A trajectory tracking control method, device and medium of an autonomous vehicle

Abstract

The embodiment of the specification discloses a trajectory tracking control method, equipment and medium of an automatic driving vehicle, the method comprises: acquiring the ideal trajectory and the actual trajectory of the automatic driving vehicle to determine the tracking error of the automatic driving vehicle; determining the boundary condition of the tracking error according to the preset decreasing function, and converting the tracking error based on the transformation of the boundary condition to obtain the error conversion result; defining the Bellman function according to the error conversion result to obtain the target control function corresponding to the automatic driving vehicle; reconstructing the Bellman function by defining the Q function neural network to obtain the reconstructed Bellman function, so as to obtain the relationship between the to-be-solved neural network weight and the target control function; based on the estimation error of the to-be-solved neural network weight, designing a finite-time adaptive law to update the Q function neural network based on the finite-time adaptive law, and designing the optimal control of the target control function according to the updated Q function neural network.

Description

Technical Field

[0001] This specification relates to the field of vehicle automatic control technology, and in particular to a trajectory tracking control method, device and medium for an autonomous vehicle. Background Technology

[0002] In recent years, with the rapid development of intelligent transportation and artificial intelligence technologies, autonomous driving technology has received widespread attention from scholars. The key technologies for autonomous vehicles mainly include: environmental perception, behavioral decision-making, path planning, and vehicle trajectory control. Autonomous driving trajectory control methods, as a crucial technology bridging the gap between different stages of autonomous driving, are essential for ensuring the safety of autonomous driving.

[0003] The highly dynamic, nonlinear characteristics and coupling of vehicles, along with their susceptibility to external disturbances, pose significant challenges to achieving accurate path tracking control for autonomous vehicles. Currently, many classic control methods are widely used for path tracking, primarily categorized as follows: 1) Geometric motion control, mainly pure trajectory tracking and Stanley control; 2) Model-free control, mainly PID control, fuzzy control, and neural network control; 3) State feedback control, mainly LQG control, sliding mode control, and H∞ robust control. However, these methods cannot effectively consider vehicle constraints, easily leading to actuator saturation or even dynamic instability in autonomous vehicles. Furthermore, existing online synchronous control methods for autonomous vehicles all require dynamic modeling of the system or the design of relevant identifiers to estimate system dynamics online, which increases computational load and affects system response time. In addition, calculating the optimal control solution requires the use of appropriate execution-evaluation structures, and the use of execution neural networks also increases computational load, impacting system response efficiency. Summary of the Invention

[0004] To address the aforementioned technical problems, this specification provides one or more embodiments of a trajectory tracking control method and apparatus for autonomous vehicles.

[0005] One or more embodiments of this specification employ the following technical solutions:

[0006] On the one hand, one or more embodiments of this specification provide a trajectory tracking control method for an autonomous vehicle, the method comprising:

[0007] The ideal trajectory and actual trajectory of the autonomous vehicle are obtained to determine the tracking error of the autonomous vehicle;

[0008] The tracking error is defined by a preset decreasing function, and the tracking error is transformed based on the transformation of the definition conditions to obtain the error transformation result.

[0009] Based on the error transformation result, a Bellman function is defined to obtain the target control function corresponding to the autonomous vehicle;

[0010] The Bellman function is reconstructed by defining a Q-function neural network to obtain the reconstructed Bellman function, thereby obtaining the relationship between the weights of the neural network to be solved and the target control function.

[0011] Based on the estimation error of the weights of the neural network to be solved, a finite-time adaptive law is designed to update the Q-function neural network, and the optimal control of the target control function is designed based on the updated Q-function neural network.

[0012] Optionally, in one or more embodiments of this specification, obtaining the ideal trajectory and the actual trajectory of the autonomous vehicle to determine the tracking error of the autonomous vehicle specifically includes:

[0013] A motion model of the autonomous vehicle is constructed based on its motion parameters; wherein, the motion model is:

[0014] Where x(t) is the horizontal position of the vehicle's center of mass in the inertial reference frame, y(t) represents the vertical position of the vehicle's center of mass in the inertial reference frame, θ(t) represents the direction of the vehicle's center of mass, and v x (t) represents the longitudinal velocity of the vehicle's center of mass within the vehicle's chassis, w x (t) represents the yaw rate of the vehicle's center of mass within the chassis frame, and d r It is the direct distance from the center of gravity to the rear axle in a vehicle;

[0015] Based on the fixed longitudinal speed v of the autonomous vehicle r (t) and fixed yaw rate w r (t) and the motion model, determine the ideal trajectory of the autonomous vehicle; wherein, the ideal trajectory is:

[0016] Where, x r (t) is the ideal horizontal position of the vehicle's center of mass in the inertial reference frame, y r (t) is the ideal perpendicular position of the vehicle's center of mass in the inertial reference frame, θ r (t) represents the ideal direction of the vehicle's center of gravity;

[0017] The driving data of the autonomous vehicle is collected to determine the actual trajectory of the autonomous vehicle, and the tracking error of the autonomous vehicle is determined based on the difference between the ideal trajectory and the actual trajectory.

[0018] Optionally, in one or more embodiments of this specification, determining the tracking error of the autonomous vehicle based on the difference between the ideal trajectory and the actual trajectory specifically includes:

[0019] Based on the difference between the ideal trajectory and the actual trajectory, the error vector of the autonomous vehicle is determined; wherein, the error vector is... x e (t), y e (t) and θ e (t) represent the tracking errors for the horizontal position, vertical position, and vehicle direction, respectively, where A = cos(θ(t)) and B = sin(θ(t)).

[0020] The error dynamics of the autonomous vehicle are determined based on the error vector and a preset nonlinear dynamic function, and the error dynamics are used as the tracking error; wherein, the tracking error is: s(x)=[x e (t),y e (t),θ e (t)] T Indicates tracking error. Let f(x) be the tracking control function for the autonomous vehicle, and g(x) be nonlinear dynamic functions.

[0021] Optionally, in one or more embodiments of this specification, the tracking error is transformed based on the transformation of the defining conditions to obtain an error transformation result, specifically including:

[0022] Define an inverse function for the transformed error corresponding to the tracking error, and define an error formula for the transformed tracking error based on the inverse function; wherein the error formula is: z represents the error transformation result, N(z) is the inverse function, and ρ(t) is the decreasing smoothing function.

[0023] The inverse function formula is determined based on the properties of the inverse function, and the error formula is transformed based on the inverse function formula to obtain the error transformation result; wherein, the error transformation result... a>0 is a positive integer. This is used to represent the relationship between tracking error and a decreasing smoothing function.

[0024] Optionally, in one or more embodiments of this specification, the Bellman function is reconstructed by defining a Q-function neural network to obtain a reconstructed Bellman function, thereby obtaining the relationship between the weights of the neural network to be solved and the target control function, specifically including:

[0025] Based on the preset activation function, the weights of the neural network to be solved, and the approximation error of the Q-function neural network, the definition formula of the Q-function neural network is obtained; wherein, the definition formula is: Q(z)=W T η(z)+ε(z), where η(z) is the activation function, W is the weight of the neural network to be solved, and ε(z) is the approximation error of the Q-function neural network, and the approximation error is bounded;

[0026] The neurons of the Q-function neural network are constructed based on preset basis functions; wherein, the neurons of the Q-function neural network are: vec(·) is a vectorization operation, η zz η zu η uu W is a basis function. zz W zu W uu These are the weights for the neural network corresponding to different basis functions;

[0027] The Bellman function is reconstructed based on the neurons of the Q-function neural network to obtain a reconstructed Bellman function, which is then used to determine the relationship between the weights of the neural network to be solved and the target control function; wherein, the reconstructed Bellman function is:

[0028] k(z,u) is the integral strengthening term, Δη(t) = η(z(t)) - η(z(tT)), ε z =ε z (z(t))-ε z (z(tT)).

[0029] Optionally, in one or more embodiments of this specification, a finite-time adaptive law is designed based on the estimation error of the weights of the neural network to be solved, specifically including:

[0030] Define auxiliary variables; wherein, the auxiliary variables include: a first auxiliary variable and a second auxiliary variable;

[0031] The solution for the first auxiliary variable and the second auxiliary variable is determined based on the preset parameters of the auxiliary variable;

[0032] Based on the estimated weights of the neural network to be solved, and the solutions of the first and second auxiliary variables, a third auxiliary variable is constructed to determine the finite-time adaptive law based on the third auxiliary variable and a preset learning gain; wherein, the finite-time adaptive law is: P1 is the solution for the first auxiliary variable, Q1 is the solution for the second auxiliary variable, and Γ1>0 is the preset learning gain.

[0033] Optionally, in one or more embodiments of this specification, after constructing a third auxiliary variable based on the estimation of the weights of the neural network to be solved, the solutions of the first auxiliary variable and the second auxiliary variable, the method further includes:

[0034] Calculate the minimum eigenvalue of the third auxiliary variable;

[0035] If the minimum eigenvalue is determined to be less than zero, a perturbation signal is added during the construction of the target control function to obtain an updated target control function.

[0036] If the minimum eigenvalue is determined to be greater than zero, then the finite-time adaptive law is constructed based on the third auxiliary variable and the preset learning gain.

[0037] Optionally, in one or more embodiments of this specification, updating the Q-function neural network based on the finite-time adaptive law, and designing the optimal control of the target control function based on the updated Q-function neural network, specifically includes:

[0038] The weights of the unsolved neural network in the Q-function neural network are determined based on the effective time adaptive law, and the current neuron of the Q-function neural network is determined based on the weights of the unsolved neural network.

[0039] By extracting the current neurons of the Q-function neural network and determining the optimal control of the target control function based on the relationship between the weights of the neural network to be solved and the target control function; wherein, the optimal control is: R -1 This represents the inverse operation on the weight matrix of the transient control, and diag represents taking the diagonal matrix.

[0040] This specification provides one or more embodiments of a trajectory tracking control device for an autonomous vehicle, the device comprising:

[0041] At least one processor; and,

[0042] A memory communicatively connected to the at least one processor; wherein,

[0043] The memory stores instructions executable by the at least one processor, which, when executed by the at least one processor, enable the at least one processor to:

[0044] Establish a motion model for the autonomous vehicle, and obtain the ideal trajectory of the autonomous vehicle based on the motion model;

[0045] The driving data of the autonomous vehicle is collected to determine the actual trajectory of the autonomous vehicle, and the tracking error of the autonomous vehicle is determined based on the ideal trajectory and the actual trajectory.

[0046] The tracking error is defined by a preset decreasing function, and the tracking error is transformed based on the transformation of the definition conditions to obtain the error transformation result.

[0047] Based on the error transformation result, a Bellman function is defined to obtain the target control function corresponding to the autonomous vehicle;

[0048] The Bellman function is reconstructed by defining a Q-function neural network to obtain the reconstructed Bellman function, thereby obtaining the relationship between the weights of the neural network to be solved and the target control function.

[0049] Based on the estimation error of the weights of the neural network to be solved, a finite-time adaptive law is designed to update the Q-function neural network, and the optimal control of the target control function is designed based on the updated Q-function neural network.

[0050] This specification provides one or more embodiments of a non-volatile computer storage medium storing computer-executable instructions, wherein the computer-executable instructions are configured as follows:

[0051] Establish a motion model for the autonomous vehicle, and obtain the ideal trajectory of the autonomous vehicle based on the motion model;

[0052] The driving data of the autonomous vehicle is collected to determine the actual trajectory of the autonomous vehicle, and the tracking error of the autonomous vehicle is determined based on the ideal trajectory and the actual trajectory.

[0053] The tracking error is defined by a preset decreasing function, and the tracking error is transformed based on the transformation of the definition conditions to obtain the error transformation result.

[0054] Based on the error transformation result, a Bellman function is defined to obtain the target control function corresponding to the autonomous vehicle;

[0055] The Bellman function is reconstructed by defining a Q-function neural network to obtain the reconstructed Bellman function, thereby obtaining the relationship between the weights of the neural network to be solved and the target control function.

[0056] Based on the estimation error of the weights of the neural network to be solved, a finite-time adaptive law is designed to update the Q-function neural network, and the optimal control of the target control function is designed based on the updated Q-function neural network.

[0057] The above-described at least one technical solution adopted in the embodiments of this specification can achieve the following beneficial effects:

[0058] By establishing a dynamic tracking error for autonomous vehicles, the tracking error and subsequent tracking control are no longer based on complete system dynamic information. The concept of a predefined performance function is introduced, where the boundary conditions for the tracking error are determined based on a preset decreasing function. This transforms the boundary conditions into unrestricted conditions, allowing the tracking error to gradually converge to zero in steady state, thus reducing computational costs by eliminating the need to consider the acquisition of system dynamics. Furthermore, the introduction of a Q-function neural network algorithm further relaxes the requirements for the autonomous vehicle's system dynamics, eliminating the need for direct online updates. The target control function is updated based on the reconstructed Bellman equation corresponding to the updated Q-function neural network, obtaining the optimal tracking control for the autonomous vehicle. This algorithm abandons the execution neural network used in traditional algorithms, simplifying computation and improving computational speed while maintaining control accuracy. Attached Figure Description

[0059] To more clearly illustrate the technical solutions in the embodiments or prior art of this specification, the drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0060] Figure 1 A schematic flowchart of a trajectory tracking control method for an autonomous vehicle provided in an embodiment of this specification;

[0061] Figure 2 This is a dynamic schematic diagram of an autonomous vehicle in an application scenario provided by an embodiment of this specification.

[0062] Figure 3 This specification provides a schematic diagram of a trajectory tracking control algorithm for an autonomous vehicle, as illustrated in an embodiment.

[0063] Figure 4 This is a schematic diagram illustrating an embodiment of the present specification for evaluating the convergence of neural network weights;

[0064] Figure 5 This is a schematic diagram illustrating the vehicle's trajectory in an application scenario provided by an embodiment of this specification.

[0065] Figure 6 This is a schematic diagram comparing the tracking errors of the two controllers provided in the embodiments of this specification;

[0066] Figure 7 A schematic diagram of the structure of a trajectory tracking control device for an autonomous vehicle provided in an embodiment of this specification;

[0067] Figure 8 This is a schematic diagram of the internal structure of a non-volatile storage medium provided in the embodiments of this specification. Detailed Implementation

[0068] This specification provides an embodiment of a trajectory tracking control method, device, and medium for an autonomous vehicle.

[0069] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this specification, and not all embodiments. Based on the embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this specification.

[0070] like Figure 1 The diagram shown is a schematic flowchart of a trajectory tracking control method for an autonomous vehicle provided in one or more embodiments of this specification. Figure 1 As can be seen, in one or more embodiments of this specification, a trajectory tracking control method for an autonomous vehicle includes the following steps:

[0071] S101: Obtain the ideal trajectory and actual trajectory of the autonomous vehicle to determine the tracking error of the autonomous vehicle.

[0072] The main purpose of tracking control is to enable the system state to track the desired trajectory given a tracking control action. Therefore, in order to achieve optimal tracking control of autonomous vehicles without estimating system dynamics, the embodiments in this specification first need to obtain the tracking error of the autonomous vehicle so that subsequent tracking control can be obtained based on the tracking error. That is, firstly, the ideal trajectory and the actual trajectory of the autonomous vehicle are obtained, and then the tracking error of the autonomous vehicle is determined based on the difference between the ideal trajectory and the actual trajectory.

[0073] Specifically, in one or more embodiments of this specification, obtaining the ideal trajectory and the actual trajectory of the autonomous vehicle to determine the tracking error of the autonomous vehicle includes the following steps:

[0074] First, based on the motion parameters of the autonomous vehicle, including lateral and longitudinal motion parameters, a motion model of the autonomous vehicle is constructed. The kinematic equations of the motion model for the rear-wheel-drive autonomous vehicle are shown in formula (1) below:

[0075]

[0076] It should be noted that: x(t) is the horizontal position of the vehicle's center of mass in the inertial reference frame, y(t) represents the vertical position of the vehicle's center of mass in the inertial reference frame, θ(t) represents the direction of the vehicle's center of mass, and v... x (t) represents the longitudinal velocity of the vehicle's center of mass within the vehicle's chassis, w x (t) represents the yaw rate about the Z-axis perpendicular to the xy plane, and d r It is the direct distance from the center of gravity to the rear axle in a vehicle.

[0077] Then based on the fixed longitudinal speed v of the autonomous vehicle r (t) and fixed yaw rate w r (t) and the motion model are used to determine the ideal trajectory of the autonomous vehicle. That is, it is assumed that the ideal trajectory is achieved through a vehicle with a fixed longitudinal velocity v. r (t) and yaw rate w r When (t) is generated, the ideal trajectory dynamics are established as shown in the following formula (2):

[0078]

[0079] Where, x r (t) is the ideal horizontal position of the vehicle's center of mass in the inertial reference frame, y r (t) is the ideal perpendicular position of the vehicle's center of mass in the inertial reference frame, θ r (t) represents the ideal direction of the vehicle's center of mass. At this point, by collecting driving data from the autonomous vehicle, its actual trajectory is obtained, and the tracking error of the autonomous vehicle is determined based on the difference between the ideal trajectory and the actual trajectory.

[0080] Furthermore, in one or more embodiments of this specification, the tracking error of the autonomous vehicle is determined based on the difference between the ideal trajectory and the actual trajectory, specifically including the following process:

[0081] First, based on the difference between the ideal trajectory and the actual trajectory, the error vector of the autonomous vehicle is determined. That is, x is defined in the vehicle's local coordinate system. e (t), y e (t) and θ e (t) represents the tracking errors for the horizontal position, vertical position, and vehicle direction, respectively, thus establishing the error vector. The error vector is shown in formula (3) below:

[0082]

[0083] Where, x e(t), y e (t) and θ e (t) represent the tracking errors for the horizontal position, vertical position, and vehicle direction, respectively, where A = cos(θ(t)) and B = sin(θ(t)).

[0084] like Figure 2 The diagram shows a dynamic representation of an autonomous vehicle. After obtaining the error vector, the error dynamics of the autonomous vehicle can be determined based on the error vector and a preset nonlinear dynamic function, thus using the error dynamics as the tracking error; as shown in formula (4), the tracking error is:

[0085]

[0086] Where s(x)=[x e (t),y e (t),θ e (t)] T Indicates tracking error. This is the tracking control function for the autonomous vehicle.

[0087] S102: Determine the boundary conditions of the tracking error according to the preset decreasing function, and transform the tracking error based on the transformation of the boundary conditions to obtain the error transformation result.

[0088] Based on the tracking error formula (4) from step S101 above, it can be seen that the tracking error includes the system dynamics f(x) and g(x). Therefore, in order to reduce the large computational cost incurred in calculating and estimating the system dynamics, and to allow the tracking error to gradually converge to zero in the steady state, this specification introduces the idea of ​​a defined performance function. Specifically, in one or more embodiments of this specification, the boundary conditions of the tracking error are determined according to a preset decreasing function. Thus, by transforming the boundary conditions into unrestricted conditions, the tracking error is transformed to obtain the error transformation result. Based on the transformation of the boundary conditions, the tracking error can be transformed as follows: Figure 5 As shown, it gradually converges to zero in steady state, which means that the process of obtaining the system dynamics does not need to be considered, thus reducing the computational cost.

[0089] The process of determining the criteria for tracking error based on a preset decreasing function includes the following steps:

[0090] First, define the decreasing smoothing function as shown in formula (5):

[0091] ρ(t)=(ρ(0)-ρ(∞))e -kt +ρ(∞) (5);

[0092] Where ρ(0)>ρ(∞) and k>0 are positive definite constants, and ρ(0) and ρ(∞) satisfy... The tracking error s can then be defined based on the following conditions:

[0093]

[0094] Where a>0 is a positive constant, and -aρ and aρ are the upper and lower bounds, respectively. To transform the boundary conditions into unrestricted terms for subsequent optimal tracking control analysis, in one or more embodiments of this specification, the process of transforming the tracking error based on the transformation of the boundary conditions to obtain the error transformation result specifically includes the following steps:

[0095] Define the inverse function N(z) of the transformed error corresponding to the tracking error, and then define the error formula after the tracking error is transformed based on the inverse function N(z); where the error formula is as shown in the following formula (7):

[0096]

[0097] Where z represents the error transformation result, N(z) is the inverse function, and ρ(t) is the decreasing smoothing function. Then, the inverse function formula is determined based on the properties of N(z), and the error transformation result is obtained by transforming the error formula based on the inverse function formula. The properties of the inverse function N(z) can be summarized as follows:

[0098] Therefore, based on this, the inverse function can be defined as:

[0099]

[0100] According to formulas (7) and (8), the error conversion result is:

[0101]

[0102] in, This is used to represent the relationship between tracking error and the decreasing smoothing function. Based on the above process, the tracking error is... Within the range of upper and lower bounds, it is transformed into a non-restricted term condition. This process allows the tracking error to gradually approach zero in steady state without requiring a precise initial error.

[0103] S103: Define a Bellman function based on the error conversion result to obtain a target control function corresponding to the autonomous vehicle.

[0104] The Bellman equation is a necessary condition for the optimization of dynamic programming mathematical optimization methods. This equation can express "the value of the decision problem at a specific time" as "the reward from the initial choice is equal to the value of the decision problem derived from the initial choice". In this way, the dynamic optimization problem is transformed into simple subproblems, which obey the "optimization principle" proposed by Bellman. In order to simplify the optimal tracking control problem, the Bellman function is defined according to the error transformation result obtained in step S102 above in the embodiments of this specification, and then the target control function corresponding to the autonomous vehicle is obtained. That is, in one or more embodiments of this specification, the process of establishing the target control function is as follows: the Bellman function is defined as shown in the following formula (10):

[0105]

[0106] Where, r(z(τ),u(τ))=z T Qz+u T Ru represents the utility function, and T>0 represents the sampling time.

[0107] S104: The Bellman function is reconstructed by defining a Q-function neural network to obtain the reconstructed Bellman function, thereby obtaining the relationship between the weights of the neural network to be solved and the target control function.

[0108] Since the Bellman function is difficult to solve, this embodiment defines a Q-function neural network to reconstruct the Bellman function, allowing the Q-function neural network to approximate the Bellman function infinitely. The reconstructed Bellman function is then used to obtain the relationship between the neural network weights and the target control function, facilitating subsequent updates and optimizations to achieve the optimal target control function and realize optimal tracking control for autonomous vehicles. Introducing the Q-function neural network algorithm further relaxes the dynamic requirements of the autonomous vehicle system, eliminating the need for dynamic system updates and allowing direct online updates. Furthermore, this algorithm eliminates the execution neural network used in traditional algorithms, simplifying computation and improving computational speed while maintaining control accuracy.

[0109] Specifically, in one or more embodiments of this specification, a reconstructed Bellman function is obtained by reconstructing the Bellman function through a Q-function neural network, in order to obtain the relationship between the weights of the neural network to be solved and the target control function. This specifically includes the following steps:

[0110] Based on the preset activation function, the weights of the neural network to be solved, and the approximation error of the Q-function neural network, the definition formula of the Q-function neural network is obtained. The definition formula is:

[0111] Q(z) = W Tη(z)+ε(z) (11);

[0112] Wherein, η(z):R n →R N Let W be the activation function, N be the number of neurons, W be the evaluation weights of the neural network, and ε(z) be the approximation error of the neural network. In this paper, it is assumed that the approximation error ε(z) and its derivative are bounded. Then, neurons of the Q-function neural network are constructed based on the preset basis functions, that is, W is... T η(z) uses data T zz (z), T zu (z,u), T uu The structure is as shown in Formula 12 below. The neurons of the Q-function neural network are:

[0113]

[0114] Where vec(·) is the vectorization operation, η zz η zu η uu W is an independent basis function. zz W zu W uu The data in the equation corresponds to the neural network weights for different basis functions, so the data can be used for the design of subsequent adaptive laws.

[0115] After obtaining the above formula (12), in order to infinitely approximate the Bellman function and obtain the optimal Bellman function to achieve optimal tracking control, the embodiments of this specification reconstruct the Bellman function based on the neurons of the Q-function neural network to obtain the reconstructed Bellman function, thereby determining the relationship between the weights of the neural network to be solved and the target control function based on the reconstructed Bellman function. It should be noted that the reconstructed Bellman function is:

[0116]

[0117] Where k(z,u) is the integral reinforcement term, Δη(t) = η(z(t)) - η(z(tT)), and the error ε z =ε z (z(t))-ε z (z(tT)) is bounded.

[0118] S105: Based on the estimation error of the weights of the neural network to be solved, design a finite-time adaptive law to update the Q-function neural network, and design the optimal control of the target control function based on the updated Q-function neural network.

[0119] In order to design an online adaptive law based on the adaptive sliding mode technique to realize the online update of the evaluation neural network and thus achieve optimal tracking control of autonomous vehicles, the embodiments of this specification design a finite-time adaptive law based on the estimation error of the weights of the neural network to be solved, and then update the Q-function neural network according to the obtained finite-time adaptive law. Then, according to the reconstructed Bellman equation corresponding to the updated Q-function neural network, the target control function is updated to obtain the optimal tracking control of the autonomous vehicle.

[0120] Specifically, in one or more embodiments of this specification, a finite-time adaptive law is designed based on the estimation error of the weights of the neural network to be solved, which specifically includes the following process:

[0121] First, define auxiliary variables; these include: a first auxiliary variable P1 and a second auxiliary variable Q1; where P1∈R N×N ,Q1∈R N The specific formula is shown in formula (14) below:

[0122]

[0123] Where l1>0 is a design parameter, therefore, the solution for the first auxiliary variable and the second auxiliary variable is determined according to the preset parameters of the auxiliary variables as follows:

[0124]

[0125] At this point, the actual neural network is defined as:

[0126]

[0127] in, and These are estimates of Q and W, respectively.

[0128] Then, based on the estimated weights of the neural network to be solved, and the solutions of the first and second auxiliary variables, a third auxiliary variable is constructed. Based on this third auxiliary variable and the preset learning gain, the finite-time adaptive law is determined. The finite-time adaptive law is:

[0129]

[0130] in, P1 is the solution for the first auxiliary variable, Q1 is the solution for the second auxiliary variable, and Γ1>0 is the preset learning gain.

[0131] Furthermore, in one or more embodiments of this specification, to avoid redundant computational loads caused by invalid analysis calculations, such as... Figure 3As shown, after constructing a third auxiliary variable based on the estimated weights of the neural network to be solved and the solutions of the first and second auxiliary variables, the method further includes the following steps: First, calculate the minimum eigenvalue of the third auxiliary variable. If the minimum eigenvalue is determined to be less than zero, then a perturbation signal is added during the construction of the target control function to obtain an updated target control function. If the minimum eigenvalue is determined to be greater than zero, then a finite-time adaptive law is constructed based on the third auxiliary variable and a preset learning gain.

[0132] Furthermore, in one or more embodiments of this specification, updating the Q-function neural network based on the finite-time adaptive law, and designing the optimal control of the target control function based on the updated Q-function neural network, specifically includes the following process:

[0133] Based on the effective time adaptive law, the weights of the unsolved neural network in the Q-function neural network are determined, and the current neuron of the Q-function neural network is determined according to the weights of the unsolved neural network. Then, by extracting the current neuron of the Q-function neural network and based on the relationship between the weights of the unsolved neural network and the target control function, the optimal control of the target control function is determined. That is, the optimal control of the autonomous vehicle is designed according to the obtained finite-time adaptive law as follows:

[0134]

[0135] Among them, R -1 This represents the inverse operation on the weight matrix of the transient control, and diag represents taking the diagonal matrix.

[0136] like Figure 3 The diagram shows a schematic flowchart of a trajectory tracking control algorithm for an autonomous vehicle provided in an embodiment of this specification. Based on the diagram, the following processes are included: establishing a tracking error model for the autonomous vehicle based on the kinematic equations and desired trajectory of the rear-wheel-drive autonomous vehicle; establishing a tracking target function based on the error transformation of a specified performance function; designing a Q-function and constructing the Bellman equation; and designing an online adaptive law based on neural network estimation error to realize the online update of the evaluation neural network, thereby achieving optimal tracking control for the autonomous vehicle.

[0137] based on Figure 4 and Figure 5 The diagrams illustrating the convergence of neural network weights and the vehicle trajectory show that the error between the ideal trajectory and the actual trajectory obtained by this method gradually approaches zero, indicating stable convergence of the video network weights. The diagrams comparing the tracking errors under the two controllers further illustrate this. Figure 6As can be seen, after comparing the control accuracy of the method proposed in this embodiment with that of the nominal control, it can be seen that the proposed method is closer to the reference value than other methods, that is, it has a better tracking control effect.

[0138] like Figure 7 As shown in the diagram, this specification provides a schematic diagram of the structure of a trajectory tracking control device for an autonomous vehicle. Figure 7 As can be seen, in one or more embodiments of this specification, a trajectory tracking control device for an autonomous vehicle includes:

[0139] At least one processor; and,

[0140] A memory communicatively connected to the at least one processor; wherein,

[0141] The memory stores instructions executable by the at least one processor, which, when executed by the at least one processor, enable the at least one processor to:

[0142] Establish a motion model for the autonomous vehicle, and obtain the ideal trajectory of the autonomous vehicle based on the motion model;

[0143] The driving data of the autonomous vehicle is collected to determine the actual trajectory of the autonomous vehicle, and the tracking error of the autonomous vehicle is determined based on the ideal trajectory and the actual trajectory.

[0144] The tracking error is defined by a preset decreasing function, and the tracking error is transformed based on the transformation of the definition conditions to obtain the error transformation result.

[0145] Based on the error transformation result, a Bellman function is defined to obtain the target control function corresponding to the autonomous vehicle;

[0146] The Bellman function is reconstructed by defining a Q-function neural network to obtain the reconstructed Bellman function, thereby obtaining the relationship between the weights of the neural network to be solved and the target control function.

[0147] Based on the estimation error of the weights of the neural network to be solved, a finite-time adaptive law is designed to update the Q-function neural network, and the optimal control of the target control function is designed based on the updated Q-function neural network.

[0148] like Figure 8 As shown in the figure, this specification provides a schematic diagram of the internal structure of a non-volatile storage medium, which is composed of... Figure 8 As can be seen, one or more embodiments of this specification provide a non-volatile storage medium storing computer-executable instructions, which are capable of:

[0149] Establish a motion model for the autonomous vehicle, and obtain the ideal trajectory of the autonomous vehicle based on the motion model;

[0150] The driving data of the autonomous vehicle is collected to determine the actual trajectory of the autonomous vehicle, and the tracking error of the autonomous vehicle is determined based on the ideal trajectory and the actual trajectory.

[0151] The tracking error is defined by a preset decreasing function, and the tracking error is transformed based on the transformation of the definition conditions to obtain the error transformation result.

[0152] Based on the error transformation result, a Bellman function is defined to obtain the target control function corresponding to the autonomous vehicle;

[0153] The Bellman function is reconstructed by defining a Q-function neural network to obtain the reconstructed Bellman function, thereby obtaining the relationship between the weights of the neural network to be solved and the target control function.

[0154] Based on the estimation error of the weights of the neural network to be solved, a finite-time adaptive law is designed to update the Q-function neural network, and the optimal control of the target control function is designed based on the updated Q-function neural network.

[0155] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the embodiments of apparatus, devices, and non-volatile computer storage media are basically similar to the method embodiments, so the descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0156] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0157] The above description is merely one or more embodiments of this specification and is not intended to limit this specification. Various modifications and variations can be made to the one or more embodiments of this specification by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of one or more embodiments of this specification should be included within the scope of the claims of this specification.

Claims

1. A trajectory tracking control method for an autonomous vehicle, characterized in that, The method includes: The ideal trajectory and actual trajectory of the autonomous vehicle are obtained to determine the tracking error of the autonomous vehicle; The tracking error is defined by a preset decreasing function, and the tracking error is transformed based on the transformation of the definition conditions to obtain the error transformation result. Based on the error transformation result, a Bellman function is defined to obtain the target control function corresponding to the autonomous vehicle; The Bellman function is reconstructed by defining a Q-function neural network to obtain the reconstructed Bellman function, thereby obtaining the relationship between the weights of the neural network to be solved and the target control function. Based on the estimation error of the weights of the neural network to be solved, a finite-time adaptive law is designed to update the Q-function neural network, and the optimal control of the target control function is designed based on the updated Q-function neural network.

2. The trajectory tracking control method for an autonomous vehicle according to claim 1, characterized in that, The process of obtaining the ideal trajectory and the actual trajectory of the autonomous vehicle to determine the tracking error of the autonomous vehicle specifically includes: A motion model of the autonomous vehicle is constructed based on its motion parameters; wherein, the motion model is: Where x(t) is the horizontal position of the vehicle's center of mass in the inertial reference frame, y(t) represents the vertical position of the vehicle's center of mass in the inertial reference frame, θ(t) represents the direction of the vehicle's center of mass, and v x (t) represents the longitudinal velocity of the vehicle's center of mass within the vehicle's chassis, w x (t) represents the yaw rate of the vehicle's center of mass within the chassis frame, and d r It is the direct distance from the center of gravity to the rear axle in a vehicle; Based on the fixed longitudinal speed v of the autonomous vehicle r (t) and fixed yaw rate w r (t) and the motion model, determine the ideal trajectory of the autonomous vehicle; wherein, the ideal trajectory is: Where, x r (t) is the ideal horizontal position of the vehicle's center of mass in the inertial reference frame, y r (t) is the ideal perpendicular position of the vehicle's center of mass in the inertial reference frame, θ r (t) represents the ideal direction of the vehicle's center of gravity; The driving data of the autonomous vehicle is collected to determine the actual trajectory of the autonomous vehicle, and the tracking error of the autonomous vehicle is determined based on the difference between the ideal trajectory and the actual trajectory.

3. The trajectory tracking control method for an autonomous vehicle according to claim 2, characterized in that, The tracking error of the autonomous vehicle is determined based on the difference between the ideal trajectory and the actual trajectory, specifically including: Based on the difference between the ideal trajectory and the actual trajectory, the error vector of the autonomous vehicle is determined; wherein, the error vector is... x e (t), y e (t) and θ e (t) represent the tracking errors for the horizontal position, vertical position, and vehicle direction, respectively, where A = cos(θ(t)) and B = sin(θ(t)). The error dynamics of the autonomous vehicle are determined based on the error vector and a preset nonlinear dynamic function, and the error dynamics are used as the tracking error; wherein, the tracking error is: s(x)=[x e (t),y e (t),θ e (t)] T Indicates tracking error. Let f(x) be the tracking control function for the autonomous vehicle, and g(x) be nonlinear dynamic functions.

4. The trajectory tracking control method for an autonomous vehicle according to claim 1, characterized in that, The tracking error is transformed based on the transformation of the defined conditions to obtain the error transformation result, specifically including: Define an inverse function for the transformed error corresponding to the tracking error, and define an error formula for the transformed tracking error based on the inverse function; wherein the error formula is: z represents the error transformation result, N(z) is the inverse function, and ρ(t) is the decreasing smoothing function. The inverse function formula is determined based on the properties of the inverse function, and the error formula is transformed based on the inverse function formula to obtain the error transformation result; wherein, the error transformation result... a>0 is a positive integer. This is used to represent the relationship between tracking error and a decreasing smoothing function.

5. The trajectory tracking control method for an autonomous vehicle according to claim 1, characterized in that, The step of reconstructing the Bellman function by defining a Q-function neural network to obtain the reconstructed Bellman function, and thus obtaining the relationship between the weights of the neural network to be solved and the target control function, specifically includes: Based on the preset activation function, the weights of the neural network to be solved, and the approximation error of the Q-function neural network, the definition formula of the Q-function neural network is obtained; wherein, the definition formula is: Q(z)=W T η(z)+ε(z), where η(z) is the activation function, W is the weight of the neural network to be solved, and ε(z) is the approximation error of the Q-function neural network, and the approximation error is bounded; The neurons of the Q-function neural network are constructed based on preset basis functions; wherein, the neurons of the Q-function neural network are: vec(·) is a vectorization operation, η zz η zu η uu W is a basis function. zz W zu W uu These are the weights for the neural network corresponding to different basis functions; The Bellman function is reconstructed based on the neurons of the Q-function neural network to obtain a reconstructed Bellman function, which is then used to determine the relationship between the weights of the neural network to be solved and the target control function; wherein, the reconstructed Bellman function is: k(z,u) is the integral strengthening term, Δη(t) = η(z(t)) - η(z(tT)), ε z =ε z (z(t))-ε z (z(tT)).

6. The trajectory tracking control method for an autonomous vehicle according to claim 5, characterized in that, Based on the estimation error of the weights of the neural network to be solved, a finite-time adaptive law is designed, specifically including: Define auxiliary variables; wherein, the auxiliary variables include: a first auxiliary variable and a second auxiliary variable; The solution for the first auxiliary variable and the second auxiliary variable is determined based on the preset parameters of the auxiliary variable; Based on the estimated weights of the neural network to be solved, and the solutions of the first and second auxiliary variables, a third auxiliary variable is constructed to determine the finite-time adaptive law based on the third auxiliary variable and a preset learning gain; wherein, the finite-time adaptive law is: P1 is the solution for the first auxiliary variable, Q1 is the solution for the second auxiliary variable, and Γ1>0 is the preset learning gain.

7. The trajectory tracking control method for an autonomous vehicle according to claim 6, characterized in that, After constructing a third auxiliary variable based on the estimated weights of the neural network to be solved, the solutions of the first auxiliary variable and the second auxiliary variable, the method further includes: Calculate the minimum eigenvalue of the third auxiliary variable; If the minimum eigenvalue is determined to be less than zero, a perturbation signal is added during the construction of the target control function to obtain an updated target control function. If the minimum eigenvalue is determined to be greater than zero, then the finite-time adaptive law is constructed based on the third auxiliary variable and the preset learning gain.

8. The trajectory tracking control method for an autonomous vehicle according to claim 5, characterized in that, The Q-function neural network is updated based on the finite-time adaptive law, and the optimal control of the target control function is designed based on the updated Q-function neural network, specifically including: The weights of the unsolved neural network in the Q-function neural network are determined based on the effective time adaptive law, and the current neuron of the Q-function neural network is determined based on the weights of the unsolved neural network. By extracting the current neurons of the Q-function neural network and determining the optimal control of the target control function based on the relationship between the weights of the neural network to be solved and the target control function; wherein, the optimal control is: R -1 This represents the inverse operation on the weight matrix of the transient control, and diag represents taking the diagonal matrix.

9. A trajectory tracking and control device for an autonomous vehicle, characterized in that, The device includes: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to: Establish a motion model for the autonomous vehicle, and obtain the ideal trajectory of the autonomous vehicle based on the motion model; The driving data of the autonomous vehicle is collected to determine the actual trajectory of the autonomous vehicle, and the tracking error of the autonomous vehicle is determined based on the ideal trajectory and the actual trajectory. The tracking error is defined by a preset decreasing function, and the tracking error is transformed based on the transformation of the definition conditions to obtain the error transformation result. Based on the error transformation result, a Bellman function is defined to obtain the target control function corresponding to the autonomous vehicle; The Bellman function is reconstructed by defining a Q-function neural network to obtain the reconstructed Bellman function, thereby obtaining the relationship between the weights of the neural network to be solved and the target control function. Based on the estimation error of the weights of the neural network to be solved, a finite-time adaptive law is designed to update the Q-function neural network, and the optimal control of the target control function is designed based on the updated Q-function neural network.

10. A non-volatile storage medium storing computer-executable instructions, characterized in that, The computer-executable instructions are capable of: Establish a motion model for the autonomous vehicle, and obtain the ideal trajectory of the autonomous vehicle based on the motion model; The driving data of the autonomous vehicle is collected to determine the actual trajectory of the autonomous vehicle, and the tracking error of the autonomous vehicle is determined based on the ideal trajectory and the actual trajectory. The tracking error is defined by a preset decreasing function, and the tracking error is transformed based on the transformation of the definition conditions to obtain the error transformation result. Based on the error transformation result, a Bellman function is defined to obtain the target control function corresponding to the autonomous vehicle; The Bellman function is reconstructed by defining a Q-function neural network to obtain the reconstructed Bellman function, thereby obtaining the relationship between the weights of the neural network to be solved and the target control function. Based on the estimation error of the weights of the neural network to be solved, a finite-time adaptive law is designed to update the Q-function neural network, and the optimal control of the target control function is designed based on the updated Q-function neural network.

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