CN114415523B - Vehicle cooperative motion control method and system - Google Patents

Vehicle cooperative motion control method and system Download PDF

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CN114415523B
CN114415523B CN202210320927.8A CN202210320927A CN114415523B CN 114415523 B CN114415523 B CN 114415523B CN 202210320927 A CN202210320927 A CN 202210320927A CN 114415523 B CN114415523 B CN 114415523B
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CN114415523A (en
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吴绍斌
李德润
龚建伟
卢佳兴
冯时
齐建永
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Huidong Planet Beijing Technology Co ltd
Beijing Institute of Technology BIT
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Abstract

The invention relates to a vehicle cooperative motion control method and system. The method comprises the steps of establishing a cooperative vehicle position relation model according to reference tracks of all vehicles in a cooperative vehicle queue; establishing a cooperative vehicle communication topological network model according to the cooperative vehicle position relation model and the communication directed graph of the vehicles in the cooperative vehicle queue; determining a vehicle kinematic model; determining a noise boundary and a robust invariant set of a vehicle kinematics model according to the vehicle kinematics model and the driving data of the vehicle; establishing a robust feedback controller; establishing a nominal model predictive controller; determining a robust model predictive controller for the vehicle based on the robust feedback controller and the nominal model predictive controller; and finishing cooperative control of the cooperative vehicle queue according to the robust model prediction controller and the cooperative vehicle communication topology network model. The invention can realize robust and reliable motion control of the expected formation keeping function of a plurality of unmanned vehicles under the condition of external disturbance and model mismatch.

Description

Vehicle cooperative motion control method and system
Technical Field
The invention relates to the field of vehicle control, in particular to a vehicle cooperative motion control method and system.
Background
With the development of software and hardware technologies of unmanned vehicles and the improvement of application requirements, the cooperative motion of unmanned vehicles is concerned widely. The unmanned vehicle control amount is generated by using a certain control technology, so that a determined number of vehicles move according to a pre-generated path and a corresponding formation is maintained, which is one of the core contents of the coordinated movement. Model Predictive Control (MPC) is widely used in cooperative motion Control of unmanned vehicles due to predictability, constraint and feedback. However, the traditional centralized MPC model is complex and has a plurality of constraint conditions, and the solving time is difficult to ensure the requirement of real-time performance. Based on this, Robust Distributed MPC (RDMPC) deployment considering prediction Model mismatch, external parameter uncertainty (such as road surface unevenness, wind resistance change and the like) and random disturbance is very necessary in unmanned vehicle cooperative motion Control.
The existing RDMPC is mainly applied to the fixed-distance running of a vehicle queue considering fuel economy, traffic smoothness, safety and communication delay, and does not consider a queue shape changing function when vehicles run cooperatively (namely, only longitudinal following is considered, and transverse control is not considered). The existing RDMPC uses a min-max method and a linear matrix inequality method more, and has the function of solving a conservative type and cannot give full play to the historical driving data of the unmanned vehicle.
Therefore, feedback control based on a robust invariant set is not considered in the prior art, unmanned vehicle driving data cannot be fully utilized, and robust and reliable motion control of multiple unmanned vehicles with an expected formation keeping function under the condition of external disturbance and model mismatch cannot be realized.
Based on the above problems, it is urgently needed to provide a vehicle cooperative motion control method or system for robust and reliable motion control, which considers the feedback control based on the robust invariant set, fully utilizes the driving data of the unmanned vehicle, and realizes that the multi-unmanned vehicle has the expected formation retention function under the condition of external disturbance and model mismatch.
Disclosure of Invention
The invention aims to provide a vehicle cooperative motion control method and system, which can realize robust and reliable motion control of multiple unmanned vehicles with an expected formation keeping function under the conditions of external disturbance and model mismatch.
In order to achieve the purpose, the invention provides the following scheme:
a vehicle cooperative motion control method comprising:
establishing a cooperative vehicle position relation model according to the reference track of each vehicle in the cooperative vehicle queue; the cooperative vehicle position relationship establishing model is the relative position relationship of two vehicle nodes in the cooperative vehicle queue;
establishing a cooperative vehicle communication topological network model according to the cooperative vehicle position relation model and the communication directed graph of the vehicles in the cooperative vehicle queue; the cooperative vehicle communication topological network model is a communication relation of vehicles in a cooperative vehicle queue;
determining a vehicle kinematics model of a vehicle in the collaborative vehicle fleet;
determining a maximum error boundary value of the state quantity and a robust invariant set of the vehicle kinematics model according to the vehicle kinematics model and the driving data of the vehicle; taking the maximum error boundary value of the state quantity as a noise boundary of the vehicle kinematics model;
establishing a robust feedback controller according to a noise boundary and a robust invariant set of a vehicle kinematic model;
constructing an optimization problem according to the prediction model, the cost function, the reference track, the collaborative vehicle position relation model and the control quantity constraint of the vehicle; establishing a nominal model prediction controller according to the optimization problem;
determining a robust model predictive controller for the vehicle based on the robust feedback controller and the nominal model predictive controller; sequentially establishing robust model prediction controllers of all vehicles in the cooperative vehicle queue;
determining the control quantity of the corresponding vehicle according to the robust model prediction controller; and completing cooperative control of the cooperative vehicle queue according to the cooperative vehicle communication topology network model.
Optionally, the establishing of the collaborative vehicle position relationship model according to the reference trajectory of each vehicle in the collaborative vehicle queue specifically includes the following formula:
Figure 661275DEST_PATH_IMAGE001
；
wherein,
Figure 748180DEST_PATH_IMAGE002
for following vehicle nodes
Figure 628411DEST_PATH_IMAGE003
And a followed vehicle
Figure 407624DEST_PATH_IMAGE004
The distance between the centers of mass of the two,
Figure 500345DEST_PATH_IMAGE005
is composed of
Figure 441756DEST_PATH_IMAGE004
、
Figure 899413DEST_PATH_IMAGE003
Centroid connecting line and following vehicle node
Figure 559065DEST_PATH_IMAGE003
The angular deviation of the course of the heading,
Figure 721056DEST_PATH_IMAGE006
for being followed by vehicle
Figure 451727DEST_PATH_IMAGE004
The global coordinates of the position are determined,
Figure 345865DEST_PATH_IMAGE007
for following vehicle nodes
Figure 929031DEST_PATH_IMAGE003
The global coordinates of the position are determined,
Figure 691450DEST_PATH_IMAGE008
is the vehicle heading angle.
Optionally, the determining a vehicle kinematics model of a vehicle in the collaborative vehicle train specifically includes:
establishing a vehicle kinematic model of the vehicle in a Cartesian coordinate system;
establishing a vehicle kinematic model of the vehicle in a curve coordinate system;
determining a state quantity and a control quantity according to a vehicle kinematic model in a Cartesian coordinate system and a vehicle kinematic model in a curve coordinate system, and further determining a vehicle nonlinear kinematic model;
according to the nonlinear kinematics model of the vehicle, determining a linear kinematics model of the vehicle by utilizing Taylor expansion to carry out linearization;
and carrying out discretization processing on the vehicle linear kinematics model.
Optionally, the establishing a robust feedback controller according to the noise boundary and the robust invariant set of the vehicle kinematics model specifically includes:
solving a Riccati equation by using an iterative method, and determining feedback gain;
and determining a feedback control quantity according to the noise boundary, the robust invariant set and the feedback gain of the vehicle kinematic model, and further completing the establishment of the robust feedback controller.
A vehicle coordinated motion control system comprising:
the cooperative vehicle position relation model establishing module is used for establishing a cooperative vehicle position relation model according to the reference track of each vehicle in the cooperative vehicle queue; the cooperative vehicle position relationship establishing model is the relative position relationship of two vehicle nodes in the cooperative vehicle queue;
the cooperative vehicle communication topological network model establishing module is used for establishing a cooperative vehicle communication topological network model according to the cooperative vehicle position relation model and the communication directed graph of the vehicles in the cooperative vehicle queue; the cooperative vehicle communication topological network model is a communication relation of a cooperative vehicle queue vehicle;
the vehicle kinematic model determining module is used for determining a vehicle kinematic model of a vehicle in the cooperative vehicle queue;
the noise boundary and robust invariant set determining module is used for determining a maximum error boundary value of the state quantity and a robust invariant set of the vehicle kinematic model according to the vehicle kinematic model and the driving data of the vehicle; taking the maximum error boundary value of the state quantity as a noise boundary of the vehicle kinematic model;
the robust feedback controller establishing module is used for establishing a robust feedback controller according to a noise boundary and a robust invariant set of the vehicle kinematics model;
the nominal model prediction controller establishing module is used for establishing an optimization problem according to a prediction model, a cost function, a reference track, a collaborative vehicle position relation model and a control quantity constraint of the vehicle; establishing a nominal model prediction controller according to the optimization problem;
the robust model prediction controller establishing module is used for determining a robust model prediction controller of the vehicle according to the robust feedback controller and the nominal model prediction controller; sequentially establishing robust model prediction controllers of all vehicles in the cooperative vehicle queue;
the cooperative control completion module is used for determining the control quantity of the corresponding vehicle according to the robust model prediction controller; and completing cooperative control of the cooperative vehicle queue according to the cooperative vehicle communication topology network model.
Optionally, the collaborative vehicle position relationship model building module specifically includes the following formula:
Figure 545137DEST_PATH_IMAGE001
；
wherein,
Figure 344597DEST_PATH_IMAGE002
for following vehicle nodes
Figure 179173DEST_PATH_IMAGE003
And a followed vehicle
Figure 417387DEST_PATH_IMAGE004
The distance between the centers of mass of the two,
Figure 860001DEST_PATH_IMAGE005
is composed of
Figure 689417DEST_PATH_IMAGE004
、
Figure 748640DEST_PATH_IMAGE003
Centroid connecting line and following vehicle node
Figure 728228DEST_PATH_IMAGE003
The angular deviation of the course direction is,
Figure 819157DEST_PATH_IMAGE006
for being followed by vehicle
Figure 553894DEST_PATH_IMAGE004
The global coordinates of the position are determined,
Figure 772517DEST_PATH_IMAGE007
for following vehicle nodes
Figure 883693DEST_PATH_IMAGE003
The global coordinates of the position are determined,
Figure 566478DEST_PATH_IMAGE008
is the vehicle heading angle.
Optionally, the vehicle kinematics model determination module specifically includes:
the vehicle kinematic model establishing unit is used for establishing a vehicle kinematic model of the vehicle in a Cartesian coordinate system;
the vehicle kinematic model building unit under the curve coordinate system is used for building a vehicle kinematic model of the vehicle under the curve coordinate system;
the vehicle nonlinear kinematic model determining unit is used for determining state quantity and control quantity according to a vehicle kinematic model in a Cartesian coordinate system and a vehicle kinematic model in a curve coordinate system so as to determine a vehicle nonlinear kinematic model;
the vehicle linear kinematics model determining unit is used for determining a vehicle linear kinematics model in a linearization manner by using Taylor expansion according to the vehicle nonlinear kinematics model;
and the vehicle linear kinematics model discretization processing unit is used for performing discretization processing on the vehicle linear kinematics model.
Optionally, the robust feedback controller establishing module specifically includes:
the feedback gain determining unit is used for solving the Riccati equation by using an iterative method and determining the feedback gain;
and the robust feedback controller establishing unit is used for determining the feedback control quantity according to the noise boundary, the robust invariant set and the feedback gain of the vehicle kinematic model so as to complete the establishment of the robust feedback controller.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
according to the vehicle cooperative motion control method and system provided by the invention, a feedback controller considering a robust invariant set is designed on the basis of a multi-objective optimization model predictive controller, so that the robust model predictive controller is constructed. Compared with the existing distributed model prediction control method applied to vehicle cooperative motion control, the method can fully consider the influence of model mismatch and parameter uncertainty on motion control, so that the unmanned vehicle still has unsophisticated path tracking performance and formation performance under disturbance.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic flow chart of a vehicle cooperative motion control method according to the present invention;
FIG. 2 is a schematic illustration of a collaborative vehicle positional relationship description;
FIG. 3 is a robust model predictive controller architecture diagram;
FIG. 4 is a schematic view of a kinematic model of an unmanned vehicle;
FIG. 5 is a diagram of a kinematic model of the Frenet of an unmanned vehicle;
fig. 6 is a schematic structural diagram of a vehicle cooperative motion control system provided by the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a vehicle cooperative motion control method and system, which can realize robust and reliable motion control of multiple unmanned vehicles with an expected formation keeping function under the conditions of external disturbance and model mismatch.
In order to make the aforementioned objects, features and advantages of the present invention more comprehensible, the present invention is described in detail with reference to the accompanying drawings and the detailed description thereof.
Fig. 1 is a schematic flow chart of a vehicle cooperative motion control method provided by the present invention, and as shown in fig. 1, the vehicle cooperative motion control method provided by the present invention includes:
s101, establishing a cooperative vehicle position relation model according to the reference track of each vehicle in the cooperative vehicle queue and as shown in FIG. 2; the cooperative vehicle position relationship establishing model is the relative position relationship of two vehicle nodes in the cooperative vehicle queue;
s101 specifically includes the following formula:
Figure 472117DEST_PATH_IMAGE001
；
wherein,
Figure 505932DEST_PATH_IMAGE002
for following vehicle nodes
Figure 152290DEST_PATH_IMAGE003
And a followed vehicle
Figure 955161DEST_PATH_IMAGE004
The distance between the centers of mass of the two,
Figure 31701DEST_PATH_IMAGE005
is composed of
Figure 83971DEST_PATH_IMAGE004
、
Figure 536949DEST_PATH_IMAGE003
Centroid connecting line and following vehicle node
Figure 194326DEST_PATH_IMAGE003
The angular deviation of the course direction is,
Figure 707347DEST_PATH_IMAGE006
for a followed vehicle
Figure 450175DEST_PATH_IMAGE004
The global coordinates of the position are determined,
Figure 461773DEST_PATH_IMAGE007
for following vehicle nodes
Figure 239236DEST_PATH_IMAGE003
The global coordinates of the position are determined,
Figure 329683DEST_PATH_IMAGE008
is the vehicle heading angle.
S102, establishing a cooperative vehicle communication topological network model according to the cooperative vehicle position relation model and the communication directed graph of the vehicles in the cooperative vehicle queue; the cooperative vehicle communication topological network model is a communication relation of vehicles in a cooperative vehicle queue;
in the process of
Figure 559807DEST_PATH_IMAGE009
In a vehicle cooperation queue formed by unmanned vehicles to communicate with a directed graph
Figure 89008DEST_PATH_IMAGE010
Representing an unmanned inter-vehicle communication relationship. Wherein the vertex set in the directed graph is used for communication
Figure 720978DEST_PATH_IMAGE011
Representing a set of vehicle nodes, with sets of edges in a directed graph of communications
Figure 310222DEST_PATH_IMAGE012
Representing communication interaction relationship between vehicles, using communication directed graph
Figure 87030DEST_PATH_IMAGE013
Of a neighboring matrix
Figure 419922DEST_PATH_IMAGE014
And representing the communication relationship, distance relationship and angle relationship among the vehicle nodes.
Figure 906398DEST_PATH_IMAGE014
Is defined as:
Figure 932123DEST_PATH_IMAGE015
. Wherein,
Figure 871260DEST_PATH_IMAGE016
a binary quantity representing an edge of the directed graph, namely:
Figure 7843DEST_PATH_IMAGE017
；
wherein, if
Figure 348826DEST_PATH_IMAGE018
Then side is determined
Figure 545452DEST_PATH_IMAGE019
To indicate the vehicle
Figure 906639DEST_PATH_IMAGE020
Vehicle incapable of receiving
Figure 581334DEST_PATH_IMAGE021
When the prediction information of
Figure 42402DEST_PATH_IMAGE022
And
Figure 144350DEST_PATH_IMAGE023
is arranged as
Figure 100002_DEST_PATH_IMAGE024
(ii) a If it is
Figure 792501DEST_PATH_IMAGE025
Then edge to edge
Figure 270886DEST_PATH_IMAGE026
To indicate the vehicle
Figure 849111DEST_PATH_IMAGE020
Can receive the vehicle
Figure 856381DEST_PATH_IMAGE021
When the prediction information of
Figure 522986DEST_PATH_IMAGE022
And
Figure 211587DEST_PATH_IMAGE023
setting as a preset value. For convenience of representation, the adjacency matrix is defined
Figure 647248DEST_PATH_IMAGE027
While defining a cooperative distance matrix
Figure 825419DEST_PATH_IMAGE028
And cooperation angle matrix
Figure 979320DEST_PATH_IMAGE029
Indicating the positional relationship between cooperating vehicles.
S103, determining a vehicle kinematics model of a vehicle in the cooperative vehicle queue;
s103 specifically comprises the following steps:
as shown in fig. 4, a vehicle kinematics model of the vehicle in a cartesian coordinate system is established:
Figure 796579DEST_PATH_IMAGE030
；
wherein,
Figure 883484DEST_PATH_IMAGE031
is the global coordinate of the position of the vehicle,
Figure 763715DEST_PATH_IMAGE032
is the angle of the heading of the vehicle,
Figure 873753DEST_PATH_IMAGE033
as the speed of the vehicle, is,
Figure 232054DEST_PATH_IMAGE034
the yaw angular velocity;
as shown in fig. 5, a vehicle kinematics model of the vehicle in a curvilinear coordinate system is established:
Figure 314410DEST_PATH_IMAGE035
；
wherein,
Figure 99964DEST_PATH_IMAGE036
the position of the vehicle is indicated,
Figure 959948DEST_PATH_IMAGE037
indicating deviation in vehicle heading (i.e. vehicle heading deviation)
Figure 856359DEST_PATH_IMAGE038
，
Figure 121119DEST_PATH_IMAGE039
As reference point courseA corner),
Figure 139890DEST_PATH_IMAGE040
is the reference point curvature.
In a curvilinear coordinate system, using
Figure 490100DEST_PATH_IMAGE036
The vehicle position is described. Wherein,
Figure 190203DEST_PATH_IMAGE041
represents the distance the vehicle has traveled along the baseline (i.e., the arc length traveled from the baseline starting point);
Figure 309469DEST_PATH_IMAGE042
indicating vehicle normal displacement (i.e., relative to baseline)
Figure 436825DEST_PATH_IMAGE041
Normal deviation of position). Coordinates in a curvilinear coordinate system
Figure 271401DEST_PATH_IMAGE036
And coordinates in a Cartesian coordinate system
Figure 775195DEST_PATH_IMAGE031
Can be converted into each other.
Determining a state quantity and a control quantity according to a vehicle kinematic model in a Cartesian coordinate system and a vehicle kinematic model in a curve coordinate system, and further determining a vehicle nonlinear kinematic model;
definition of
Figure 14546DEST_PATH_IMAGE043
For state variables, define
Figure 578383DEST_PATH_IMAGE044
For the control variables, the general form of the nonlinear kinematics model of the vehicle is then expressed as:
Figure 106447DEST_PATH_IMAGE045
；
according to the nonlinear kinematics model of the vehicle, determining a linear kinematics model of the vehicle by utilizing Taylor expansion to carry out linearization;
at a reference point (defining the state quantity at the reference point as
Figure 945090DEST_PATH_IMAGE046
Defining the control quantity at the reference point as
Figure 38948DEST_PATH_IMAGE047
And (3) carrying out linearization by using Taylor expansion to obtain a vehicle linear kinematics model:
Figure 976948DEST_PATH_IMAGE048
and carrying out discretization processing on the vehicle linear kinematics model.
To be provided with
Figure 520537DEST_PATH_IMAGE049
At a sampling time interval of
Figure 631713DEST_PATH_IMAGE050
The discretization of the time can obtain:
Figure 845657DEST_PATH_IMAGE051
；
wherein,
Figure 751296DEST_PATH_IMAGE052
，
Figure 113007DEST_PATH_IMAGE053
。
in an ackerman-steered vehicle, there are the following additional relationships:
Figure 496715DEST_PATH_IMAGE054
；
wherein,
Figure 565165DEST_PATH_IMAGE055
is the turning angle of the front wheel,
Figure 907285DEST_PATH_IMAGE056
the wheelbase of the front axle and the rear axle of the vehicle. Further converting the control quantity of the kinematic model of the unmanned Ackerman steering vehicle into the control quantity of the kinematic model of the unmanned Ackerman steering vehicle
Figure 428396DEST_PATH_IMAGE057
. The control quantity at the reference point is expressed as
Figure 636302DEST_PATH_IMAGE058
。
In the crawler differential steering unmanned vehicle, the following relationship is provided:
Figure 559259DEST_PATH_IMAGE059
；
wherein,
Figure 9963DEST_PATH_IMAGE060
，
Figure 18370DEST_PATH_IMAGE061
the speeds of the left and right crawler belts are respectively,
Figure 9460DEST_PATH_IMAGE062
the center distance of the two side tracks can be used for converting the control quantity of a kinematic model of the unmanned track differential steering vehicle into the control quantity of the kinematic model of the unmanned track differential steering vehicle
Figure 786923DEST_PATH_IMAGE063
The control quantity at the reference point is expressed as
Figure 205266DEST_PATH_IMAGE064
。
Considering bounded perturbations
Figure 435391DEST_PATH_IMAGE065
In the case ofThe general form of the linear kinematics model of the vehicle is restated as follows:
Figure 492821DEST_PATH_IMAGE066
；
wherein,
Figure 124790DEST_PATH_IMAGE067
is expressed as an actual state quantity which,
Figure 41931DEST_PATH_IMAGE068
is the actual control quantity. Without bounded perturbation
Figure 24930DEST_PATH_IMAGE065
The nominal linear kinematics model of the vehicle is expressed as:
Figure 357823DEST_PATH_IMAGE069
；
wherein,
Figure 844299DEST_PATH_IMAGE070
in order to be the nominal system state,
Figure 135603DEST_PATH_IMAGE071
the nominal control quantity is indicated.
S104, determining a maximum error boundary value of the state quantity and a robust invariant set of the vehicle kinematics model according to the vehicle kinematics model and the driving data of the vehicle; taking the maximum error boundary value of the state quantity as a noise boundary of the vehicle kinematic model;
due to model mismatch (deviation of the built vehicle model and a real vehicle system) and external uncertainty (random disturbance of a road surface, wind resistance and the like). True system state
Figure 340319DEST_PATH_IMAGE072
Output system state of the predictive model
Figure 414586DEST_PATH_IMAGE073
A deviation occurs as shown in the following formula:
Figure 18218DEST_PATH_IMAGE074
；
wherein,
Figure 214844DEST_PATH_IMAGE075
and
Figure 641277DEST_PATH_IMAGE076
are respectively at
Figure 581551DEST_PATH_IMAGE077
The vehicle state quantity and the control quantity measured at the moment;
a robust invariant set of post-computing systems. The following constraints are first defined for the system:
Figure 308199DEST_PATH_IMAGE078
；
defining a one-step robust reachable set:
Figure 410147DEST_PATH_IMAGE079
；
i.e. at all inputs
Figure 589456DEST_PATH_IMAGE080
Disturbance of
Figure 395738DEST_PATH_IMAGE081
Below, all
Figure 711312DEST_PATH_IMAGE082
Can be linearly kinematically modeled
Figure 246812DEST_PATH_IMAGE083
Mapping into collections
Figure 913416DEST_PATH_IMAGE084
。
Figure 398755DEST_PATH_IMAGE085
Specifically represented by the formula:
Figure 631154DEST_PATH_IMAGE086
；
wherein,
Figure 278167DEST_PATH_IMAGE087
for the linear state feedback control law, it will be established in step five.
Robust invariant set of system
Figure 432067DEST_PATH_IMAGE088
It can be calculated from table 1:
TABLE 1
Figure 252256DEST_PATH_IMAGE089
Defining the collective operations Minkowski summation and Pontryagin differencing. Define two polyhedrons
Figure 808002DEST_PATH_IMAGE090
And
Figure 419725DEST_PATH_IMAGE091
the minkowski summation is expressed as:
Figure 529763DEST_PATH_IMAGE092
；
the pointryagin differencing is expressed as:
Figure 419222DEST_PATH_IMAGE093
；
s105, establishing a robust feedback controller according to the noise boundary and the robust invariant set of the vehicle kinematic model;
s105 specifically includes:
solving a Riccati equation by using an iterative method, and determining feedback gain;
and determining a feedback control quantity according to the noise boundary, the robust invariant set and the feedback gain of the vehicle kinematic model, and further completing the establishment of the robust feedback controller.
In order to eliminate the deviation between the real system state and the nominal system state, a robust feedback controller is established. For linear states the feedback control law is generally of the form:
Figure 563895DEST_PATH_IMAGE094
；
in the proven matrix
Figure 615028DEST_PATH_IMAGE095
Controllable and observable (setting matrix)
Figure 477942DEST_PATH_IMAGE096
As an identity matrix), the control law of the Linear Quadratic Regulator (LQR) is selected
Figure 639933DEST_PATH_IMAGE097
As a steady state feedback gain of the error system, namely:
Figure 232588DEST_PATH_IMAGE098
；
wherein,
Figure 454622DEST_PATH_IMAGE099
in order to feed back the control quantity,
Figure 536323DEST_PATH_IMAGE097
solving by adopting the following method;
solving the solution of the Riccati equation by using an iterative method
Figure 174109DEST_PATH_IMAGE100
：
Figure 293374DEST_PATH_IMAGE101
；
By using
Figure 14206DEST_PATH_IMAGE102
Solving for feedback gain
Figure 851712DEST_PATH_IMAGE103
：
Figure 621085DEST_PATH_IMAGE104
；
And can further be in
Figure 798119DEST_PATH_IMAGE105
Determining feedback control quantity in control period starting at moment
Figure 627535DEST_PATH_IMAGE106
；
S106, constructing an optimization problem according to the prediction model, the cost function, the reference track, the cooperative vehicle position relation model and the control quantity constraint of the vehicle; establishing a nominal model prediction controller according to the optimization problem;
the cost function needs to ensure that the unmanned vehicle can accurately and stably track the expected path, reduce energy consumption as much as possible, and simultaneously keep a preset position relation with other unmanned vehicles. The following objective function is designed:
Figure 683828DEST_PATH_IMAGE107
；
wherein,
Figure 319209DEST_PATH_IMAGE108
to predict the time domain, the cost function is firstThe second item reflects the following ability of the vehicle to the reference track, the third item and the fourth item reflect the smooth degree of the controlled variable and the energy consumption of the controlled variable actuator, and the fourth item and the fifth item reflect the ability of the unmanned vehicle to finish the cooperative motion.
Figure 413067DEST_PATH_IMAGE109
、
Figure 413384DEST_PATH_IMAGE110
、
Figure 163165DEST_PATH_IMAGE111
、
Figure 8761DEST_PATH_IMAGE112
、
Figure 222705DEST_PATH_IMAGE113
Is the weight coefficient of each term.
The constraints are divided into equality constraints and inequality constraints. The equality constraint is a prediction model of the system, and the inequality constraint considers the control quantity extreme value constraint and the control quantity increment constraint. The control quantity limit value constraint is expressed as follows:
Figure 456240DEST_PATH_IMAGE114
；
the control amount increment constraint is expressed by the following formula:
Figure 490055DEST_PATH_IMAGE115
；
by integrating the prediction model, the cost function and the constraint, the optimization problem is constructed as follows:
Figure 404922DEST_PATH_IMAGE116
；
Figure 673705DEST_PATH_IMAGE117
Figure 750245DEST_PATH_IMAGE118
Figure 271356DEST_PATH_IMAGE119
Figure 52230DEST_PATH_IMAGE120
Figure 240766DEST_PATH_IMAGE121
Figure 691470DEST_PATH_IMAGE122
Figure 434298DEST_PATH_IMAGE123
Figure 690967DEST_PATH_IMAGE124
Figure 796327DEST_PATH_IMAGE125
Figure 480249DEST_PATH_IMAGE126
Figure 996460DEST_PATH_IMAGE127
in that
Figure 728924DEST_PATH_IMAGE128
Solving the optimization problem in the control period of the moment start to obtain a control sequence
Figure 892052DEST_PATH_IMAGE129
Controlling the first control quantity of the sequence
Figure 481296DEST_PATH_IMAGE130
The sum of the reference control quantity is used as a nominal model to predict the output quantity of the controller, namely:
Figure 526613DEST_PATH_IMAGE131
；
s107, as shown in the figure 3, determining a robust model prediction controller of the vehicle according to the robust feedback controller and the nominal model prediction controller; sequentially establishing robust model prediction controllers of all vehicles in the cooperative vehicle queue;
namely, it is
Figure 859505DEST_PATH_IMAGE132
；
S108, determining the control quantity of the corresponding vehicle according to the robust model prediction controller; and completing cooperative control of the cooperative vehicle queue according to the cooperative vehicle communication topology network model.
Fig. 6 is a schematic structural diagram of a vehicle cooperative motion control system provided by the present invention, and as shown in fig. 6, the vehicle cooperative motion control system provided by the present invention includes:
a collaborative vehicle position relationship model establishing module 601, configured to establish a collaborative vehicle position relationship model according to a reference trajectory of each vehicle in the collaborative vehicle queue; the cooperative vehicle position relationship model is established as the relative position relationship of two vehicle nodes in the cooperative vehicle queue;
a collaborative vehicle communication topological network model building module 602, configured to build a collaborative vehicle communication topological network model according to the collaborative vehicle position relationship model and the communication directed graph of the vehicles in the collaborative vehicle queue; the cooperative vehicle communication topological network model is a communication relation of vehicles in a cooperative vehicle queue;
a vehicle kinematics model determination module 603 configured to determine a vehicle kinematics model of a vehicle in the collaborative vehicle fleet;
a noise boundary and robust invariant set determination module 604 for determining a maximum error boundary value of the state quantity and a robust invariant set of the vehicle kinematics model according to the vehicle kinematics model and the driving data of the vehicle; taking the maximum error boundary value of the state quantity as a noise boundary of the vehicle kinematics model;
a robust feedback controller establishing module 605, configured to establish a robust feedback controller according to the noise boundary and the robust invariant set of the vehicle kinematics model;
a nominal model predictive controller building module 606 for building an optimization problem according to the predictive model, the cost function, the reference trajectory, the collaborative vehicle position relationship model and the controlled variable constraint of the vehicle; establishing a nominal model prediction controller according to the optimization problem;
a robust model predictive controller building module 607 for determining a robust model predictive controller for the vehicle based on the robust feedback controller and the nominal model predictive controller; sequentially establishing robust model prediction controllers of all vehicles in the cooperative vehicle queue;
a cooperative control completion module 608 for determining a control quantity of the corresponding vehicle according to the robust model prediction controller; and completing cooperative control of the cooperative vehicle queue according to the cooperative vehicle communication topology network model.
The collaborative vehicle position relationship model building module 601 specifically includes the following formula:
Figure 877140DEST_PATH_IMAGE001
；
wherein,
Figure 840547DEST_PATH_IMAGE002
for following vehicle nodes
Figure 310843DEST_PATH_IMAGE003
And a followed vehicle
Figure 444497DEST_PATH_IMAGE004
The distance between the centers of mass of the two,
Figure 378955DEST_PATH_IMAGE005
is composed of
Figure 575581DEST_PATH_IMAGE004
、
Figure 470856DEST_PATH_IMAGE003
Centroid connecting line and following vehicle node
Figure 411130DEST_PATH_IMAGE003
The angular deviation of the course direction is,
Figure 137777DEST_PATH_IMAGE006
for being followed by vehicle
Figure 567622DEST_PATH_IMAGE004
The global coordinates of the position are determined,
Figure 746930DEST_PATH_IMAGE007
for following vehicle nodes
Figure 490895DEST_PATH_IMAGE003
The global coordinates of the position are determined,
Figure 9732DEST_PATH_IMAGE008
is the vehicle heading angle.
The vehicle kinematics model determination module 603 specifically includes:
the vehicle kinematic model establishing unit is used for establishing a vehicle kinematic model of the vehicle in a Cartesian coordinate system;
the vehicle kinematic model building unit under the curve coordinate system is used for building a vehicle kinematic model of the vehicle under the curve coordinate system;
the vehicle nonlinear kinematic model determining unit is used for determining state quantity and control quantity according to a vehicle kinematic model in a Cartesian coordinate system and a vehicle kinematic model in a curvilinear coordinate system so as to determine a vehicle nonlinear kinematic model;
the vehicle linear kinematics model determining unit is used for determining a vehicle linear kinematics model in a linearization manner by using Taylor expansion according to the vehicle nonlinear kinematics model;
and the vehicle linear kinematics model discretization processing unit is used for discretizing the vehicle linear kinematics model.
The robust feedback controller establishing module 605 specifically includes:
the feedback gain determining unit is used for solving the Riccati equation by using an iterative method and determining the feedback gain;
and the robust feedback controller establishing unit is used for determining the feedback control quantity according to the noise boundary, the robust invariant set and the feedback gain of the vehicle kinematic model so as to complete the establishment of the robust feedback controller.
In the present specification, the embodiments are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the description of the method part.
The principle and the embodiment of the present invention are explained by applying specific examples, and the above description of the embodiments is only used to help understanding the method and the core idea of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (8)

1. A vehicle cooperative motion control method characterized by comprising:
establishing a cooperative vehicle position relation model according to the reference track of each vehicle in the cooperative vehicle queue; the cooperative vehicle position relationship establishing model is the relative position relationship of two vehicle nodes in the cooperative vehicle queue;
establishing a cooperative vehicle communication topological network model according to the cooperative vehicle position relation model and the communication directed graph of the vehicles in the cooperative vehicle queue; the cooperative vehicle communication topological network model is a communication relation of vehicles in a cooperative vehicle queue;
determining a vehicle kinematics model of a vehicle in the collaborative vehicle fleet;
determining a maximum error boundary value of the state quantity and a robust invariant set of the vehicle kinematics model according to the vehicle kinematics model and the driving data of the vehicle; taking the maximum error boundary value of the state quantity as a noise boundary of the vehicle kinematic model;
establishing a robust feedback controller according to a noise boundary and a robust invariant set of a vehicle kinematic model;
constructing an optimization problem according to the prediction model, the cost function, the reference track, the collaborative vehicle position relation model and the control quantity constraint of the vehicle; establishing a nominal model prediction controller according to the optimization problem;
determining a robust model predictive controller for the vehicle based on the robust feedback controller and the nominal model predictive controller; sequentially establishing robust model prediction controllers of all vehicles in the cooperative vehicle queue;
determining the control quantity of the corresponding vehicle according to the robust model prediction controller; and completing cooperative control of the cooperative vehicle queue according to the cooperative vehicle communication topology network model;
the constructed optimization problem specifically comprises the following formula:
Figure DEST_PATH_IMAGE001
；
Figure DEST_PATH_IMAGE002
Figure DEST_PATH_IMAGE003
Figure DEST_PATH_IMAGE005
Figure DEST_PATH_IMAGE007
Figure DEST_PATH_IMAGE009
Figure DEST_PATH_IMAGE011
Figure DEST_PATH_IMAGE013
Figure DEST_PATH_IMAGE015
Figure DEST_PATH_IMAGE016
Figure DEST_PATH_IMAGE017
Figure DEST_PATH_IMAGE018
；
the nominal model predictive controller specifically includes the following equation:
Figure DEST_PATH_IMAGE019
；
wherein,
Figure DEST_PATH_IMAGE020
in order to predict the time domain,
Figure DEST_PATH_IMAGE021
、
Figure DEST_PATH_IMAGE022
、
Figure DEST_PATH_IMAGE023
、
Figure DEST_PATH_IMAGE024
、
Figure DEST_PATH_IMAGE025
in order to be the weight coefficient,
Figure DEST_PATH_IMAGE026
in order to control the amount of the liquid,
Figure DEST_PATH_IMAGE027
for the purpose of reference to the control quantity,
Figure DEST_PATH_IMAGE028
the output of the controller is predicted for the nominal model,
Figure DEST_PATH_IMAGE029
in order to restrict the extreme value of the control quantity,
Figure DEST_PATH_IMAGE030
in order to control the quantity increment constraint,
Figure DEST_PATH_IMAGE031
is composed of
Figure 189360DEST_PATH_IMAGE031
The time of day.
2. The vehicle cooperative motion control method according to claim 1, wherein the establishing of the cooperative vehicle position relationship model according to the reference trajectory of each vehicle in the cooperative vehicle queue specifically includes the following formula:
Figure DEST_PATH_IMAGE032
；
wherein,
Figure DEST_PATH_IMAGE033
for following vehicle nodes
Figure DEST_PATH_IMAGE034
And a followed vehicle
Figure DEST_PATH_IMAGE035
The distance between the centers of mass of the two,
Figure DEST_PATH_IMAGE036
is composed of
Figure 256149DEST_PATH_IMAGE035
、
Figure 768033DEST_PATH_IMAGE034
Centroid connecting line and following vehicle node
Figure 983114DEST_PATH_IMAGE034
The angular deviation of the course direction is,
Figure DEST_PATH_IMAGE037
for being followed by vehicle
Figure 432812DEST_PATH_IMAGE035
The global coordinates of the position are determined,
Figure DEST_PATH_IMAGE038
for following vehicle nodes
Figure 945702DEST_PATH_IMAGE034
The global coordinates of the position are determined,
Figure DEST_PATH_IMAGE039
is the vehicle heading angle.
3. The method according to claim 1, wherein the determining a vehicle kinematic model of a vehicle in the coordinated vehicle train specifically comprises:
establishing a vehicle kinematic model of the vehicle in a Cartesian coordinate system;
establishing a vehicle kinematic model of the vehicle in a curve coordinate system;
determining a state quantity and a control quantity according to a vehicle kinematic model in a Cartesian coordinate system and a vehicle kinematic model in a curve coordinate system, and further determining a vehicle nonlinear kinematic model;
according to the nonlinear kinematics model of the vehicle, determining a linear kinematics model of the vehicle by utilizing Taylor expansion to carry out linearization;
and carrying out discretization processing on the vehicle linear kinematics model.
4. The vehicle cooperative motion control method according to claim 1, wherein the establishing of the robust feedback controller according to the noise boundary and the robust invariant set of the vehicle kinematics model specifically comprises:
solving a Riccati equation by using an iterative method, and determining a feedback gain;
and determining a feedback control quantity according to the noise boundary, the robust invariant set and the feedback gain of the vehicle kinematic model, and further completing the establishment of the robust feedback controller.
5. A vehicle coordinated motion control system, characterized by comprising:
the cooperative vehicle position relation model establishing module is used for establishing a cooperative vehicle position relation model according to the reference track of each vehicle in the cooperative vehicle queue; the cooperative vehicle position relationship establishing model is the relative position relationship of two vehicle nodes in the cooperative vehicle queue;
the cooperative vehicle communication topological network model establishing module is used for establishing a cooperative vehicle communication topological network model according to the cooperative vehicle position relation model and the communication directed graph of the vehicles in the cooperative vehicle queue; the cooperative vehicle communication topological network model is a communication relation of vehicles in a cooperative vehicle queue;
the vehicle kinematic model determining module is used for determining a vehicle kinematic model of a vehicle in the collaborative vehicle queue;
the noise boundary and robust invariant set determining module is used for determining a maximum error boundary value of the state quantity and a robust invariant set of the vehicle kinematic model according to the vehicle kinematic model and the driving data of the vehicle; taking the maximum error boundary value of the state quantity as a noise boundary of the vehicle kinematic model;
the robust feedback controller establishing module is used for establishing a robust feedback controller according to a noise boundary and a robust invariant set of the vehicle kinematics model;
the nominal model prediction controller establishing module is used for establishing an optimization problem according to a prediction model, a cost function, a reference track, a collaborative vehicle position relation model and a control quantity constraint of the vehicle; establishing a nominal model prediction controller according to the optimization problem;
the robust model prediction controller establishing module is used for determining a robust model prediction controller of the vehicle according to the robust feedback controller and the nominal model prediction controller; sequentially establishing robust model prediction controllers of all vehicles in the cooperative vehicle queue;
the cooperative control completion module is used for determining the control quantity of the corresponding vehicle according to the robust model prediction controller; and completing cooperative control of the cooperative vehicle queue according to the cooperative vehicle communication topology network model;
the constructed optimization problem specifically comprises the following formula:
Figure 534596DEST_PATH_IMAGE001
；
Figure 920578DEST_PATH_IMAGE002
Figure 637998DEST_PATH_IMAGE003
Figure 16896DEST_PATH_IMAGE005
Figure 237792DEST_PATH_IMAGE007
Figure 60255DEST_PATH_IMAGE009
Figure 750125DEST_PATH_IMAGE011
Figure 152287DEST_PATH_IMAGE013
Figure 8116DEST_PATH_IMAGE015
Figure 735901DEST_PATH_IMAGE016
Figure 959072DEST_PATH_IMAGE017
Figure 381570DEST_PATH_IMAGE018
；
the nominal model predictive controller specifically includes the following formula:
Figure 639376DEST_PATH_IMAGE019
；
wherein,
Figure 475745DEST_PATH_IMAGE020
in order to predict the time domain,
Figure 701058DEST_PATH_IMAGE021
、
Figure 913865DEST_PATH_IMAGE022
、
Figure 26178DEST_PATH_IMAGE023
、
Figure 49760DEST_PATH_IMAGE024
、
Figure 981943DEST_PATH_IMAGE025
in order to be a weight coefficient of the image,
Figure 60758DEST_PATH_IMAGE026
in order to control the amount of the liquid,
Figure 480107DEST_PATH_IMAGE027
for the purpose of reference to the control quantity,
Figure 720595DEST_PATH_IMAGE028
the output of the controller is predicted for the nominal model,
Figure 374298DEST_PATH_IMAGE029
in order to restrict the extreme value of the control quantity,
Figure 991224DEST_PATH_IMAGE030
in order to control the quantity increment constraint,
Figure 15812DEST_PATH_IMAGE031
is composed of
Figure 676469DEST_PATH_IMAGE031
The moment of time.
6. The vehicle cooperative motion control system according to claim 5, wherein the cooperative vehicle position relationship model building module specifically includes the following formula:
Figure 786507DEST_PATH_IMAGE032
；
wherein,
Figure 207124DEST_PATH_IMAGE033
for following vehicle nodes
Figure 633689DEST_PATH_IMAGE034
And a followed vehicle
Figure 419242DEST_PATH_IMAGE035
The distance between the centers of mass of the two,
Figure 78894DEST_PATH_IMAGE036
is composed of
Figure 224573DEST_PATH_IMAGE035
、
Figure 286070DEST_PATH_IMAGE034
Centroid connecting line and following vehicle node
Figure 39262DEST_PATH_IMAGE034
The angular deviation of the course direction is,
Figure 606117DEST_PATH_IMAGE037
for a followed vehicle
Figure 368536DEST_PATH_IMAGE035
The global coordinates of the position are determined,
Figure 471490DEST_PATH_IMAGE038
for following vehicle nodes
Figure 661163DEST_PATH_IMAGE034
The global coordinates of the position are determined,
Figure 233090DEST_PATH_IMAGE039
is the vehicle heading angle.
7. The vehicle cooperative motion control system according to claim 5, wherein the vehicle kinematics model determination module specifically includes:
the vehicle kinematic model establishing unit is used for establishing a vehicle kinematic model of the vehicle in a Cartesian coordinate system;
the vehicle kinematic model building unit under the curve coordinate system is used for building a vehicle kinematic model of the vehicle under the curve coordinate system;
the vehicle nonlinear kinematic model determining unit is used for determining state quantity and control quantity according to a vehicle kinematic model in a Cartesian coordinate system and a vehicle kinematic model in a curve coordinate system so as to determine a vehicle nonlinear kinematic model;
the vehicle linear kinematics model determining unit is used for determining a vehicle linear kinematics model in a linearization manner by using Taylor expansion according to the vehicle nonlinear kinematics model;
and the vehicle linear kinematics model discretization processing unit is used for discretizing the vehicle linear kinematics model.
8. The vehicle coordinated motion control system according to claim 5, wherein the robust feedback controller establishment module specifically comprises:
the feedback gain determining unit is used for solving the Riccati equation by using an iterative method and determining the feedback gain;
and the robust feedback controller establishing unit is used for determining the feedback control quantity according to the noise boundary, the robust invariant set and the feedback gain of the vehicle kinematic model so as to complete the establishment of the robust feedback controller.
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