Optimal trajectory tracking control method for incomplete constraint wheeled mobile robot based on Fourier physical information neural network

Abstract

The invention belongs to the field of intelligent control and robot control, and discloses an incomplete constraint wheeled mobile robot optimal trajectory tracking control method based on a Fourier physical information neural network, and the method comprises the steps: obtaining an incomplete constraint kinematics model and a cost function of a robot through constructing a control problem description analyzer; analyzing and deducing an optimal control law by using an optimal control constraint builder, eliminating an upper definite bound operator in an HJB equation, and generating an explicit optimal control constraint; then constructing a Fourier physical information neural network controller, and embedding the explicit constraint into a training process to obtain a high-precision approximate value function and a gradient thereof; and finally, a control instruction generator generates linear velocity and angular velocity instructions based on the gradient and sends the linear velocity and angular velocity instructions to a driving unit. According to the method, the problems of difficulty in solving an HJB equation and spectrum deviation of network training in a traditional method can be effectively solved, and reduction of robot trajectory tracking errors and smoothing of control instructions under complex working conditions are realized.

Description

Technical Field

[0001] This application belongs to the field of intelligent control and robot control, specifically relating to an optimal trajectory tracking control method for a nonholonomic constrained wheeled mobile robot based on a Fourier physical information neural network. Background Technology

[0002] In trajectory tracking control of nonholonomically constrained wheeled mobile robots, the robot's pose state (position and heading angle) is typically used as the system state, and linear velocity and angular velocity are used as control inputs. By constructing running cost functions and terminal cost functions, the trajectory tracking control problem is formulated as an optimal control problem. Dynamic programming yields the Hamiltonian-Jacobi-Bellman (HJB) equations for solving the value function and optimal control law. However, HJB equations are generally difficult to solve analytically, and traditional numerical discretization methods in scenarios involving online generation of linear and angular velocity commands incur high computational costs. Furthermore, if repeated numerical optimization around the extremum conditions of the Hamiltonian is required during the solution or training process, convergence efficiency can easily decrease, affecting the real-time output and smoothness of control commands. Existing physical information neural network methods can incorporate equation residuals as constraints into training, but without suitable high-frequency feature representations, the network may exhibit spectral bias, leading to insufficient learning of high-frequency components of the value function, thus affecting the trajectory tracking error reduction effect. Summary of the Invention

[0003] The purpose of this application is to overcome the shortcomings of the prior art and provide an optimal trajectory tracking control method for a nonholonomically constrained wheeled mobile robot based on a Fourier physical information neural network. By generating explicit optimal control constraints for neural network training and obtaining an approximate value function and its gradient, the linear velocity command and angular velocity command of the wheeled mobile robot are generated, thereby reducing trajectory tracking error and smoothing control commands.

[0004] To achieve the above objectives, this application employs the following technical solution:

[0005] This invention provides an optimal trajectory tracking control method for a nonholonomic constrained wheeled mobile robot based on a Fourier physical information neural network, comprising:

[0006] A control problem description parser is constructed to acquire trajectory tracking control problem description data. This data includes the kinematic equations, running cost function, terminal cost function, and spatiotemporal information of the wheeled mobile robot's pose state. The pose state spatiotemporal information includes time domain information and pose state domain information, with the pose state domain information including position and heading angle.

[0007] An optimal control constraint builder is constructed to deduce the optimal control law based on the trajectory tracking control problem description data. The optimal control law is then substituted into the value function constraint to eliminate the supremacy operation in the optimality solution, thereby generating explicit optimal control constraints for neural network training.

[0008] A Fourier physical information neural network controller is constructed to build an improved network model based on the spatiotemporal information of the pose state, including a learnable Fourier feature embedding layer and a multilayer perceptron. The explicit optimal control constraints are embedded into this model for training to obtain an approximate value function and its gradient. The Fourier physical information neural network is a network model that combines Fourier feature embedding representation with a physical information neural network; the network includes Fourier feature mapping, value function approximation based on a multilayer perceptron, and gradient calculation based on automatic differentiation.

[0009] A control command generator is constructed to generate linear velocity and angular velocity commands for a wheeled mobile robot based on the gradient of the approximate value function and the optimal control law output by the optimal control constraint builder.

[0010] Through the above construction process, the approximate value function and its gradient are used to characterize the optimal trajectory tracking control strategy of the wheeled mobile robot, thereby reducing trajectory tracking error and smoothing control commands.

[0011] A further improvement of this application is that: the trajectory tracking control problem description data includes the kinematic equations of the wheeled mobile robot, the running cost function, the terminal cost function, and the spatiotemporal information of the pose state; the spatiotemporal information of the pose state includes time domain information and pose state domain information, and the pose state domain information includes position and heading angle.

[0012] A further improvement of this application is that the optimal control constraint builder includes:

[0013] Hamiltonian definition unit, wherein the input of the Hamiltonian definition unit is the kinematic equation of the wheeled mobile robot. Operating cost function and costate vector ,in Let be the system state vector. To control the input vector, It is a value function, and ;

[0014] The optimal control law derivation unit, whose input is the Hamiltonian output by the Hamiltonian definition unit. ;

[0015] The control constraint reconstruction unit receives the Hamiltonian output by the Hamiltonian definition unit as its input. The optimal control law output by the optimal control law derivation unit ;

[0016] A further improvement of this application is that, in step 3, the Fourier physical information neural network controller is used to establish an improved network model containing a learnable Fourier feature embedding layer and a multilayer perceptron based on the spatiotemporal information of the pose state, and to embed explicit nonlinear partial differential equation constraints into the model for training to obtain an approximate value function and its gradient; wherein, the improved network model is the network structure used by the Fourier physical information neural network controller for approximating the value function, and the Fourier physical information neural network controller includes:

[0017] The Fourier feature mapping unit, whose input is a spatiotemporal coordinate vector based on pose state spatiotemporal domain information. The output of the Fourier feature mapping unit is a feature vector. ;

[0018] The neural network operation unit, wherein the input of the neural network operation unit is the feature vector output by the Fourier feature mapping unit. The feature vector output by the Fourier feature mapping unit The approximate value function output by the neural network operation unit is then passed through it. ;

[0019] An automatic differential gradient unit, wherein the input of the automatic differential gradient unit is the approximate value function output by the neural network operation unit. The output of the automatic differential gradient unit is the partial derivative information of the approximate value function with respect to time and state;

[0020] The equation residual calculation unit receives the explicit optimal control constraints output by the control constraint reconstruction unit and the approximate value function output by the neural network operation unit as inputs. The partial derivative information output by the automatic differential gradient unit, and the output of the equation residual calculation unit is the equation residual. ;

[0021] The network weight update unit receives the equation residuals output by the equation residual calculation unit as its input. Approximate value function output by the neural network operation unit and the terminal cost function obtained by the control problem description parser. The network weight update unit is used to calculate the terminal cost function constraint error based on the terminal's pose state spatiotemporal information, and to construct a loss function by combining the equation residuals to update the network parameters.

[0022] A further improvement of this application is that the control command generator includes:

[0023] The control command generator includes a control law mapping unit, the input of which is the optimal control function mapping relationship output by the optimal control law derivation unit. Approximate value function output by the neural network operation unit and the gradient output by the automatic differential gradient unit .

[0024] A further improvement of this application is that the operation process of the Hamiltonian definition unit is as follows:

[0025] According to the kinematic equations of wheeled mobile robots Operating cost function and costate vector Calculate the Hamiltonian

[0026]

[0027] In the formula, For time variables, Let be the system state vector. To control the input vector, It is a value function, and .

[0028] A further improvement of this application is that the calculation process of the optimal control law derivation unit is as follows:

[0029] According to Hamiltonian For control input vector Find the partial derivatives and set them to zero, then analytically calculate the optimal control law.

[0030]

[0031] In the formula, The optimal control function mapping relationship obtained through analysis

[0032] A further improvement of this application is that the operation process of the control constraint reconstruction unit is as follows:

[0033] Optimal control law Substitute Hamiltonian Eliminate the supremum operator and compute the optimized Hamiltonian. :

[0034]

[0035] The following explicit nonlinear partial differential equation is used as the explicit optimal control constraint:

[0036]

[0037] In the formula, Let be the partial derivative of the value function with respect to time.

[0038] A further improvement of this application is that: the kinematic equations of the wheeled mobile robot satisfy nonholonomic constraints, the pose state vector is a three-dimensional vector composed of position and heading angle, the control input vector is a two-dimensional vector composed of linear velocity and angular velocity, and the kinematic equations include nonlinear terms related to heading angle.

[0039] A further improvement of this application is that the operation process of the Fourier feature mapping unit is as follows:

[0040] Based on the input spatiotemporal coordinate vector Learnable frequency matrix and frequency scaling factor Calculate the first Fourier characteristic components

[0041]

[0042] In the formula, For including time variables and state variables The joint input vector, Let be the frequency parameter matrix to be trained, and The frequency parameter matrix to be trained The row vectors The preset frequency scaling factor, This is the global amplitude coefficient;

[0043] A further improvement of this application is that the operation process of the neural network operation unit is as follows:

[0044] Its input is the output of the Fourier feature mapping unit; a multilayer perceptron model is constructed, including an input layer, several fully connected hidden layers, and an output layer; the feature vector is... The input data stream passes through weighted summations and nonlinear activation functions in each hidden layer to extract high-dimensional nonlinear features. Finally, an approximate value function is obtained by linear mapping from the output layer. ,in These are the learnable parameters of the network.

[0045] A further improvement of this application is that the calculation process of the automatic differential gradient unit is as follows:

[0046] Its input is the output of the neural network's computational units; based on the computational graph mechanism of the deep learning framework, the network parameters are locked. Calculate using the backpropagation chain rule Regarding time partial derivatives and the state gradient .

[0047] A further improvement of this application is that the operation process of the equation residual calculation unit is as follows:

[0048] Based on the approximate value function output by the neural network operation unit The partial derivative information output by the automatic differential gradient unit is combined with the explicit nonlinear partial differential equation output by the control constraint reconstruction unit to calculate the equation residuals. :

[0049]

[0050] In the formula, For the set of learnable parameters of a neural network, This is the gradient of the approximate value function with respect to the state;

[0051] A further improvement of this application is that the operation process of the network weight update unit is as follows: based on the equation residual Sum of terminal cost function objective value Calculate the total loss function And perform a minimized update:

[0052]

[0053] In the formula, and These are the weighting coefficients. For the number of internal distribution points, Assign the number of terminal points. For terminal cost function, This refers to the terminal moment.

[0054] A further improvement of this application is that the operation process of the control law mapping unit is as follows: based on the approximate value function output by the neural network operation unit... The gradient output by the automatic differential gradient unit And the mapping relationship of the optimal control function output by the optimal control law derivation unit. Calculate the actual control commands :

[0055]

[0056] in The control input vector The actual value will be the actual control command. The commands are decomposed into linear velocity commands and angular velocity commands, which are then sent to the drive unit of the wheeled mobile robot to drive the actuator to complete trajectory tracking control.

[0057] This application provides an optimal trajectory tracking control device for a nonholonomically constrained wheeled mobile robot based on a Fourier physical information neural network. The device includes:

[0058] A control problem description parser is used to obtain trajectory tracking control problem description data, which includes the kinematic equations of the wheeled mobile robot, the running cost function, the terminal cost function, and the spatiotemporal information of the pose state.

[0059] An optimal control constraint builder is used to analytically derive the optimal control law and eliminate Hamiltonian loss based on the trajectory tracking control problem description data. Jacobi The supremum operator in the Bellman equations generates explicit optimal control constraints;

[0060] A Fourier physical information neural network controller is used to establish an improved network model containing a learnable Fourier feature embedding layer and a multilayer perceptron based on the spatiotemporal information of the pose state, and to embed the explicit optimal control constraint into the model for training to obtain an approximate value function and its gradient.

[0061] A control command generator is used to generate linear velocity and angular velocity commands for a wheeled mobile robot based on the gradient of the approximate value function and the optimal control law output by the optimal control constraint builder.

[0062] The beneficial effects of this application are:

[0063] This application improves the ability to represent high-frequency components in the value function by introducing a learnable Fourier feature embedding layer into the Fourier physical information neural network controller, thereby enhancing the approximation accuracy of the approximate value function and its gradient.

[0064] This application uses an optimal control constraint builder to analytically derive the optimal control law and generate explicit optimal control constraints, enabling the training process to calculate the equation residuals without performing supremum operations, thereby reducing the numerical optimization steps around the Hamiltonian extremum conditions.

[0065] This application generates linear velocity and angular velocity commands based on the gradient of the approximate value function and the optimal control law through a control command generator, and sends them to the drive unit of the wheeled mobile robot, thereby reducing trajectory tracking error and smoothing control commands. Attached Figure Description

[0066] Figure 1 This is a flowchart of the control method in an embodiment of this application.

[0067] Figure 2 This is a schematic diagram of the improved network model structure in the embodiments of this application.

[0068] Figure 3 This is a schematic diagram of the overall structure of the control method device according to an embodiment of this application.

[0069] Figure 4 In the embodiment of this application, the state variables are fixed in the baseline HJB problem. and At that time, the generated approximate value function A schematic diagram of the two-dimensional slice distribution.

[0070] Figure 5 For embodiments of this application, in the case of fixed state variables and The point-to-point absolute error distribution between the approximate value function and the analytical solution is shown in the figure. Detailed Implementation

[0071] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0072] like Figure 1 As shown, this application discloses an optimal trajectory tracking control method for a nonholonomically constrained wheeled mobile robot based on a Fourier physical information neural network. The control method includes a control problem description parser, an optimal control constraint builder, a Fourier physical information neural network controller, and a control command generator. The control method includes the following steps:

[0073] Step 1: Obtain trajectory tracking control problem description data through a control problem description parser. The trajectory tracking control problem description data includes the kinematic equations of the wheeled mobile robot. Operating cost function Terminal cost function And pose state spatiotemporal information, the pose state spatiotemporal information includes time domain information and pose state domain information, the pose state domain information includes position and heading angle;

[0074] Step 2: Based on the description data of the trajectory tracking control problem, the optimal control law is analytically derived. This optimal control law is then substituted into the value function constraints to eliminate the supremacy operation in the optimality solution, generating explicit optimal control constraints for neural network training. The optimal control constraint builder includes a Hamiltonian definition unit, an optimal control law derivation unit, and a control constraint reconstruction unit.

[0075] Step 2.1: Define the Hamiltonian unit, whose inputs are the system dynamics equations, the operating cost function, and the costate vector; the operation process of the Hamiltonian unit is as follows: based on the kinematic equations of the wheeled mobile robot... Operating cost function and costate vector Calculate the Hamiltonian

[0076]

[0077] In the formula, For time variables, Let be the system state vector. To control the input vector, It is a value function, and .

[0078] Step 2.2: The optimal control law derivation unit, whose input is the output of the Hamiltonian definition unit; the operation process of the optimal control law derivation unit is as follows: based on the Hamiltonian... For control input vector Find the partial derivatives and set them to zero, then analytically calculate the optimal control law.

[0079]

[0080] In the formula, This is the mapping relationship of the optimal control function obtained through analysis.

[0081] Step 2.3: The control constraint reconstruction unit, whose inputs are the outputs of the Hamiltonian definition unit and the optimal control law derivation unit; the operation process of the control constraint reconstruction unit is as follows: The optimal control law... Substitute Hamiltonian Eliminate the supremum operator and compute the optimized Hamiltonian. :

[0082]

[0083] Step 2.4: Use explicit nonlinear partial differential equations as explicit optimal control constraints:

[0084]

[0085] In the formula, Value function Regarding time The partial derivatives, Value function Regarding the system state vector The gradient;

[0086] Step 3: Construct an improved network model based on the spatiotemporal information of pose state, which includes a learnable Fourier feature embedding layer and a multilayer perceptron. Embed the explicit optimal control constraints generated in Step 2 into the network model for training to obtain the approximate value function and the gradient of the approximate value function.

[0087] like Figure 3 As shown, the control method of this application includes a Fourier physical information neural network controller, used to complete the approximation and training of the value function under explicit optimal control constraints; wherein, the improved network model structure inside the controller for approximating the value function is as follows: Figure 2 As shown, it includes a Fourier feature mapping unit, a neural network operation unit, and an automatic differential gradient unit. During training, the controller also includes an equation residual calculation unit and a network weight update unit to calculate the equation residuals and update the network parameters based on explicit optimal control constraints. Step 3 specifically includes the following steps:

[0088] Step 3.1: The Fourier feature mapping unit takes a spatiotemporal coordinate vector as its input. The operation process of the Fourier feature mapping unit is as follows: based on the input spatiotemporal coordinate vector... Frequency parameter matrix to be trained and frequency scaling factor Calculate the first Fourier characteristic components

[0089]

[0090] In the formula, For including time variables and state variables The joint input vector, Let be the frequency parameter matrix to be trained, and The frequency parameter matrix to be trained The row vectors The preset frequency scaling factor, This is the global amplitude coefficient.

[0091] Step 3.2: The neural network operation unit takes the output of the Fourier feature mapping unit as its input; the operation process of the neural network operation unit is as follows: The feature vector... Input a multilayer perceptron (MLP) and output an approximate value function. ,in This is the set of learnable parameters for a neural network.

[0092] Step 3.3: Automatic gradient differentiation unit, whose input is the output of the neural network operation unit; the operation process of the automatic gradient differentiation unit is as follows: calculating using automatic differentiation technology. Regarding time partial derivatives and the state gradient .

[0093] Step 3.4: The equation residual calculation unit receives the outputs of the explicit equation reconstruction unit, the neural network operation unit, and the automatic differential gradient unit as inputs; based on the approximate value function output by the neural network operation unit... The partial derivative information output by the automatic differential gradient unit is combined with the explicit nonlinear partial differential equation output by the control constraint reconstruction unit to calculate the equation residuals. :

[0094]

[0095] In the formula, For the set of learnable parameters of a neural network, This is the gradient of the approximate value function with respect to the state.

[0096] Step 3.5: The network weight update unit takes the output of the equation residual calculation unit and the terminal cost function as inputs. The operation process of the network weight update unit is as follows: based on the equation residual... Sum of terminal cost function objective value Calculate the total loss function And perform a minimized update:

[0097]

[0098] In the formula, and These are the weighting coefficients. For the number of internal distribution points, Assign the number of terminal points. For terminal cost function, This refers to the terminal moment.

[0099] Step 4: Based on the approximate value function gradient obtained in Step 3 and the optimal control law in Step 2, generate the linear velocity and angular velocity commands for the wheeled mobile robot. Specifically, the input to the control law mapping unit is the optimal control function mapping relationship output by the optimal control law derivation unit. Approximate value function output by the neural network operation unit and the gradient output by the automatic differential gradient unit Based on the approximate value function output by the neural network operation unit The gradient output by the automatic differential gradient unit And the mapping relationship of the optimal control function output by the optimal control law derivation unit. Calculate the actual control commands :

[0100]

[0101] in The control input vector The actual value will be the actual control command. The commands are decomposed into linear velocity commands and angular velocity commands, which are then sent to the drive unit of the wheeled mobile robot to drive the actuator to complete trajectory tracking control.

[0102] To verify the effectiveness of the present invention, a nonlinear system of a three-dimensional wheeled mobile robot that satisfies nonholonomic constraints was selected for verification.

[0103] (1) Selection of system model parameters: The system state vector is defined as , respectively corresponding to the robot's x-coordinate y-axis and heading angle The control input vector is defined as follows: , respectively corresponding to linear velocity and angular velocity System dynamics equations Specifically, it can be expanded as follows:

[0104]

[0105] Running cost function Adopting a quadratic form:

[0106]

[0107] in, The state weight matrix is... To control the weight matrix. Terminal cost function. Defined as:

[0108]

[0109] in, This is the terminal weight matrix. The system's spatiotemporal domain is defined as: time... Location coordinates heading angle Initial moment Terminal time .

[0110] (2) Explicit equation construction results: Hamiltonian Defined as:

[0111]

[0112] in, Let it be a costate vector. According to the Hamiltonian extremum condition... ,Right now Analytical calculation of the optimal control law :

[0113]

[0114] Substituting the optimal control law into the Hamiltonian to eliminate the supremum operator, we obtain the explicit HJB partial differential equation constraints:

[0115]

[0116] (3) Neural network parameter selection: Network structure: Contains one Fourier feature embedding layer (mapping dimension) ), 3 fully connected hidden layers, each containing 32 neurons, with the activation function selected as... Training parameters: number of internal collocations Terminal configuration number Weight parameters: , Optimizer: Adam optimizer, learning rate set to The number of iterations is 5000.

[0117] (4) Simulation result analysis: such as Figure 4 As shown, given that the value function of a nonholonomically constrained wheeled mobile robot is defined in the four-dimensional spatiotemporal domain (time... With state In a system, full-dimensional visualization cannot be directly performed. Therefore, this embodiment selects the horizontal axis of the system status. and heading angle A specific physical section shows an approximate value function. Over time and ordinate The changing relationship. From Figure 4 As can be seen from the data, the generated value function surface on this slice is smooth and continuous, clearly reflecting the evolution of the optimal cost with time and longitudinal displacement under the straight-line, no-yaw condition. Moreover, the boundary conditions are handled properly, and no obvious numerical calculation oscillations are observed.

[0118] like Figure 5 As shown, it illustrates the corresponding Figure 4 Slicing conditions ( The point-to-point absolute error distribution is shown in the figure. Axis representation On the plane, the error magnitude between the approximate value function obtained by the neural network and the analytical solution is shown. The results show that even with the introduction of slice constraints, the error of this method on the critical state path is still controlled at an extremely low level (shown in the figure). The error distribution exhibits uniform high-frequency texture features (level), indicating that the Fourier feature embedding layer effectively captures the fine structure of the value function on a specific manifold in the state space, verifying the solution accuracy and generalization ability of the proposed control method when dealing with high-dimensional nonlinear systems.

[0119] This embodiment also provides an approximate solution device for the HJB equation based on a Fourier physical information neural network, the device comprising:

[0120] A control problem description parser is used to acquire trajectory tracking control problem description data, which includes the kinematic equations of a wheeled mobile robot. Operating cost function Terminal cost function And the spatiotemporal information of pose state;

[0121] An optimal control constraint builder is used to analytically derive the optimal control law and eliminate Hamiltonian loss based on the trajectory tracking control problem description data. Jacobi The supremum operator in the Bellman equations generates explicit optimal control constraints;

[0122] A Fourier physical information neural network controller is used to establish an improved network model containing a learnable Fourier feature embedding layer and a multilayer perceptron based on the spatiotemporal information of the pose state, and to embed the explicit optimal control constraint into the model for training to obtain an approximate value function and its gradient.

[0123] A control command generator is used to generate linear velocity and angular velocity commands for a wheeled mobile robot based on the gradient of the approximate value function and the optimal control law output by the optimal control constraint builder.

[0124] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0125] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0126] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0127] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0128] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimal trajectory tracking control of a nonholonomically constrained wheeled mobile robot based on a Fourier physical information neural network, the control method comprising a control problem description parser, an optimal control constraint builder, a Fourier physical information neural network controller, and a control command generator, characterized in that: The control method includes the following steps: Step 1: Obtain trajectory tracking control problem description data through the control problem description parser. The trajectory tracking control problem description data includes the kinematic equations, running cost function, terminal cost function, and spatiotemporal information of the pose state of the wheeled mobile robot. Step 2: Based on the trajectory tracking control problem description data, deduce the optimal control law, substitute the optimal control law into the value function constraint to eliminate the supremacy operation in the optimality solution, and generate explicit optimal control constraints for neural network training. Step 3: Construct an improved network model based on the spatiotemporal information of pose state, which includes a learnable Fourier feature embedding layer and a multilayer perceptron. Embed the explicit optimal control constraints generated in Step 2 into the network model for training to obtain the approximate value function and the gradient of the approximate value function. Step 4: Based on the gradient of the approximate value function obtained in Step 3 and the optimal control law in Step 2, generate the linear velocity command and angular velocity command for the wheeled mobile robot. Step 5: Use the approximate value function and its gradient to characterize the optimal trajectory tracking control strategy of the wheeled mobile robot, thereby reducing trajectory tracking error and smoothing control commands.

2. The optimal trajectory tracking control method for a nonholonomic constrained wheeled mobile robot based on a Fourier physical information neural network according to claim 1, characterized in that: The optimal control constraint builder is used to generate explicit nonlinear partial differential equation constraints based on the problem description data by analytically deriving the optimal control law and eliminating the supremum operator in the Hamilton-Jacobi-Bellman equations, including: Hamiltonian definition unit, wherein the input of the Hamiltonian definition unit is the kinematic equation of the wheeled mobile robot. Operating cost function and costate vector ,in Let be the system state vector. To control the input vector, It is a value function, and ; The optimal control law derivation unit, whose input is the Hamiltonian output by the Hamiltonian definition unit. ; The control constraint reconstruction unit receives the Hamiltonian output by the Hamiltonian definition unit as its input. The optimal control law output by the optimal control law derivation unit .

3. The optimal trajectory tracking control method for a nonholonomic constrained wheeled mobile robot based on a Fourier physical information neural network according to claim 2, characterized in that: Step 2 specifically includes the following steps: Step 2.1: Based on the kinematic equations of the wheeled mobile robot Operating cost function and costate vector Calculate the Hamiltonian : In the formula, For time variables, Let be the system state vector. To control the input vector, Value function, costate vector ; Step 2.2, based on Hamiltonian For control input vector Find the partial derivative and let The value is zero; the optimal control law is calculated analytically. In the formula, The mapping relationship of the optimal control function obtained by analysis; Step 2.3: Apply the optimal control law obtained in Step 2.

2. Substitute Hamiltonian Calculate the optimized Hamiltonian : Step 2.4: Use explicit nonlinear partial differential equations as explicit optimal control constraints: In the formula, Value function Regarding time The partial derivatives, Value function Regarding the system state vector The gradient.

4. The optimal trajectory tracking control method for a nonholonomic constrained wheeled mobile robot based on a Fourier physical information neural network according to claim 3, characterized in that: In step 3, the Fourier physical information neural network controller is used to establish an improved network model based on the spatiotemporal information of the pose state, which includes a learnable Fourier feature embedding layer and a multilayer perceptron. Explicit nonlinear partial differential equation constraints are embedded into this model for training to obtain an approximate value function and its gradient. The improved network model is the network structure used by the Fourier physical information neural network controller for approximating the value function. The Fourier physical information neural network controller includes: The Fourier feature mapping unit, whose input is a spatiotemporal coordinate vector based on pose state spatiotemporal domain information. The output of the Fourier feature mapping unit is a feature vector. ; The neural network operation unit, wherein the input of the neural network operation unit is the feature vector output by the Fourier feature mapping unit. The feature vector output by the Fourier feature mapping unit The approximate value function output by the neural network operation unit is then passed through it. ; An automatic differential gradient unit, wherein the input of the automatic differential gradient unit is the approximate value function output by the neural network operation unit. The output of the automatic differential gradient unit is the partial derivative information of the approximate value function with respect to time and state; The equation residual calculation unit receives the explicit optimal control constraints output by the control constraint reconstruction unit and the approximate value function output by the neural network operation unit as inputs. The partial derivative information output by the automatic differential gradient unit, and the output of the equation residual calculation unit is the equation residual. ; The network weight update unit receives the equation residuals output by the equation residual calculation unit as its input. Approximate value function output by the neural network operation unit and the terminal cost function obtained by the control problem description parser. The network weight update unit is used to calculate the terminal cost function constraint error based on the terminal's pose state spatiotemporal information, and to construct a loss function by combining the equation residuals to update the network parameters.

5. The optimal trajectory tracking control method for a nonholonomic constrained wheeled mobile robot based on a Fourier physical information neural network according to claim 4, characterized in that: Step 3 specifically includes the following steps: Step 3.1: Convert the robot coordinate vector to a spacetime coordinate vector. Frequency parameter matrix to be trained and preset frequency scaling factor Input Fourier feature map unit, calculate the first Fourier characteristic components In the formula, For including time variables and system state vector The joint input vector, Let be the frequency parameter matrix to be trained, and The frequency parameter matrix to be trained The row vectors The preset frequency scaling factor, For global amplitude coefficients, Step 3.2: Convert the feature vector Input a multilayer perceptron (MLP) and output an approximate value function. And the partial derivative information output by the automatic differential gradient unit, where This is the set of learnable parameters for a neural network. Step 3.3: Calculate the approximate value function using automatic differentiation techniques. Time variable partial derivatives and the system state vector gradient ; Step 3.4: Based on the approximate value function The partial derivative information output by the automatic differential gradient unit is combined with the explicit nonlinear partial differential equation output by the control constraint reconstruction unit to calculate the equation residuals. : Step 3.5: Based on the equation residuals Sum of terminal cost function objective value Calculate the total loss function And perform a minimal update: In the formula, and These are the weighting coefficients. For the number of internal distribution points, Assign the number of terminals. For terminal cost function, This refers to the terminal moment.

6. The optimal trajectory tracking control method for a nonholonomic constrained wheeled mobile robot based on a Fourier physical information neural network according to claim 1, characterized in that: The control command generator is used to generate linear velocity and angular velocity commands for the wheeled mobile robot based on the gradient of the approximate value function and the optimal control law output by the optimal control constraint builder. It includes a control law mapping unit, the input of which is the optimal control function mapping relationship output by the optimal control law derivation unit. Approximate value function output by the neural network operation unit and the gradient output by the automatic differential gradient unit .

7. The optimal trajectory tracking control method for a nonholonomic constrained wheeled mobile robot based on a Fourier physical information neural network according to claim 6, characterized in that: Step 4 specifically includes the following steps: Step 4.1: Based on the approximate value function output by the neural network operation unit. The gradient output by the automatic differential gradient unit And the mapping relationship of the optimal control function output by the optimal control law derivation unit. Calculate the actual control commands : In the formula, To control the input vector The actual value of is a two-dimensional vector composed of linear velocity command and angular velocity command; Step 4.2: Transfer the actual control command Decompose the commands into linear velocity and angular velocity commands, and extract the actual control commands. The first component is used as the linear velocity command to extract the actual control command. The second component is used as the angular velocity command; Step 4.3: Send the linear velocity command and angular velocity command to the drive unit of the wheeled mobile robot to drive the actuator to complete the trajectory tracking control.

8. An electronic device, characterized in that, It includes a processor and a storage medium; the storage medium is used to store instructions; the processor is used to operate according to the instructions to perform the steps of the method according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1-7.

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