CN114379583A - Automatic driving vehicle trajectory tracking system and method based on neural network dynamics model - Google Patents
Automatic driving vehicle trajectory tracking system and method based on neural network dynamics model Download PDFInfo
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Abstract
The invention discloses an automatic driving vehicle track tracking system and method based on a neural network dynamic model, which comprises a neural network vehicle dynamic model part, a vehicle dynamic data acquisition part (comprising a driving simulator and a virtual simulation platform CarSim simulation data acquisition process, real world automatic driving vehicle data acquisition), a training part of the neural network model and a model prediction control algorithm design, wherein the neural network vehicle dynamic model part comprises a neural network vehicle dynamic model part, a vehicle dynamic data acquisition part and a simulation control algorithm design part; by combining the established neural network vehicle dynamics prediction model with the model predictive control algorithm, compared with an end-to-end control algorithm, the control algorithm provided by the invention has higher interpretability. And the tracking control of the expected track can be realized under different road conditions and running conditions, the path tracking precision is ensured, the transverse and longitudinal stability is considered simultaneously, and the method lays a foundation for developing a high-performance motion controller for an automatic driving vehicle.
Description
Technical Field
The invention relates to the technical field of automatic driving of intelligent vehicles, in particular to an automatic driving vehicle track tracking system and method based on a neural network dynamic model.
Background
With the continuous upgrading of the 'new and quadruple' of automobiles and the rapid development of artificial intelligence technology, the automatic driving vehicle becomes the trend of the traditional automobile industry revolution and the research hotspot of the world vehicle engineering. Autonomous vehicles are expected to free people from cumbersome long distance driving, and have great potential in reducing traffic congestion and reducing traffic accidents. Autonomous vehicles are generally composed of environment-aware, path planning, and control execution systems, where the construction of vehicle models is critical to trajectory planning and control, which is the basis for high-safety and high-reliability trajectory tracking control.
Currently, trajectory tracking control of an autonomous vehicle is mainly divided into control methods based on a vehicle kinematic model and control methods based on a vehicle dynamic model. The controller designed based on the vehicle kinematic model can ensure certain control performance under the working conditions of low speed and small curvature. However, when the vehicle body speed is high and the road curvature is large, the dynamic characteristics of the vehicle itself are not considered, resulting in a decrease in the control performance and a deterioration in the running quality. The controller designed based on the vehicle dynamics model cannot sufficiently consider the vertical motion of the vehicle when the vehicle is running at a high speed, the suspension motion characteristics, and the longitudinal-lateral coupling relationship of the force of the tire due to the simplification of the vehicle model. Such models are mostly built based on differential equations, and since the real-world vehicle has high degrees of freedom, the models are usually simplified into two-degree-of-freedom or three-degree-of-freedom vehicle dynamics models. Although this approach reduces computational complexity, the vehicle dynamics model employed generally does not adequately account for vertical vehicle motion at high vehicle speeds, suspension motion characteristics, and tire force longitudinal-lateral coupling relationships. Therefore, when the vehicle runs at a high speed, a large track tracking error is generated, and the actual requirement of high-level automatic driving of the intelligent vehicle cannot be met.
Disclosure of Invention
In order to solve the technical problems, the invention provides an automatic driving vehicle track tracking system based on a neural network vehicle dynamic model, which mainly comprises a neural network vehicle dynamic model part, a vehicle dynamic data acquisition part (comprising a driving simulator and a virtual simulation platform CarSim simulation data acquisition process, and real world automatic driving vehicle data acquisition), a training part of the neural network model and model prediction control algorithm design.
The neural network vehicle dynamics model part designs a neural network model with delay input by using a feedforward neural network, a hidden layer of the model is two layers, each layer is provided with 100 neurons, an activation layer selects a Softplus activation function, and the input of the model adopts vehicle control and state information at two moments so as to predict the first derivative of the yaw rate and the lateral speed of the vehicle.
And the vehicle dynamics data acquisition part establishes a real-time virtual simulation platform through the driving simulator and the CarSim, selects the automatic driving test map Mcity and acquires data based on the normal driving behaviors of human beings. Since the road curvature of the vehicle has a great influence on the handling performance of the vehicle, in order to collect complete data, the vehicle is driven to run on different roads including a straight road, a curved road and the like, and single lane change and double lane change are performed.
In the real world vehicle data acquisition process, the automatic driving vehicle is controlled by a human driver to perform linear motion, curvilinear motion, single lane change, double lane change and the like.
Based on a feedforward neural network vehicle dynamics prediction model training part, an obtained virtual experiment platform simulation data set and real vehicle data of the real world are combined and divided into an 80% training set, a 10% verification set and a 10% testing set. The penalty function is chosen as the MSE penalty function, the optimizer is chosen as Adam, the batch size is set to 1000, and the learning rate is set to 0.0003. And training the network model based on the Pythrch deep learning framework.
And designing a model predictive control algorithm part based on the trained neural network vehicle dynamics model, and solving on line through rolling optimization to obtain the optimal front wheel corner so as to realize the tracking of the reference track.
Based on the tracking system, the invention also provides an automatic driving vehicle track tracking method based on the neural network vehicle dynamics model, which comprises the following steps:
s1: establishing a neural network vehicle dynamics model; the method comprises the following steps:
s1.1, firstly, establishing a nonlinear single-track model of the vehicle; specifically, the method comprises the following steps:
the vehicle is turned by the front wheel, a vehicle body coordinate system is located in a vehicle bilateral symmetry plane, the origin of the vehicle mass center is o, the x axis is the vehicle longitudinal axis, the y axis is the vehicle lateral direction, the z axis meets the right hand rule and is perpendicular to the oxy direction, a stress balance equation of the vehicle around the y axis and the z axis is obtained according to the Newton's law, and the nonlinear vehicle dynamic model can be expressed by the following differential equation:
where m is the vehicle mass, vxAnd vyRespectively the longitudinal acceleration and the lateral acceleration of the mass center under the vehicle body coordinate system, IzIs the moment of inertia of the vehicle about the z-axis,/fAnd lrDistances from the center of mass of the vehicle to the front axle and the rear axle, respectively, FxfAnd FxrThe resultant of the longitudinal forces of the tire acting on the front axle and the rear axle, respectively, FyfAnd FyrThe resultant of the lateral forces of the tires acting on the front and rear axles of the vehicle, r is the yaw rate of the vehicle,
is the first derivative of the yaw rate of the vehicle,
as the first derivative of the lateral speed of the vehicle, deltafIs a front wheel corner;
the non-linear characteristics generated during the running of the vehicle under different road conditions are caused by the tires during the turning, so that the Fiala model of the tires is introduced, and the lateral force F of the tiresyThe calculation formula of (2) is as follows:
wherein α is the slip angle of the tire, CαFor the cornering stiffness of the tyre, u is the coefficient of friction between the tyre and the ground, FzThe resultant force of the vertical forces of the tires;
Fzf、Fzrrespectively neglecting the vertical load of the front wheel and the vertical load of the rear wheel under the condition of transverse load displacement and longitudinal load displacement;
s1.2: determining the inputs of a feedforward neural network model based on the nonlinear single-track model of the vehicle as the yaw rate r and the lateral speed v of the vehicleyLongitudinal velocity vxFront wheel corner deltafThe output of the model being the first derivative of the yaw rate
First derivative of longitudinal velocity
The neural network vehicle dynamics model specifically adopts the following structure: the first layer is an input layer, and the input layer has 8 characteristic inputs, namely the yaw rate r at the current momenttLateral velocity vy,tLongitudinal velocity vx,tFront wheel corner deltaf,tAnd yaw rate r at the previous timet-1Lateral velocity vy,t-1Longitudinal velocity vx,t-1Front wheel corner deltaf,t-1(ii) a The second layer is an FC1 full-connection network layer, and the hidden layer is designed to have 100 hidden units; the third layer is an activation layer, and the activation function is selected as a Softplus function; the fourth layer is an FC2 full-connection network layer, and the hidden layer is designed to have 100 hidden units; the fifth layer is an activation layer, and the activation function is selected to be a Softplus function; the sixth layer is an output layer which is designed to have 2 neurons, and the output is the first derivative of the yaw rate at the current moment
First derivative of vehicle lateral velocity
The forward calculation method of the designed neural network vehicle dynamics model is as follows:
xt＝(r,vy,vx,δf)
ht＝[xt,xt-1]
θ＝(w1,b1,w2,b2,w3,b3)
wherein x istVehicle state information for a single time step, htContaining the current and last time vehicle status information, a1,a2Theta is a parameter learned by the network and w is an activation layer Softplus function expression1,b1,w2,b2,w3,b3For weights and offsets of intermediate layers of the network, z1For the output of the first hidden layer of the network, z2Hiding the output of the layer for the second layer of the network.
And
is defined as:
and
the Δ t is 0.03s, which is the sampling frequency of the data;
s2, acquiring vehicle dynamics data, including simulation data acquisition based on a driving simulator and a virtual simulation platform CarSim and real world automatic driving vehicle data acquisition;
establishing a real-time virtual simulation platform through a driving simulator and CarSim, selecting an automatic driving test map Mcity, collecting data based on normal driving behaviors of human beings, and driving vehicles to run on different roads including straight roads, curved roads and the like for collecting complete data and carrying out single-lane transformation and double-lane transformation; in real world vehicle data acquisition, an automatic driving vehicle is controlled by a human driver to perform linear motion, curvilinear motion, single lane transformation and double lane transformation;
s3, training a neural network vehicle dynamics model;
combining the obtained virtual simulation platform data set with real vehicle data of the real world, dividing the combined virtual simulation platform data set into an 80% training set, a 10% verification set and a 10% testing set, setting a loss function as an MSE (mean square error) loss function, setting an optimizer as Adam, setting a batch size as 1000, setting a learning rate as 0.0003, and training a network model based on a Pythrch deep learning framework;
the MSE loss function is specifically designed as follows:
in the formula r, vyRespectively the measured yaw rate and lateral speed of the vehicle,
first derivatives of vehicle yaw rate and lateral velocity predicted by the neural network vehicle dynamics model, Δ t being the sampling time, N being the number of samples, first derivatives of vehicle yaw rate and lateral velocity predicted by the neural network vehicle dynamics model
Yaw-rate and lateral-rate measurements r, v obtained by the CarSim softwareyPerforming Euler integration to obtain the predicted values of the yaw rate and the lateral rate at the next moment
htThe vehicle state information of the current moment and the last moment is contained, and theta is a parameter learned by the network;
s4, designing a model predictive control algorithm; and obtaining the optimal front wheel rotation angle through rolling optimization on-line solving, and realizing the tracking of the reference track.
Further, the model predictive control algorithm is specifically designed as follows:
based on the neural network vehicle dynamics model, establishing an automatic driving vehicle path tracking system model as
xt＝(r,vy,vx,δf)
ht＝[xt,xt-1]
In the formula, xtVehicle state information for a single time step, htContaining the current and last vehicle status information, fNNFor the neural network vehicle dynamics model that is built,
is the heading angle, v, of the vehiclexAnd vyRespectively the longitudinal acceleration and the lateral acceleration of the mass center under a vehicle body coordinate system, r is the yaw velocity of the vehicle, deltafIs the turning angle of the front wheel,
is the first derivative of the yaw rate of the vehicle,
is the first derivative of the lateral speed of the vehicle,
is the first derivative of the heading angle of the vehicle,
and
first derivatives of the longitudinal and lateral vehicle displacements, respectively;
the yaw angular velocity r and the lateral velocity vyLongitudinal velocity vxLongitudinal displacement X and lateral displacement Y course angle
As state variables of the system, i.e.
Front wheel corner deltafAs a control variable of the system, i.e. u ═ δf]Input of the system
Discretizing the described automatic driving vehicle track model by using an Euler formula to obtain a discrete dynamic model of the system
y(k)＝C·S(k)
In the form of matrix
Is the sampling time, TSIs a sampling time, and TSSame as the virtual data sampling time, TS0.03S for t, S (k-1) is the last time state of the system, S (k) is the current time state of the system, F is the established trajectory tracking system model, F is the current time state of the system, F is the current time of the system, F is the current time of the system, F is the current time of the system, F is the current time of the current time, F is longer than F, F is the current time is longer than the current time is longer, F is longer than the current time, the current time is longer, F is longer, F is the system is longer, F is the system is the current time is the same as the current time is longer, F is the current time, F is the system is the same as the sameNNFor the established neural network vehicle dynamics model, r (k), vy(k),vx(k),δf(k) Respectively yaw rate, lateral rate, longitudinal rate, front wheel angle, r (k-1), v, of the vehicle at the current sampling time ky(k-1),vx(k-1),δf(k-1) yaw rate, lateral rate, longitudinal rate, front wheel angle,
respectively a first derivative of the longitudinal position, a first derivative of the transverse position and a first derivative of the course angle of the vehicle at the moment k;
defining the prediction time domain of an automatic driving vehicle track model as p, the control time domain as c, wherein p is more than or equal to c, and the vehicle is in [ k +1, k + p ]]The dynamics in the prediction time domain can be obtained based on the current state of the vehicle, the state at the last moment and the prediction model, namely at the moment of k + p, the state of the vehicle is
At the kth sampling instant, the optimal input sequence of the system is obtained as
U(K)＝[u(k|k),u(k+1|k),…,u(k+p-1|k)]T
At the kth sampling instant, the predicted output of the system is
Y(K)＝[y(k|k),y(k+1|k),…,y(k+p|k)]T
At the k-th sampling moment, the reference input sequence of the system is
R(K)＝[rref(k|k),rref(k+1|k),…,rref(k+p|k)]T
At the kth sampling moment, y (k) is used as an initial value predicted by a control system, namely y (k | k) ═ y (k), the controller predicts the output of the system in a future period of time through a prediction model, designs the optimal performance index expected to be reached by the controller, obtains the control output by solving the optimal control problem with constraint, corrects the predicted output according to the output of the system in the next period, and completes the control period;
in the design process of the model predictive control algorithm, the trackability and the comfort of the vehicle are considered, and in order to keep good track tracking of the automatic driving vehicle, the expected output on the input tracking of the system, namely the output longitudinal displacement X, the lateral displacement Y and the course angle of the system, is required to be enabled
Tracking the desired lateral displacement XrefLongitudinal displacement YrefAnd course angle
The control targets are:
in the formula Q1,Q2,Q3To optimize the weights in the target, Q is increased1,Q2The path tracking performance can be improved;
in order to reduce the rate of change of the control action to ensure the comfort of the passengers, the control targets are:
wherein M is the weight of the optimization target, and the weight coefficient can be adjusted according to the requirement;
obtaining a total optimization objective function:
in addition, constraint conditions for control quantity should be considered in MPC solving process
umin≤δf≤umax
Δumin≤Δδf≤Δumax
In the formula umin，umaxRespectively the minimum value and the maximum value of the front wheel rotation angle, delta u, obtained in the MPC solution processmin，ΔumaxRespectively obtaining the minimum change rate and the maximum change rate of the front wheel rotation angle obtained in the MPC solving process;
for the control stability of the vehicle body, a constraint condition is applied to the first derivative of the yaw rate
In the formula
First derivative of yaw rate, mu friction coefficient of road, g acceleration of gravity, vxIs the longitudinal velocity.
The invention has the beneficial effects that:
1. the invention provides a data acquisition method based on a driving simulator and a CarSim real-time virtual simulation platform, and lays a data foundation for building a vehicle dynamics model. Data of real-time response of vehicle dynamics are obtained by the driver using a driving simulator to maneuver the vehicle in the high fidelity vehicle dynamics software CarSim. And the freedom degree selection range of the vehicle dynamics simulation data is wide, and the data acquisition cost is reduced.
2. The invention provides a neural network vehicle dynamics prediction model designed based on a feedforward neural network, which consists of four simple layers of feedforward neural networks, reduces the calculation cost compared with a deep neural network, can accurately identify various complex dynamics behaviors in the vehicle running process, and can learn unmodeled vehicle dynamic responses, such as vertical motion of a vehicle in high-speed running, suspension motion characteristics and the longitudinal and transverse coupling relation of the force of a tire.
3. By combining the established neural network vehicle dynamics prediction model with the model predictive control algorithm, compared with an end-to-end control algorithm, the control algorithm provided by the invention has higher interpretability. And the tracking control of the expected track can be realized under different road conditions and running conditions, the path tracking precision is ensured, the transverse and longitudinal stability is considered simultaneously, and the method lays a foundation for developing a high-performance motion controller for an automatic driving vehicle.
Drawings
FIG. 1 is a flow chart of autonomous vehicle trajectory tracking based on a neural network vehicle dynamics model;
FIG. 2 is a non-linear single-track model of an autonomous vehicle;
FIG. 3 is a vehicle dynamics prediction model based on a feed-forward neural network;
FIG. 4 is a vehicle dynamics data acquisition module;
FIG. 5 is a diagram of a vehicle dynamics prediction model training architecture based on a feedforward feedback neural network;
FIG. 6 is a flow chart of an autonomous vehicle trajectory tracking control algorithm based on neural network vehicle dynamics model predictive control.
Detailed Description
The invention will be further explained with reference to the drawings.
Fig. 1 is a flowchart of an intelligent vehicle trajectory tracking algorithm based on neural network vehicle dynamics model predictive control, including model training and trajectory tracking based on model predictive control, as follows:
model training: the data acquisition process of the driving simulator and the CarSim simulation platform and the real vehicle data acquisition process are adopted. And designing a vehicle dynamics prediction model based on the feedforward neural network and training the model by using the acquired data.
Trajectory tracking based on model predictive control: and designing a model predictive control algorithm by using the trained neural network vehicle dynamics model, and solving on line through rolling optimization to obtain the optimal front wheel corner so as to realize the tracking control of the reference track.
FIG. 2 is a non-linear single-track model of a vehicle. The vehicle nonlinear single-track model makes the following idealized assumptions:
(1) assuming that the vehicle is traveling on a flat road surface, only the lateral and longitudinal movements of the vehicle are considered, and the vertical movements of the vehicle are ignored.
(2) Assuming that the suspension system of the vehicle is a rigid body, the motion of the suspension and its effect on the coupling relationship are ignored.
(3) The coupling relationship of the lateral and longitudinal tire forces of the vehicle is ignored.
(4) The lateral load displacement and the longitudinal load displacement of the vehicle are ignored.
(5) Neglecting the effect of the track width on the turning radius, a bicycle model is used to describe the motion of the vehicle.
(6) The influence of the air resistance on the yaw characteristic of the vehicle is not considered.
Based on the above assumptions, the vehicle has motion only in the x-o-y plane. The vehicle is turned by the front wheel, a coordinate system of the vehicle body is positioned in a bilateral symmetry plane of the vehicle, the origin of the center of mass of the vehicle is o, the x axis is the longitudinal axis of the vehicle, the y axis is the lateral direction of the vehicle, and the z axis meets the right-hand rule and is vertical to the oxy direction. According to Newton's law, a stress balance equation of the vehicle on the y axis and around the z axis is obtained. The nonlinear vehicle dynamics model can be expressed as the following differential equation:
where m is the vehicle mass, vxAnd vyRespectively the longitudinal acceleration and the lateral acceleration of the mass center under the vehicle body coordinate system, IzIs the moment of inertia of the vehicle about the z-axis,/fAnd lrDistances from the center of mass of the vehicle to the front axle and the rear axle, respectively, FxfAnd FxrThe resultant of the longitudinal forces of the tire acting on the front axle and the rear axle, respectively, FyfAnd FyrWheels acting on the front and rear axles of the vehicle, respectivelyThe resultant of the lateral forces of the tires, r is the yaw rate of the vehicle,
is the first derivative of the yaw rate of the vehicle,
as the first derivative of the lateral speed of the vehicle, deltafIs the corner of the front wheel.
The non-linear characteristics generated during the running of the vehicle under different road conditions are caused by the tires during the turning, so that the Fiala model of the tires is introduced, and the lateral force F of the tiresyThe calculation formula of (2) is as follows:
wherein α is the slip angle of the tire, CαFor the cornering stiffness of the tyre, u is the coefficient of friction between the tyre and the ground, FzThe resultant force of the vertical forces of the tires is obtained.
Fzf、FzrThe vertical load of the front wheel and the vertical load of the rear wheel are respectively under the condition that the transverse load displacement and the longitudinal load displacement of the vehicle are ignored.
Determining the inputs of a feedforward neural network model based on the nonlinear single-track model of the vehicle as the yaw rate r and the lateral speed v of the vehicleyLongitudinal velocity vxFront wheel corner deltafThe output of the model being the first derivative of the yaw rate
First derivative of longitudinal velocity
FIG. 3 is a vehicle dynamics prediction model of a basis feedforward neural network. A neural network vehicle dynamics model with time delay input is designed by utilizing a feedforward neural network, and compared with the traditional nonlinear single-rail mode, the model can learn unmodeled vehicle dynamics changes, such as vertical motion of a vehicle, suspension motion characteristics and longitudinal-transverse coupling relation of tire force when the vehicle runs at a high speed.
The neural network vehicle dynamics model specifically adopts the following structure: the first layer is an input layer, and the input layer has 8 characteristic inputs, namely the yaw rate r at the current momenttLateral velocity vy,tLongitudinal velocity vx,tFront wheel corner deltaf,tAnd yaw rate r at the previous timet-1Lateral velocity vy,t-1Longitudinal velocity vx,t-1Front wheel corner deltaf,t-1. The second layer is FC1 full connection network layer, and the hidden layer design has 100 hidden units. The third layer is an activation layer, and the activation function is selected to be a Softplus function. The fourth layer is FC2 full connection network layer, and the hidden layer design has 100 hidden units. The fifth layer is an activation layer, and the activation function is selected to be a Softplus function. The sixth layer is an output layer which is designed to have 2 neurons, and the output is the first derivative of the yaw rate at the current moment
First derivative of vehicle lateral velocity
The forward calculation method of the designed neural network vehicle dynamics model is as follows:
xt＝(r,vy,vx,δf)
ht＝[xt,xt-1]
θ＝(w1,b1,w2,b2,w3,b3)
wherein x istVehicle state information for a single time step, htIncluding the vehicle status information at the current time and the previous time. a is1,α2And theta is a parameter learned by the network for activating the layer Softplus function expression. w is a1,b1,w2,b2,w3,b3For weights and offsets of intermediate layers of the network, z1For the output of the first hidden layer of the network, z2Hiding the output of the layer for the second layer of the network.
And
is defined as:
and
data acquisition with Δ t of 0.03sThe sample frequency.
FIG. 4 is a vehicle dynamics data acquisition module. Vehicle parameters in vehicle dynamics simulation software CarSim are modified according to vehicle parameters of an automatically driven vehicle in the real world. A real-time simulation platform is established by the driving simulator and the CarSim, an automatic driving test map Mcity is selected, and data based on the normal driving habits of human beings are collected. Since the road curvature of the vehicle has a great influence on the handling performance of the vehicle, in order to collect complete data, the vehicle is driven to run on different roads including a straight road, a curved road and the like, and single lane change and double lane change are performed.
In the real world vehicle data acquisition process, a human driver is used to control the autonomous vehicle to perform linear motion, curvilinear motion, single lane change, double lane change and the like.
FIG. 5 is a block diagram of a vehicle dynamics prediction model training based on a feed-forward neural network. The method comprises the steps of training vehicle dynamics simulation data and real vehicle data which are acquired by using CarSim software and are based on human normal driving behaviors, and dividing an obtained data set into an 80% training set, a 10% verification set and a 10% testing set. The loss function is selected as an MSE loss function, the optimizer is selected as Adam, the batch size is set to be 1000, the learning rate is set to be 0.0003, the network model is trained based on a Pythroch deep learning framework, and the loss function of the model is as follows:
in the formula r, vyRespectively the measured yaw rate and lateral speed of the vehicle,
and the first derivatives of the yaw rate and the lateral speed of the vehicle predicted by the neural network vehicle dynamic model, wherein delta t is sampling time, and N is the number of samples. First derivatives of vehicle yaw rate and lateral speed predicted using neural network vehicle dynamics models
Yaw-rate and lateral-rate measurements r, v obtained by the CarSim softwareyPerforming Euler integration to obtain the predicted values of the yaw rate and the lateral rate at the next moment
htThe vehicle state information at the current time and the last time is included, and theta is a parameter learned by the network.
FIG. 6 is a flow chart of an autonomous vehicle trajectory tracking control algorithm based on neural network vehicle dynamics model predictive control. Based on the established neural network vehicle dynamics model, the autonomous vehicle path tracking system model may be expressed as
xt＝(r,vy,vx,δf)
ht＝[xt,xt-1]
In the formula, xtVehicle state information for a single time step, htIncluding the vehicle status information at the current time and the previous time. f. ofNNAnd establishing a neural network vehicle dynamics model.
Is the heading angle, v, of the vehiclexAnd vyRespectively the longitudinal acceleration and the lateral acceleration of the mass center under a vehicle body coordinate system, r is the yaw velocity of the vehicle, deltafIs the corner of the front wheel.
Is the first derivative of the yaw rate of the vehicle,
is the first derivative of the lateral speed of the vehicle,
is the first derivative of the heading angle of the vehicle,
and
the first derivatives of the longitudinal and lateral vehicle displacement, respectively.
The yaw angular velocity r and the lateral velocity vyLongitudinal velocity vxLongitudinal displacement X and lateral displacement Y course angle
As state variables of the system, i.e.
Front wheel corner deltafAs a control variable of the system, i.e. u ═ δf]Input of the system
Discretizing the described automatic driving vehicle track model by using an Euler formula to obtain a discrete dynamic model of the system
y(k)＝C·S(k)
In the form of matrix
Is the sampling time, TSIs a sampling time, and TSSame as the virtual data sampling time, TSΔ t is 0.03 s. S (k-1) is the last time state of the system, and S (k) is the current time state of the system. F is the established trajectory tracking system model, FNNAnd establishing a neural network vehicle dynamics model. r (k), vy(k),vx(k),δf(k) Respectively yaw velocity, lateral velocity, longitudinal velocity, and front wheel turning angle of the vehicle at the current sampling time k. r (k-1), vy(k-1),vx(k-1),δfAnd (k-1) respectively representing the yaw rate, the lateral speed, the longitudinal speed and the front wheel turning angle of the vehicle at the moment k-1 before the current sampling moment k.
The first derivative of the longitudinal position, the first derivative of the transverse position and the first derivative of the heading angle of the vehicle at the moment k are respectively.
In the invention, the prediction time domain of the automatic driving vehicle track model is defined as p, the control time domain is defined as c, and p is more than or equal to c. The vehicle is at [ k +1, k + p ]]The dynamics within the prediction horizon may be derived based on the current state of the vehicle, the state at the previous time, and the prediction model. That is, at the time k + p, the state of the vehicle is
Thus, at the kth sampling instant, the optimal input sequence for the system is available as
U(K)＝[u(k|k),u(k+1|k),…,u(k+p-1|k)]T
At the kth sampling instant, the predicted output of the system is
Y(K)＝[y(k|k),y(k+1|k),…,y(k+p|k)]T
At the k-th sampling moment, the reference input sequence of the system is
R(K)＝[rref(k|k),rref(k+1|k),…,rref(k+p|k)]T
At the k-th sampling time, y (k) is used as an initial value predicted by the control system, i.e., y (k | k) ═ y (k). The controller predicts the output of the system in a period of time in the future through a prediction model, designs the optimal performance index which the controller hopes to achieve, obtains the control output by solving the optimal control problem with constraint, corrects the prediction output according to the system output in the next period, and completes the control period.
In the process of designing the model predictive control algorithm, the performances of the vehicle such as tracking performance, comfort and the like are considered. To maintain good trajectory tracking of an autonomous vehicle, it is desirable to have the inputs of the system track the desired outputs, i.e., the output longitudinal displacement X, lateral displacement Y, and heading angle of the system
Tracking the desired lateral displacement XrefLongitudinal displacement YrefAnd course angle
The control targets are as follows:
in the formula Q1,Q2,Q3To optimize the weights in the target, σ is increased1,Q2The path tracking performance can be obviously improved.
In order to reduce the change rate of the control action and ensure the comfort of passengers, the control targets are as follows:
wherein M is the weight of the optimization target, and the weight coefficient can be adjusted according to the requirement.
To sum up, the overall optimization objective function is obtained, i.e.
In addition, constraint conditions for control quantity should be considered in MPC solving process
umin≤δf≤umax
Δumin≤Δδf≤Δumax
In the formula umin，umaxRespectively the minimum value and the maximum value of the front wheel rotation angle obtained in the MPC solving process. Δ umin，ΔumaxRespectively the minimum change rate and the maximum change rate of the front wheel rotation angle obtained in the MPC solving process. For the control stability of the vehicle body, a constraint condition is applied to the first derivative of the yaw rate
In the formula
First derivative of yaw rate, mu friction coefficient of road, g acceleration of gravity, vxIs the longitudinal velocity.
Therefore, the required optimization problem with constraints is established, a joint simulation model is established through CarSim and Matlab/Simulink, and a nonlinear optimization solver fmincon is applied to solve an optimization equation on line to obtain the controlled variable.
The above-listed series of detailed descriptions are merely specific illustrations of possible embodiments of the present invention, and they are not intended to limit the scope of the present invention, and all equivalent means or modifications that do not depart from the technical spirit of the present invention are intended to be included within the scope of the present invention.
Claims (10)
1. An automatic driving vehicle track tracking system based on a neural network dynamic model is characterized by comprising a neural network vehicle dynamic model part, a vehicle dynamic data acquisition part, a training part of the neural network model and a model prediction control algorithm part;
the neural network vehicle dynamics model part: a neural network model with delay input is designed by using a feedforward neural network, a hidden layer of the model is two layers, each layer is provided with 100 neurons, an activation layer selects a Softplus activation function, and the input of the model adopts vehicle control and state information at two moments so as to predict the first derivative of the yaw angular velocity and the lateral velocity of the vehicle;
the vehicle dynamics data acquisition section: the method comprises the steps of acquiring simulation data based on a driving simulator and a virtual simulation platform CarSim and acquiring real-world automatic driving vehicle data, establishing a real-time virtual simulation platform through the driving simulator and the CarSim, selecting an automatic driving test map Mtry, acquiring data based on normal driving behaviors of human beings, and performing single lane transformation and double lane transformation on driving vehicles running on different roads including straight roads, curved roads and the like in order to collect complete data; in real world vehicle data acquisition, an automatic driving vehicle is controlled by a human driver to perform linear motion, curvilinear motion, single lane transformation and double lane transformation;
the training part of the neural network model comprises the following steps: combining the obtained virtual simulation platform data set with real vehicle data of the real world, dividing the combined virtual simulation platform data set into an 80% training set, a 10% verification set and a 10% testing set, setting a loss function as an MSE (mean square error) loss function, setting an optimizer as Adam, setting a batch size as 1000, setting a learning rate as 0.0003, and training a network model based on a Pythrch deep learning framework;
the model predictive control algorithm part: and obtaining the optimal front wheel rotation angle through rolling optimization on-line solving, and realizing the tracking of the reference track.
2. The system of claim 1, wherein the neural network vehicle dynamics model portion determines the inputs to the feedforward neural network model as the yaw rate r and the lateral velocity v of the vehicle based on the nonlinear single-track model of the vehicleyLongitudinal velocity vxFront wheel corner deltafThe output of the model being the first derivative of the yaw rate
First derivative of longitudinal velocity
3. The system of claim 2, wherein the vehicle nonlinear single-track model is selected from the group consisting of: the vehicle is set as front wheel steering, a vehicle body coordinate system is located in a vehicle bilateral symmetry plane, the origin of the vehicle mass center is o, the x axis is the vehicle longitudinal axis, the y axis is the vehicle lateral direction, and the z axis meets the right hand rule and is vertical to the oxy direction; according to Newton's law, a stress balance equation of the vehicle on the y axis and around the z axis is obtained, and the nonlinear vehicle dynamic model can be expressed by the following differential equation:
where m is the vehicle mass, vxAnd vyRespectively the longitudinal acceleration and the lateral acceleration of the mass center under the vehicle body coordinate system, IzIs the moment of inertia of the vehicle about the z-axis,/fAnd lrDistances from the center of mass of the vehicle to the front axle and the rear axle, respectively, FxfAnd FxrThe resultant of the longitudinal forces of the tire acting on the front axle and the rear axle, respectively, FyfAnd FyrThe resultant of the lateral forces of the tires acting on the front and rear axles of the vehicle, r is the yaw rate of the vehicle,
is the first derivative of the yaw rate of the vehicle,
as the first derivative of the lateral speed of the vehicle, deltafIs a front wheel corner;
introduction into the Fiala model of the tire, the tire lateral force FyThe calculation formula of (2) is as follows:
wherein α is the slip angle of the tire, CαFor the cornering stiffness of the tyre, u is the coefficient of friction between the tyre and the ground, FzThe resultant force of the vertical forces of the tires;
Fzf、Fzrthe vertical load of the front wheel and the vertical load of the rear wheel are respectively under the condition that the transverse load displacement and the longitudinal load displacement of the vehicle are ignored.
4. The automatic driving vehicle trajectory tracking system based on the neural network dynamic model as claimed in claim 2, wherein the specific structure of the neural network vehicle dynamic model is:
the first layer is an input layer, and the input layer has 8 characteristic inputs, namely a yaw rate rt and a lateral rate v at the current momenty，tLongitudinal velocity vx，tFront wheel corner deltaf，tAnd yaw rate r at the previous timet-1Lateral velocity vy，t-1Longitudinal velocity vx，t-1Front wheel corner deltaf，t-1；
The second layer is an FC1 full-connection network layer, and the hidden layer is designed to have 100 hidden units;
the third layer is an activation layer, and the activation function is selected as a Softplus function;
the fourth layer is an FC2 full-connection network layer, and the hidden layer is designed to have 100 hidden units;
the fifth layer is an activation layer, and the activation function is selected to be a Softplus function;
the sixth layer is an output layer which is designed to have 2 neurons, and the output is the first derivative of the yaw rate at the current moment
First derivative of vehicle lateral velocity
5. The system of claim 4, wherein the forward calculation method of the neural network vehicle dynamics model is as follows:
xt＝(r，vy，vx，δf)
ht＝[xt，xt-1]
θ＝(w1，b1，w2，b2，w3，b3)
wherein x istVehicle state information for a single time step, htContaining the current and last time vehicle status information, a1，a2Theta is a parameter learned by the network and w is an activation layer Softplus function expression1，b1，w2，b2，w3，b3For weights and offsets of intermediate layers of the network, z1For the output of the first hidden layer of the network, z2Hiding the output of the layer for the second layer of the network.
And
is defined as:
and
the Δ t is 0.03s, which is the sampling frequency of the data.
6. The system of claim 1, wherein the training portion of the neural network model is configured to design the MSE loss function as follows:
in the formula r, vyRespectively the measured yaw rate and lateral speed of the vehicle,
first derivatives of vehicle yaw rate and lateral velocity predicted by the neural network vehicle dynamics model, Δ t being the sampling time, N being the number of samples, first derivatives of vehicle yaw rate and lateral velocity predicted by the neural network vehicle dynamics model
Yaw-rate and lateral-rate measurements r, v obtained by the CarSim softwareyPerforming Euler integration to obtain the predicted values of the yaw rate and the lateral rate at the next moment
htThe vehicle state information at the current time and the last time is included, and theta is a parameter learned by the network.
7. The neural network dynamics model-based autonomous vehicle trajectory tracking system of claim 1, wherein the model predictive control algorithm portion, based on the established neural network vehicle dynamics model, designs an autonomous vehicle path tracking system model represented as
xt＝(r，vy，vx，δf)
ht＝[xt，xt-1]
In the formula, xtVehicle state information for a single time step, htContaining the current and last vehicle status information, fNNFor the neural network vehicle dynamics model that is built,
is the heading angle, v, of the vehiclexAnd vyRespectively the longitudinal acceleration and the lateral acceleration of the mass center under a vehicle body coordinate system, r is the yaw velocity of the vehicle, deltafIs the turning angle of the front wheel,
is yaw rate of vehicleThe first derivative of the order of the first,
is the first derivative of the lateral speed of the vehicle,
is the first derivative of the heading angle of the vehicle,
and
first derivatives of the longitudinal and lateral vehicle displacements, respectively;
the yaw angular velocity r and the lateral velocity vyLongitudinal velocity vxLongitudinal displacement X and lateral displacement Y course angle
As state variables of the system, i.e.
Front wheel corner deltafAs a control variable of the system, i.e. u ═ δf]Input of the system
Discretizing the described automatic driving vehicle track model by using an Euler formula to obtain a discrete dynamic model of the system
y(k)＝C·S(k)
In the form of matrix
k is the sampling time and is TSIs a sampling time, and TSSame as the virtual data sampling time, TSΔ t is 0.03 s; s (k-1) is the state of the system at the last moment, S (k) is the state of the system at the current moment, F is the established trajectory tracking system model, FNNFor the established neural network vehicle dynamics model, r (k), vy(k)，vx(k)，δf(k) Respectively yaw rate, lateral rate, longitudinal rate, front wheel angle, r (k-1), v, of the vehicle at the current sampling time ky(k-1)，vx(k-1)，δf(k-1) yaw rate, lateral rate, longitudinal rate, front wheel angle,
respectively a first derivative of the longitudinal position, a first derivative of the transverse position and a first derivative of the course angle of the vehicle at the moment k;
defining the prediction time domain of an automatic driving vehicle track model as p, the control time domain as c, wherein p is more than or equal to c, and the vehicle is in [ k +1, k + p ]]The dynamics in the prediction time domain can be obtained based on the current state of the vehicle, the state of the vehicle at the previous moment and the prediction model, namely, at the moment k + p, the state of the vehicle is x (k + p) ═ F (F)NN(r(k)，vy(k)，vx(k)，δf(k)，r(k-1)，vy(k-1)，vx(k-1)，δf(k-1))，Xk，Yk，
u(k+1)，…，u(k+c)，…，u(k+p-1))；
At the kth sampling instant, the optimal input sequence of the system is obtained as
U(K)＝[u(k|k)，u(k+1|k)，…，u(k+p-1|k)]T
At the kth sampling instant, the predicted output of the system is
Y(K)＝[y(k|k)，y(k+1|k)，…，y(k+p|k)]T
At the k-th sampling moment, the reference input sequence of the system is
R(K)＝[rref(k|k)，rref(k+1|k)，...，rref(k+p|k)]T
At the k-th sampling time, y (k) is used as an initial value predicted by the control system, namely y (k | k) ═ y (k); the controller predicts the output of the system in a period of time in the future through a prediction model, designs the optimal performance index which the controller hopes to achieve, obtains the control output by solving the optimal control problem with constraint, corrects the prediction output according to the system output in the next period, and completes the control period.
8. The system of claim 7, wherein in the design of the model predictive control algorithm, to maintain good trajectory tracking of the autonomous vehicle, the expected outputs on the input tracking of the system, namely the output longitudinal displacement X, the lateral displacement Y and the heading angle of the system, are required to make the input tracking of the system follow
Tracking the desired lateral displacement XrefLongitudinal displacement YrefAnd course angle
The control targets are as follows:
in the formula Q1，Q2，Q3To optimize the weights in the target, Q is increased1，Q2The path tracking performance can be improved;
in order to reduce the change rate of control action and ensure the comfort of passengers, the control targets are as follows:
wherein M is the weight of the optimization target, and the weight coefficient can be adjusted according to the requirement;
to sum up, the overall optimization objective function is obtained, i.e.
In addition, constraint conditions for control quantity should be considered in MPC solving process
umin≤δf≤umax
Δumin≤Δδf≤Δumax
In the formula umin，umaxRespectively the minimum value and the maximum value of the front wheel rotation angle, delta u, obtained in the MPC solution processmin，ΔumaxRespectively obtaining the minimum change rate and the maximum change rate of the front wheel rotation angle obtained in the MPC solving process; for the control stability of the vehicle body, a constraint condition is applied to the first derivative of the yaw rate
In the formula
First derivative of yaw rate, mu friction coefficient of road, g acceleration of gravity, vxIs the longitudinal velocity.
9. An automatic driving vehicle track tracking method based on a neural network dynamic model is characterized by comprising the following steps:
s1: establishing a neural network vehicle dynamics model; the method comprises the following steps:
s1.1, firstly, establishing a nonlinear single-track model of the vehicle; specifically, the method comprises the following steps:
the vehicle is turned by the front wheel, a vehicle body coordinate system is located in a vehicle bilateral symmetry plane, the origin of the vehicle mass center is o, the x axis is the vehicle longitudinal axis, the y axis is the vehicle lateral direction, the z axis meets the right hand rule and is perpendicular to the oxy direction, a stress balance equation of the vehicle around the y axis and the z axis is obtained according to the Newton's law, and the nonlinear vehicle dynamic model can be expressed by the following differential equation:
where m is the vehicle mass, vxAnd vyRespectively the longitudinal acceleration and the lateral acceleration of the mass center under the vehicle body coordinate system, IzIs the moment of inertia of the vehicle about the z-axis,/fAnd lrDistances from the center of mass of the vehicle to the front axle and the rear axle, respectively, FxfAnd FxrThe resultant of the longitudinal forces of the tire acting on the front axle and the rear axle, respectively, FyfAnd FyrThe resultant of the lateral forces of the tires acting on the front and rear axles of the vehicle, r is the yaw rate of the vehicle,
is the first derivative of the yaw rate of the vehicle,
as the first derivative of the lateral speed of the vehicle, deltafIs a front wheel corner;
the non-linear characteristics generated during the running of the vehicle under different road conditions are caused by the tires during the turning, so that the Fiala model of the tires is introduced, and the lateral force F of the tiresyThe calculation formula of (2) is as follows:
wherein α is the slip angle of the tire, CαFor the cornering stiffness of the tyre, u is the coefficient of friction between the tyre and the ground, FzThe resultant force of the vertical forces of the tires;
Fzf、Fzrrespectively neglecting the vertical load of the front wheel and the vertical load of the rear wheel under the condition of transverse load displacement and longitudinal load displacement;
s1.2: determining the inputs of a feedforward neural network model based on the nonlinear single-track model of the vehicle as the yaw rate r and the lateral speed v of the vehicleyLongitudinal velocity vxFront wheel corner deltafThe output of the model being the first derivative of the yaw rate
First derivative of longitudinal velocity
The neural network vehicle dynamics model specifically adopts the following structure: the first layer is an input layer, and the input layer has 8 characteristic inputs, namely the yaw rate r at the current momenttLateral velocity vy，tLongitudinal velocity vx，tFront wheel corner deltaf，tAnd yaw rate r at the previous timet-1Lateral velocity vy，t-1Longitudinal velocity vx，t-1Front wheel corner deltaf，t-1(ii) a The second layer is an FC1 full-connection network layer, and the hidden layer is designed to have 100 hidden units; the third layer is an activation layer, and the activation function is selected as a Softplus function; the fourth layer is an FC2 full-connection network layer, and the hidden layer is designed to have 100 hidden units; the fifth layer is an activation layer, and the activation function is selected to be a Softplus function; the sixth layer is an output layer which is designed to have 2 neurons, and the output is the first derivative of the yaw rate at the current moment
First derivative of vehicle lateral velocity
The forward calculation method of the designed neural network vehicle dynamics model is as follows:
xt＝(r，vy，vx，δf)
ht＝[xt，xt-1]
θ＝(w1，b1，w2，b2，w3，b3)
wherein x istVehicle state information for a single time step, htContaining the current and last time vehicle status information, a1，a2Theta is a parameter learned by the network and w is an activation layer Softplus function expression1，b1，w2，b2，w3，b3For weights and offsets of intermediate layers of the network, z1For the output of the first hidden layer of the network, z2Hiding the output of the layer for the second layer of the network.
And
is defined as:
and
the Δ t is 0.03s, which is the sampling frequency of the data;
s2: acquiring vehicle dynamics data, including simulation data acquisition based on a driving simulator and a virtual simulation platform CarSim and real world automatic driving vehicle data acquisition;
establishing a real-time virtual simulation platform through a driving simulator and CarSim, selecting an automatic driving test map Mcity, collecting data based on normal driving behaviors of human beings, and driving vehicles to run on different roads including straight roads, curved roads and the like for collecting complete data and carrying out single-lane transformation and double-lane transformation; in real world vehicle data acquisition, an automatic driving vehicle is controlled by a human driver to perform linear motion, curvilinear motion, single lane transformation and double lane transformation;
s3: training a neural network vehicle dynamics model;
combining the obtained virtual simulation platform data set with real vehicle data of the real world, dividing the combined virtual simulation platform data set into an 80% training set, a 10% verification set and a 10% testing set, setting a loss function as an MSE (mean square error) loss function, setting an optimizer as Adam, setting a batch size as 1000, setting a learning rate as 0.0003, and training a network model based on a Pythrch deep learning framework;
the MSE loss function is specifically designed as follows:
in the formula r, vyRespectively the measured yaw rate and lateral speed of the vehicle,
first derivatives of vehicle yaw rate and lateral velocity predicted by the neural network vehicle dynamics model, Δ t being the sampling time, N being the number of samples, first derivatives of vehicle yaw rate and lateral velocity predicted by the neural network vehicle dynamics model
Yaw-rate and lateral-rate measurements r, v obtained by the CarSim softwareyPerforming Euler integration to obtain the predicted values of the yaw rate and the lateral rate at the next moment
htThe vehicle state information of the current moment and the last moment is contained, and theta is a parameter learned by the network;
s4: designing a model predictive control algorithm; and obtaining the optimal front wheel rotation angle through rolling optimization on-line solving, and realizing the tracking of the reference track.
10. The method of claim 9, wherein the model predictive control algorithm is specifically designed as follows:
based on the neural network vehicle dynamics model, establishing an automatic driving vehicle path tracking system model as
xt＝(r，vy，vx，δf)
ht＝[xt，xt-1]
In the formula, xtVehicle state information for a single time step, htContaining the current and last vehicle status information, fNNFor the neural network vehicle dynamics model that is built,
is the heading angle, v, of the vehiclexAnd vyRespectively the longitudinal acceleration and the lateral acceleration of the mass center under a vehicle body coordinate system, r is the yaw velocity of the vehicle, deltafIs the turning angle of the front wheel,
is the first derivative of the yaw rate of the vehicle,
is the first derivative of the lateral speed of the vehicle,
is the first derivative of the heading angle of the vehicle,
and
first derivatives of the longitudinal and lateral vehicle displacements, respectively;
the yaw angular velocity r and the lateral velocity vyLongitudinal velocity vxLongitudinal displacement X and lateral displacement Y course angle
As state variables of the system, i.e.
Front wheel corner deltafAs a control variable of the system, i.e. u ═ δf]Input of the system
Discretizing the described automatic driving vehicle track model by using an Euler formula to obtain a discrete dynamic model of the system
y(k)＝C·S(k)
In the form of matrix
k is the sampling time and is TSIs a sampling time, and TSSame as the virtual data sampling time, TS＝Δt＝0.03S, S (k-1) is the state of the system at the last moment, S (k) is the state of the system at the current moment, F is the established trajectory tracking system model, FNNFor the established neural network vehicle dynamics model, r (k), vy(k)，vx(k)，δf(k) Respectively yaw rate, lateral rate, longitudinal rate, front wheel angle, r (k-1), v, of the vehicle at the current sampling time ky(k-1)，vx(k-1)，δf(k-1) yaw rate, lateral rate, longitudinal rate, front wheel angle,
respectively a first derivative of the longitudinal position, a first derivative of the transverse position and a first derivative of the course angle of the vehicle at the moment k;
defining the prediction time domain of an automatic driving vehicle track model as p, the control time domain as c, wherein p is more than or equal to c, and the vehicle is in [ k +1, k + p ]]The dynamics in the prediction time domain can be obtained based on the current state of the vehicle, the state of the vehicle at the previous moment and the prediction model, namely, at the moment k + p, the state of the vehicle is x (k + p) ═ F (F)NN(r(k)，vy(k)，vx(k)，δf(k)，r(k-1)，vy(k-1)，vx(k-1)，δf(k-1))，Xk，Yk，
u(k+1)，…，u(k+c)，…，u(k+p-1))，
At the kth sampling instant, the optimal input sequence of the system is obtained as
U(K)＝[u(k|k)，u(k+1|k)，…，u(k+p-1|k)]T
At the kth sampling instant, the predicted output of the system is
Y(K)＝[y(k|k)，y(k+1|k)，…，y(k+p|k)]T
At the k-th sampling moment, the reference input sequence of the system is
R(K)＝[rref(k|k)，rref(k+1|k)，...，rref(k+p|k)]T
At the kth sampling moment, y (k) is used as an initial value predicted by a control system, namely y (k | k) ═ y (k), the controller predicts the output of the system in a future period of time through a prediction model, designs the optimal performance index expected to be reached by the controller, obtains the control output by solving the optimal control problem with constraint, corrects the predicted output according to the output of the system in the next period, and completes the control period;
in the design process of the model predictive control algorithm, the trackability and the comfort of the vehicle are considered, and in order to keep good track tracking of the automatic driving vehicle, the expected output on the input tracking of the system, namely the output longitudinal displacement X, the lateral displacement Y and the course angle of the system, is required to be enabled
Tracking the desired lateral displacement XrefLongitudinal displacement YrefAnd course angle
The control targets are:
in the formula Q1，Q2，Q3To optimize the weights in the target, Q is increased1，Q2The path tracking performance can be improved;
in order to reduce the rate of change of the control action to ensure the comfort of the passengers, the control targets are:
wherein M is the weight of the optimization target, and the weight coefficient can be adjusted according to the requirement;
obtaining a total optimization objective function:
in addition, constraint conditions for control quantity should be considered in MPC solving process
umin≤δf≤umax
Δumin≤Δδf≤Δumax
In the formula umin，umaxRespectively the minimum value and the maximum value of the front wheel rotation angle, delta u, obtained in the MPC solution processmin，ΔumaxRespectively obtaining the minimum change rate and the maximum change rate of the front wheel rotation angle obtained in the MPC solving process;
for the control stability of the vehicle body, a constraint condition is applied to the first derivative of the yaw rate
In the formula
First derivative of yaw rate, mu friction coefficient of road, g acceleration of gravity, vxIs the longitudinal velocity.
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Cited By (5)
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