CN111240327B - Intelligent vehicle iteration track tracking control method based on variable rate model - Google Patents
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- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
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- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
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Abstract
The invention discloses an intelligent vehicle iteration track tracking control method based on a variable rate model, which belongs to the field of intelligent vehicle control and adopts different sampling frequencies to establish the variable rate model; after the variable speed model is established, by repeating this operation a plurality of times using iterative learning control as a method of gradually determining the transient driving correct steering input, high-precision and stable path tracking is realized. The idea of the variable rate model proposed by the present invention results in an augmented model using multiple rates, including perturbations. The state considered in the shift rate model in the case where the increase in computational complexity is not large includes the state considered in the single-rate model, so that the control using the shift rate model can find a solution that is not inferior to the control using the single-rate model. The provided iterative trajectory tracking control idea is used as a method for gradually determining the correct steering input of the transient driving maneuver, and the tracking performance is improved by repeating for multiple times and utilizing the information obtained by the previous iteration.
Description
Technical Field
The invention belongs to the field of intelligent vehicle control, and particularly relates to a control method of an intelligent vehicle under a repetitive track.
Background
With the rapid development of computer information processing technology, the unmanned vehicle technology based on high-efficiency environment perception is rapidly improved, wherein the important aim is to improve the path tracking precision and the running speed of the intelligent vehicle, so that the intelligent vehicle has good stability and safety under a high-speed condition. Under the working conditions with fixed and repeatable tracks, such as formula racing, airport bus-trip and agricultural seeding harvesting vehicles, the traditional controller only utilizes the current error to control the running track, and does not fully utilize historical information to improve the running speed and track tracking precision.
In the traditional intelligent vehicle path tracking process, the design of the control system generally considers that the same sampling frequency is kept in the control system, so that the modeling and the subsequent analysis design of the whole control system are simple. However, for smart vehicles, the control system is large and complex, making it difficult to make all the operating rates the same, even for some processes impossible. At this time, if different sampling frequencies are used in the control system, this can improve the control effect of the system, and at the same time, can reduce the control cost of the system.
Disclosure of Invention
Aiming at the problems, the invention provides a path tracking control method of an intelligent vehicle, which constructs a variable rate model by using different sampling frequencies in a system, utilizes iterative learning control as a method for gradually determining the correct steering input of transient driving after the variable rate model is constructed, tracks a path, repeats the operation for multiple times, and utilizes the information obtained by previous iteration to improve the reference tracking performance. The tracking precision and stability of the path are improved.
The invention has the beneficial effects that:
1. the idea of the variable rate model proposed by the present invention is to obtain an augmented model using multi-rate objects containing perturbations. Since the state quantity and the controlled variable are both integral multiples of the original ones, and the states considered in the shift rate model include the states considered in the single-rate model when the computational complexity is not increased so much, the latter solution set should be a subset of the former solution set, and thus the control using the shift rate model can find a solution that is not inferior to the control using the single-rate model.
2. The invention provides an iterative trajectory tracking control idea, which is a method for gradually determining the correct steering input of a transient driving maneuver, and improves the reference tracking performance by repeating the maneuver operation for multiple times and utilizing the information obtained by the previous iteration.
Drawings
FIG. 1 is a logic block diagram of the control principle of the present invention;
Detailed Description
The invention will be further explained with reference to the drawings.
As shown in FIG. 1, the practice of the present invention includes the following
Step1: establishing a variable Rate model
In a typical intelligent vehicle control system, the same sampling frequency is typically used by the system, which facilitates control system modeling and corresponding analytical design processes, but is impractical for complex operating conditions. If the sampling period is too large, the sampled signal may be distorted; if the sampling period is too small, the calculation amount is greatly increased, and the calculation load of the whole control system is increased. Aiming at the situation, the invention adopts different sampling frequencies in the system, thus improving the control effect of the system and reducing the cost.
In practical application, the system is usually a continuous system, and when the system is controlled, the system needs to be sampled to obtain a corresponding discrete model, and then the controller is designed. This results in that only the states of the sampling points are considered in the optimization of the system without considering the states between the sampling points, and therefore even if the state values of the sampling points reach the desired values, the states between the sampling points may not reach the desired values, resulting in the existence of ripples between the sampling points. Since complete elimination of ripple is essentially impossible, it can be done to find ways to reduce it. In the design of the controller, only the states of the sampling points are usually considered in the performance index, and the state between two adjacent sampling points directly influences the amplitude of the ripple. If the sampling frequency is increased, the sampling interval is reduced, and the change of the state is also reduced, which is a good method for reducing the ripple, but the more control quantity is required, so that the difficulty of implementing the control quantity in the control process is greatly increased. Therefore, the invention introduces a variable speed model in the design of the controller, so that more states can be considered without increasing the control frequency. The control quantity remains constant during a sampling interval, so that the implementation is not complicated.
Firstly, establishing a piecewise affine dynamic model of longitudinal and transverse forces of a vehicle, simultaneously considering the transverse force and the longitudinal force, carrying out piecewise affine processing on a nonlinear transverse and longitudinal force model, and carrying out tire cornering angle alpha i Force F acting in a lateral direction of the tire yi Is divided into three linear representations
Wherein, C i1 And C i2 Cornering stiffness of the piecewise affine expression for the ith tire lateral force; f. of i1 And f i2 A constant term of the piecewise affine expression is used for the lateral force of the ith wheel; alpha is alpha pi1 ，α pi2 Is a segmentation point;
the longitudinal slip ratio k of the tire i Force F in the longitudinal direction of the tire xi Is divided into three linear representations
Wherein, K i1 And K i2 The longitudinal stiffness of the piecewise affine expression for the ith tire longitudinal force; g is a radical of formula i1 And g i2 A constant term of the piecewise affine expression is used for the lateral force of the ith wheel; k is a radical of formula pi1 ，k pi2 Is a segmentation point;
the dynamic model obtained from the piecewise affine dynamic model is as follows:
wherein
Is a longitudinal path of the vehicleThe derivative is a function of the time of the first,
is the reciprocal of the lateral error of the distance from the center of mass to the path of the automobile, kappa is the road curvature, delta psi is the course angle error, V x 、V y Beta and r are respectively the longitudinal speed, the transverse speed, the mass center slip angle and the yaw angle speed of the automobile. F xf 、F xr Longitudinal forces of the front and rear wheels, respectively, F yf 、F yr The lateral force of the front wheel and the rear wheel, m is the mass of the vehicle body, a, b and IZ are the wheelbase and the rotational inertia around the Z axis
Constructing a state space equation on the basis of considering the disturbance:
e＝C c x (10)
wherein the state quantity x is represented by (V) x V y r delta psi e) and the transverse and longitudinal dynamic characteristics, A c Is a state matrix, B c Is a control quantity matrix, u is a control quantity, D c Is a disturbance quantity matrix, d is a disturbance quantity, C c Is an output quantity matrix; taking T as a sampling period to perform sampling, a corresponding discrete time model can be obtained:
x(k+1)＝A d x(k)+B d u(k)+D d d (11)
e(k)＝C c x(k) (12)
wherein A is d Is a discrete state matrix, B d As a matrix of discrete controlled quantities, D d As a matrix of discrete disturbance variables
Assuming the period of disturbance is Td, then
d(k)＝d(k-Td) (13)
The relationship between the perturbations is therefore:
the new augmented state matrix is introduced as:
z(k)＝(x k d(k) d(k-1) … d(k-Td+1)) (15)
the augmentation model is therefore:
z(k+1)＝Az(k)+Bu(k) (16)
e(k)＝Cx(k) (17)
wherein
After obtaining the augmentation model, a rate-of-change model is obtained. The rate m is chosen here, i.e. the model used by the controller is sampled with a sampling period of T/m. The control system is shown in figure 1, wherein PWA is the dynamic model of the previous formulas (3) to (8), and RPC (T/r) is the short term variable rate model. Since the sampling period is shortened, the number of state values and disturbances actually sampled in the same time period is m times the original number. Therefore, the equation for the system disturbance after using the variable rate model becomes:
wherein N = (1 \82301; 1) 1×r 。
The augmented state vector is:
z′(k)＝(x k d′(k) d′(k-1) … d′(k-Td+1)) (20)
so that the rate of change is augmented by
z′(k+1)＝A′z(k)+B′u(k) (21)
e(k)＝C′z(k) (22)
Wherein:
establishing an iterative variable rate augmentation model:
e j (k)＝C′z j (k) (25)
where k =1, \8230;, N is the number of samples, j =1, \8230;, M is the number of iterations, the inputs and outputs are stacked into an array and correlated by matrix multiplication:
e j ＝(e j (0) … e j (N)) (28)
where P is the Toeplitz matrix:
P＝CA k-1 B (29)
step2: iterative learning controller
The steering dynamics for a given turn is represented by equation (26) given the error response e for the completed turn j In the case of (2), the learning steering input of the next round is determined
The iterative learning algorithm framework is as follows:
where Q is an NxN filter matrix and L is an NxN learning matrix, the matrices Q and L will be obtained by a quadratic optimal (Q-ILC) learning controller.
Learning steering input
Is determined by minimizing the quadratic cost function in the next iteration:
wherein
T, R, S are N × N weight matrices, and superscript T denotes a transpose matrix, which function allows weighting of competing targets to minimize tracking error and variation in control amount. The filter matrix and learning matrix are as follows:
Q＝(P T TP+R+S) -1 (P T TP+S) (32)
L＝(P T TP+S) -1 P T TP(T 1/2 P) -1 T 1/2 (33)
one advantage of quadratic optimal control design is that the Q and L of the controller matrix take into account the dynamics P matrix. This enables the iterative learning algorithm to account for changes in steering dynamics due to changes in vehicle speed.
The above-listed detailed description is only a specific description of a possible embodiment of the present invention, and they are not intended to limit the scope of the present invention, and equivalent embodiments or modifications made without departing from the technical spirit of the present invention should be included in the scope of the present invention.
Claims (1)
1. An intelligent vehicle iteration track tracking control method based on a variable rate model is characterized in that the variable rate model is established by adopting different sampling frequencies; after the variable speed model is established, iterative learning control is used as a method for gradually determining the correct steering input of the transient driving, and the operation is repeated for multiple times to realize high-precision and stable path tracking;
the method for establishing the variable speed model comprises the steps of establishing a piecewise affine dynamic model of the longitudinal and transverse forces of the vehicle, wherein the piecewise affine dynamic model of the longitudinal and transverse forces of the vehicle comprises the following steps: dividing a relation curve of the tire slip angle and the tire lateral force into three sections to be linearly represented
Wherein, C i1 And C i2 Cornering stiffness of the piecewise affine expression for the ith tire lateral force; f. of i1 And f i2 A constant term of the piecewise affine expression is used for the lateral force of the ith wheel; alpha (alpha) ("alpha") pi1 ，α pi2 Is a segmentation point;
and
dividing a relation curve of the tire longitudinal slip ratio and the tire longitudinal force into three segments to be linearly represented
Wherein, K i1 And K i2 The longitudinal stiffness of the piecewise affine expression for the ith tire longitudinal force; g is a radical of formula i1 And g i2 Segmenting a constant term of an affine expression for the ith wheel lateral force; k is a radical of formula pi1 ，k pi2 Is a segmentation point;
the method of establishing a variable rate model further comprises: the dynamic model is built according to the piecewise affine dynamic model as follows:
wherein
Is the derivative of the longitudinal path of the car,
is the lateral error derivative of the distance from the center of mass of the automobile to the path, kappa is the road curvature, delta psi is the course angle error, V x 、V y Beta and r are respectively the longitudinal speed, the transverse speed, the mass center slip angle and the yaw angle speed of the automobile;
the method of establishing a variable rate model further comprises: and constructing a state space equation containing disturbance quantity according to the dynamic model:
e＝C c x (10)
wherein the state quantity x is represented by (V) x V y r delta psie) by taking the longitudinal and transverse dynamic characteristics into comprehensive consideration, A c Is a state matrix, B c For controlling a quantity matrix, D c As a disturbance quantity matrix, C c An output quantity matrix is obtained;
and (3) setting T as a sampling period to sample, and d as a disturbance quantity to obtain a corresponding discrete time model:
x(k+1)＝A d x(k)+B d u(k)+D d d (11)
e(k)＝C c x(k) (12)
wherein A is d Is a discrete state matrix, B d As a matrix of discrete controlled quantities, D d The matrix is a disturbance quantity matrix after dispersion;
the method of establishing a variable rate model further comprises: an augmentation model is established as follows
Let the disturbance period be Td, then
d(k)＝d(k-Td) (13)
The relationship between the disturbances is established as:
the new augmented state matrix is introduced as:
z(k)＝(x k d(k) d(k-1)…d(k-Td+1)) (15)
the established augmentation model is as follows:
z(k+1)＝Az(k)+Bu(k) (16)
e(k)＝Cx(k) (17)
wherein
The method of establishing a variable rate model further comprises: according to the augmentation model, establishing a variable speed augmentation model:
assuming that the sampling rate is r, i.e. the model used by the controller is sampled by the sampling period of T/r, the equation of the system disturbance becomes:
wherein N = (1 \ 82301; 1) 1×r ；
The augmented state vector is:
z′(k)＝(x k d′(k) d′(k-1)…d′(k-Td+1)) (20)
the variable speed rate augmentation model is
z′(k+1)＝A′z(k)+B′u(k) (21)
e(k)＝C′z(k) (22)
Wherein:
the method of establishing a variable rate model further comprises: establishing an iterative variable rate augmentation model:
e j (k)＝C′z j (k) (25)
where k =1, \8230;, N is the number of samples, j =1, \8230;, M is the number of iterations, the inputs and outputs are stacked into an array and correlated by matrix multiplication:
e j ＝(e j (0)…e j (N)) (28)
where P is the Toeplitz matrix:
P＝CA k-1 B (29)；
the method for iterative learning control comprises the following steps:
by using the formula
Representing a given revolutionTo dynamics, at a given completed turn of error response e j In the case of (2), the learning steering input of the next round is determined
The iterative learning algorithm framework is as follows:
where Q is an NxN filter matrix and L is an NxN learning matrix, the matrices Q and L will be obtained by a quadratic optimal (Q-ILC) learning controller;
learning steering input
Is determined by minimizing the quadratic cost function in the next iteration:
wherein
T, R, S are weight matrices of NxN, which function allows weighting competing targets to minimize tracking error and variation in control quantities; the filter matrix and the learning matrix are as follows:
Q＝(P T TP+R+S) -1 (P T TP+S) (32)
L＝(P T TP+S) -1 P T TP(T 1/2 P) -1 T 1/2 (33)。
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