CN114625002B - Vehicle transverse and longitudinal integrated control method based on model predictive control - Google Patents
Vehicle transverse and longitudinal integrated control method based on model predictive control Download PDFInfo
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Abstract
The invention discloses a vehicle transverse and longitudinal integrated control method based on model predictive control, which comprises the following steps: designing a fastest differential tracker and establishing an error model based on a two-degree-of-freedom model of the vehicle; predicting a vehicle state of the vehicle for a period of time in the future according to the prediction module; selecting a matching point according to the predicted vehicle state, and calculating the transverse and longitudinal errors of the vehicle; designing a model predictive controller and obtaining a target steering wheel input quantity and a target acceleration input quantity; and calculating the feedforward control quantity, and obtaining the final controller output quantity according to the feedforward control quantity, the target steering wheel input quantity and the target acceleration input quantity. The model predictive controller designed by the invention can calculate the optimal control quantity while considering the constraint problem of the state, and avoid the potential unsafe problem caused by the fact that the final calculation result is out of the constraint range because the constraint problem of the vehicle state is not considered.
Description
Technical Field
The invention relates to the field of vehicle control, in particular to a vehicle transverse and longitudinal integrated control method based on model predictive control.
Background
Automated driving assistance systems have evolved rapidly in recent years, and existing automated driving frameworks are largely comprised of four major modules, namely perception, decision making, planning and control. The control acts as a module for directly interacting with the vehicle, where it plays a very important role. The control layer may be generally divided into lateral and longitudinal controls. Lateral control achieves a desired position and attitude by changing the steering wheel of the vehicle and longitudinal control achieves a desired speed of the vehicle by providing vehicle acceleration. The two functions together to control the vehicle.
At present, the prior art is mostly based on transverse and longitudinal split control strategies of control methods such as PID, LQR and the like. For example, a "parameter adaptive lateral movement LQR control method for an automatic driving automobile" disclosed in chinese patent literature, the publication number CN110568758a, specifically includes the following steps: acquiring target path information, vehicle position information and vehicle state information required by a transverse motion control system in real time; processing and converting the acquired data; determining a controller parameter in a current state according to the collected data information and a formulated LQR control parameter adjustment strategy based on a path tracking error and a vehicle-road position relationship; according to the determined controller parameters, the steering control quantity of the automatic driving automobile is calculated and transmitted to a steering actuator for execution.
For another example, an "automatic driving acceleration control method based on an adaptive PID algorithm" disclosed in chinese patent literature, its bulletin number CN112947047a, includes the steps of: acquiring vehicle running information, and calculating PID control torque_PID, ramp compensation Torque torque_slope, friction torque_ Friction and acceleration feedforward Torque torque_ Feedforward, wherein the friction torque_ Friction comprises air resistance torque_ AirFriction; PID control torque_PID, ramp compensation torque_slope, friction torque_ Friction, and acceleration feedforward Torque torque_ Feedforward are summed to get a combined Torque torque_total, which is then used to control vehicle acceleration.
The patent 'a parameter self-adaptive transverse movement LQR control method of an automatic driving automobile' adds an LQR controller parameter calculation adjustment strategy based on a path tracking error and a vehicle-path position relationship on the basis of an automatic driving transverse LQR controller, so that the improvement of the path tracking precision and the improvement of the controller self-adaptability are realized; the patent 'an automatic driving acceleration control method based on a self-adaptive PID algorithm' effectively improves the rapidity and the precision index of the acceleration tracking of an automatic driving vehicle, so that the vehicle runs smoothly, the experience is improved, the safety coefficient of the vehicle is greatly improved, but the constraint problem of the vehicle state is not considered by the method and the method, and the final calculation result is out of the constraint range, so that potential unsafe exists.
Disclosure of Invention
The invention provides a vehicle transverse and longitudinal integrated control method based on model predictive control, which aims to solve the problem that the constraint problem of the vehicle state is not considered in the prior art, so that the final calculation result is out of the constraint range and has potential unsafe problem.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
A vehicle transverse and longitudinal integrated control method based on model predictive control comprises the following steps: s1: designing a fastest differential tracker and establishing an error model based on a two-degree-of-freedom model of the vehicle; s2: predicting a vehicle state of the vehicle for a period of time in the future according to the prediction module; s3: selecting a matching point according to the predicted vehicle state, and calculating the transverse and longitudinal errors of the vehicle; s4: designing a model predictive controller and obtaining a target steering wheel input quantity and a target acceleration input quantity; s5: and calculating the feedforward control quantity, and obtaining the final controller output quantity according to the feedforward control quantity, the target steering wheel input quantity and the target acceleration input quantity. The invention introduces a fastest differential tracker, and 'softens' the received track, thereby greatly relieving the situation of controlling the jump of the expected quantity caused by unsmooth track connection; the prediction module of the vehicle is added, the concept of pre-aiming is reflected in feedback, and the stability of an algorithm is ensured; the model predictive controller is designed, and the transverse and longitudinal directions of the vehicle are controlled simultaneously, so that various problems that one of the transverse and longitudinal separate designs is poor in effect, the other controller with better original effect is poor, the control parameters are repeatedly repeated, and the control parameters are difficult to adjust are avoided; the model predictive controller designed by the invention can calculate the optimal control quantity while considering the constraint problem of the state, and avoid the potential unsafe problem caused by the fact that the final calculation result is out of the constraint range because the constraint problem of the vehicle state is not considered.
As a preferred scheme of the present invention, the fastest differential tracker in S1 is designed as follows:
Wherein fhan (x 1,x2,r0,h0) is the fastest synthesis function, expressed as follows:
. Wherein h is a sampling period, k represents a kth sampling period, k+1 represents a kth+1th sampling period, v is an input signal, and x 1、x2 are v, Filtered results,/>Is the differentiation of v, r 0 is the speed factor, h 0 is the filter factor, r 0 and h 0 are the parameters to be designed, l, d and s l、a0、a1,a2、y、sy are intermediate variables, sign (x) is the sign function.
As a preferable scheme of the invention, the error model establishment process in the S1 is as follows: the expression of the two-degree-of-freedom model of the vehicle is as follows:
Let e d = d be the value, Through Frenet coordinate conversion, a two-degree-of-freedom model is combined, and the position error e s and the speed error e v are considered, so that the following transverse and longitudinal error models are obtained:
. Wherein a and b are distances from a front and rear axis to a center of gravity, phi is a yaw angle, v x is a vehicle longitudinal speed, C f,Cr is a front and rear wheel cornering stiffness, I z is moment of inertia, m is vehicle weight, y is lateral displacement, delta f is a front wheel corner, e d =d is a lateral error, theta r is a desired heading angle, s is displacement, v is a vehicle centroid speed, For heading angle error, e s is position error and e v is speed error.
As a preferred embodiment of the present invention, the prediction module in S2 is designed as follows:
. Wherein t pre is the predicted time, (x, y) is the current positioning coordinate of the vehicle, (x pre,ypre) is the predicted coordinate of the vehicle after t pre seconds from the current time, θ, S is the course angle, yaw angle and displacement of the vehicle,/>, respectivelyV pre is the predicted yaw angle and speed of the vehicle, respectively.
As a preferred embodiment of the present invention, the calculation formula of the horizontal-vertical error in S3 is as follows:
. Where (x, y) is the predicted position of the vehicle in S2, (x m,ym) is the position of the matching point, e s、ev is the position error and the speed error, respectively, For vehicle centroid speed vector expression, when the vehicle is in a steady state, the centroid slip angle is zero, which can be regarded as heading angle=yaw angle,/>For the heading angle predicted by the vehicle in S2, θ m is the heading angle of the matching point,/> For the speed of the matching point, θ r＝θm+kmes, the heading angle of the projected point, k m the curvature of the matching point,The speed of the vehicle.
As a preferred embodiment of the present invention, the S4 is specifically as follows:
Neglecting The influence of the discrete two-degree-of-freedom model is:
x(k+1)＝Ax(k)+Bu(k)
Wherein, K represents the kth sampling period, k+1 represents the kth+1th sampling period, and N periods are predicted backward, which can be obtained:
x(k+1)＝Ax(k)+Bu(k)
x(k+2)＝A2x(k)+ABu(k)+Bu(k+1)
x(k+3)＝A3x(k)+A2Bu(k)+ABu(k+1)+Bu(k+2)
x(k+4)＝A4x(k)+A3Bu(k)+A2Bu(k+1)+ABu(k+2)+Bu(k+3)
…
x (k+n) =a Nx(k)+AN-1 Bu (k) + … +bu (k+n-1), let
The prediction model is obtained as:
X＝Mx(k)+DU
Consider the following cost function:
consider steering wheel constraints and acceleration delta constraints:
solving for optimum by quadratic programming And taking the first state quantity u (k) = [ delta f,Δρ]T ] to obtain the following target steering wheel input quantity/>And a target acceleration input amount ρ:
。
Wherein I is an identity matrix, Are all intermediate variables, p is a relaxation factor, q is a relaxation factor coefficient,/>For/>Delta fmin、δfmax is the minimum value and the maximum value of the front wheel rotation angle delta f, delta rho min、Δρmax is the minimum value and the maximum value of the target acceleration change value delta a, u is the output of the controller, u (k) is the output of the kth sampling period of the controller, delta f and delta rho are the rotation angle and the acceleration change value of the front wheel of the vehicle respectively, n tran is the transmission ratio of the steering wheel and the front wheel of the vehicle, and a pre is the acceleration value of the output of the controller of the previous period. The invention introduces a relaxation factor into the cost function, and greatly improves the real-time performance of control while ensuring that the control precision loss is not great.
As a preferred embodiment of the present invention, the S5 specifically is: the feedforward control amount is calculated as follows:
Where K m is the curvature of the matching point and K 3 =k (3) is the third solution of the Riccati equation, which is based on the two-degree-of-freedom vehicle model-related parameters and the current vehicle speed alone, the feed-forward module functions to cancel out The impact on the system, i.e. making the steady state error 0, results in the final controller output:
. Wherein a and b are distances from the front and rear axles to the center of gravity, v x is the longitudinal speed of the vehicle, and m is the vehicle weight. The invention enables the actual track of the vehicle to track the expected track without overshoot by controlling the front wheel rotation angle delta f and the acceleration rho, and ensures the driving comfort in the process.
Therefore, the invention has the following beneficial effects: the invention introduces a fastest differential tracker, and 'softens' the received track, thereby greatly relieving the situation of controlling the jump of the expected quantity caused by unsmooth track connection; the prediction module of the vehicle is added, the concept of pre-aiming is reflected in feedback, and the stability of an algorithm is ensured; the model predictive controller is designed, and the transverse and longitudinal directions of the vehicle are controlled simultaneously, so that various problems that one of the transverse and longitudinal separate designs is poor in effect, the other controller with better original effect is poor, the control parameters are repeatedly repeated, and the control parameters are difficult to adjust are avoided; the model predictive controller designed by the invention can calculate the optimal control quantity and simultaneously consider the constraint problem of the state, so that the problem that the final calculation result is out of the constraint range and potential unsafe is generated due to the constraint problem of the state of the vehicle which is not considered is avoided; the invention introduces a relaxation factor into the cost function, and greatly improves the real-time performance of control while ensuring that the control precision loss is not great; the invention enables the actual track of the vehicle to track the expected track without overshoot by controlling the front wheel rotation angle delta f and the acceleration rho, and ensures the driving comfort in the process.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is an overall flow chart of an embodiment of the present invention;
FIG. 3 is a functional block diagram of an algorithm of the present invention;
FIG. 4 is a schematic illustration of a two degree of freedom model of a vehicle of the present invention;
Fig. 5 is a schematic view of the setpoint of the present invention.
Detailed Description
The invention is further described below with reference to the drawings and detailed description.
As shown in fig. 1, a vehicle transverse and longitudinal integrated control method based on model predictive control includes: s1: designing a fastest differential tracker and establishing an error model based on a two-degree-of-freedom model of the vehicle; s2: predicting a vehicle state of the vehicle for a period of time in the future according to the prediction module; s3: selecting a matching point according to the predicted vehicle state, and calculating the transverse and longitudinal errors of the vehicle; s4: designing a model predictive controller and obtaining a target steering wheel input quantity and a target acceleration input quantity; s5: and calculating the feedforward control quantity, and obtaining the final controller output quantity according to the feedforward control quantity, the target steering wheel input quantity and the target acceleration input quantity. The invention introduces a fastest differential tracker, and 'softens' the received track, thereby greatly relieving the situation of controlling the jump of the expected quantity caused by unsmooth track connection; the prediction module of the vehicle is added, the concept of pre-aiming is reflected in feedback, and the stability of an algorithm is ensured; the model predictive controller is designed, and the transverse and longitudinal directions of the vehicle are controlled simultaneously, so that various problems that one of the transverse and longitudinal separate designs is poor in effect, the other controller with better original effect is poor, the control parameters are repeatedly repeated, and the control parameters are difficult to adjust are avoided; the model predictive controller designed by the invention can calculate the optimal control quantity and simultaneously consider the constraint problem of the state, so that the problem that the final calculation result is out of the constraint range and potential unsafe is generated due to the constraint problem of the state of the vehicle which is not considered is avoided; the invention introduces a relaxation factor into the cost function, and greatly improves the real-time performance of control while ensuring that the control precision loss is not great; the invention enables the actual track of the vehicle to track the expected track without overshoot by controlling the front wheel rotation angle delta f and the acceleration rho, and ensures the driving comfort in the process.
In particular, the object of the invention is to allow the actual trajectory of the vehicle to track the desired trajectory quickly without overshooting by controlling the front wheel steering angle (via the steering wheel) δ f and the acceleration ρ, and to ensure driving comfort in the process. The algorithm of the invention needs to enable the transverse error, the transverse error change rate, the longitudinal error, the speed error, the course angle error and the course angle error change rate of the actual vehicle and the plan to be converged to 0, and simultaneously takes the input quantities delta f and rho with the values and the change rates as small as possible. The overall flow chart of the invention is shown in fig. 2, the algorithm principle block diagram is shown in fig. 3, and the overall process is as follows: the planning module gives out the expected track point information, and controls to find a matching point through the closest point matching principle, so that the relevant information of the projection point is combined, the vehicle is differenced from the current vehicle state, and the error is input into the MPC to obtain the target front wheel steering angle and the acceleration increment. In addition, in order to eliminate steady-state errors due to the model, a feedforward control amount is also required, and the two control laws δ f and Δρ are calculated by combining the feedforward control amount and the feedforward control amount. In addition, for comfort, it is desirable to have a certain predictability of control, so a prediction module for the own vehicle is added, and then the actual error is the error of the predicted vehicle state and the desired vehicle state.
More specifically, the first step: designing a fastest differential tracker, arranging an excessive tracking process for the system, and establishing an error model of transverse distance, course angle, displacement and speed based on a two-degree-of-freedom model of the vehicle through Frenet coordinate conversion; the fastest differential tracker is designed as follows:
Wherein h is a sampling period, k represents a kth sampling period, k+1 represents a kth+1th sampling period, v is an input signal, and x 1、x2 are v, Filtered results,/>For the differentiation of v, r 0、h0 is a speed factor and a filtering factor, respectively, and fhan (x 1,x2,r0,h0) is the fastest synthesis function, and the expression is:
Wherein l, d and s l、a0、a1,a2、y、sy are all intermediate variables, sign (x) is a sign function, and the expression is as follows:
the design process of the error model of the transverse distance, the course angle, the displacement and the speed is as follows: the two-degree-of-freedom model of the vehicle is shown in fig. 4, and the expression is established as follows:
wherein a, b is the distance from the front and rear axes to the center of gravity, V x is the vehicle longitudinal speed, C f,Cr is the front and rear wheel cornering stiffness, I z is the moment of inertia, m is the vehicle weight, y is the lateral displacement, and δ f is the front wheel turning angle. Let e d = d,/>Since the planned given trajectory is smoother, it can be approximated as/>Then there are:
bringing the above formula into a two-degree-of-freedom model, and supplementing according to the form And/>And the position error e s and the speed error e v are considered to obtain the following transverse and longitudinal error models:
Wherein/> U= [ delta f,Δρ]T,ed =d is the lateral error,/>Is yaw angle, theta r is the desired heading angle, s is displacement, v is vehicle centroid speed,/>For heading angle error, e s is position error and e v is speed error.
And a second step of: designing a vehicle prediction module, and predicting a vehicle state of the vehicle for a period of time in the future according to the prediction module; the vehicle prediction module is designed as follows:
Wherein t pre is the predicted time, (x, y) is the current positioning coordinate of the vehicle, (x pre,ypre) is the predicted coordinate of the vehicle after t pre seconds, calculated from the current time, theta, S is the course angle, yaw angle and displacement of the vehicle,/>, respectivelyV pre is the predicted yaw angle and speed of the vehicle, respectively.
And a third step of: taking matching points, calculating projection points, and finishing the calculation of horizontal and longitudinal errors; the selection point schematic diagram is shown in fig. 5, and the matching point is selected by the following method: and traversing the expected track point, and selecting the point closest to the predicted vehicle position as a matching point P m. Assuming that the curvature between the matching point and the projection point is a fixed value, calculating the transverse and longitudinal errors at the projection point:
Where (x, y) is the predicted position of the vehicle in the second step, (x m,ym) is the position of the matching point, e s、ev is the position error and the speed error, respectively, For vehicle centroid speed vector expression, when the vehicle is in a steady state, the centroid slip angle is zero, which can be regarded as heading angle=yaw angle,/>For the heading angle predicted by the vehicle in the second step, θ m is the heading angle of the matching point,/>For the speed of the matching point, θ r＝θm+kmes is the heading angle of the projected point, k m is the curvature of the matching point,/>The speed of the vehicle.
Fourth step: designing a model predictive controller and obtaining a target steering wheel input quantity and a target acceleration input quantity; neglecting transverse-longitudinal error modelsMiddle/>The influence on the system, the discrete two-degree-of-freedom model is designed as follows:
x(k+1)＝Ax(k)+Bu(k)
Where k represents the kth sampling period, k+1 represents the kth+1 sampling period, and I is the identity matrix. Predicting N cycles backward, the following can be obtained:
x(k+1)＝Ax(k)+Bu(k)
x(k+2)＝A2x(k)+ABu(k)+Bu(k+1)
x(k+3)＝A3x(k)+A2Bu(k)+ABu(k+1)+Bu(k+2)
x(k+4)＝A4x(k)+A3Bu(k)+A2Bu(k+1)+ABu(k+2)+Bu(k+3)
…
x(k+N)＝ANx(k)+AN-1Bu(k)+…+Bu(k+N-1)
Order the The prediction model is x=mx (k) +du. Consider the following cost function:
Wherein the method comprises the steps of Is a state weight matrix,/>Is an output weight matrix. Record/>The cost function may be written as:
X=mx (k) +du is taken into the above solution into a standard quadratic programming form:
Wherein the method comprises the steps of Since x (k) T Gx (k) is determined by the state at kT time (initial state), it is not considered. I.e. consider the following cost function:
Because the real-time control requirement is higher and the number of mpc iterations is more, in order to reduce the number of iterations, mpc is enabled to find the optimal solution as soon as possible, and a relaxation factor is introduced into the original cost function, namely
Wherein the method comprises the steps of Are intermediate variables, p is a relaxation factor, and q is a relaxation factor coefficient. Steering wheel constraints and acceleration delta constraints are then considered:
Wherein the method comprises the steps of For/>Delta fmin、δfmax is the minimum and maximum value of the front wheel rotation angle delta f, deltaa min、Δamax is the minimum and maximum value of the target acceleration change value deltaa, and q is the relaxation factor coefficient. Solving the optimal/>, through quadratic programming Where u is the controller output and u (k) is the output of the kth sampling period of the controller. Then, taking the first state quantity u (k) = [ delta f,Δρ]T, wherein delta f and delta rho are respectively the rotation angle and acceleration change value of the front wheel of the vehicle, and finally obtaining the following target steering wheel input quantity/>And a target acceleration input amount ρ:
n tran is the transmission ratio of the steering wheel and the front wheel of the vehicle, and a pre is the acceleration value output by the controller in the previous period.
Fifth step: calculating a feedforward control quantity, and obtaining a final controller output quantity according to the feedforward control quantity, a target steering wheel input quantity and a target acceleration input quantity; the feedforward control amount is calculated as follows:
Wherein a and b are distances from front and rear axes to the center of gravity, v x is vehicle longitudinal speed, m is vehicle weight, K m is curvature of a matching point, K 3 =k (3) is a discrete two-degree-of-freedom model x (k+1) =ax (K) +bu (K), and the cost function is: a third solution of the Riccati equation under J lqr＝x(k)TQx(k)+u(k-1)T Ru (k-1), where x (k) is the state of the kth cycle of the vehicle, u (k-1) is the controller output of the kth-1 cycle of the vehicle, Q is a sub-state weight matrix, R is a sub-output weight matrix, and Q, R in the mpc controller is the same variable. The feedforward module is used for counteracting The effect on the system is to make the steady state error 0. The final controller output can then be obtained:
The existing control module depends on an upper planning module, and the smoothness of the track given by planning can be ensured in the period, but the smoothness of the joint of the track given in the previous period cannot be ensured; the invention introduces a fastest differential tracker, and 'softens' the received track, thereby greatly relieving the situation of controlling the jump of the expected quantity caused by unsmooth track connection.
Because the algorithm driving is only in the moment of error, the algorithm driving lacks foresight, the foresight of the driving of a driver is generally simulated in a pre-aiming feedforward mode, and the feedback thought of the method and the algorithm is split, so that the stability of the algorithm is difficult to ensure; the prediction module of the vehicle is added, the concept of pre-aiming is reflected in feedback, and the stability of an algorithm is ensured.
The horizontal and longitudinal control of the vehicle can achieve theoretical decoupling under the Frenet coordinate system, but the decoupling is established in a certain range of error control of the horizontal and longitudinal control, and when the vehicle is in some complex road conditions, the error is often not guaranteed to be small enough, and at the moment, the horizontal and longitudinal control can be mutually influenced, so that the control effect of the vehicle is not ideal; the design model predictive controller can control the transverse direction and the longitudinal direction of the vehicle simultaneously, and can give consideration to the effects of the two, so that various problems that one controller is poor in effect and the other controller is poor in original effect and is repeated, control parameters are difficult to adjust and the like caused by the transverse direction and the longitudinal direction separated design are avoided.
The existing transverse and longitudinal control algorithm is mainly based on PID and LQR, and cannot consider the constraint problem of the vehicle state, so that the final calculation result is out of the constraint range, and potential unsafe exists. The model predictive controller designed by the invention can calculate the optimal control quantity and simultaneously consider the constraint problem of the state.
Model predictive control (Model predictive control, MPC for short) is more robust than LQR, but its computational complexity is much higher, and the control module of the vehicle is highly demanding in terms of facts, and it is a difficulty how to quickly converge the required states and meet the control requirements. The invention introduces a relaxation factor into the cost function, and greatly improves the real-time performance of control while ensuring that the control precision loss is not great.
The invention designs the fastest differential tracker, which 'flexibly' controls the target value and prevents the jump; the vehicle prediction module is designed, the problem that the algorithm vehicle control lacks perspective relative to the human vehicle control is solved from the angle of closed loop, the conventional pre-aiming feedforward method is replaced, and the overall stability of the algorithm is ensured; compared with the conventional calculation mode of the course angle of the projection point, the method directly takes the course angle of the matching point as the target course angle, the invention assumes the fixed curvature between the matching point and the projection point, and the course angle of the projection point is calculated more accurately through geometry to be taken as the target course angle of the vehicle, thereby improving the reliability of the algorithm; and a relaxation factor is added into the MPC cost function, so that the iterative speed of the algorithm is greatly increased, and the real-time requirement of control is met.
The foregoing is merely illustrative of specific embodiments of the present invention, and the scope of the present invention is not limited thereto, but any changes or substitutions that do not undergo the inventive effort should be construed as falling within the scope of the present invention.
Claims (6)
1. A vehicle transverse and longitudinal integrated control method based on model predictive control is characterized by comprising the following steps:
S1: designing a fastest differential tracker and establishing an error model based on a two-degree-of-freedom model of the vehicle;
s2: predicting a vehicle state of the vehicle for a period of time in the future according to the prediction module;
s3: selecting a matching point according to the predicted vehicle state, and calculating the transverse and longitudinal errors of the vehicle;
S4: designing a model predictive controller and obtaining a target steering wheel input quantity and a target acceleration input quantity; the discrete two-degree-of-freedom model is:
x(k+1)＝Ax(k)+Bu(k)
Wherein, And/>Is a parameter of the error model; k represents a kth sampling period, and k+1 represents a kth+1 sampling period; i is an identity matrix; predicting N cycles backwards, and obtaining a prediction model as follows:
X＝Mx(k)+DU
Consider the following cost function:
Are intermediate variables, p is a relaxation factor, and q is a relaxation factor coefficient; /(I)
Q is a state weight matrix, R is an output weight matrix;
consider steering wheel constraints and acceleration delta constraints:
Wherein the method comprises the steps of For/>Delta fmin、δfmax is the minimum and maximum value of the front wheel rotation angle delta f, delta rho min、Δρmax is the minimum and maximum value of the target acceleration change value delta rho, and the optimal value is obtained through quadratic programmingAnd taking the first state quantity u (k) = [ delta f,Δρ]T ] to obtain the following target steering wheel input quantity/>And a target acceleration input amount ρ:
n tran is the transmission ratio of the steering wheel and the front wheel of the vehicle, and a pre is the acceleration value output by the controller in the previous period; s5: and calculating the feedforward control quantity, and obtaining the final controller output quantity according to the feedforward control quantity, the target steering wheel input quantity and the target acceleration input quantity.
2. The vehicle transverse and longitudinal integrated control method based on model predictive control according to claim 1, wherein the fastest differential tracker in S1 is designed as follows:
Wherein h is a sampling period, k represents a kth sampling period, k+1 represents a kth+1th sampling period, v is an input signal, and x 1、x2 are v, Filtered results,/>R 0、h0 is a velocity factor and a filter factor, respectively, where fhan (x 1,x2,r0,h0) is the fastest synthesis function, expressed as follows:
Wherein l, d, s l、a0、a1,a2、y、sy are all intermediate variables and sign (x) is a sign function.
3. The vehicle transverse and longitudinal integrated control method based on model predictive control according to claim 1 or 2, wherein the error model establishing process in S1 is as follows:
the expression of the two-degree-of-freedom model of the vehicle is as follows:
Wherein a and b are distances from the front and rear axes to the center of gravity, Is yaw angle, v x is longitudinal speed of the vehicle, C f,Cr is lateral deflection rigidity of front and rear wheels, I z is moment of inertia, m is vehicle weight, y is transverse displacement, delta f is front wheel rotation angle, and the formula/>Through Frenet coordinate conversion, a two-degree-of-freedom model is combined, and the position error e s and the speed error e v are considered, so that the following transverse and longitudinal error models are obtained:
e d is the transverse error, which is the error in the transverse direction, Is yaw angle, theta r is the desired heading angle, s is displacement, v is vehicle centroid speed,/>For the heading angle error, e s is a position error, e v is a speed error, and Δρ is an acceleration change value.
4. The vehicle transverse and longitudinal integrated control method based on model predictive control according to claim 1, wherein the predictive module in S2 is designed as follows:
Wherein t pre is the predicted time, (x, y) is the current positioning coordinate of the vehicle, (x pre,ypre) is the predicted coordinate of the vehicle after t pre seconds, calculated from the current time, theta, S is the course angle, yaw angle and displacement of the vehicle,/>, respectivelyV pre is the predicted yaw angle and speed of the vehicle, respectively.
5. The vehicle transverse and longitudinal integrated control method based on model predictive control according to claim 1, wherein the transverse and longitudinal error calculation formula in S3 is as follows:
Where (x, y) is the position predicted by the vehicle in the prediction module, (x m,ym) is the position of the matching point, e s、ev is the position error and the speed error, respectively, For vehicle centroid speed vector expression, when the vehicle is in a steady state, the centroid slip angle is zero, which can be regarded as heading angle=yaw angle,/>For the heading angle predicted by the vehicle in the prediction module, θ m is the heading angle of the matching point,For the speed of the matching point, θ r＝θm+kmes is the heading angle of the projected point, k m is the curvature of the matching point,The speed of the vehicle.
6. The vehicle transverse and longitudinal integrated control method based on model predictive control according to claim 1, wherein the step S5 is specifically: the feedforward control amount is calculated as follows:
Wherein a and b are distances from front and rear axles to center of gravity, v x is longitudinal speed of the vehicle, m is vehicle weight, K m is curvature of a matching point, K 3 =k (3) is a third solution of Riccati equation, the solution is based on two-degree-of-freedom vehicle model related parameters and current vehicle speed only, and the feedforward module is used for counteracting The impact on the system, i.e. making the steady state error 0, results in the final controller output:
c f,Cr is the cornering stiffness of the front and rear wheels.
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