Robust trajectory tracking control method, device and program product for autonomous vehicle

Abstract

This application provides a robust trajectory tracking control method, device, and program product for autonomous vehicles, relating to the field of autonomous driving technology. The method includes: constructing a vehicle dynamics model; decomposing the vehicle dynamics model to obtain a nominal model and an uncertain model; using the Koopman operator to increase the dimensionality of the uncertain model to obtain a finite-dimensional model; linearly superimposing the nominal model and the finite-dimensional model to obtain a fused model; decomposing the fused model into a finite-dimensional model and a disturbance model; constructing a nominal controller, a finite-dimensional controller, and a disturbance controller; using the nominal controller, the finite-dimensional controller, and the disturbance controller to generate a target control quantity, and using the target control quantity to control the target vehicle's movement. This can improve the problem of insufficient robustness of traditional autonomous driving control methods under extreme conditions.

Description

Technical Field

[0001] This invention relates to the field of autonomous driving technology, and more specifically, to a robust trajectory tracking control method, device, and program product for autonomous vehicles. Background Technology

[0002] As autonomous driving technology advances to more advanced levels, the safety of vehicle motion control under extreme conditions such as high-speed, low-adhesion surfaces and emergency obstacle avoidance has become a core challenge. Current autonomous driving trajectory tracking control primarily employs a mechanistic model-driven approach, constructing a linearized vehicle dynamics model based on Newton's laws of motion and combining it with model predictive control algorithms to achieve trajectory tracking. However, under extreme conditions, the vehicle tires enter the nonlinear region, and the system exhibits strong coupling and strong nonlinear characteristics. The prediction accuracy of the linear mechanistic model decreases significantly, leading to excessively conservative controller output, increased tracking errors, and even instability phenomena such as vehicle sideslip and fishtailing.

[0003] To improve model accuracy, some studies have introduced purely data-driven methods, directly fitting vehicle dynamics characteristics through black-box models such as neural networks. However, purely data-driven methods suffer from poor interpretability and a lack of clear safety boundaries, failing to theoretically guarantee the robust stability of the system and making it difficult to meet the functional safety and expected functional safety requirements of autonomous driving. Furthermore, existing fusion-driven methods are mostly simple model weighted superpositions, failing to fully consider the propagation and evolution of modeling errors, and thus cannot achieve deep integration of mechanisms and data, leaving the control performance still needing improvement. Summary of the Invention

[0004] In view of this, the purpose of this application is to provide a robust trajectory tracking control method, device and program product for autonomous vehicles, which can improve the problem of insufficient robustness of traditional autonomous driving control methods under extreme conditions.

[0005] To achieve the above technical objectives, the technical solution adopted in this application is as follows: In a first aspect, embodiments of this application provide a robust trajectory tracking control method for autonomous vehicles, including: Construct a vehicle dynamics model that characterizes the driving state of the target vehicle; The vehicle dynamics model is decomposed to obtain a nominal model that characterizes the linear characteristics of the target vehicle's driving and an uncertain model that characterizes the nonlinear characteristics of the target vehicle's driving. The uncertainty model is increased in dimension using the Koopman operator to obtain a finite-dimensional increased model; The nominal model and the finite-dimensional model are linearly superimposed to obtain a fusion model; The fusion model is decomposed into the finite up-dimensional model and a perturbation model that characterizes the modeling error of the fusion model; Construct the nominal controller corresponding to the nominal model, the dimensionality-upgraded controller corresponding to the finite dimensionality-upgraded model, and the disturbance controller corresponding to the disturbance model, respectively. The target control quantity is generated using the nominal controller, the dimensionality upgrade controller, and the disturbance controller, and the target control quantity is used to control the driving of the target vehicle.

[0006] In conjunction with the first aspect, in some alternative implementations, the vehicle dynamics model is represented as follows:

[0007] In the formula, express Real-time state of the target vehicle. The true state quantity at any given moment , in, Indicates longitudinal velocity tracking error. This indicates the lateral position tracking error. This represents the rate of change of the lateral position tracking error. Indicates the heading angle tracking error. The rate of change of the heading angle tracking error. Indicates the actual control quantity. This represents the actual amount of disturbance. This represents the actual mapping function.

[0008] In conjunction with the first aspect, in some optional embodiments, the vehicle dynamics model is decomposed to obtain a nominal model characterizing the linear characteristics of the target vehicle's driving, and an uncertain model characterizing the nonlinear characteristics of the target vehicle's driving, including: Based on the vehicle dynamics model, construct the nominal model:

[0009] In the formula, express The nominal state quantity at time t. express The nominal state quantity at time t. Indicates the nominal control quantity. , These represent the system matrix and the control matrix, respectively. The linear mapping function representing the nominal model; Based on the vehicle dynamics model, construct the uncertain model:

[0010] In the formula, express Uncertain state quantities at time, express Uncertain state quantities at time, , Indicates an uncertain control quantity. , This represents the disturbance amount in an uncertain model.

[0011] In conjunction with the first aspect, in some optional implementations, the uncertain model is upgraded using the Koopman operator to obtain a finite-dimensional upgraded model, including: Based on the aforementioned uncertainty model, a state dimensionality-upgrading function is constructed using the Koopman operator; A finite-dimensional state upgrade function is constructed by extracting a basis function of a preset dimension from the state upgrade function, wherein the preset dimension is greater than the dimension of the uncertain state quantity in the uncertain model. Based on the finite-dimensional state dimensionality increase function and the uncertain model, an initial dimensionality increase model is constructed, which is expressed as follows:

[0012] In the formula, express The upgraded state quantity at any given moment. express The upgraded state quantity at any given moment. Represents the state variable of the upgraded dimension. Indicates the preset dimension. Describes the function for increasing the dimensionality of a finite-dimensional state. This indicates the control quantity for dimensional expansion. , Represents the initial upgraded system matrix. This represents the initial upgraded control matrix. This represents the dimension of the uncertain control quantity in an uncertain model. Let be the initial inverse mapping matrix. The dimension representing the uncertain state quantity in an uncertain model; Obtain the operating parameters of the target vehicle during its driving process; Based on the initial upgraded system matrix, the initial upgraded control matrix, and the initial inverse mapping matrix, a least squares optimization problem is constructed, and the least squares optimization problem is solved using the operating parameters to obtain the target upgraded system matrix, the target upgraded control matrix, and the target inverse mapping matrix; The initial dimensionality-upgrading system matrix, the initial dimensionality-upgrading control matrix, and the initial inverse mapping matrix in the initial dimensionality-upgrading model are replaced with the target dimensionality-upgrading system matrix, the target dimensionality-upgrading control matrix, and the target inverse mapping matrix to obtain the finite dimensionality-upgrading model.

[0013] In conjunction with the first aspect, in some optional implementations, the fusion model is decomposed into the finite-dimensional upscaling model and a perturbation model characterizing the modeling error of the fusion model, including: Based on the modeling error and the finite dimensionality upgrade model, an accurate dimensionality upgrade model is constructed, which is represented as follows:

[0014] In the formula, express The precise upgraded state quantity at any given moment. express The precise upgraded state quantity at any given moment. This indicates the precise dimensional control quantity. Indicates modeling error; Based on the finite dimensionality upgrade model and the exact dimensionality upgrade model, an initial model is determined, which is represented as follows:

[0015] In the formula, express The perturbation state quantity at any given moment. express The perturbation state quantity at any given moment. , This represents the disturbance control quantity. ; The initial model is reconstructed using the feedback gain matrix to obtain the perturbation model, which is represented as follows:

[0016] In the formula, , The feedback gain matrix is ​​represented by solving linear matrix inequalities. get, .

[0017] In conjunction with the first aspect, in some optional implementations, a nominal controller corresponding to the nominal model, a dimension-upgrading controller corresponding to the finite dimension-upgrading model, and a disturbance controller corresponding to the disturbance model are respectively constructed, including: The nominal controller is constructed with the goal of minimizing the nominal state tracking error and the nominal control consumption. The dimensionality-upgrading controller is constructed with the goal of minimizing the state tracking error and the control consumption in dimensionality-upgrading. Based on the disturbance model, a disturbance controller is constructed. .

[0018] In conjunction with the first aspect, in some optional implementations, a target control quantity is generated using the nominal controller, the dimensionality-upgrading controller, and the disturbance controller, and the target control quantity is used to control the driving of the target vehicle, including: The nominal controller is used to generate a nominal control quantity; The dimensionality-upgrading controller is used to generate dimensionality-upgrading control quantities; The disturbance control quantity is generated using the disturbance controller. The target control quantity is obtained by linearly superimposing the nominal control quantity, the upgraded control quantity, and the disturbance control quantity. The vehicle's movement is controlled using the target control variable.

[0019] Secondly, embodiments of this application also provide an electronic device, which includes a processor and a memory coupled to each other. The memory stores a computer program, and when the computer program is executed by the processor, the electronic device performs the above-described method.

[0020] Thirdly, embodiments of this application also provide a computer program product, including a computer program that implements the above-described method when executed by a processor.

[0021] The invention employing the above technical solution has the following advantages: The technical solution provided in this application first constructs a vehicle dynamics model representing the driving state of the target vehicle, and decomposes the vehicle dynamics model to obtain a nominal model and an uncertain model. Then, the uncertain model is upgraded in dimensionality using the Koopman operator to obtain a finite-dimensional upgraded model. Subsequently, the nominal model and the finite-dimensional upgraded model are linearly superimposed to obtain a fusion model, which is then decomposed into a finite-dimensional upgraded model and a disturbance model representing the modeling error of the fusion model. Then, a nominal controller corresponding to the nominal model, an upgraded controller corresponding to the finite-dimensional upgraded model, and a disturbance controller corresponding to the disturbance model are constructed respectively. Finally, the nominal controller, the upgraded controller, and the disturbance controller are used to generate a target control quantity, and the target control quantity is used to control the driving of the target vehicle. In this way, the problem of insufficient robustness of traditional autonomous driving control methods under extreme conditions can be improved. Attached Figure Description

[0022] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0023] Figure 1A structural block diagram of an electronic device provided in an embodiment of this application.

[0024] Figure 2 This is one of the flowcharts illustrating the robust trajectory tracking control method for autonomous vehicles provided in this application.

[0025] Figure 3 This is the second flowchart illustrating the robust trajectory tracking control method for autonomous vehicles provided in this application embodiment.

[0026] Figure 4 This is a schematic diagram of the finite-dimensional upgrade model construction process provided in the embodiments of this application.

[0027] Icons: 100 - Electronic device; 101 - Processor; 102 - Memory. Detailed Implementation

[0028] The present application will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that similar or identical parts are referred to by the same reference numerals in the drawings or description. Implementations not shown or described in the drawings are forms known to those skilled in the art. In the description of this application, terms such as "first" and "second" are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0029] Example 1

[0030] Please refer to Figure 1 This application provides an electronic device 100 that may include a processor 101 and a memory 102. The memory 102 stores a computer program, which, when executed by the processor 101, enables the electronic device 100 to perform corresponding steps in the following robust trajectory tracking control method for autonomous vehicles.

[0031] In this embodiment, the processor 101 can be an integrated circuit chip with signal processing capabilities. The processor 101 can be a general-purpose processor. For example, the processor 101 can be a central processing unit (CPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components, capable of implementing or executing the methods, steps, and logic block diagrams disclosed in the embodiments of this application.

[0032] The memory 102 can be, but is not limited to, random access memory, read-only memory, programmable read-only memory, erasable programmable read-only memory, electrically erasable programmable read-only memory, etc. In this embodiment, the memory 102 can be used to store vehicle dynamics models, nominal models, uncertain models, finite-dimensional models, fused models, disturbance models, nominal controllers, finite-dimensional controllers, disturbance controllers, target control variables, etc. Of course, the memory 102 can also be used to store programs, which the processor 101 executes after receiving an execution instruction.

[0033] In this embodiment, the electronic device 100 can be a personal computer, a laptop computer, a vehicle controller integrated into a vehicle, etc. A vehicle dynamics model characterizing the driving state of the target vehicle is constructed, and the vehicle dynamics model is decomposed to obtain a nominal model characterizing the linear characteristics of the target vehicle's driving, and an uncertain model characterizing the nonlinear characteristics of the target vehicle's driving. Then, the uncertain model is upgraded using the Koopman operator to obtain a finite-dimensional upgraded model, and the nominal model and the finite-dimensional upgraded model are linearly superimposed to obtain a fused model. The fused model is then decomposed into a finite-dimensional upgraded model and a disturbance model characterizing the modeling error of the fused model. Subsequently, a nominal controller, an upgraded controller, and a disturbance controller are constructed respectively. Finally, using the nominal controller, the upgraded controller, and the disturbance controller, a target control quantity is generated, and the target control quantity is used to control the driving of the target vehicle.

[0034] Understandable, Figure 1 The electronic device 100 shown is only a schematic diagram; the electronic device 100 may also include components that are more... Figure 1 More components are shown. Figure 1 The components shown can be implemented using hardware, software, or a combination thereof.

[0035] It should be noted that those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the electronic device 100 described above can be referred to the corresponding steps in the following method, and will not be elaborated further here.

[0036] Example 2

[0037] Please refer to Figure 2 This application also provides a robust trajectory tracking control method for autonomous vehicles, which can be applied to electronic device 100 and executed or implemented by electronic device 100. The robust trajectory tracking control method for autonomous vehicles may include the following steps: Step 210: Construct a vehicle dynamics model that characterizes the driving state of the target vehicle; Step 220: Decompose the vehicle dynamics model to obtain a nominal model that characterizes the linear characteristics of the target vehicle's driving and an uncertain model that characterizes the nonlinear characteristics of the target vehicle's driving. Step 230: Use the Koopman operator to increase the dimensionality of the uncertain model to obtain a finite-dimensional model; Step 240: Linearly superimpose the nominal model and the finite-dimensional model to obtain the fused model; Step 250: Decompose the fusion model into the finite up-dimensional model and a perturbation model that characterizes the modeling error of the fusion model; Step 260: Construct the nominal controller corresponding to the nominal model, the dimensionality upgrade controller corresponding to the finite dimensionality upgrade model, and the disturbance controller corresponding to the disturbance model, respectively. Step 270: Using the nominal controller, the dimensionality upgrade controller, and the disturbance controller, a target control quantity is generated, and the target control quantity is used to control the driving of the target vehicle.

[0038] In the above implementation, a vehicle dynamics model representing the driving state of the target vehicle is first constructed, and then decomposed into a nominal model and an uncertain model. Next, the uncertain model is upgraded using the Koopman operator to obtain a finite-dimensional upgraded model. Subsequently, the nominal model and the finite-dimensional upgraded model are linearly superimposed to obtain a fused model, which is then decomposed into a finite-dimensional upgraded model and a perturbation model representing the modeling error of the fused model. Then, a nominal controller corresponding to the nominal model, a finite-dimensional upgraded controller corresponding to the finite-dimensional upgraded model, and a perturbation controller corresponding to the perturbation model are constructed respectively. Finally, using the nominal controller, the finite-dimensional upgraded controller, and the perturbation controller, a target control quantity is generated, and this target control quantity is used to control the target vehicle's driving. This approach can improve the insufficient robustness of traditional autonomous driving control methods under extreme conditions.

[0039] Please refer to Figure 3 The following section will elaborate on each step of the robust trajectory tracking control method for autonomous vehicles: In step 210, the real system model (i.e., the vehicle dynamics model, or simply the real system) is first constructed, as follows: Real vehicle dynamics models are described using nonlinear discrete state-space equations:

[0040] In the formula, express Real-time state of the target vehicle. The true state quantity at any given moment , in For longitudinal velocity tracking error, The actual longitudinal velocity at the vehicle's center of gravity, The desired longitudinal velocity at the reference trajectory point; Let y represent the lateral position tracking error, and y represent the actual lateral position of the vehicle in the global coordinate system. The desired lateral position on the reference trajectory; The rate of change of the lateral position tracking error represents the speed at which the vehicle approaches the reference trajectory; For heading angle tracking error, This represents the vehicle's actual heading angle in the global coordinate system. The expected heading angle at the reference trajectory point; This represents the rate of change of the heading angle tracking error. Actual control quantity. ,in For the total longitudinal resultant external force, The steering angle of the front wheels; This represents the actual disturbance amount; The transformation mapping function for the real system is referred to simply as the real mapping function. Because the controlled vehicle system (i.e., the target vehicle) contains internal and external uncertainties caused by adverse factors, the real mapping function... It is inherently nonlinear, encompassing internal uncertainties such as time-varying parameters, longitudinal and lateral coupled dynamics, and unmodeled dynamics, as well as external uncertainties such as sensor noise and environmental interference.

[0041] In this embodiment, each error can be understood as the difference between the real-time driving state of the vehicle and the reference trajectory pre-generated by the vehicle controller (including the path used to guide the vehicle's driving and the expected values ​​of parameters such as longitudinal speed, lateral position, and heading angle).

[0042] Furthermore, based on the above description, it can be seen that the true mapping function It exhibits high nonlinearity and complexity, and its specific mathematical expression is unknown. Furthermore, theoretically, it is impossible to give an exact expression that satisfies the true mapping function. The response is always perfectly consistent with that of a real vehicle in the real world. Based on this, the final result of the control always contains an error, and the control error is related to the function... The degree of nonlinearity is proportional to the actual mapping function, although the true mapping function cannot be given. While a precise expression for the actual vehicle dynamics model is not available, based on observations of the target vehicle's dynamic response in real-world conditions, and considering actuator specifications or performance limitations, it can be determined that each variable in the real system (i.e., the vehicle dynamics model) necessarily has boundary constraints within the operational design conditions. Therefore, due to the central symmetry characteristics of the vehicle system, reasonable assumptions can be made regarding the actual state variables. Actual control quantity and the actual disturbance amount All are subject to centrally symmetric bounded constraints, with the center being zero. Therefore, the constraints for constructing the vehicle dynamics model are as follows:

[0043] In the formula, , , These are the shape generators for the corresponding sets. The logic for determining the shape generator is as follows: First, the physical boundaries of the vehicle's state variables are determined based on the vehicle's inherent physical parameters (such as body size, mass, wheelbase, tire lateral stiffness, etc.); then, the design operating conditions (such as vehicle speed range) are considered. , range of road surface adhesion coefficient (etc.) Determine the maximum possible fluctuation range of each state variable and control variable; finally, with the origin as the center, combine these boundary values ​​and fluctuation amplitudes into a generator matrix of a fully symmetric polytope, thereby constructing a constraint set containing all possible values.

[0044] In step 220, the vehicle dynamics model is decomposed into a nominal model and an uncertain model. Based on the three-degree-of-freedom vehicle dynamics model (i.e., the vehicle dynamics model), a linear time-invariant nominal mechanism model (i.e., the nominal model) is constructed, as shown below:

[0045] In the formula, express The nominal state quantity at time t. for The nominal state quantity at time t. This refers to the nominal control variables. The nominal model (or nominal system) is an idealized digital twin model of the real target vehicle. It is constructed based on first principles (Newtonian mechanics) and reasonable simplification assumptions, completely ignoring various uncertainties in the real world (such as tire nonlinearity, wind resistance, parameter perturbations, etc.), and reflects the expected motion behavior of the vehicle under ideal conditions. Nominal state variables. Defined as the nominal tracking error relative to the reference trajectory; , , The nominal total longitudinal net external force and the nominal front wheel steering angle are given.

[0046] Nominal system matrix and control matrix The continuous system matrix of the trajectory tracking error model , The sampling time was obtained by discretization using the zero-order hold method. The discretization calculation formula is as follows:

[0047] The specific expression for the matrix of the continuous system is:

[0048] In the formula, This refers to the vehicle's longitudinal speed. Vehicle parameters include: total vehicle mass. (kg), distance from front axle to center of gravity (m), distance from rear axle to center of mass (m), moment of inertia about the z-axis Front wheel equivalent lateral stiffness Rear wheel equivalent lateral stiffness The above variables are taken from parameters of a specific vehicle (the target vehicle in this example). and After discretization, the result can be completely determined. and The value.

[0049] The constraints of the nominal system are also expressed in a fully symmetric multicellular form:

[0050] , Do not use the shape generator for the corresponding set.

[0051] In this embodiment, the uncertain system model (or uncertain system) is constructed as follows: Define uncertain state quantities Uncertain control quantity Then the state-space equation of the uncertain system is:

[0052] In the formula, This is a nonlinear mapping function for an uncertain system, inheriting all the nonlinear characteristics of the real system. The disturbance quantity of the uncertain system... Constraint range Determined in the following ways: Data Acquisition: Using high-fidelity vehicle dynamics simulation software or a real vehicle test platform, input and output data of the real system are collected within the designed operating conditions (set vehicle speed range, road surface adhesion coefficient range). The input and output data may include the real state variables at the current moment. Actual control quantity and the actual state quantity at the next moment. ; Sample Calculation: Based on the definition of a real system, calculate the sample disturbance at each moment using the following formula:

[0053] because The above equation also gives the amount of uncertain disturbance. Sample values; Set construction: All calculated results Sample collection is performed by containing all sample points in the smallest possible fully symmetric polytope, i.e.:

[0054] Among them, shape generator The principle for determining the generator's F-norm is to minimize the size of the generator's F-norm while ensuring that all sample points are included, thereby reducing the conservatism of the controller design. The above process is completed offline; the controller only needs to be queried when running online. The value.

[0055] Therefore, the constraints of the uncertain system are:

[0056] In the formula, , , These are the shape generators for the corresponding sets. Indicates uncertain disturbance quantity Dimensions.

[0057] In step 230, the Koopman operator maps the finite-dimensional nonlinear system to an infinite-dimensional linear space through a nonlinear dimension-upgrading function, allowing the upgraded state to evolve linearly. This embodiment extends the Koopman operator to controlled systems, achieving linearized modeling of nonlinear uncertain systems. The dimension-upgrading process of the uncertain model in this embodiment is as follows: Step 231, Koopman operator embedding of the controlled system: To extend the Koopman operator theory to controlled systems with control inputs, we define the extended state:

[0058] in, For the uncertain state of the system at the current moment; From the current moment The sequence of uncertain control variables extending to the infinite future. The introduction of this extended state allows the controlled system mapping to be written in an autonomous form without explicit control inputs: This satisfies the application conditions of the standard Koopman operator.

[0059] Based on this, construct an extended dimension-upgrading function:

[0060] In the formula, For state-level upscaling functions, derived from polynomial basis functions constitute; Let be the uncertain control quantity at the current moment. The above design ensures that the evolution of the uncertain system's dimensionality depends only on the uncertain control quantity at the current moment, effectively avoiding the difficulties in handling infinite-dimensional control sequences.

[0061] Extended Koopman operator Satisfies a linear evolutionary relationship:

[0062] in, To extend the Koopman operator matrix, its specific value is obtained by regression calculation on the collected input and output data using the improved extended dynamic mode decomposition algorithm described in subsequent step S233. This operator equates the dynamic evolution of the original nonlinear system to a linear transformation in an increased-dimensional space.

[0063] Step 232, Construction of the finite-dimensional upgrade model (or finite-dimensional upgrade system): like Figure 4 As shown, the first 15 nonlinear basis functions of the state-level upscaling function are extracted, and a finite-dimensional state-level upscaling function is defined. Its specific basis functions are:

[0064] in The five components correspond to the uncertain state quantity. (Upgraded state quantity) Dimensional control quantity Constructing a finite-dimensional upgrade system:

[0065] In the formula, This is the upgraded system matrix (i.e., the initial upgraded system matrix that has not yet been solved). This is the upgraded control matrix (i.e., the initial upgraded control matrix that has not yet been solved). It is the inverse mapping matrix (i.e. the initial inverse mapping matrix that has not been solved) to realize the bidirectional mapping between the upgraded state and the original uncertain state.

[0066] Step 233: Improve the extended dynamic mode decomposition algorithm to solve for the upgraded system matrix: Data Acquisition and Preprocessing: High-fidelity vehicle dynamics simulation software CarSim / Real Vehicle was used to collect real system input and output data within the design operating conditions, covering the operating range of the vehicle speed-road adhesion coefficient design domain. The sampling frequency was 1 / A total of 1 million data points were collected at Hz. These data were then substituted into the nominal model to calculate the nominal output. Subtracting the nominal output from the nominal output yielded the uncertain system dataset. .

[0067] Constructing the optimization problem: Define a least squares optimization problem and introduce a LASSO regularization term to achieve matrix sparsity:

[0068] In the formula, the data matrix , , Regularization parameters , This embodiment can be flexibly configured according to actual conditions. =0.001、 =0.001.

[0069] Solving for the matrix: The optimization problem is transformed into a matrix inversion problem using normal equations, and the coordinate descent method is used to obtain the matrix of the upgraded system. Dimensional control matrix and inverse mapping matrix LASSO regularization causes approximately 30% of the elements in the matrix to be zero, effectively reducing the model complexity.

[0070] It should be noted that the extended Koopman operator matrix mentioned in step 231 The finite-dimensional approximation is the upgraded system matrix described in step 232. The specific value is determined by the improved extended dynamic mode decomposition algorithm described in this step, that is: based on the collected uncertain system dataset. Using finite-dimensional state-level upscaling functions Mapping uncertain state variables to a high-dimensional space to construct a data matrix By solving the least squares optimization problem with LASSO regularization and using the coordinate descent method, the finite-dimensional approximate expression of this operator can be obtained.

[0071] In step 240, the mechanism-data fusion model is constructed as follows: By linearly superimposing the nominal mechanism model (i.e., the nominal model) and the data model (i.e., the finite-dimensional model), the predicted output of the fusion model is obtained:

[0072] The fusion model exhibits a bilinear time-invariant form, combining the stability of a mechanistic model with the accuracy of a data model.

[0073] In step 250, the fusion model is decomposed into a finite-dimensional upscaling model and a perturbation model representing the modeling error of the fusion model. Specifically: First, consider the Koopman modeling error. Constructing an accurate Koopman system, also known as an accurate dimensionality-upgrading model:

[0074] In the formula, express The precise state quantity at any given moment. for The precise Koopman state at time t (i.e., the precise state quantity) represents the precise state of the uncertain system in the higher-dimensional space. The Koopman modeling error (or simply modeling error) characterizes the dynamic difference between a finite-dimensional upgraded system and an exact Koopman system. The constraints on the modeling error are expressed using a fully symmetric polytopic form: , This is the shape generator for the corresponding set.

[0075] The following formula is used to calculate:

[0076] in , and All of these can be calculated from the collected real system data. Constraints on modeling errors. All calculated values ​​are contained within a fully symmetric polytope that is as small as possible. The sampling points are used to determine the location.

[0077] Then, the exact Koopman system is decomposed into two independent sub-models: a finite-dimensional upgraded system and a perturbation system (i.e., the perturbation model). The dimensional upgrading system has been constructed in step 232 above, and the perturbation model is designed as follows: Define the disturbance state quantity Disturbance control quantity The perturbation model is as follows:

[0078] Introducing a feedback gain matrix To reconstruct the perturbed system into an autonomous system: Let ,but:

[0079] in, By solving the linear matrix inequality (LMI) of the upgraded system We obtain the formula, Those that meet the above LMI requirements This ensures the asymptotic stability of the disturbed system.

[0080] In step 260, a three-layer control architecture is constructed based on the nominal model, the finite-dimensional model, and the perturbation model, including: Nominal Controller: Design a model predictive controller for a nominal mechanism system, with the optimization objective being to minimize the nominal state tracking error and control computation cost.

[0081]

[0082] in, To predict the time domain, To control the time domain, the decision variables for this optimization problem are the nominal control quantity sequences. and the first relaxation factor , The first relaxation factor The weighting coefficients. To predict the sequence of nominal state variables in the time domain; and It is a positive definite weight matrix; The weights are the relaxation factor. , For robust tube constraints of the nominal system, , This is the shape generator for the corresponding set.

[0083] Dimensional Upgrade Controller: For a dimensional upgrade data system, a model predictive controller (MPC) is designed. The optimization objective and constraints are similar to those of the nominal controller. Therefore, the control optimization problem for this system is as follows:

[0084]

[0085] Among them, the decision variables are sequences of upgraded control quantities. Second relaxation factor . To predict the sequence of upgraded state variables in the time domain; and It is a positive definite weight matrix; The weighting coefficient of the second relaxation factor; Robust tube constraints for dimensional upgrading systems , This is the shape generator for the corresponding set.

[0086] Disturbance Controller: Design a state feedback controller for a disturbed system, with the feedback gain matrix as the decision variable. :

[0087] in This is the disturbance control variable. This is a perturbation state variable.

[0088] The robust constraint design for each controller is as follows: Based on the theory of fully symmetric multitopic sets, the minimum robust positive invariant set of Koopman modeling error is calculated. Since... The Neumann series converges, and we have The reachable set of the perturbation model in the infinite time domain is:

[0089] Robust tube constraints are designed for the nominal model and the finite-dimensional upgraded model using Pontnia difference operations: The constraint is a nominal robust tube constraint:

[0090] The constraint is a finite-dimensional robust tube constraint:

[0091] In the formula, This is for the Pontnia gold difference operation.

[0092] In step 270, nominal control quantities are generated using the nominal controller, the dimension-upgrading controller, and the disturbance controller, respectively. Dimensional control quantity and disturbance control quantity ; The final target control quantity acting on the real vehicle is a linear superposition of the three control quantities:

[0093] In the formula, the actual control quantity (i.e., the target control quantity) nominal control quantity Dimensional control quantity and disturbance control quantity It consists of three elements. Among them, and The systems in question are all of LTI form and have known system matrices; the disturbance control quantity... The disturbed system contains uncertainties. Transforming the above equation into a set expression, we can see that the constraints of the three control variables should satisfy the following relationship:

[0094] This completes the design of the three-layer controller. The target control quantity is generated by superimposing the control quantities output by the three-layer controller, and finally the target vehicle is controlled based on the target control quantity.

[0095] Example 3

[0096] This application also provides a computer program product, including a computer program. When executed by processor 101, the computer program can implement the robust trajectory tracking control method for autonomous vehicles described in the above embodiments.

[0097] Based on the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by hardware or by using software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of this application can be embodied in the form of a software product. This software product can be stored in a non-volatile storage medium (such as CD-ROM, USB flash drive, mobile hard drive, etc.) and includes several instructions to cause a computer device (such as a personal computer, server, or network device, etc.) to execute the methods described in the various implementation scenarios of this application.

[0098] In summary, this application provides a robust trajectory tracking control method, device, and program product for autonomous vehicles. In this technical solution, a vehicle dynamics model characterizing the driving state of the target vehicle is first constructed, and then decomposed to obtain a nominal model and an uncertain model. Then, the uncertain model is upgraded using the Koopman operator to obtain a finite-dimensional upgraded model. Subsequently, the nominal model and the finite-dimensional upgraded model are linearly superimposed to obtain a fusion model, which is then decomposed into a finite-dimensional upgraded model and a disturbance model characterizing the modeling error of the fusion model. Then, a nominal controller corresponding to the nominal model, a dimensional upgrade controller corresponding to the finite-dimensional upgraded model, and a disturbance controller corresponding to the disturbance model are constructed respectively. Finally, the nominal controller, the dimensional upgrade controller, and the disturbance controller are used to generate a target control quantity, and this target control quantity is used to control the driving of the target vehicle. Thus, this technical solution retains the interpretability and robustness of the mechanistic model (nominal model) and effectively captures the nonlinear characteristics of the vehicle under extreme conditions through a data-driven approach (referencing the finite-dimensional upgraded model construction process), significantly improving trajectory tracking accuracy and driving safety, and is applicable to the motion control of autonomous vehicles under both normal and extreme conditions.

[0099] In the embodiments provided in this application, it should be understood that the disclosed methods can also be implemented in other ways. The method embodiments described above are merely illustrative. For example, the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of methods and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, program segment, or part of code, which includes one or more executable instructions for implementing a specified logical function. It should also be noted that each block in a block diagram and / or flowchart, and combinations of blocks in block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions. Furthermore, the functional modules in the various embodiments of this application can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0100] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A robust trajectory tracking control method for autonomous vehicles, characterized in that, include: Construct a vehicle dynamics model that characterizes the driving state of the target vehicle; The vehicle dynamics model is decomposed to obtain a nominal model that characterizes the linear characteristics of the target vehicle's driving, and an uncertain model that characterizes the nonlinear characteristics of the target vehicle's driving. The uncertainty model is increased in dimension using the Koopman operator to obtain a finite-dimensional increased model; The nominal model and the finite-dimensional model are linearly superimposed to obtain a fusion model; The fusion model is decomposed into the finite up-dimensional model and a perturbation model that characterizes the modeling error of the fusion model; Construct the nominal controller corresponding to the nominal model, the dimension-upgraded controller corresponding to the finite dimension-upgraded model, and the disturbance controller corresponding to the disturbance model, respectively. The target control quantity is generated using the nominal controller, the dimensionality upgrade controller, and the disturbance controller, and the target control quantity is used to control the driving of the target vehicle.

2. The method according to claim 1, characterized in that, The vehicle dynamics model is represented as follows: In the formula, express Real-time state of the target vehicle. The true state quantity at any given moment , in, Indicates longitudinal velocity tracking error. This indicates the lateral position tracking error. This represents the rate of change of the lateral position tracking error. Indicates the heading angle tracking error. The rate of change of the heading angle tracking error. Indicates the actual control quantity. This represents the actual amount of disturbance. This represents the actual mapping function.

3. The method according to claim 1, characterized in that, The vehicle dynamics model is decomposed to obtain a nominal model characterizing the linear characteristics of the target vehicle's movement, and an uncertain model characterizing the nonlinear characteristics of the target vehicle's movement, including: Based on the vehicle dynamics model, construct the nominal model: In the formula, express The nominal state quantity at time t. express The nominal state quantity at time t. Indicates the nominal control quantity. , These represent the system matrix and the control matrix, respectively. The linear mapping function representing the nominal model; Based on the vehicle dynamics model, construct the uncertain model: In the formula, express Uncertain state quantities at time, express Uncertain state quantities at time, , Indicates an uncertain control quantity. , This represents the disturbance amount in an uncertain model.

4. The method according to claim 1, characterized in that, The uncertain model is upgraded using the Koopman operator to obtain a finite-dimensional upgraded model, including: Based on the aforementioned uncertainty model, a state dimensionality-upgrading function is constructed using the Koopman operator; A finite-dimensional state upgrade function is constructed by extracting a basis function of a preset dimension from the state upgrade function, wherein the preset dimension is greater than the dimension of the uncertain state quantity in the uncertain model. Based on the finite-dimensional state dimensionality increase function and the uncertain model, an initial dimensionality increase model is constructed, which is expressed as follows: In the formula, express The upgraded state quantity at any given moment. express The upgraded state quantity at any given moment. Represents the state variable of the upgraded dimension. Indicates the preset dimension. Describes the function for increasing the dimensionality of a finite-dimensional state. This indicates the control quantity for dimensional expansion. , Represents the initial upgraded system matrix. This represents the initial upgraded control matrix. This represents the dimension of the uncertain control quantity in an uncertain model. Let be the initial inverse mapping matrix. The dimension representing the uncertain state quantity in an uncertain model; Obtain the operating parameters of the target vehicle during its driving process; Based on the initial upgraded system matrix, the initial upgraded control matrix, and the initial inverse mapping matrix, a least squares optimization problem is constructed, and the least squares optimization problem is solved using the operating parameters to obtain the target upgraded system matrix, the target upgraded control matrix, and the target inverse mapping matrix; The initial dimensionality-upgrading system matrix, the initial dimensionality-upgrading control matrix, and the initial inverse mapping matrix in the initial dimensionality-upgrading model are replaced with the target dimensionality-upgrading system matrix, the target dimensionality-upgrading control matrix, and the target inverse mapping matrix to obtain the finite dimensionality-upgrading model.

5. The method according to claim 4, characterized in that, The fusion model is decomposed into the finite-dimensional upscaling model and a perturbation model representing the modeling error of the fusion model, including: Based on the modeling error and the finite dimensionality upgrade model, an accurate dimensionality upgrade model is constructed, which is represented as follows: In the formula, express The precise upgraded state quantity at any given moment. express The precise upgraded state quantity at any given moment. This indicates the precise dimensional control quantity. Indicates modeling error; Based on the finite dimensionality upgrade model and the exact dimensionality upgrade model, an initial model is determined, which is represented as follows: In the formula, express The perturbation state quantity at any given moment. express The perturbation state quantity at any given moment. , This represents the disturbance control quantity. ; The initial model is reconstructed using the feedback gain matrix to obtain the perturbation model, which is represented as follows: In the formula, , The feedback gain matrix is ​​represented by solving linear matrix inequalities. get, .

6. The method according to claim 5, characterized in that, Constructing the nominal controller corresponding to the nominal model, the dimensionality-upgraded controller corresponding to the finite dimensionality-upgraded model, and the perturbation controller corresponding to the perturbation model, respectively, includes: The nominal controller is constructed with the goal of minimizing the nominal state tracking error and the nominal control consumption. The dimensionality-upgrading controller is constructed with the goal of minimizing the state tracking error and the control consumption in dimensionality-upgrading. Based on the disturbance model, a disturbance controller is constructed. .

7. The method according to claim 1, characterized in that, Using the nominal controller, the dimensionality-upgrading controller, and the disturbance controller, a target control quantity is generated, and the target control quantity is used to control the movement of the target vehicle, including: The nominal controller is used to generate a nominal control quantity; The dimensionality-upgrading controller is used to generate dimensionality-upgrading control quantities; The disturbance control quantity is generated using the disturbance controller. The target control quantity is obtained by linearly superimposing the nominal control quantity, the upgraded control quantity, and the disturbance control quantity. The vehicle's movement is controlled using the target control variable.

8. An electronic device, characterized in that, The electronic device includes a processor and a memory coupled together, the memory storing a computer program that, when executed by the processor, causes the electronic device to perform the method as described in any one of claims 1-7.

9. A computer program product, characterized in that, Includes a computer program that, when executed by a processor, implements the method as described in any one of claims 1-7.

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