CN113433942B - Long-axis vehicle path tracking control method based on optimal course angle - Google Patents
Long-axis vehicle path tracking control method based on optimal course angle Download PDFInfo
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Abstract
The invention discloses a long-axis vehicle path tracking control method based on an optimal course angle. The method comprises the following steps: selecting state quantity and control quantity of a control system according to a kinematics model of the long-axis vehicle, establishing a tracking error equation of a reference state point, establishing an integral deviation model of the long-axis vehicle and a reference path, solving to obtain the maximum value of integral deviation according to a coordinate transformation method so as to determine the optimal course angle of the long-axis vehicle in steering, establishing an MPC path tracking controller based on a pose error equation between the course angle and an actual vehicle, determining the optimal front wheel corner of the long-axis vehicle in the steering process by solving a cost function in the controller, and further controlling the vehicle to run along the reference path. The invention realizes the long-axis vehicle path tracking control, enables the running track of the front wheel to be closer to the reference path, effectively reduces the sweeping area of the front wheel of the long-axis vehicle in the steering process, and improves the trafficability of the long-axis vehicle in a narrow area.
Description
Technical Field
The invention belongs to the field of intelligent vehicle path tracking, and particularly relates to a long-axis vehicle path tracking control method based on an optimal course angle.
Background
The intelligent vehicle path tracking control technology is a hotspot of current research, but research objects mainly comprise passenger vehicles, the research on commercial vehicles is insufficient, and the realization of path tracking control of long-axis vehicles is an important component of intelligent traffic. The vehicle parameters of the long-axis vehicle are obviously different from those of a passenger vehicle, the long-axis vehicle is easy to collide with the road environment in the steering process in the narrow area, meanwhile, the current common path tracking control technologies such as PID, pure tracking and MPC control algorithms simplify the vehicle into mass points for control research, but for the long-axis vehicle, the algorithm cannot reflect the steering characteristic of the long-axis vehicle, so that the method has the defects.
The invention patent No. CN202011557293.5 of China, published in 2020, 12 and 24, discloses a route tracking Control method based on a Lyapunov-MPC, a tracking error model between a target value and a desired value is established according to a vehicle dynamics model, an LMPC controller is designed based on a CLF (Control Lyapunov Function) theory, an auxiliary tracking Control law is designed by utilizing a backstep method and is converted into a constraint condition in an MPC optimization process, and the closed-loop stability of the whole system is guaranteed theoretically. However, this method only considers the stability and robustness of the vehicle in the path tracking process, and cannot guarantee that a safe area exists between the long-axis vehicle and the narrow road environment.
In summary, the main problems existing in the current long-axis vehicle path tracking process are as follows: when the long-axis vehicle is simply researched as particle control, the characteristics of the long-axis vehicle cannot be reflected, and the long-axis vehicle is easy to collide with the road environment in the steering process of a narrow area.
Disclosure of Invention
The invention aims to provide a long-axis vehicle path tracking control method based on an optimal course angle, which can reduce the integral deviation between a long-axis vehicle and a reference path, so that the long-axis vehicle can safely pass through a narrow area without collision.
The technical solution for realizing the purpose of the invention is as follows: a long-axis vehicle path tracking control method based on an optimal course angle is characterized by comprising the following steps:
step S1: establishing a kinematics model of a long-axis vehicle according to speed constraints of front and rear wheels of the vehicle, then selecting state quantity and control quantity of the vehicle, and establishing an error equation of a model predictive control MPC algorithm;
step S2: establishing an overall deviation model between the long-axis vehicle and the reference path according to the given reference path, and solving by a coordinate transformation method to obtain the most value of the overall deviation model so as to determine the optimal course angle between the long-axis vehicle and the reference path;
and step S3: establishing an MPC path tracking controller according to the error equation in the step S1 and the optimal course angle in the step S2, establishing a prediction equation expression, then establishing a cost function according to the feedback quantity of the actual state of the vehicle and the reference quantity in the ideal state, and solving the cost function to obtain the optimal corner of the front wheel of the long-axis vehicle in the path tracking process;
and step S4: and judging whether the vehicle finishes walking the given reference path or not, if not, repeating the steps S2 and S3 until all the reference points are finished, and finally obtaining the running tracks of the front wheels and the rear wheels.
Compared with the prior art, the invention has the following points:
(1) According to the method, the vehicle is not considered as a single particle to be researched, but the integral deviation between the long-axis vehicle and the reference path is considered, the optimal course angle between the long-axis vehicle and the reference path is determined by solving the integral deviation model, and finally, the vehicle path tracking control is realized, and compared with the course angle under the given reference path, the optimal course angle enables the front wheel tracking track of the vehicle to be closer to the given reference path, the sweeping area of the long-axis vehicle in the steering process is reduced, and the long-axis vehicle can pass through a narrow area without collision.
(2) The MPC path tracking controller designed by the method can determine the optimal control quantity of the vehicle in the path tracking process through the constraint of the control quantity and the rolling optimization of the control time domain, and can ensure that the vehicle stably and accurately tracks the reference path.
Drawings
FIG. 1 is a flow chart of a long-axis vehicle path tracking method of the present invention.
FIG. 2 is a diagram of a vehicle kinematic model according to the present invention.
FIG. 3 is a graph of the overall deviation between the vehicle of the present invention and a reference path.
FIG. 4 is a flow chart of an MPC control algorithm of the present invention.
FIG. 5 is a graph of the reference heading angle and the optimal heading angle for the double-shift line condition.
FIG. 6 is a front wheel track diagram under the double-shift working condition.
Detailed Description
The present invention is described in further detail below with reference to the attached drawing figures.
As shown in fig. 1-6, a long-axis vehicle path tracking control method based on an optimal heading angle includes the following steps:
step S1: establishing a kinematic model of a long-axis vehicle according to speed constraints of front and rear wheels of the vehicle, then selecting state quantity and control quantity of the vehicle, and establishing an error equation of a Model Predictive Control (MPC) algorithm;
step S2: establishing an overall deviation model between the long-axis vehicle and the reference path according to the given reference path, and solving by a coordinate transformation method to obtain the most value of the overall deviation model so as to determine the optimal course angle between the long-axis vehicle and the reference path;
and step S3: establishing an MPC path tracking controller according to the error equation in the step S1 and the optimal course angle in the step S2, determining a prediction equation expression, then establishing a cost function according to the feedback quantity of the actual state of the vehicle and the reference quantity in the ideal state, and solving the cost function to obtain the optimal rotation angle of the front wheel of the long-axis vehicle in the path tracking process;
and step S4: and judging whether the vehicle finishes walking the given reference path or not, if not, repeating the steps S2 and S3 until all the reference points are finished, and finally obtaining the running tracks of the front wheels and the rear wheels.
Step S5: in order to verify the method, a simulation model is built on MATLAB/SIMULINK and TRUCKSIM software simulation platforms, and finally the effectiveness of the method is proved through results.
Specifically, as shown in fig. 2, the front and rear wheel speed constraint solving step in step S1 is:
firstly, a vehicle model is simplified into a single-axle bicycle model, namely, two front wheels and two rear wheels are combined into a single wheel, a vehicle coordinate system is defined, the rear wheel of the vehicle is the origin of the vehicle coordinate system, the vehicle advancing direction is an x-axis, the left side is a y-direction when the vehicle advances towards the x-axis direction, and then the speeds of the front wheels and the rear wheels are constrained as follows:
wherein X f ，Y f Indicating the coordinates of the front wheel position in the geodetic coordinate system. The solving step of the vehicle kinematic model comprises the following steps:
first, the speed at the rear wheel position is determined to be:
then, according to the position relation of the front wheel and the rear wheel, the following can be obtained:
finally, the vehicle yaw rate omega can be determined according to the expressions (1), (2) and (3):
the final vehicle kinematic model obtained is then:
wherein X r ，Y r As position coordinates of the rear wheels of the vehicle in the geodetic coordinate system, v r The running speed of the rear wheel, L is the vehicle axial length, theta is the included angle between the vehicle axial line and the geodetic coordinate system, namely the vehicle course angle, delta is the front wheel rotating angle, and r is the position of the rear wheel.
The above expression is written in the general form:
wherein the state quantity is xi = [ X = r ,Y r ,θ]The controlled variable is u = [ v = r ,δ]。
Further, the error equation establishing process in step S1 includes the steps of:
first a reference path is given, i.e. a set of coordinate values derived by the GPS.
Then it can be known from (6) that on a given reference path, any point coordinate satisfies (5), and therefore the equation of state at the reference position is expressed as:
where a is indicated at the reference path position. The Taylor expansion transformation of equation (6) at the reference path can obtain:
subtracting (8) from (7) yields the error equation in the MPC controller:
the above equation is a continuous equation expression of an error equation, and in order to design the MPC controller, the state equation can be obtained by discretizing the above equation by using an euler method:
wherein
T is discrete sampling time, k represents a discrete value, and the value is 1,2 … n.
The control target of the system is that the position of the rear wheel of the vehicle is as close to the reference position as possible, and the output equation of the system is:
wherein the content of the first and second substances,
further, as shown in fig. 3, the optimal heading angle obtaining step in step S2 includes:
firstly, the overall deviation between the vehicle and the reference path is defined, when the rear wheel of the vehicle is on the reference path, the position of the front wheel of the vehicle is determined by the axial length and the vehicle heading angle, therefore, different heading angles correspond to different positions of the front wheel under the same rear wheel position, at the moment, a perpendicular line is drawn from the reference track to the front wheel, and then the axial length of the vehicle, the area enclosed by the perpendicular line and the reference track is defined as the overall deviation between the vehicle and the reference path, such as a shaded part shown in fig. 3. As described above, different heading angles can determine the overall deviation between different long-axis vehicles and the reference path, so that there exists a heading angle that minimizes the overall deviation between the long-axis vehicle and the reference trajectory, i.e., the heading angle at this time is defined as the optimal heading angle. The expression for the overall deviation can be found from fig. 3 as:
wherein xoy is a vehicle coordinate system with an origin o at the rear wheel, p (x) is an expression of the reference path in the vehicle coordinate system, and theta t And determining a reference path heading angle at the current origin position by the given reference path, wherein epsilon is a change value of the heading angle, and an optimal heading angle between the long-axis vehicle and the reference track can be determined by solving the minimum value of the overall deviation in order to reduce the calculated amount epsilon and take a smaller positive value.
In order to solve the overall deviation function between the long-axis vehicle and the reference path, a method of converting a vehicle coordinate system into a geodetic coordinate system is used for solving, wherein a point on the vehicle coordinate system is translated and rotated to obtain a coordinate on the geodetic coordinate system, and then the transformation form is as follows:
wherein, as shown in FIG. 3, XOY is a geodetic coordinate system, f (X) is a reference path expression in the coordinate system, and X r ，y r Is the coordinate of the origin of the vehicle coordinate system under the geodetic coordinate system, the final objective function is expressed as:
the parameter in the objective function after the integration of the above formula is only theta, the maximum value of the objective function can be determined according to the value range of the parameter theta, and the maximum value is used
Indicating an optimal heading angle between the reference path and the long axis vehicle. The MPC path tracking controller can be designed after the optimal heading angle is determined at this point.
As shown in fig. 4, a design flow of the MPC controller is shown, and the MPC controller is designed according to the error equation and the optimal heading angle in step S3, and the specific implementation steps are as follows:
first, a new state quantity needs to be redefined in order to establish a prediction equation, and the deviation state quantity and the controlled variable are defined as a new state, which is expressed as follows:
where γ (k | t) is the new state quantity of the system at the current time,
is the state quantity of the error equation at the current moment,
the previous value of the controlled variable in the error equation at the present time.
A new state space expression can now be built from the above state equation,
wherein the content of the first and second substances,
where n is the dimension of the state quantity, m is the dimension of the control quantity, I m Is a unit array. For the convenience of calculation, the following assumptions were made
A k,t ＝A t,t ,k＝1,2,…t+N-1；B k,t ＝B t,t ,k＝1,2,…t+N-1；C k,t ＝C t,t ,k＝1,2,…t+N-1，
A new predicted output expression can thus be derived:
Y(t)＝ψ t γ(t|t)+Θ t ΔU(t) (17)
wherein each symbol is represented as:
wherein N is p To predict the time domain, N c To control the time domain.
The final established cost function is as follows:
as can be seen from the cost function, the first term of the formula represents the tracking ability of the system for a given path, Q is a weight matrix, the second term represents the constraint ability of the system for control increment, the control quantity is ensured to be as small as possible, R is the weight matrix, and the final rho weight coefficient and the relaxation factor epsilon are added to prevent the situation of no solution. The minimum value of the objective function can be obtained through a QP solver carried by the MATLAB, and the optimal control output of the system can be determined.
In order to obtain a better control effect, the control increment and the control quantity need to be constrained, and the actual running condition of the vehicle needs to be considered in the vehicle path tracking process, so the constraint form of the controller is as follows:
wherein
Denotes the kronecker product, I m Is a unit array.
ΔU min ，ΔU max Minimum and maximum values of the control increment, U min ，U max The minimum value and the maximum value in the control time domain are respectively set, and the values of the parameters are determined by an actual control system.
Obtaining a control input increment of
The first element of the series is applied to the controlled system as the actual control increment as follows:
u(t)＝u(t-1)+Δu t (21)
the optimal front wheel rotation angle delta output by the MPC control system can be obtained from the formula (21), and the steps are repeated after the next control period is entered, so that the tracking control of the vehicle on the given path can be realized.
Step S4, judging whether the vehicle finishes walking the given reference path or not, if not, repeating the steps S2 and S3 until all the reference points are finished, and finally obtaining the running tracks of the front wheels and the rear wheels
In step S5, an MPC controller model is built on MATLAB/SIMULINK, an optimal course angle solving model is built, joint simulation verification is performed by using a vehicle model of a long-axis vehicle in truksim, whether the vehicle completes path tracking control is judged through actual pose feedback, and vehicle front and rear wheel driving trajectories are obtained according to truksim output, fig. 5 shows that a front wheel trajectory is closer to a given reference path under the optimal course angle, a sweeping area of a front wheel is smaller in the driving process, and it is proved that the deviation between the whole vehicle and the reference path can be reduced more by the front and rear wheel trajectories of the optimal course angle than a result under the reference course angle under the double-line moving condition, the trafficability of the long-axis vehicle in a narrow area is improved, and the effective traveling of the proposed method is verified.
Claims (2)
1. A long-axis vehicle path tracking control method based on an optimal course angle is characterized by comprising the following steps:
step S1: establishing a kinematics model of a long-axis vehicle according to speed constraints of front and rear wheels of the vehicle, then selecting state quantity and control quantity of the vehicle, and establishing an error equation of a model predictive control MPC algorithm;
the step S1 specifically includes the following steps:
step S11: the solving steps of the speed constraint of the front wheel and the rear wheel are as follows:
simplify the vehicle model to unipolar bicycle model, be exactly merge two front wheels and two rear wheels into single wheel, define the vehicle coordinate system, the vehicle rear wheel is the origin of vehicle coordinate system, is the x axle along the vehicle direction of advance, and the left side is the y direction when towards the x axle direction, then the speed constraint of front and rear wheels is:
wherein X f ，Y f Coordinates representing the position of the front wheel in a geodetic coordinate system;
step S12: the solving step of the vehicle kinematic model comprises the following steps:
first, the speed at the rear wheel position is determined to be:
then, according to the position relation of the front wheel and the rear wheel, the following can be obtained:
finally, the vehicle yaw rate omega can be determined according to the expressions (1), (2) and (3):
step S13: the final vehicle kinematics model obtained is:
wherein X r ，Y r As position coordinates of the rear wheels of the vehicle in the geodetic coordinate system, v r The driving speed of a rear wheel, L is the axial length of the vehicle, theta is the included angle between the axis of the vehicle and a geodetic coordinate system, namely the heading angle of the vehicle, delta is the rotation angle of a front wheel, and r is the position of the rear wheel;
the above expression is written in the general form:
wherein the state quantity is xi = [ X ] r ,Y r ,θ]The controlled variable is u = [ v ] r ,δ]；
Step S14: establishing an error equation of a model predictive control MPC algorithm:
firstly, a reference path is given, namely a group of coordinate values obtained by a GPS;
then it can be known from (6) that on a given reference path, any point coordinate satisfies (5), and therefore the equation of state at the reference position is expressed as:
where a is at the reference path position; the taylor expansion transform of equation (6) at the reference path can obtain:
subtracting (8) from (7) yields the error equation in the MPC controller:
the above equation is a continuous equation expression of an error equation, and in order to design an MPC controller, a state equation can be obtained by discretizing the above equation by using an euler method:
wherein
T is discrete sampling time, k represents a value at a discrete position, and the value is 1,2 … n;
the control target of the system is that the position of the rear wheel of the vehicle is as close to the reference position as possible, and the output equation of the system is:
wherein the content of the first and second substances,
step S2: establishing an overall deviation model between the long-axis vehicle and the reference path according to the given reference path, and solving by a coordinate transformation method to obtain the most value of the overall deviation model so as to determine the optimal course angle between the long-axis vehicle and the reference path;
the step S2 of establishing an overall deviation model between the long-axis vehicle and the reference path specifically includes:
defining the integral deviation between a vehicle and a reference path, when a rear wheel of the vehicle is on the reference path, determining the position of a front wheel of the vehicle by the axial length and the heading angle of the vehicle, so that different heading angles under the same rear wheel position correspond to different positions of the front wheel, making a vertical line from a reference track to the front wheel at the moment, defining the axial length of the vehicle, the area enclosed by the vertical line and the reference track as the integral deviation between the vehicle and the reference path, and defining a heading angle to minimize the integral deviation between a long-axis vehicle and the reference track, namely defining the heading angle at the moment as an optimal heading angle;
the expression for the overall deviation is:
wherein xoy is a vehicle coordinate system with an origin o at the rear wheel, p (x) is an expression of the reference path in the vehicle coordinate system, and theta t Determining a course angle of a reference path at the current origin position by a given reference path, wherein epsilon is a change value of the course angle, and a smaller positive value is taken for reducing the calculated quantity epsilon;
the step S2 of solving by a coordinate transformation method to obtain a maximum value of the overall deviation model to determine an optimal heading angle between the long-axis vehicle and the reference path specifically includes:
and (3) solving by using a method of converting the vehicle coordinate system into a geodetic coordinate system, wherein the coordinates on the geodetic coordinate system can be obtained by translating and rotating points on the vehicle coordinate system, and the conversion form is as follows:
wherein XOY is a geodetic coordinate system, f (X) is a reference path expression in the coordinate system, and X r ，y r Is the coordinate of the origin of the vehicle coordinate system under the geodetic coordinate system, the final objective function is expressed as:
the parameter in the objective function after the integration of the above formula is only theta, the maximum value of the objective function can be determined according to the value range of the parameter theta, and the maximum value is used
Representing an optimal heading angle between the reference path and the long-axis vehicle;
and step S3: establishing an MPC path tracking controller according to the error equation in the step S1 and the optimal course angle in the step S2, establishing a prediction equation expression, then establishing a cost function according to the feedback quantity of the actual state of the vehicle and the reference quantity in the ideal state, and solving the cost function to obtain the optimal corner of the front wheel of the long-axis vehicle in the path tracking process;
the step S3 specifically comprises the following steps:
to establish the prediction equation, a new state quantity needs to be newly defined, and the deviation state quantity and the controlled variable are defined as a new state, which is expressed as follows:
where γ (k | t) is the new state quantity of the system at the current time,
is the state quantity of the error equation at the current moment,
the previous value of the controlled variable in the error equation at the current moment;
a new state space expression can now be built from the above state equation,
wherein the content of the first and second substances,
where n is the dimension of the state quantity, m is the dimension of the control quantity, I m Is a unit array; for the convenience of calculation, the following assumptions were made
A k,t ＝A t,t ,k＝1,2,…t+N-1；B k,t ＝B t,t ,k＝1,2,…t+N-1；C k,t ＝C t,t ,k＝1,2,…t+N-1，
A new predicted output expression can thus be derived:
Y(t)＝ψ t γ(t|t)+Θ t △U(t) (17)
wherein each symbol is represented as:
wherein N is p To predict the time domain, N c Is a control time domain;
the final established cost function is as follows:
according to the cost function, a first term of the formula represents the tracking capacity of the system to a given path, Q is a weight matrix, a second term represents the constraint capacity of the system to a control increment, the control quantity is ensured to be as small as possible, R is the weight matrix, and the final rho weight coefficient and the relaxation factor epsilon are added to prevent the situation of no solution; the minimum value of the objective function can be obtained through a QP solver carried by the MATLAB, and the optimal control output of the system can be determined;
and constraining the control increment and the control quantity, wherein the actual running condition of the vehicle needs to be considered in the vehicle path tracking process, and the constraint form of the controller is as follows:
wherein
Denotes the kronecker product, I m Is a unit array;
△U min ，△U max minimum and maximum values of the control increment, U, respectively min ，U max Respectively set as the minimum value and the maximum value in the control time domain, and the values of the parameters are determined by an actual control system;
obtaining a control input increment of
The first element of the control input increment of equation (20) is applied to the controlled system as the actual control increment as follows:
u(t)＝u(t-1)+△u t (21)
the optimal front wheel steering angle delta output by the MPC control system can be obtained from the formula (21), and the steps are repeated after the next control period is entered, so that the tracking control of the vehicle on the given path can be realized;
and step S4: and judging whether the vehicle finishes walking the given reference path or not, if not, repeating the steps S2 and S3 until all the reference points are finished, and finally obtaining the running tracks of the front wheels and the rear wheels.
2. The method of claim 1, further comprising the steps of:
step S5: the method comprises the steps of building an MPC controller model on MATLAB/SIMULINK, solving a model for an optimal course angle, performing joint simulation verification by using a vehicle model of a long-axis vehicle in TRUCKSIM, judging whether the vehicle completes path tracking control or not through actual pose feedback, obtaining driving tracks of front wheels and rear wheels of the vehicle according to the output of the TRUCKSIM, and finally, proving that the scanning area between the whole vehicle and a reference path can be reduced by the tracks of the front wheels and the rear wheels under the optimal course angle compared with the result under the reference course angle, so that the trafficability of the long-axis vehicle in a narrow area is improved.
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