CN116224769B - PID consistency control method for unmanned automobile formation - Google Patents
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Abstract
The invention discloses a PID consistency control method for unmanned automobile formation, which comprises the following steps: step 1, establishing a state space model of a positive multi-intelligent system of an unmanned automobile formation system; step 2, establishing a distributed PID control protocol of the unmanned automobile formation system; step 3, designing an integral part of a distributed PID control protocol; step 4, designing a condition for stable operation of the unmanned automobile formation system; step 5, a positive verification process of the unmanned automobile formation system; and 6, verifying the consistency of the unmanned automobile formation system. The invention realizes that each vehicle in the unmanned vehicle formation system keeps a relatively stable pose and a motion state between itself and an automatic driving vehicle running nearby, so that the unmanned vehicle formation system can normally run.
Description
Technical Field
The invention belongs to the technical field of automatic driving and modern control, and particularly relates to a PID consistency control method for unmanned automobile formation.
Background
In the technical field of automatic driving, unmanned automobile formation driving is a common control form technology, and has obvious effects of relieving road congestion in the future, improving road traffic capacity and reducing traffic accidents. The problem of unmanned car formation mainly aims at that a plurality of unmanned cars are in complex and changeable traffic environments, and the form speed and the steering of the unmanned cars are regulated, so that the geometrical pose and the motion state of the unmanned cars are kept relatively stable between the unmanned cars and the adjacent automatic cars, and the consistent running behavior taking wireless communication as a tie between the unmanned cars is realized. The term "consistency" is meant to mean that the states or targets of the individual agents in the multi-agent system are ultimately consistent via a suitable distributed control law. For unmanned vehicles formation, each unmanned vehicle is taken as an intelligent body, and information interaction is carried out among the unmanned vehicles through communication topology. The system for forming the unmanned vehicles, as shown in fig. 1, is an example of six unmanned vehicles, and the figure also represents a communication topological diagram of the system for forming the unmanned vehicles, a wire between vehicles indicates that the two unmanned vehicles can communicate with each other, and a wire between vehicles indicates that the two unmanned vehicles cannot communicate with each other.
In many practical applications, the unmanned vehicle formation moves in a fixed area, and the unmanned formation problem of limited area can be modeled by a plurality of intelligent agents, namely, the track of the vehicle formation is limited to move in a non-negative image limit, and the modeling also becomes limited modeling. The use of multi-agent systems to model formation problems has become very popular, such as in formation flights. The controller having a proportional-integral-derivative control law is called a PID controller. Since the introduction of PID controllers into the engineering field, it has become a core technology and is widely used in industrial engineering. Compared with other control strategies, the PID controller has the advantages of simple structure, good stability, reliable operation, convenient adjustment, easy understanding by engineers and the like. In an unmanned automobile formation system, all unmanned automobiles in the system are required to have consistent behaviors or change according to a certain rule so as to meet the requirements of unmanned automobile formation. The PID controller (proportional-integral-derivative controller) is to set a proportional unit P, an integral unit I and a derivative unit D to carry out deviation adjustment on the whole control system, so that the actual value of the controlled variable is consistent with the preset value of the process requirement. Compared with a PI controller, the PID controller has the advantage of improving the steady-state performance of the system, and provides a negative real zero point, so that the PID controller has greater superiority in improving the dynamic performance of the system. The P part in the PID controller can reduce the steady-state error of the system, so that the control precision of the system is improved, the I part can improve the steady-state performance of the system, and the D part can improve the dynamic performance of the system. At present, research on PID control protocols of multiple intelligent agents exists, but the research is carried out on the basis of a general multi-intelligent agent system (non-positive multi-intelligent agent system), if the general multi-intelligent agent system is used for modeling an unmanned automobile formation system, redundant negative quantity parts are caused, and further system resources are wasted. In order to solve the problems, the invention aims to consider the problem of the consistency of the unmanned automobile formation system by modeling the unmanned automobile formation system by adopting a positive multi-agent system and realizing the unmanned automobile formation system through a PID control protocol.
Disclosure of Invention
Aiming at the problems, the invention establishes a state space model of the unmanned automobile formation system by utilizing the modern control theory technology, is based on a PID protocol, is a distributed PID control protocol of the unmanned automobile formation system, analyzes the positive and consistency of the distributed PID control protocol, and ensures that each automobile in the unmanned automobile formation system can maintain relatively stable geometric pose and motion state. In conclusion, the design of the unmanned automobile formation system based on the positive multi-agent system modeling and the distributed PID control protocol has important scientific research significance and practical application significance.
The invention aims at solving the problem of consistency control of vehicles in an unmanned automobile formation system, researches the unmanned automobile formation system by using a distributed PID control protocol, and provides a PID consistency control method for unmanned automobile formation.
The method comprises the following specific steps:
step 1, acquiring geometric pose data which is the running state of a vehicle in an unmanned automobile formation system, and establishing a state space model of a positive multi-intelligent system of the unmanned automobile formation system, wherein the form is as follows:
x i (k+1)＝Ax i (k)+Bu i (k),
y i (k)＝Cx i (k),i∈1,2,...,N
wherein ,indicating the running state of the ith vehicle at the time k,control input representing the next operating state of the ith vehicle at time k, +.>And (5) representing the pose of the ith vehicle acquired by the sensor at the moment k. />Is a known system matrix. />And representing the number of the automobiles in the unmanned automobile formation system. />Respectively representing n-dimensional, r-dimensional and s-dimensional column vectors, n×n-dimensional, n×r-dimensional and s×n-dimensional matrixes and positive integer sets. [ x ] i1 (k),x i2 (k),...,x in (k)] T Representing vector x i1 (k),x i2 (k),...,x in (k)]Is a transpose of (a).
Step 2, a distributed PID control protocol of the unmanned automobile formation system is established, and the establishment form is as follows:
wherein ,Kp1 ,K p2 ,K I and KD All are gain matrices of the PID control protocol to be designed;is a matrix related to the communication topology between the agents, if the ith agent and the jth agent can communicate, then +.>Otherwise the first set of parameters is selected,the dimension of the system is related to the number of the intelligent agents in the multi-intelligent system (namely, the system is as same as the number of the vehicles in the unmanned vehicle formation system); e, e i(k) and Δyi (k) Respectively the integral and differential parts of the distributed PID control protocol, and deltay i (k)＝y i (k)-y i (k-1)。
Step 3, designing an integral part of a distributed PID control protocol, wherein the integral part has the following construction form:
e i (k)＝Cx i (k-1)+(1-α)e i (k-1),
where α is a small tuning parameter and α > 0.
And 4, designing the conditions for the stable operation of the unmanned automobile formation system as follows:
the design constant alpha is more than 0 and less than or equal to 1,vector v 1 ＞0,v' 1＞0, and />The vector quantity is used to determine the vector quantity, so that
η + +η-+v' 2 -αv 2 ＜0, (7)
For any iota=1, 2, …, r, then under the distributed PID control protocol in step 2, the unmanned vehicle formation system achieves positive and consistent performance with a gain matrix of
And satisfy the following
wherein ,i.e. l max and lmin Representing matrices separatelyMaximum and minimum elements of the diagonal; 1 r R-dimensional column vector representing 1 for all elements,/->R-dimensional column vectors representing 1 for the first element and 0 for the remaining elements, 0 representing a vector or matrix with all elements being 0; vector quantityThe superscript + in (a) indicates that all elements of the vector are positive, the vectorThe superscript in (a) indicates that all elements of the vector are negative, and (2)>Respectively represent vectorsUpper bound of->Respectively represent vector +.>Is defined below.
And 5, a positive verification process of the unmanned automobile formation system is as follows:
5.1 the integral part of the PID control protocol constructed in the step 2 and the PID control protocol constructed in the step 3 can be obtained according to the state space model of the unmanned automobile formation system constructed in the step 1
wherein ,is a Cronecker product operator, I N and Is Identity matrices of dimensions N x N and s x s, respectively, and
5.2 reamFrom step 5.1, it can be obtained
wherein ,
definition matrixThe diagonal matrix and the off-diagonal matrix of (a) are:
and
5.3 from conditions (1) - (4) in step 4, 0 < alpha.ltoreq.1 and C.gtoreq.0:
thus, the first and second substrates are bonded together,therefore, unmanned car queuing systems are positive.
And 6, verifying the consistency of the unmanned automobile formation system, wherein the verifying process is as follows:
6.1 selecting a Linear residual positive Lyapunov function wherein , the difference of (2) is:
6.2 combining steps 5.2 and 6.1, one can obtain
wherein ,
from the following components wherein ,/>Representation matrix->Elements of the ith row and jth column of (c) can be obtained
6.3 from condition (5) in step 4:
the method further comprises the following steps:
6.4 from conditions (6) - (8) in step 4:
further, omega is less than 0, gamma is less than 0, and pi is less than 0. Combining the step 6.2 to obtain
Therefore, the unmanned automobile formation system is consistent, namely, the relative stable pose and motion state between each automobile and the automatic driving automobile running nearby in the unmanned automobile formation system are realized.
The beneficial effects of the invention are as follows:
the invention provides a PID consistency control method for unmanned automobile formation. Information interaction between different vehicles is achieved by means of the communication topological graph and graph theory knowledge. A distributed PID control protocol is designed by means of the constructed linear residual Lyapunov function and matrix decomposition technology, the positive and the consistency of the distributed PID control protocol are analyzed, and the purpose that the relative stable pose and motion state between each vehicle and the nearby automatic driving vehicles in the unmanned automobile formation system are kept is achieved, so that the unmanned automobile formation system can normally operate.
Drawings
Fig. 1 is a diagram of an unmanned vehicle formation system.
Fig. 2 is a mathematical model block diagram based on an unmanned vehicle formation system.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
The invention aims at solving the problem of consistency control of vehicles in an unmanned automobile formation system, researches the unmanned automobile formation system by using a distributed PID control protocol, and provides a distributed PID control protocol method of the unmanned automobile formation system based on positive multi-agent system modeling. The specific implementation mode is as follows:
step 1, acquiring geometric pose data which is the running state of a vehicle in an unmanned automobile formation system, and establishing a state space model of a positive multi-intelligent system of the unmanned automobile formation system, wherein the form is as follows:
x i (k+1)＝Ax i (k)+Bu i (k),
y i (k)＝Cx i (k),i∈1,2,…,N
wherein ,indicating the running state of the ith vehicle at the time k,control input representing the next operating state of the ith vehicle at time k, +.>And (5) representing the pose of the ith vehicle acquired by the sensor at the moment k. />Is a known system matrix. />And representing the number of the automobiles in the unmanned automobile formation system. />Respectively representing n-dimensional, r-dimensional and s-dimensional column vectors, n×n-dimensional, n×r-dimensional and s×n-dimensional matrixes and positive integer sets. />Representing vector x i1 (k),x i2 (k),…,x in (k)]Is a transpose of (a).
Step 2, a distributed PID control protocol of the unmanned automobile formation system is established, and the establishment form is as follows:
wherein ,Kp1 ,K p2 ,K I and KD All are gain matrices of the PID control protocol to be designed;is a matrix related to the communication topology between the agents, if the ith agent and the jth agent can communicate, then +.>Otherwise the first set of parameters is selected,the dimension of which is related to the number of agents in the multi-agent system (i.e., as many vehicles as in the unmanned vehicle formation system), as shown in fig. 2; e, e i(k) and Δyi (k) Respectively the integral and differential parts of the distributed PID control protocol, and deltay i (k)＝y i (k)-y i (k-1)。
Step 3, designing an integral part of a distributed PID control protocol, wherein the integral part has the following construction form:
e i (k)＝Cx i (k-1)+(1-α)e i (k-1),
where α is a small tuning parameter and α > 0.
And 4, designing the conditions for the stable operation of the unmanned automobile formation system as follows:
the design constant alpha is more than 0 and less than or equal to 1,vector v 1 ＞0,v' 1＞0, and />The vector quantity is used to determine the vector quantity, so that
For any iota=1, 2..r, then under the distributed PID control protocol in step 2, the unmanned car queuing system achieves positive and consistent performance with a gain matrix of
And satisfy the following
wherein ,i.e. l max and lmin Representing matrices separatelyMaximum and minimum elements of the diagonal; 1 r R-dimensional column vector representing 1 for all elements,/->R-dimensional column vectors representing 1 for the first element and 0 for the remaining elements, 0 representing a vector or matrix with all elements being 0; vector quantitySuperscript in (3) + All elements representing the vector are positive, the vectorThe superscript in (a) indicates that all elements of the vector are negative, and (2)>Respectively represent vector +.>Upper bound of->Respectively represent vector +.>Is defined below.
And 5, a positive verification process of the unmanned automobile formation system is as follows:
5.1 the integral part of the PID control protocol constructed in the step 2 and the PID control protocol constructed in the step 3 can be obtained according to the state space model of the unmanned automobile formation system constructed in the step 1
wherein ,is a Cronecker product operator, I N and Is Identity matrices of dimensions N x N and s x s, respectively, and
5.2 reamFrom step 5.1, it can be obtained
wherein ,
definition matrixThe diagonal matrix and the off-diagonal matrix of (a) are:
and
5.3 from conditions (1) - (4) in step 4, 0 < alpha.ltoreq.1 and C.gtoreq.0:
thus, the first and second substrates are bonded together,therefore, unmanned car queuing systems are positive.
And 6, verifying the consistency of the unmanned automobile formation system, wherein the verifying process is as follows:
6.1 selecting a Linear residual positive Lyapunov function wherein , the difference of (2) is:
6.2 combining steps 5.2 and 6.1, one can obtain
wherein ,
from the following components wherein ,/>Representation matrix->Elements of the ith row and jth column of (c) can be obtained
6.3 from condition (5) in step 4:
the method further comprises the following steps:
6.4 from conditions (6) - (8) in step 4:
further, omega is less than 0, gamma is less than 0, and pi is less than 0. Combining the step 6.2 to obtain
Therefore, the unmanned automobile formation system is consistent, namely, the relative stable pose and motion state between each automobile and the automatic driving automobile running nearby in the unmanned automobile formation system are realized.
Claims (3)
1. The PID consistency control method for the unmanned automobile formation is characterized by comprising the following steps of:
step 1, a positive multi-intelligent system state space model of an unmanned automobile formation system is established, and the structural form is as follows:
x i (k+1)＝Ax i (k)+Bu i (k),
y i (k)＝Cx i (k),i∈1,2,...,N
wherein ,indicating the operating state of the ith vehicle at time k, < >>Control input representing the next operating state of the ith vehicle at time k, +.>When k is expressedThe pose of the ith vehicle acquired by the sensor is carved, < >>Is a known system matrix, +.>Indicating the number of cars in the unmanned car platoon system,/-> Respectively representing n-dimension, r-dimension, s-dimension column vectors, n x n-dimension, n x r-dimension, s x n-dimension matrix, positive integer set,/->Representing vector x i1 (k),x i2 (k),...,x in (k)]Is a transpose of (2);
step 2, a distributed PID control protocol of the unmanned automobile formation system is established, and the establishment form is as follows:
wherein ,Kp1 ,K p2 ,K I and KD All are gain matrices of the PID control protocol to be designed;is a matrix related to the communication topology between the agents, if the ith agent and the jth agent can communicate, then +.>Otherwise the first set of parameters is selected,the dimension is related to the number of the intelligent agents in the multi-intelligent system; e, e i(k) and Δyi (k) Respectively the integral and differential parts of the distributed PID control protocol, and deltay i (k)＝y i (k)-y i (k-1)；
Step 3, designing an integral part of a distributed PID control protocol, wherein the integral part has the following construction form:
e i (k)＝Cx i (k-1)+(1-α)e i (k-1),
wherein α is a small tuning parameter and α > 0;
step 4, designing a condition for stable operation of the unmanned automobile formation system, wherein the construction method comprises the following steps:
the design constant alpha is more than 0 and less than or equal to 1,vector-> and />Vector (S)> So that
For any iota=1, 2..r, then under the distributed PID control protocol in step 2, the unmanned car queuing system achieves positive and consistent performance with a gain matrix of
And satisfy the following
wherein ,i.e. l max and lmin Respectively represent matrix->Maximum and minimum elements of the diagonal; 1 r R-dimensional column vector representing 1 for all elements,/->R-dimensional column vectors representing 1 for the first element and 0 for the remaining elements, 0 representing a vector or matrix with all elements being 0; vector->o + ,/>η + ，/> θ + ，/>Superscript in (3) + All elements representing the vector are positive, vector +.>o - ，/>η - ，/> θ - ，/>Superscript in (3) - All elements representing the vector are negative, < >>Respectively represent vector +.>Is defined by the upper bound of (c),θ + ,θ - respectively represent vector +.>Lower bound of (2);
step 5, a positive verification process of the unmanned automobile formation system;
and 6, verifying the consistency of the unmanned automobile formation system.
2. The PID consistency control method of unmanned vehicle formation according to claim 1, wherein the positive verification process of the unmanned vehicle formation system in step 5 is constructed as follows:
5.1 the integral part of the PID control protocol constructed in the step 2 and the PID control protocol constructed in the step 3 can be obtained according to the state space model of the unmanned automobile formation system constructed in the step 1
wherein ,is a Cronecker product operator, I N and Is Identity matrices of dimensions N x N and s x s, respectively, and
5.2 reamFrom step 5.1, it can be obtained
wherein ,
definition matrixThe diagonal matrix and the off-diagonal matrix of (a) are:
and
5.3 from conditions (1) - (4) in step 4, 0 < alpha.ltoreq.1 andthe method can obtain:
thus, the first and second substrates are bonded together,therefore, unmanned car queuing systems are positive.
3. The PID consistency control method of unmanned vehicle formation according to claim 2, wherein the consistency verification process of the unmanned vehicle formation system in step 6 is constructed as follows:
6.1 selecting a Linear residual positive Lyapunov function wherein ,
is the difference of (2)The method is divided into:
6.2 combining steps 5.2 and 6.1, one can obtain
wherein ,
from the following components wherein ,/>Representation matrix->Elements of the ith row and jth column of (c) can be obtained
6.3 from condition (5) in step 4:
the method further comprises the following steps:
6.4 from conditions (6) - (8) in step 4:
further can obtainCombining the step 6.2 to obtain
Therefore, the unmanned automobile formation system is consistent, namely, the relative stable pose and motion state between each automobile and the automatic driving automobile running nearby in the unmanned automobile formation system are realized.
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