, existing fixed-parameter control methods are difficult to adapt to complex and variable working conditions. Using Bayesian optimization alone has the problems of heavy online computational burden and insufficient real-time performance, while using neural networks alone is limited by the quality of training samples and it is difficult to guarantee the optimality of parameter tuning results. Summary of the Invention

[0006] To address the aforementioned problems, the present invention aims to provide a trajectory tracking autonomous control method that integrates Bayesian optimization and radial basis function neural networks. This method achieves complementary advantages by: using Bayesian optimization for global optimization in the offline phase to compensate for insufficient training sample quality in the neural network; and using a dual radial basis function neural network for rapid inference in the online phase to avoid the excessive computational burden of Bayesian optimization. This allows the control system to obtain near-globally optimal control parameters and quickly adapt to different initial deviations and dynamic operating conditions during actual operation, thereby improving trajectory tracking accuracy, reducing control energy consumption, and enhancing the system's real-time adaptive capability.

[0007] The technical solution of this invention is: a trajectory tracking autonomous control method integrating Bayesian optimization and radial basis function neural networks, specifically including the following steps:

[0008] Construct a trajectory tracking controller for the controlled object;

[0009] Offline optimization of controller parameters is performed based on Bayesian optimization algorithm;

[0010] Construct an offline training sample library for a two radial basis function neural network;

[0011] Construct and train a two radial basis function neural network model;

[0012] Based on the trained biradial basis function neural network model, autonomous control of the trajectory tracking of the controlled object is achieved.

[0013] Compared with the prior art, the advantages of the present invention are as follows:

[0014] (1) This invention obtains the optimal parameters of the controller under multiple working conditions in an offline state through the Bayesian optimization algorithm; at the same time, it designs a dual radial basis neural network model to learn online and quickly output the control parameter increments under the corresponding working conditions, thereby realizing the transfer from offline high-precision optimization capability to online real-time autonomous parameter tuning capability.

[0015] (2) Compared with the method of directly running Bayesian optimization online, the present invention transfers the calculation of the time-consuming controller optimal parameters to the offline stage. In the online stage, only forward inference of the two radial basis function neural network is required to obtain the control parameters, which significantly reduces the online calculation burden and meets the real-time requirements of trajectory tracking control. Moreover, compared with the traditional manual parameter tuning or fixed parameter control method, the present invention automatically constructs the optimal parameter sample library through the Bayesian optimization algorithm, gets rid of the dependence on manual experience, and improves the parameter optimization efficiency and global search capability;

[0016] (3) The present invention designs a dual radial basis function neural network model. After the first radial basis function neural network acts on the outer loop controller, it constructs the new expected motion state quantity and the expected motion state increment output by the outer loop controller as coupling feature quantities, which serve as part of the input of the second radial basis function neural network. This enables the second radial basis function neural network to perceive the load change caused by the adjustment of the outer loop controller parameters on the inner loop controller tracking the expected motion state quantity, thereby realizing the coupled tuning of the parameters of the inner and outer loop controllers.

[0017] (4) The neural network sample training library of the present invention is derived from the optimal controller parameters obtained by Bayesian optimization. Compared with the method of adaptive parameter tuning using neural networks, the parameter increment obtained by the present invention has a clearer optimization target and higher control performance.

[0018] (5) The present invention incorporates trajectory tracking error and control energy consumption into the optimization objective through a multi-objective cost function, so that the output controller parameters can not only improve tracking accuracy, but also suppress control input oscillation, reduce the risk of actuator saturation and reduce system operating energy consumption. Attached Figure Description

[0019] Figure 1 This is a diagram of a two-radial basis function neural network structure.

[0020] Figure 2 For the Bayesian optimization iterative convergence process;

[0021] Figure 3 The diagram shows the training state; (a) is the outer loop neural network regression, (b) is the mean square error of the outer loop neural network, (c) is the inner loop neural network regression, and (d) is the mean square error of the inner loop neural network.

[0022] Figure 4 To optimize the simulation results before and after, (a) is the position error in the x direction, (b) is the position error in the y direction, (c) is the position error in the z direction, (d) is the pitch tracking error, (e) is the yaw tracking error, (f) is the thrust, (g) is the pitch rudder deflection, (h) is the yaw rudder deflection, and (i) is the control energy. Detailed Implementation

[0023] The purpose of this invention is to provide a trajectory tracking autonomous control method that integrates Bayesian optimization and radial basis function neural networks, so as to realize online autonomous adjustment of trajectory tracking control system parameters, effectively reduce trajectory tracking error and control energy, and improve control performance.

[0024] First, this invention provides a trajectory tracking autonomous control method that integrates Bayesian optimization and radial basis function neural networks, the steps of which include:

[0025] S1: Construct a trajectory tracking controller for the controlled object.

[0026] Based on the hierarchical control principle, a two-layer trajectory tracking controller for the controlled object is constructed. The controller consists of an outer-loop kinematic controller and an inner-loop dynamic controller, achieving decoupled control in different dimensions. The outer-loop kinematic controller controls the displacement of the controlled object in the x, y, and z directions. The inputs are the position errors in these three directions, and the outputs are the desired motion state variables. The desired motion state variable can be the desired velocity, desired acceleration, desired attitude angle, or desired angular velocity. In practical applications, it can be selected and adjusted according to different controlled objects and task requirements. It characterizes how the controlled object should move to reduce position error. This is also the target that the inner-loop dynamics controller tracks. The inner-loop dynamics controller is used for motion state regulation of the controlled object, and its input is the motion state variable error. ,in This represents the actual motion state of the controlled object. The output is the final control command, such as thrust and rudder deflection angle; thus achieving decoupled closed-loop control of position and attitude.

[0027] S2: Offline optimization of controller parameters based on Bayesian optimization algorithm;

[0028] The Bayesian optimization algorithm is used to perform offline optimization of the core parameters of the controller, and the Gaussian process surrogate model is used to reduce the computational cost of simulation evaluation, balancing parameter search efficiency and optimization accuracy. The specific steps are as follows:

[0029] S201: Construct a multi-objective cost function;

[0030] To balance trajectory tracking control accuracy and system control energy consumption, and to avoid control defects caused by optimizing a single performance index, this invention designs a multi-objective cost function that integrates tracking error and control energy consumption. This cost function consists of two parts: a tracking accuracy index established using the integral absolute error, and a control energy index established using the sum of squared integrals. The multi-objective cost function is as follows:

[0031] ;

[0032] In the formula, The total integral absolute error; To control the sum of squares of the energy integral; , where is the weighting coefficient, indicating the priority of performance metric allocation.

[0033] Due to position tracking error ( ) and attitude tracking error ( The smaller this index is, the smaller the deviation between the control system and the reference trajectory. Its expression is as follows:

[0034] ;

[0035] In the formula, The actual three-axis position of the controlled object. The desired three-axis position of the controlled object. These are the actual pitch angle and actual yaw angle of the controlled object, respectively. Let t be the desired pitch angle and desired yaw angle of the controlled object, t be time, and T be the total duration of a single trajectory tracking control simulation.

[0036] This represents the energy consumption for control; the smaller this indicator, the less energy the control system outputs. To eliminate optimization bias caused by differences in the dimensions of different indicators, the energy consumption for control is... After normalization to ensure consistent dimensions, the expression is as follows:

[0037]

[0038] In the formula, The longitudinal control force output generated by the system at time t. This is the maximum longitudinal control force limit allowed by the system. , The actual deflection angle of the control mechanism (such as rudder or elevator) at time t. , This is the maximum allowable deflection angle limit for the control mechanism.

[0039] Set weight coefficients Prioritize ensuring basic control performance; Avoid excessive energy consumption. In practical applications, adjustments can be made according to different controlled objects and task requirements.

[0040] S202: Define the parameter space of the parameters to be optimized and construct the initial historical dataset. ;

[0041] Based on parameter tuning experience, the parameters to be optimized for the inner and outer loop controllers are defined. The parameter space. N sets of initial parameters are randomly selected internally. Construct the initial parameter set The initial parameter set is used to perform realistic simulation calculations in the inner and outer loop controllers for trajectory tracking, and then the cost function value corresponding to each set of parameters is solved. Construct a Bayesian optimization of the initial historical dataset ;

[0042] S203: Construct a Gaussian process surrogate model, and then calculate the parameters to be optimized. Predicted objective function value

[0043] To address the high-cost evaluation challenge in controller parameter optimization—namely, the high computational cost of evaluating the objective function value corresponding to any controller parameter—this invention constructs a Gaussian process as a low-computational-cost surrogate model to replace the original simulation system, thereby fitting the controller parameters to be optimized. With the objective function value The nonlinear mapping relationship between them.

[0044] (1) Establish a prior model

[0045] First, consider the optimization parameters. With the objective function value The mapping relationship establishes a priori assumptions, namely, that it follows a Gaussian process distribution as follows:

[0046] ;

[0047] In the formula, GP(·,·) represents a Gaussian process; It is a mean function, usually set to a constant or zero; The covariance kernel function is used to measure the variance between any two points in the parameter space. and The similarity between the corresponding objective function values ​​is expressed as follows:

[0048] ;

[0049] In the formula, For signal variance, For length scale, Represents two sets of controller parameter vectors and Euclidean distance in the parameter domain It is a natural exponential function.

[0050] The physical meaning of this prior assumption is that, in the parameter space, similar controller parameters should have similar performance characteristics, meaning the objective function value has spatial continuity and smoothness. Based on this assumption, when the actual performance of some controller parameter points is known, Bayesian inference can be used to determine the optimal parameters of the controller. To predict the performance.

[0051] (2) Construct the predicted objective function value Compared with historical objective function values joint Gaussian distribution relationship

[0052] For any given optimization parameters Construct the prediction objective function value corresponding to this parameter. Compared with historical objective function values Joint Gaussian distribution relationship:

[0053]

[0054] In the formula, For the set A column vector composed of medium values, Parameters that have been measured The covariance matrix between them, whose element in the i-th row and j-th column is ; Parameters to be optimized Its own prior variance; Parameters to be optimized Compared with measured parameters The covariance vector between them.

[0055] (3) Utilizing the joint Gaussian distribution relationship, through historical datasets Solve for the parameters to be optimized Predicted objective function value .

[0056] Its posterior conditional probability distribution is:

[0057]

[0058] In the formula, Given the current historical dataset, its corresponding average prediction performance With uncertainty prediction variance The results are obtained using the following formulas:

[0059]

[0060]

[0061] In the formula: That is, to predict the objective function value. ; This represents the variance of the prediction uncertainty; a larger value indicates a lower reliability of the prediction.

[0062] Therefore, there is no need to run time-consuming simulations for each candidate parameter; the predicted mean can be used directly. As parameters to be optimized The corresponding predicted objective function value And utilize the prediction variance The reliability of the prediction is characterized; only the next set of candidate parameters selected by the acquisition function is simulated to achieve a global prediction of parameter performance with extremely low computational cost.

[0063] S204: Construct the acquisition function and iteratively solve for the optimal parameters of the controller;

[0064] The parameter space is iteratively searched by relying on the acquisition function. By solving for the maximum value of the acquisition function, the next set of optimal parameter points to be evaluated is obtained, thus completing the efficient iterative search of the controller parameter space.

[0065] This invention selects the desired improved EI as the acquisition function, and defines... The current historical minimum objective function value, i.e., the current optimal objective function value, is the parameter to be optimized for any controller. Improvement of the objective function in a single iteration It can be represented as:

[0066] ;

[0067] In the formula, This is a preset minimum positive constant, used to adjust the global exploration capability during the parameter search process and reduce the probability of the algorithm getting stuck in local optima;

[0068] Due to the parameters to be optimized Its objective function value has not yet been evaluated through actual simulation. Under the Gaussian process surrogate model, the mean is... Standard deviation is The Gaussian distribution, therefore the acquisition function Defined as the improvement of the objective function within a single iteration The mathematical expectation, that is:

[0069]

[0070] In the formula, The probability density function is the standard normal distribution. The cumulative distribution function of the standard normal distribution; For Gaussian surrogate models in parameters The standard deviation of the performance prediction at that location. It is the relative improvement after normalization.

[0071] By designing the acquisition function described above, an effective trade-off can be achieved between exploring the unknown region of the parameter to be optimized and utilizing the current optimal parameter region within a limited number of simulation iterations. This avoids blind searching and local optima, thereby efficiently retrieving the optimal controller parameters that minimize the multi-objective cost function.

[0072] The optimal controller parameters obtained in step S2 are not only used for one-time offline tuning, but also serve as a sample database for the radial basis function neural network. By matching the characteristics of different operating conditions with their corresponding Bayesian optimization controller parameters, the optimal controller parameters are then optimized. By pairing, this invention solidifies the global search results of Bayesian optimization into data samples that can be learned by neural networks, enabling radial basis function neural networks to quickly approximate the optimization output of Bayesian optimization in the online stage, thereby forming a functional coupling relationship between Bayesian optimization and radial basis function neural networks.

[0073] S3: Construct a sample library for offline training of a two radial basis function neural network;

[0074] S301: Apply multiple sets of random initial deviations to the controlled object to simulate the actual working condition disturbances such as initial position deviation and initial attitude deviation that exist in the actual operation process, and obtain multiple sets of initial deviation working conditions.

[0075] S302: For each set of initial deviation conditions, the Bayesian optimization algorithm described in step S2 is called to complete the offline tuning of the controller's optimal parameters, obtaining the controller's optimal parameters under each condition and the new expected motion state quantities corresponding to the outer loop controller's optimal parameters under each condition. and expected motion state increment .

[0076] S303: Collect the operating characteristics (i.e., initial deviation), optimal controller parameter data, expected motion state quantities and expected motion state increments corresponding to different initial deviation operating conditions, integrate them to generate a sample set, and finally construct a complete offline database that can be directly used for the training, testing and verification of radial basis neural networks.

[0077] S4: Constructing a two radial basis function neural network model

[0078] To address the inner and outer loop adjustment requirements of a dual-layer trajectory tracking controller, a dual radial basis function neural network model is designed to achieve precise adaptive adjustment of the inner and outer loop controller parameters.

[0079] The first radial basis function neural network (outer loop network) takes the position errors in the x, y, and z directions as input and outputs the parameter increments of the outer loop kinematic controller.

[0080] The second radial basis function neural network (inner loop network) takes the motion state error of the controlled object as its input. ( (actual motion state variables of the controlled object) and new desired motion state variables and expected motion state increment The output is the increment of the parameters of the inner loop dynamic controller.

[0081] For the first radial basis function neural network (RBFNN), its inputs are the position errors in the x, y, and z directions, and its output is the increment of the outer loop controller parameters. After the RBFNN adjusts the outer loop controller parameters, the outer loop controller will generate a new desired motion state quantity. and expected motion state increment .

[0082] A joint input is constructed for the second radial basis function neural network; the input of the second radial basis function neural network is the motion state error. Expected state of motion and expected motion state increment The output is the incremental parameter of the inner loop controller. The specific structure diagram is shown below. Figure 1 As shown.

[0083] In this invention, the first radial basis function neural network (RBFNN) does not directly transmit an abstract network output to the second RBFNN. Instead, it first generates an outer-loop control parameter increment based on the position error. This parameter increment, when applied to the outer-loop controller, changes the desired motion state quantity output by the outer-loop controller. Since the desired motion state quantity is precisely the tracking target of the inner-loop controller, the change in the outer-loop output can reflect the change in tracking load caused by the outer-loop parameter tuning to the inner loop.

[0084] S5: Offline training;

[0085] The training objective of the described dual radial basis function (DBF) neural network model is not to directly learn the motion trajectory of the controlled object, but rather to learn the nonlinear mapping relationship between the operating condition characteristics obtained by Bayesian optimization and the optimal parameter increments of the controller. The outer-loop DBF neural network is used to learn the mapping relationship between the initial position deviation and the optimal parameter increments of the outer-loop kinematic controller, while the inner-loop DBF neural network is used to learn the mapping relationship between the motion state quantity error and the desired change in the outer-loop motion state quantity and the optimal parameter increments of the inner-loop dynamic controller. Therefore, the dual DBF neural network can directly output control parameter increments that approximate the Bayesian optimization results based on its current network inputs.

[0086] S501: Dataset Partitioning and Network Hyperparameter Configuration

[0087] Based on the offline database constructed in step S2, the database is divided into training data, validation data, and test data in a ratio of 70%, 15%, and 15%, respectively. These are used for iterative updates of network parameters, verification of training effectiveness, and detection of generalization ability.

[0088] A unified dual radial basis function (RBF) neural network topology was configured: the network consisted of a single hidden layer with 20 neurons, and the output layer had 15 neurons. The hidden layer activation function was set to a radial basis function (RBF) Gaussian, and the output layer activation function was set to Purelin. Network weights were initialized using the `initwb` function. The network learning rate was uniformly set to 0.01, the maximum number of training iterations was set to 3000, and mean squared error was used as the network training loss function to accurately measure the error between the network output parameters and the true optimal parameters.

[0089] S502: Network Iterative Training and Model Storage

[0090] The network is trained, validated, and tested sequentially using three types of datasets that have been divided, until the network loss function converges and the test set error meets the preset accuracy requirements. After training, the bi-branch radial basis function neural network model that has been double-validated by the validation set and the test set and has achieved the required generalization performance is retained for use in subsequent online control processes.

[0091] S6: Autonomous control for trajectory tracking of the controlled object based on the trained biradial basis function neural network model.

[0092] S601: During the actual motion of the controlled object, the position error and motion state error of the controlled object are used as inputs to call the trained dual radial basis neural network model.

[0093] S602: Real-time parallel output of the outer loop kinematic controller parameter increment and the inner loop dynamic controller parameter increment of the dual radial basis neural network model;

[0094] S603: The parameter increments output by the dual radial basis function neural network model are superimposed with the controller's baseline parameters to obtain the optimal control parameters that are adapted to the current operating conditions in real time.

[0095] S604: Transmits the optimal control parameters to the inner and outer loop control systems of the controlled object, outputs control commands to drive the controlled object to run, and finally completes the full-process high-precision trajectory tracking control task.

[0096] In the offline phase, this invention utilizes Bayesian optimization for global optimization to compensate for the insufficient quality of training samples in neural networks. In the online phase, it employs a two-radial basis function (RBF) neural network for rapid inference to avoid the excessive computational burden of Bayesian optimization, thus achieving a complementary advantage. Specifically, in the offline phase, under various initial deviation conditions, the weighted sum of trajectory tracking error and control energy consumption is used as the optimization objective. Bayesian optimization is used to search for the optimal controller parameters, and the operating condition characteristics (i.e., initial deviation) and the corresponding optimal parameters form a high-quality sample library. In the online control phase, the RBF neural network learns and fits the nonlinear mapping relationship between the operating condition characteristics and the optimal control parameters, and outputs the corresponding controller parameter adjustment amount in real time based on the current operating condition characteristics. Thus, this invention transforms the global optimization capability of Bayesian optimization into the rapid online inference capability of neural networks, achieving autonomous adaptation and real-time adjustment of controller parameters to changes in operating conditions while avoiding repetitive and costly online optimization calculations.

[0097] Example

[0098] Using MATLAB software for simulation, the effectiveness of the autonomous control method that integrates Bayesian optimization and radial basis neural network was demonstrated for trajectory tracking control of UUV (Unmanned Underwater Vehicle).

[0099] Bayesian optimization is used to optimize controller parameters offline, generating a sample library. The convergence process of Bayesian optimization is as follows: Figure 2 As shown;

[0100] Training a biradial basis function neural network, with an outer loop neural network for regression, is as follows: Figure 3 As shown in (a), the mean square error of the outer loop neural network is as follows: Figure 3 As shown in (b), the inner loop neural network regression is as follows: Figure 3 As shown in (c), the mean square error of the inner loop neural network is as follows: Figure 3 As shown in (d);

[0101] Unify the initial conditions of the simulation and control the initial position and initial attitude parameters of the object;

[0102] The increments of the outer loop kinematic controller parameters and the inner loop dynamic controller parameters are output by the radial basis neural network, and are summed with the reference coefficients to obtain the autonomous control system parameters;

[0103] The parameters of the autonomous control system output by the neural network are applied to the trajectory tracking controller of the UUV for control simulation.

[0104] Simulation results Figure 4 (a)~(c) respectively reflect the controlled object's... Errors in position direction. It can be seen that the present invention can bring the position deviation closer and eliminate it to zero in a shorter response time. (d) and (e) show that the pitch and yaw angles have extremely slight overshoots during tracking. This is because the cross-hidden feature layer coupling mapping of the present invention plays a role; in the early stages of a surge in position error, the inner loop core center automatically changes, allowing the inner loop control to intervene in time and smooth out the angle fluctuations. (f)~(h) show the total thrust. Elevator deflection With rudder deflection The operation was observed. It can be confirmed that the fixed-gain design frequently collided with the maximum rudder angle boundary during startup and sudden steering, causing high-frequency switching oscillation saturation; while the nonlinear control force curve proposed in this invention is very smooth and flat, completely confined within the maximum anti-saturation limit safety zone. Figure 4 (i) The comparison chart of integral energy consumption indicators clearly shows that the method of the present invention significantly reduces the total energy consumption of the system by avoiding useless repeated step-like work. This fully and powerfully demonstrates the superior control effectiveness and engineering application value of the trajectory tracking controller design method of the present invention.

[0105] Compared to traditional fixed-parameter control schemes, the trajectory tracking autonomous control method proposed in this invention, which integrates Bayesian optimization and radial basis function neural networks, can achieve online autonomous dynamic adjustment of controller parameters based on neural networks. This enables faster elimination of initial tracking deviations, effectively reduces steady-state tracking errors in position and attitude, results in smaller control input fluctuations, smoother system operation, and reduced useless control energy consumption. Overall trajectory tracking accuracy and dynamic response performance are significantly improved, fully demonstrating that this trajectory tracking autonomous control method possesses superior trajectory tracking control effects and engineering practical value. Although embodiments of the present invention have been shown and described above, it is understood that these embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the invention.

Claims

1. A trajectory tracking autonomous control method integrating Bayesian optimization and radial basis function neural networks, characterized in that, Includes the following steps: Construct a trajectory tracking controller for the controlled object; Offline optimization of controller parameters is performed based on Bayesian optimization algorithm; Construct an offline training sample library for a two radial basis function neural network; Construct and train a two radial basis function neural network model; Based on the trained biradial basis function neural network model, autonomous control of the trajectory tracking of the controlled object is achieved.

2. The trajectory tracking autonomous control method according to claim 1, characterized in that, In the offline optimization of controller parameters based on the Bayesian optimization algorithm, the Bayesian optimization algorithm is used to complete the offline optimization of the core controller parameters. A Gaussian process surrogate model is used to reduce the computational cost of simulation evaluation, balancing parameter search efficiency and optimization accuracy. The specific steps are as follows: Construct a multi-objective cost function; Define the parameter space of the parameters to be optimized in the controller and construct the initial parameter set; Construct a Gaussian process proxy model and calculate the predicted objective function value of the controller's parameters to be optimized; Construct an acquisition function and iteratively solve for the optimal parameters of the controller.

3. The trajectory tracking autonomous control method according to claim 2, characterized in that, The multi-objective cost function is as follows: ； In the formula, The total integral absolute error ; To control the sum of squares of the energy integral; , where is the weighting coefficient, indicating the priority of performance metric allocation.

4. The trajectory tracking autonomous control method according to claim 2, characterized in that, In constructing the Gaussian process surrogate model, a prior model is established: Treatment of optimization parameters With the objective function value The mapping relationship establishes a prior hypothesis, namely, that it follows a Gaussian process distribution as follows: ； In the formula, GP(·,·) represents a Gaussian process; It is a mean function, usually set to a constant or zero; The covariance kernel function is used to measure the variance between any two points in the parameter space. and The similarity between the corresponding objective function values.

5. The trajectory tracking autonomous control method according to claim 2, characterized in that, In constructing the Gaussian process surrogate model, the objective function value is predicted. Compared with historical objective function values The joint Gaussian distribution relationship: for any given parameters to be optimized Construct the objective function value corresponding to this parameter. Compared with historical objective function values Joint Gaussian distribution relationship: ； In the formula, For the set A column vector composed of medium values, Parameters that have been measured The covariance matrix between them, its th Line number Column elements are ; Parameters to be optimized Its own prior variance; Parameters to be optimized Compared with measured parameters The covariance vector between them.

6. The trajectory tracking autonomous control method according to claim 2, characterized in that, In constructing a Gaussian process surrogate model, the predicted objective function values ​​of the controller's optimization parameters are calculated using the joint Gaussian distribution relationship and historical datasets. Solve for the parameters to be optimized Predicted objective function value : The posterior conditional probability distribution is: ； In the formula, Given the current historical dataset, its corresponding average prediction performance With uncertainty prediction variance The results are obtained using the following formulas: ； ； In the formula: For the parameters to be optimized objective function value Predicted mean ; This represents the variance of the uncertainty in the forecast.

7. The trajectory tracking autonomous control method according to claim 2, characterized in that, In the construction of the acquisition function, define The current historical minimum objective function value, i.e., the current optimal objective function value, is the parameter to be optimized for any controller. Improvement of the objective function in a single iteration Represented as: ； In the formula, This is a preset minimum positive constant, used to adjust the global exploration capability during the parameter search process and reduce the probability of the algorithm getting stuck in local optima; Due to the parameters to be optimized The improvement of the objective function within a single iteration has not yet been evaluated through actual simulation. Under the Gaussian process surrogate model, the mean is... Standard deviation is Gaussian distribution, acquisition function Defined as the improvement of the objective function within a single iteration The mathematical expectation, that is: ； In the formula, The probability density function is the standard normal distribution. The cumulative distribution function of the standard normal distribution; For Gaussian surrogate models in parameters The standard deviation of the performance prediction at the location; It is the relative improvement after normalization.

8. The trajectory tracking autonomous control method according to claim 1, characterized in that, The specific steps for constructing a sample library for offline training of a two-radial basis function neural network are as follows: Multiple sets of random initial deviations are applied to the controlled object to simulate the initial position deviations and initial attitude deviations that exist in the actual operation process, and multiple sets of initial deviation working conditions are obtained. For each set of initial deviation conditions, the controller parameters are tuned offline using a Bayesian optimization algorithm and then simulated to obtain the optimal controller parameters under each condition, the new expected motion state variables and expected motion state increments corresponding to the optimal outer loop controller parameters under each condition. The system collects operating condition characteristics, optimal controller parameters, expected motion state variables, and expected motion state increments corresponding to different initial deviation operating conditions, integrates them to generate an operating condition sample set, and finally constructs a complete offline database that can be directly used for the training, testing, and verification of radial basis neural networks.

9. The trajectory tracking autonomous control method according to claim 1, characterized in that, The dual radial basis function neural network coupling structure includes: The first radial basis function neural network takes the position error as input and outputs the parameter increment of the outer loop kinematic controller. After the first radial basis function neural network adjusts the parameters of the outer loop controller, the outer loop controller will generate a new desired motion state quantity and a desired motion state increment. A joint input is constructed for the second radial basis function neural network; the input of the second radial basis function neural network is the motion state error, the desired motion state quantity, and the desired motion state increment, and the output is the inner loop controller parameter increment.

10. The trajectory tracking autonomous control method according to claim 1, characterized in that, The specific steps for autonomous control of trajectory tracking of the controlled object based on the trained biradial basis function neural network model are as follows: During the actual movement of the controlled object, the initial position deviation and initial attitude deviation of the controlled object are used as inputs to call the trained dual radial basis neural network model. The dual radial basis function neural network model outputs the parameter increments of the outer loop kinematic controller and the inner loop dynamic controller in real time and in parallel. The parameter increments output by the two radial basis function neural network model are superimposed with the controller's baseline parameters to obtain the optimal control parameters that are adapted to the current operating conditions in real time. The optimal control parameters are transmitted to the inner and outer loop control systems of the controlled object, and control commands are output to drive the controlled object to run, ultimately completing the high-precision trajectory tracking control task throughout the entire process.

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