A deep Gaussian vehicle dynamics model, training method, intelligent vehicle trajectory tracking control method and terminal device

Abstract

The present invention discloses a deep Gaussian vehicle dynamics model, a training method, an intelligent automobile trajectory tracking control method and a terminal device. The present invention uses a physical model to obtain the mean required in the deep Gaussian model, and uses a feedforward neural network to obtain the covariance matrix required in the deep Gaussian model. Compared with the data-driven model, the established model integrates the prior knowledge of the physical model on the basis of accurately identifying various complex dynamic behaviors during vehicle operation, thereby increasing the robustness of the model and avoiding unknown errors in the data-driven model in areas not covered by the training data. The designed trajectory tracking control algorithm has higher interpretability than the end-to-end control algorithm. In addition, the tracking control of the desired trajectory can be achieved under different road conditions and driving conditions. While ensuring the path tracking accuracy, the lateral and longitudinal stability are also taken into account, laying a good foundation for the development of high-performance motion controllers for intelligent vehicles.

Description

Technical Field

[0001] The present invention relates to the field of intelligent vehicle control, and in particular to an intelligent vehicle trajectory tracking control method and terminal equipment based on a deep Gaussian vehicle dynamics model. Background Art

[0002] With the continuous advancement of vehicle intelligence and connectivity, coupled with the rapid development of artificial intelligence (AI), smart cars have become a transformative trend in the traditional automotive industry and a research hotspot in global vehicle engineering. Smart cars promise to free people from the tedium of long-distance driving and have enormous potential to alleviate traffic congestion and accidents. Classic autonomous driving systems typically consist of perception, positioning, decision-making, trajectory planning, and control modules. Trajectory planning and control often require vehicle dynamics information to ensure safe vehicle movement. Control algorithms based on vehicle dynamics models can achieve better road utilization and increased safety, for example, enabling trajectory tracking and obstacle avoidance under varying road adhesion coefficients.

[0003] Vehicle kinematic or dynamic models based on analytical mechanics typically undergo certain simplifications during modeling. While the introduction of tire models such as magic tires and brush tires expands the model's degrees of freedom, they fail to fully capture the tire's higher-order dynamic response and relaxation effects. This makes it impossible to accurately calculate the vehicle's state at the next moment using real-time experimental data acquired during driving. While data-driven models can adapt to changes in the vehicle's external environment, they can easily overfit during training due to difficulties in acquiring training data and uneven data distribution. Furthermore, model parameters fail to correspond to real-world physical parameters, resulting in insufficient interpretability. Therefore, establishing an accurate intelligent vehicle dynamics prediction model while ensuring model interpretability and developing a trajectory tracking control algorithm based on this model are critical issues that need to be addressed. Summary of the Invention

[0004] To address these technical challenges, this paper proposes a deep Gaussian vehicle dynamics model, training method, intelligent vehicle trajectory tracking control method, and terminal device. This method primarily involves establishing the deep Gaussian model, acquiring training data using a driving simulator and the virtual simulation platform Matlab-UE4, and acquiring real-world autonomous vehicle data, training the deep Gaussian model, and designing a trajectory tracking control algorithm.

[0005] In the design of an intelligent vehicle dynamics prediction model based on a deep Gaussian process, a multi-layer feedforward neural network with delayed input receives vehicle control and state information from the current and historical moments, obtaining the covariance matrix of the state variables at the next moment. The physical model receives the current vehicle control and state information and outputs the mean value of the state variables at the next moment.

[0006] In the vehicle dynamics data acquisition module, a real-time simulation platform is established through the driving simulator and Matlab-UE4, and virtual data of normal human driving behavior is collected through the driver's manipulation.

[0007] In the real-world vehicle dynamics data acquisition module, human drivers drive smart cars under different working conditions to collect data.

[0008] During the deep Gaussian model training process, the resulting simulation dataset was divided into an 80% training set, a 10% validation set, and a 10% test set. The negative log-likelihood loss function was selected, the Adam optimizer was chosen, the batch size was set to 1000, and the learning rate was set to 0.0001. The network model was trained using the TensorFlow deep learning framework. A control algorithm was designed based on the trained deep Gaussian model. The optimal front wheel angle and torque were obtained through online rolling optimization to track the reference trajectory.

[0009] The specific contents are as follows:

[0010] A deep Gaussian vehicle dynamics model includes: a multi-layer feedforward neural network with delayed input, a nonlinear physical model, and a deep Gaussian model; the feedforward neural network receives vehicle control and state information at the current moment and historical moments to obtain a covariance matrix of state quantities at the next moment; the nonlinear physical model receives the vehicle control and state information at the current moment and outputs a mean value of state quantities at the next moment; the deep Gaussian model combines the neural network model with the vehicle dynamics physical model to predict the vehicle dynamics state at the next moment;

[0011] The structure of the feedforward neural network is as follows: the first layer is the input layer, which has 10 feature inputs, namely the yaw angular velocity r at the current moment t , lateral velocity v y,t , longitudinal velocity v x,t , front wheel turning angle δ f,t , front wheel longitudinal force F x,f,t And the yaw angular velocity r at the previous moment t-1 , lateral velocity v y,t-1 , longitudinal velocity v x,t-1 , front wheel turning angle δ f,t-1 , front wheel longitudinal force F x,f,t-1The second layer is the FC1 fully connected network layer, the hidden layer is designed to have 64 hidden units, the third layer is the activation layer, the activation function is selected as the Softplus function, the fourth layer is the FC2 fully connected network layer, the hidden layer is designed to have 64 hidden units, the fifth layer is the activation layer, the activation function is selected as the Softplus function, the sixth layer is the output layer, the design has 2 neurons, and the output is the variance σ of the yaw velocity at the next moment r,t+1 , the variance of lateral velocity The nonlinear physical model receives the current yaw rate r t , lateral velocity v y,t , longitudinal velocity v x,t , front wheel turning angle δ f,t , front wheel longitudinal force F x,f,t , the output is the mean value μ of the yaw velocity at the next moment r,t+1 , the mean lateral velocity

[0012] The nonlinear physical model includes a single track model and a tire brush model; the single track model is represented by the following differential equation:

[0013]

[0014] Where m is the vehicle mass, v x and v y are the longitudinal velocity and lateral velocity of the center of mass in the vehicle coordinate system, I z is the moment of inertia of the vehicle around the z axis, l f and l r are the distances from the vehicle's center of mass to the front and rear axles, respectively, and F xf and F xr are the resultant longitudinal forces of the tires acting on the front and rear axles, F yf and F yr are the resultant lateral forces of the tires acting on the front and rear axles of the vehicle, r is the yaw angular velocity of the vehicle, is the first-order derivative of the vehicle’s yaw velocity, is the first-order derivative of the vehicle's lateral velocity, δ f is the front wheel turning angle;

[0015] The lateral force is calculated using the brush tire model, and the tire model can be expressed by the following formula:

[0016]

[0017] Where α is the side slip angle of the tire, C α is the cornering stiffness of the tire, mμ is the friction coefficient between the tire and the ground, F z is the longitudinal force of the tire;

[0018] Front tire slip angle α f and the rear tire slip angle α r The calculation formula is:

[0019]

[0020]

[0021] Front wheel vertical force F zf and rear wheel vertical force F zr The calculation formula is:

[0022]

[0023] Where h is the height of the vehicle's center of mass, and L is the vehicle's wheelbase length.

[0024] Furthermore, the deep Gaussian model: obtains the variance required by the deep Gaussian model through a feedforward neural network, obtains the mean required by the deep Gaussian model through a vehicle dynamics physical model, models the vehicle dynamics state transition process as a deep Gaussian process, and thus establishes a deep Gaussian model N.

[0025] Furthermore, the forward calculation method of the deep Gaussian vehicle dynamics model is as follows:

[0026] x t =(r,v y ,v x ,δ f ,F xf )

[0027] h t =[x t ,x t-1 ]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] θ=(w1,b1,w2,b2,w3,b3)

[0034]

[0035]

[0036]

[0037] Among them, x t is the vehicle state and control information of a single time step, h t Contains the vehicle state and control information at the current moment and the previous moment. z1, z2 are the expressions of the network hidden layer, a1, a2 are the expressions of the activation layer Softplus function, and θ is the parameter learned by the network. w1, b1, w2, b2, w3, b3 are the weights and biases of the network middle layer. f NN is the feedforward neural network model established, f STM is the established nonlinear physical model, and N is the deep Gaussian model.

[0038] The training method for the above deep Gaussian vehicle dynamics model is as follows: the dataset is divided into an 80% training set, a 10% validation set, and a 10% test set. The loss function is the negative log-likelihood loss function, the optimizer is Adam, the batch size is set to 1000, and the learning rate is set to 0.0001. The network model is trained based on the Tensorflow learning framework. The optimization training algorithm design is as follows:

[0039]

[0040]

[0041] Where n is the number of samples in each training batch.

[0042] A trajectory tracking control method for an intelligent vehicle, including longitudinal control and lateral control;

[0043] In longitudinal control, the point mass vehicle dynamics model is adopted, which can be expressed as

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] in X k They are the longitudinal acceleration, front wheel longitudinal force, longitudinal speed, and longitudinal coordinate corresponding to the planning coordinate point calculated by the longitudinal control strategy; is the first derivative of the longitudinal coordinate; Δt is the sampling interval; k p is the proportional gain coefficient; a x,des ,v k,des are the longitudinal reference acceleration and longitudinal reference speed corresponding to the planned coordinate points; R is the tire radius; T is the torque applied to each front tire,

[0051] The longitudinal force at each moment in the optimization time domain is obtained through the above longitudinal control algorithm. N p To predict the time domain, the solved longitudinal force will be used in the lateral control algorithm, and the calculated front wheel torque T will be used for longitudinal drive;

[0052] In lateral control, the variance obtained by the deep Gaussian vehicle dynamics model is incorporated into the cost function for optimization calculation. The lateral control strategy algorithm can be expressed as follows:

[0053]

[0054] h k =[x k ,x k-1 ]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] where r k , v y,k , δ f,k , They are the yaw rate, lateral rate, front wheel angle, heading angle, first-order derivative of lateral position, first-order derivative of heading angle, and first-order derivative of lateral position of each coordinate point calculated by the lateral control strategy; is the longitudinal force corresponding to the planning reference point calculated by the longitudinal control strategy; v x,des,k is the longitudinal reference speed corresponding to the planning coordinate point;

[0061] The yaw rate r, lateral velocity v y , the longitudinal reference speed v corresponding to the planning coordinate point x,des , the longitudinal force corresponding to the planning coordinate point calculated by the longitudinal control strategy Longitudinal displacement X and lateral displacement Y, heading angle As the state variable of the system, Front wheel turning angle δ f As the control variable of the system, that is, u=[δ f ], the output of the system

[0062] Furthermore, it also includes: discretizing the lateral control strategy using the Euler formula to obtain the discrete dynamic model of the system:

[0063]

[0064] y(k)=C·S(k)

[0065] In the formula, the matrix k is the sampling time, T S is the sampling time, and T S Same as data sampling time, T S =Δt=0.02s; S(k-1) is the state of the system at the previous moment; S(k) is the state of the system at the current moment; F refers to trajectory tracking control.

[0066] Furthermore, it also includes: defining the prediction time domain of the intelligent vehicle trajectory model as p, the control time domain as c, and p≥c, the dynamics of the vehicle in the prediction time domain [p+1, k+p] can be obtained based on the current state of the vehicle and the deep Gaussian vehicle dynamics model, that is, at the time k+p, the state of the vehicle is

[0067]

[0068] At the Kth sampling moment, the optimal input sequence of the system is

[0069] U(K)=[u(k|k),u(k+1|k),…,u(k+p-1|k)] T

[0070] At the Kth sampling moment, the predicted output of the system is

[0071] Y(K)=[y(k|k),y(k+1|k),…,y(k+p|k)] T

[0072] At the Kth sampling moment, the reference input sequence of the system is

[0073] R(K)=[r ref (k|k),r ref (k+1|k),…,r ref (k+p|k)] T

[0074] At the Kth sampling moment, y(k) serves as the initial value predicted by the control system, i.e., y(k|k) = y(k). This control strategy uses a deep Gaussian vehicle dynamics model to predict the system output for a period of time in the future. The control output is obtained by solving the constrained optimal control problem. In the next cycle, the predicted output is corrected based on the system output, completing the control cycle.

[0075] Furthermore, in lateral control, the system input needs to track the desired output, that is, the system output longitudinal displacement X, lateral displacement Y and heading angle Track the desired lateral displacement X ref , longitudinal displacement Y ref and heading angle The variance calculated in the deep Gaussian vehicle dynamics model is incorporated into the constraints, and the cost function is designed as

[0076]

[0077] Where Q1, Q2, Q3, Q4, and Q5 are the weights in the optimization objective.

[0078] Furthermore, the following constraints are imposed during the process of solving the control variable front wheel angle:

[0079] u min ≤δ f ≤u max

[0080] Δu min ≤Δδ f ≤Δu max

[0081] Where u min ,u max are the minimum and maximum values ​​of the front wheel turning angle obtained during the solution process, Δu min , Δu max are the minimum and maximum rates of change of the front wheel angle obtained during the solution process.

[0082] Based on the above-mentioned deep Gaussian vehicle dynamics model and trajectory tracking control method, the present invention also proposes a vehicle terminal device, which contains program instructions of the intelligent vehicle trajectory tracking control method when executing the program.

[0083] Beneficial effects of the present invention:

[0084] 1. The present invention proposes a data acquisition method based on a driving simulator and the Matlab-UE4 real-time virtual simulation platform, which lays a data foundation for the establishment of a vehicle dynamics model and reduces the cost of data acquisition.

[0085] 2. The present invention proposes a deep Gaussian vehicle dynamics model, which uses a physical model to obtain the mean required in the deep Gaussian model, and uses a feedforward neural network to obtain the covariance matrix required in the deep Gaussian model. Compared with the data-driven model, the established model integrates the prior knowledge of the physical model on the basis of accurately identifying various complex dynamic behaviors during vehicle operation, thereby increasing the robustness of the model and avoiding unknown errors in the data-driven model in areas not covered by the training data.

[0086] 3. This invention designs a control algorithm based on the established deep Gaussian vehicle dynamics prediction model. Compared to end-to-end control algorithms, the proposed control algorithm has higher interpretability. It can also achieve desired trajectory tracking control under various road conditions and driving modes, while ensuring path tracking accuracy while also taking into account lateral and longitudinal stability. This lays a good foundation for the development of high-performance motion controllers for intelligent vehicles. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 This is a flow chart for intelligent vehicle trajectory tracking control based on a deep Gaussian vehicle dynamics model;

[0088] Figure 2 It is a nonlinear physical model integrated into the deep Gaussian vehicle dynamics model;

[0089] Figure 3 Flowchart for vehicle dynamics data collection;

[0090] Figure 4 This is the structure diagram of the deep Gaussian vehicle dynamics model;

[0091] Figure 5 Flowchart for training a deep Gaussian vehicle dynamics model;

[0092] Figure 6 Flowchart of the intelligent vehicle trajectory tracking control algorithm based on the deep Gaussian vehicle dynamics model. DETAILED DESCRIPTION

[0093] The present invention will be further described below with reference to the accompanying drawings.

[0094] Figure 1 The flowchart of the intelligent vehicle trajectory tracking control algorithm based on the deep Gaussian vehicle dynamics model includes model design and training as well as model-based trajectory tracking control, as follows:

[0095] Model Design and Training: Real-time vehicle dynamic response data is obtained using the simulation software Matlab-UE4 and real-world intelligent vehicles. A deep Gaussian vehicle dynamics model is built and trained using the model and the acquired data.

[0096] Model-based trajectory tracking: Extract the weight parameters of the trained deep Gaussian vehicle dynamics model and design a control algorithm. Through rolling optimization online solution, the optimal front wheel angle and optimal front wheel torque are obtained to achieve tracking control of the reference trajectory.

[0097] Figure 2 is the nonlinear physical model integrated into the deep Gaussian model. The nonlinear physical model of the vehicle makes the following idealized assumptions:

[0098] (1) Assuming that the vehicle is traveling on a flat road, only the lateral and longitudinal motions of the vehicle are considered, and the vertical motion of the vehicle is ignored.

[0099] (2) Assume that the vehicle's suspension system is a rigid body and ignore the movement of the suspension and its influence on the coupling relationship.

[0100] (3) Ignore the lateral and longitudinal coupling relationship of the tire.

[0101] (4) Ignore the lateral load displacement of the vehicle.

[0102] (5) The vehicle is driven by the front wheels and the friction of the rear wheels is ignored.

[0103] The nonlinear physical model mainly consists of a single track model and a tire brush model. The single track model can be expressed by the following differential equation:

[0104]

[0105] Where m is the vehicle mass, v x and v y are the longitudinal velocity and lateral velocity of the center of mass in the vehicle coordinate system, I z is the moment of inertia of the vehicle around the z axis, l f and l r are the distances from the vehicle's center of mass to the front and rear axles, respectively, and F xf and F xr are the resultant longitudinal forces of the tires acting on the front and rear axles, F yf and F yr are the resultant lateral forces of the tires acting on the front and rear axles of the vehicle, and r is the yaw angular velocity of the vehicle. is the first-order derivative of the vehicle’s yaw velocity, is the first-order derivative of the vehicle's lateral velocity, δ f is the front wheel turning angle.

[0106] The lateral force is calculated using the brush tire model. The tire model can be expressed as follows:

[0107]

[0108] Where α is the side slip angle of the tire, C α is the cornering stiffness of the tire, mμ is the friction coefficient between the tire and the ground, F z is the longitudinal force of the tire.

[0109] Front tire slip angle α f and the rear tire slip angle α r The calculation formula is:

[0110]

[0111]

[0112] Front wheel vertical force F zf and rear wheel vertical force F zr The calculation formula is:

[0113]

[0114]

[0115] Where h is the height of the vehicle's center of mass, and L is the vehicle's wheelbase length.

[0116] Figure 3 This is a flowchart for vehicle dynamics data collection. A Matlab-UE4 intelligent driving simulation platform was built based on real-world smart car parameters. An autonomous driving test map was constructed in UE4. Data based on normal human driving behavior was collected by a human driver operating a driving simulator. During the real-world smart car dynamics data acquisition process, the human driver controlled the smart car and conducted various tests on different road surfaces. Inertial sensors were used to obtain the vehicle's longitudinal velocity, lateral velocity, yaw rate, and longitudinal acceleration in real time. The steering wheel angle was obtained in real time from the steering wheel sensor and converted to the front wheel angle using the conversion relationship between the front wheel angle and the steering wheel angle. The tire force sensor was used to obtain the front wheel longitudinal force resultant in real time. The collected data was filtered using a Butterworth low-pass filter with a cutoff frequency of 6 Hz to reduce the sampling frequency and remove noise caused by high-frequency vibrations of the suspension.

[0117] Figure 4 The structure of the deep Gaussian vehicle dynamics model is shown in Figure 2. First, a multi-layer feedforward neural network with delayed input is used to receive vehicle control and state information at the current and historical moments, and obtain the covariance matrix of the state quantity at the next moment. The specific structure of the feedforward neural network is as follows: the first layer is the input layer, which has 10 feature inputs, namely the current yaw angular velocity r t , lateral velocity v y，t , longitudinal velocity v x,t , front wheel turning angle δ f,t, front wheel longitudinal force F x,f,t And the yaw angular velocity r at the previous moment t-1 , lateral velocity v y,t-1 , longitudinal velocity v x,t-1 , front wheel turning angle δ f,t-1 , front wheel longitudinal force F x,f,t-1 The second layer is the FC1 fully connected network layer, and the hidden layer is designed to have 64 hidden units. The third layer is the activation layer, and the activation function is the Softplus function. The fourth layer is the FC2 fully connected network layer, and the hidden layer is designed to have 64 hidden units. The fifth layer is the activation layer, and the activation function is the Softplus function. The sixth layer is the output layer, which is designed to have 2 neurons, and the output is the variance σ of the yaw velocity at the next moment. r,t+1 , the variance of lateral velocity The nonlinear physical model receives the current yaw rate r t , lateral velocity v y,t , longitudinal velocity v x,t , front wheel turning angle δ f,t , front wheel longitudinal force F x,f,t , the output is the mean value μ of the yaw velocity at the next moment r,t+1 , the mean lateral velocity

[0118] The forward calculation method of the designed deep Gaussian vehicle dynamics model is as follows:

[0119] x t =(r,v y ,v x ,δ f ,F xf )

[0120] h t =[x t ,x t-1 ]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126] θ=(w1,b1,w2,b2,w3,b3)

[0127]

[0128]

[0129]

[0130] Among them, x t is the vehicle state and control information of a single time step, h t Contains the vehicle state and control information at the current moment and the previous moment. z1, z2, z3 are the expressions of the network hidden layer, a1, a2 are the expressions of the activation layer Softplus function, and θ is the parameter learned by the network. w1, b1, w2, b2, w3, b3 are the weights and biases of the network middle layer. f NN is the feedforward neural network model established, f STM The nonlinear physical model is established. The variance required by the deep Gaussian model is obtained through a feedforward neural network, and the mean required by the deep Gaussian model is obtained through the vehicle dynamics physical model. The vehicle dynamics state transition process is modeled as a deep Gaussian process, thus establishing the deep Gaussian model N.

[0131] Figure 5 This is a flowchart for training a deep Gaussian vehicle dynamics model. The resulting virtual and real datasets were divided into 80% training, 10% validation, and 10% test sets. The negative log-likelihood loss function was selected, the Adam optimizer was chosen, the batch size was set to 1000, and the learning rate was set to 0.0001. The network model was trained using the TensorFlow learning framework. The optimized training algorithm is shown below:

[0132]

[0133]

[0134] Where n is the number of samples in each training batch.

[0135] Figure 6 This is a flow chart of the intelligent vehicle trajectory tracking control algorithm based on the deep Gaussian vehicle dynamics model, which is divided into two parts: longitudinal control and lateral control.

[0136] Longitudinal control uses a point mass vehicle dynamics model, which ignores the vehicle's size information and the load transfer caused by lateral and longitudinal acceleration. The specific control strategy can be expressed as

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143] in X k They are the longitudinal acceleration, front wheel longitudinal force, longitudinal speed, and longitudinal coordinate corresponding to the planning coordinate point calculated by the longitudinal control strategy; is the first derivative of the longitudinal coordinate; Δt is the sampling interval 0.02s; k p is the proportional gain coefficient; a x,des ,v k,des are the longitudinal reference acceleration and longitudinal reference speed corresponding to the planning coordinate point; R is the tire radius; T is the torque applied to each front tire. The longitudinal force at each moment in the optimization time domain is obtained through the above longitudinal control algorithm. N p The calculated longitudinal force will be used in the lateral control algorithm, and the calculated front wheel torque T will be used for longitudinal drive.

[0144] In lateral control, the variance obtained by the deep Gaussian vehicle dynamics model will be incorporated into the cost function for optimization calculation. The lateral control strategy algorithm can be expressed as follows

[0145]

[0146] h k =[x k ,x k-1 ]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152] where r k , v y,k , δ f,k , They are the yaw rate, lateral rate, front wheel angle, heading angle, first-order derivative of lateral position, first-order derivative of heading angle, and first-order derivative of lateral position of each coordinate point calculated by the lateral control strategy; is the longitudinal force corresponding to the planning reference point calculated by the longitudinal control strategy; v x,des,k is the longitudinal reference speed corresponding to the planning coordinate point.

[0153] The yaw rate r, lateral velocity v y , the longitudinal reference speed v corresponding to the planning coordinate point x,des , the longitudinal force corresponding to the planning coordinate point calculated by the longitudinal control strategy Longitudinal displacement X and lateral displacement Y, heading angle As the state variable of the system, Front wheel turning angle δ f As the control variable of the system, that is, u=[δ f ], the output of the system

[0154] The described lateral control strategy is discretized using the Euler formula to obtain the discrete dynamic model of the system:

[0155]

[0156] y(k)=C·S(k)

[0157] In the formula, the matrix k is the sampling time, T S is the sampling time, and T S Same as data sampling time, T S =Δt=0.02s; S(k-1) is the state of the system at the previous moment; S(k) is the state of the system at the current moment; F is the proposed control strategy.

[0158] In this invention, the prediction time domain of the intelligent vehicle trajectory model is defined as p, the control time domain is defined as c, and p≥c. The dynamics of the vehicle in the prediction time domain [k+1, k+p] can be obtained based on the current state of the vehicle and the deep Gaussian vehicle dynamics model. That is, at the time k+p, the state of the vehicle is

[0159]

[0160] Therefore, at the Kth sampling moment, the optimal input sequence of the system is

[0161] U(K)=[u(k|k),u(k+1|k),…,u(k+p-1|k)] T

[0162] At the Kth sampling moment, the predicted output of the system is

[0163] Y(K)=[y(k|k),y(k+1|k),…,y(k+p|k)] T

[0164] At the Kth sampling moment, the reference input sequence of the system is

[0165] R(K)=[r ref (k|k),r ref (k+1|k),…,r ref (k+p|k)] T

[0166] At the Kth sampling moment, y(k) serves as the initial value predicted by the control system, i.e., y(k|k) = y(k). This control strategy uses a deep Gaussian vehicle dynamics model to predict the system output for a period of time in the future. The control output is obtained by solving the constrained optimal control problem. In the next cycle, the predicted output is corrected based on the system output, completing the control cycle.

[0167] In the process of lateral control algorithm design, in order to maintain good trajectory tracking performance of the intelligent vehicle, it is necessary to make the system input track the desired output, that is, the system output longitudinal displacement X, lateral displacement Y and heading angle Track the desired lateral displacement X ref , longitudinal displacement Y ref and heading angle The variance calculated in the deep Gaussian vehicle dynamics model is incorporated into the constraints, and the cost function is designed as

[0168]

[0169] Where Q1, Q2, Q3, Q4, and Q5 are the weights in the optimization objective.

[0170] In addition, the constraints on the control quantity should be considered in the solution process.

[0171] u min ≤δ f ≤u max

[0172] Δu min ≤Δδ f ≤Δu max

[0173] Where u min ,u max are the minimum and maximum values ​​of the front wheel turning angle obtained during the solution process. min , Δu max are the minimum and maximum rates of change of the front wheel angle obtained during the solution process.

[0174] In this way, the required constrained optimization problem is established. A simulation model is built through Matlab / Simulink, and the open source nonlinear optimization software package Yamlip is used to solve the optimization equation online to obtain the control variable.

[0175] The series of detailed descriptions listed above are only specific descriptions of feasible implementation methods of the present invention. They are not intended to limit the scope of protection of the present invention. Any equivalent methods or changes that do not deviate from the technology of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for training a deep Gaussian vehicle dynamics model, the deep Gaussian vehicle dynamics model comprising: Multilayer feedforward neural networks with delayed input, nonlinear physical models, and deep Gaussian models; The feedforward neural network receives vehicle control and state information at the current moment and historical moments, and obtains a covariance matrix of state quantities at the next moment. The nonlinear physical model receives the vehicle control and state information at the current moment and outputs a mean value of the state quantities at the next moment. The deep Gaussian model combines a neural network model with a vehicle dynamics physical model to predict the vehicle dynamics state at the next moment. The structure of the feedforward neural network is as follows: the first layer is the input layer, which has 10 feature inputs, namely the yaw angular velocity r at the current moment t , lateral velocity v y,t , longitudinal velocity v x,t , front wheel turning angle δ f,t , front wheel longitudinal force F x,f,t And the yaw angular velocity r at the previous moment t-1 , lateral velocity v y,t-1 , longitudinal velocity v x,t-1 , front wheel turning angle δ f,t-1 , front wheel longitudinal force F x,f,t-1 The second layer is the FC1 fully connected network layer, the hidden layer is designed to have 64 hidden units, the third layer is the activation layer, the activation function is selected as the Softplus function, the fourth layer is the FC2 fully connected network layer, the hidden layer is designed to have 64 hidden units, the fifth layer is the activation layer, the activation function is selected as the Softplus function, the sixth layer is the output layer, the design has 2 neurons, and the output is the variance σ of the yaw velocity at the next moment r,t+1 , the variance of the lateral velocity The nonlinear physical model receives the current yaw rate r t , lateral velocity v y,t , longitudinal velocity v x,t , front wheel turning angle δ f,t , front wheel longitudinal force F x,f,t , the output is the mean value μ of the yaw velocity at the next moment r,t+1 , the mean lateral velocity The nonlinear physical model includes a single track model and a tire brush model; the single track model is represented by the following differential equation: Where m is the vehicle mass, v x and v y are the longitudinal velocity and lateral velocity of the center of mass in the vehicle coordinate system, I z is the moment of inertia of the vehicle around the z axis, l f and l r are the distances from the vehicle's center of mass to the front and rear axles, respectively, and F xf and F xr are the resultant longitudinal forces of the tires acting on the front and rear axles, F yf and F yr are the resultant lateral forces of the tires acting on the front and rear axles of the vehicle, r is the yaw angular velocity of the vehicle, is the first-order derivative of the vehicle’s yaw velocity, is the first-order derivative of the vehicle's lateral velocity, δ f is the front wheel turning angle; The lateral force is calculated using the brush tire model, and the tire model can be expressed by the following formula: Where α is the side slip angle of the tire, C α is the tire's cornering stiffness, μ is the friction coefficient between the tire and the ground, F z is the longitudinal force of the tire; Front tire slip angle α f and the rear tire slip angle α r The calculation formula is: Front wheel vertical force F zf and rear wheel vertical force F zr The calculation formula is: Where h is the height of the vehicle's center of mass, and L is the vehicle's wheelbase length. The dataset is divided into 80% training set, 10% validation set, and 10% test set. The loss function is the negative log-likelihood loss function. The optimizer is Adam, the batch size is set to 1000, and the learning rate is set to 0.0001. The network model is trained based on the Tensorflow learning framework. The optimization training algorithm is designed as follows: Where n is the number of samples in each training batch; h t Contains the vehicle status and control information at the current moment and the previous moment; θ is the parameter learned by the network, θ = (w1, b1, w2, b2, w3, b3), w1, b1, w2, b2, w3, b3 are the weights and biases of the middle layer of the network.

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