CN109358621B - Autonomous driving vehicle Trajectory Tracking Control method - Google Patents
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
- G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process
Abstract
A kind of autonomous driving vehicle Trajectory Tracking Control method, in the Trajectory Tracking Control modeling process of autonomous driving vehicle, it is contemplated that inevitable network delay and data packetloss problem, and general delay expression is more advantageous to the design of controller.Autonomous driving vehicle Trajectory Tracking Control design synthesis considers the uncertainty and the influence of external disturbance of vehicle dynamic model, improves the control stability of vehicle and the robustness of Trajectory Tracking Control.Solve the problems, such as the autonomous driving vehicle Trajectory Tracking Control containing network delay and data packetloss, convenience of calculation by solving linear matrix inequality.By solving convex optimization problem, the lower bound of autonomous driving vehicle Trajectory Tracking Control problem Disturbance Rejection performance indicator can be calculated, it is thus possible to obtain optimal contrail tracker.
Description
Technical field
The present invention relates to autonomous driving vehicle Trajectory Tracking Control fields, and in particular to a kind of autonomous driving vehicle track with
Track control method.
Background technique
Autonomous driving vehicle can effectively promote the driving safety of vehicle, realize better road utilization rate, and significantly
Mobile cost is reduced, provides possibility fundamentally to change traditional mode of transportation, thus, become emerging in recent years and grinds
Study carefully hot spot.One of key technology as autonomous driving vehicle, the Trajectory Tracking Control target of vehicle are how to guarantee vehicle
Under the premise of driving safety and riding comfort, by controlling the steering system of vehicle, allow the vehicle to along desired
Route running, eliminates the tracing deviation that generates in autonomous driving vehicle driving process, i.e. range deviation and angular deviation, and track
Tracking control algorithm is the key that realize Vehicle tracing control, particularly important to autonomous driving vehicle.
Existing autonomous driving vehicle Trajectory Tracking Control algorithm has fuzzy control, adaptive robust control, iterative learning
Control, Variable Structure Control, model predictive control method etc., these control methods are all based on greatly accurate mathematical model, so
And the driving cycle of autonomous driving vehicle is complicated and changeable, there is height uncertainties for actual vehicle dynamic model, and easily
It is influenced by external disturbance.Meanwhile usually there is inevitable time delay sum number in vehicle-state measurement and signals transmission
According to packet loss problem, this will will be greatly reduced the performance of controller, or even can destroy the stability of system.Thus, how to occur
In the case of network delay and data packetloss, the uncertainty and the influence of external disturbance of vehicle dynamic model are comprehensively considered,
The ideal trajectory tracing control for realizing autonomous driving vehicle is still industry and sphere of learning facing challenges problem.
Summary of the invention
To overcome the above deficiencies, the invention provides a kind of autonomous driving vehicle Trajectory Tracking Control method,
This method devises a kind of robust H∞State feedback controller realizes the ideal Trajectory Tracking Control of vehicle, meanwhile, it solves
Network delay and data packetloss problem in car status information transmission process, improve vehicle control stability and track with
The robustness of track control.
The present invention overcomes the technical solution used by its technical problem to be:
A kind of autonomous driving vehicle Trajectory Tracking Control method, includes the following steps:
A) the Vehicle tracing dynamical equation such as formula (1) is established:
Wherein,For e1Second-order differential, e1Normal direction for vehicle centroid CG to ideal path deviates, e2For the cross of vehicle
The yaw angle ψ of pivot angle ψ and reference point corresponding on reference trajectoryrDifference, yaw angle ψ be vehicle in global coordinate system XOGIt is opposite in Y
The deflection of reference axis X, O are the rotation center of vehicle,For the second-order differential of y, y is rotation center O to vehicle centroid CG's
Normal direction deviates, vxFor the longitudinal velocity of vehicle,For the first differential of yaw angle ψ, yrFor the side of reference point corresponding on reference trajectory
To deviation,For yrSecond-order differential, ψrFor the yaw angle of reference point corresponding on reference trajectory;
B) the lateral dynamical equation of vehicle such as formula (2) is established
Wherein, m is the quality of vehicle, IzIt is vehicle around the rotary inertia of z-axis, lfFor vehicle centroid to automobile front-axle away from
From lrFor the distance of vehicle centroid to vehicle rear axle,For the second-order differential of yaw angle ψ, FyfFor vehicle front-wheel lateral force, Fyr
For vehicle rear wheel lateral force, vehicle front-wheel and rear-wheel lateral force are sought by formula (3);
Fyf=2Cfαf,Fyf=-2Crαr (3)
Wherein, CfFor the cornering stiffness of vehicle front-wheel, CrFor the cornering stiffness of vehicle rear wheel, αfFor vehicle front-wheel side drift angle,
αrFor vehicle rear wheel side drift angle;
C) side velocity of vehicle is defined For the first differential of y, vehicle front wheel side is calculated by formula (4)
Drift angle αfWith vehicle rear wheel side drift angle αr;
Wherein, δfFor the steering angle of vehicle front-wheel, the lateral dynamical equation of vehicle is established by formula (5);
Wherein, T is matrix transposition,ForFirst differential,
D) e is chosen1, e2And e1, e2First differential be state variable, establish as formula (6) Trajectory Tracking Control mould
Type;
Wherein,For yrFirst differential,For ψrFirst differential,For ψrSecond-order differential,
E) the wheel steering rigidity for assuming vehicle is time-varying, establishes the multiplying property perturbation equation such as formula (7);
Cf=(1+ λf)Cf0,Cr=(1+ λr)Cr0 (7)
Wherein, λf, λrFor time-varying parameter, and meet condition | λi|≤1, i=f, r, Cf0, Cr0Respectively Cf, CrIt is nominal
Value, establishes system parameter matrix by formula (8);
A=A0+ Δ A, B=B0+ΔB (8)
Wherein, A0, B0The nominal value of respectively A, B, and Δ A, Δ B represent A, the variable quantity of B is established not by formula (9)
Determine parameter matrix;
[Δ A Δ B]=H Λ [E1 E2] (9)
Wherein, the certainty matrix that H is 4 × 9, the uncertain parameters diagonal matrix that Λ is 9 × 9, E1, E2Respectively 9 ×
4,9 × 1 constant matrices, when front and back wheel pavement friction is consistent, λf=λr, it is based on uncertain parameter expression matrix (9),
Establish the Trajectory Tracking Control model such as formula (10);
Wherein,For the first differential of x;
F) network delay and data packet-dropping model based on network control system are established, in each sampling period, sampling
Moment tkWhen time delay be expressed as τk=τsc+τca, wherein τscFor sensor-controller time delay, τcaWhen for controller-actuator
Prolong, the data packet that controller receives is indicated by formula (11);
Wherein, h indicates the sampling period, and n (k) represents sampling instant tkWhen data packetloss number, what controller received
Data packet is indicated by formula (12);
Mark τ (t)=t- (tk-lh-τk), thenAs 0 < τ (t)≤τmaxWhen, pass through public affairs
Formula (13) establishes vehicle-state feedback controller;
Wherein, K is STATE FEEDBACK CONTROL gain matrix to be designed, τmaxFor be delayed the upper bound,It is anti-for vehicle-state
Controller is presented in sampling instant tkWhen the status signal that receives;
G) choosing controlled output isC is numbers matrix, establishes such as formula (14)
Vehicle tracing closed-loop system;
The Disturbance Rejection performance indicator γ of closed-loop system (14) is calculated by formula (15),
H) the positive definite matrix X > 0 for meeting the linear matrix inequality such as formula (16) is solved,General square
Battle array Y,With quantity ∈ > 0;
Wherein, in formula (16) * be matrix symmetric element transposition,
Ξ77=-∈ I, Ξ88=-∈ I, Ξ99=-I
Vehicle-state feedback control gain matrix is sought by formula (17);
K=YX-1(17),
By solving the convex optimization problem such as formula (18)
Further, when vehicle control network system signal transmission process is without time delay and data packetloss, in step g)
Vehicle tracing closed-loop system is established by formula (19),
Wherein, KndFor feedback control gain to be designed;
The positive definite matrix for meeting linear matrix inequality (20) is solved in step h)General matrixSum number
Measure ∈0> 0,
Wherein,Controller gain matrix isγ in formula0Autonomous driving vehicle track and tracking and controlling method disturbance press down when for for time delay and data packetloss
Performance indicator processed.
The beneficial effects of the present invention are: the joint modeling of both track following model and the lateral dynamic model of vehicle, realizes
The ideal Trajectory Tracking Control of autonomous driving vehicle, meanwhile, improve the lateral stability of vehicle.In the rail of autonomous driving vehicle
In mark tracing control modeling process, it is contemplated that inevitable network delay and data packetloss problem, and general time delay table
The design of controller is more advantageous to up to formula.Autonomous driving vehicle Trajectory Tracking Control design synthesis considers vehicle dynamic model
Uncertainty and external disturbance influence, improve the control stability of vehicle and the robustness of Trajectory Tracking Control.Pass through
It solves linear matrix inequality and solves the problems, such as the autonomous driving vehicle Trajectory Tracking Control containing network delay and data packetloss,
Convenience of calculation.By solving convex optimization problem, autonomous driving vehicle Trajectory Tracking Control problem Disturbance Rejection can be calculated
The lower bound of performance indicator, it is thus possible to obtain optimal contrail tracker.
Detailed description of the invention
Fig. 1 is Vehicle tracing schematic diagram of the invention;
Fig. 2 is the Vehicle tracing control flow chart based on network control system.
Specific embodiment
1 the present invention will be further described with reference to the accompanying drawing.
A kind of autonomous driving vehicle Trajectory Tracking Control method, includes the following steps:
A) the Vehicle tracing dynamical equation such as formula (1) is established:
Wherein,For e1Second-order differential, e1Normal direction for vehicle centroid CG to ideal path deviates, e2For the cross of vehicle
The yaw angle ψ of pivot angle ψ and reference point corresponding on reference trajectoryrDifference, yaw angle ψ be vehicle in global coordinate system XOGIt is opposite in Y
The deflection of reference axis X, O are the rotation center of vehicle,For the second-order differential of y, y is rotation center O to vehicle centroid CG's
Normal direction deviates, vxFor the longitudinal velocity of vehicle,For the first differential of yaw angle ψ, yrFor the side of reference point corresponding on reference trajectory
To deviation,For yrSecond-order differential, ψrFor the yaw angle of reference point corresponding on reference trajectory.
B) the lateral dynamical equation of vehicle such as formula (2) is established
Wherein, m is the quality of vehicle, IzIt is vehicle around the rotary inertia of z-axis, lfFor vehicle centroid to automobile front-axle away from
From lrFor the distance of vehicle centroid to vehicle rear axle,For the second-order differential of yaw angle ψ, FyfFor vehicle front-wheel lateral force, Fyr
For vehicle rear wheel lateral force, vehicle front-wheel and rear-wheel lateral force are sought by formula (3);
Fyf=2Cfαf,Fyf=-2Crαr (3)
Wherein, CfFor the cornering stiffness of vehicle front-wheel, CrFor the cornering stiffness of vehicle rear wheel, αfFor vehicle front-wheel side drift angle,
αrFor vehicle rear wheel side drift angle.
C) side velocity of vehicle is defined For the first differential of y, vehicle front wheel side is calculated by formula (4)
Drift angle αfWith vehicle rear wheel side drift angle αr;
Wherein, δfFor the steering angle of vehicle front-wheel, the lateral dynamical equation of vehicle is established by formula (5);
Wherein, T is matrix transposition,ForFirst differential,
D) e is chosen1, e2And e1, e2First differential be state variable, establish as formula (6) Trajectory Tracking Control mould
Type;
Wherein,For yrFirst differential,For ψrFirst differential,For ψrSecond-order differential,
E) the wheel steering rigidity for assuming vehicle is time-varying, establishes the multiplying property perturbation equation such as formula (7);
Cf=(1+ λf)Cf0,Cr=(1+ λr)Cr0 (7)
Wherein, λf, λrFor time-varying parameter, and meet condition | λi|≤1, i=f, r, Cf0, Cr0Respectively Cf, CrIt is nominal
Value, establishes system parameter matrix by formula (8);
A=A0+ Δ A, B=B0+ΔB (8)
Wherein, A0, B0The nominal value of respectively A, B, and Δ A, Δ B represent A, the variable quantity of B is established not by formula (9)
Determine parameter matrix;
[Δ A Δ B]=H Λ [E1 E2] (9)
Wherein, the certainty matrix that H is 4 × 9, the uncertain parameters diagonal matrix that Λ is 9 × 9, E1, E2Respectively 9 ×
4,9 × 1 constant matrices, when front and back wheel pavement friction is consistent, λf=λr, it is based on uncertain parameter expression matrix (9),
Establish the Trajectory Tracking Control model such as formula (10);
Wherein,For the first differential of x.
F) with the fast development of active safety systems of vehicles, car status information can be by directly measuring to obtain.Example
Such as, yaw velocity r can be measured by onboard sensor (such as Inertial Measurement Unit) and be obtained, and the lateral deviation of vehicle, side
It can be measured and be obtained by global positioning system (GPS) to speed and deflection error.However, due to network congestion or node failure,
There are inevitable network delay and data packetloss in vehicle control system.
As shown in Fig. 2, network delay and data packet-dropping model based on network control system are established, in each sampling week
In phase, sampling instant tkWhen time delay be expressed as τk=τsc+τca, wherein τscFor sensor-controller time delay, τcaFor controller-
Actuator time delay, the data packet that controller receives are indicated by formula (11);
Wherein, h indicates the sampling period, and n (k) represents sampling instant tkWhen data packetloss number, when comprehensively considering network
Prolong the influence with data packetloss, the data packet that controller receives is indicated by formula (12);
Mark τ (t)=t- (tk-lh-τk), thenAs 0 < τ (t)≤τmaxWhen, pass through public affairs
Formula (13) establishes vehicle-state feedback controller;
Wherein, K is STATE FEEDBACK CONTROL gain matrix to be designed, τmaxFor be delayed the upper bound,It is anti-for vehicle-state
Controller is presented in sampling instant tkWhen the status signal that receives.
G) in order to complete autonomous driving vehicle Trajectory Tracking Control task, the lateral deviation e of vehicle1With deflection error e2It answers
This is smaller as much as possible.Choosing controlled output isC is numbers matrix, is established such as
The Vehicle tracing closed-loop system of formula (14);
The Disturbance Rejection performance indicator γ of closed-loop system (14) is calculated by formula (15),
H) the positive definite matrix X > 0 for meeting the linear matrix inequality such as formula (16) is solved,General square
Battle array Y,With quantity ∈ > 0;
Wherein, in formula (16) * be matrix symmetric element transposition,
Ξ77=-∈ I, Ξ88=-∈ I, Ξ99=-I
Vehicle-state feedback control gain matrix is sought by formula (17);
K=YX-1(17),
Further, by solving the available optimal contrail tracker of convex optimization problem such as formula (18),
The joint modeling of both track following model and the lateral dynamic model of vehicle, realizes the ideal rail of autonomous driving vehicle
Mark tracing control, meanwhile, improve the lateral stability of vehicle.In the Trajectory Tracking Control modeling process of autonomous driving vehicle
In, it is contemplated that inevitable network delay and data packetloss problem, and general delay expression is more advantageous to controller
Design.Autonomous driving vehicle Trajectory Tracking Control design synthesis considers the uncertainty of vehicle dynamic model and the external world is disturbed
Dynamic influence improves the control stability of vehicle and the robustness of Trajectory Tracking Control.By solving linear matrix inequality
Solve the problems, such as the autonomous driving vehicle Trajectory Tracking Control containing network delay and data packetloss, convenience of calculation.Pass through solution
The lower bound of autonomous driving vehicle Trajectory Tracking Control problem Disturbance Rejection performance indicator can be calculated in convex optimization problem, from
And available optimal contrail tracker.Further, when vehicle control network system signal transmission process is without time delay
When with data packetloss, Vehicle tracing closed-loop system is established by formula (19) in step g),
Wherein, KndFor feedback control gain to be designed;
The positive definite matrix for meeting linear matrix inequality (20) is solved in step h)General matrixSum number
Measure ∈0> 0,
Wherein,Controller gain matrix isγ in formula0Autonomous driving vehicle track and tracking and controlling method disturbance press down when for for time delay and data packetloss
Performance indicator processed.
Claims (2)
1. a kind of autonomous driving vehicle Trajectory Tracking Control method, which comprises the steps of:
A) the Vehicle tracing dynamical equation such as formula (1) is established:
Wherein,For e1Second-order differential, e1Normal direction for vehicle centroid CG to ideal path deviates, e2For the yaw angle ψ of vehicle
The yaw angle ψ of reference point corresponding on reference trajectoryrDifference, yaw angle ψ be vehicle in global coordinate system XOGRelative datum axis in Y
The deflection of X, O are the rotation center of vehicle,For the second-order differential of y, y is that the normal direction of rotation center O to vehicle centroid CG are inclined
From vxFor the longitudinal velocity of vehicle,For the first differential of yaw angle ψ, yrFor the lateral inclined of reference point corresponding on reference trajectory
From,For yrSecond-order differential, ψrFor the yaw angle of reference point corresponding on reference trajectory;
B) the lateral dynamical equation of vehicle such as formula (2) is established
Wherein, m is the quality of vehicle, IzIt is vehicle around the rotary inertia of z-axis, lfFor the distance of vehicle centroid to automobile front-axle, lr
For the distance of vehicle centroid to vehicle rear axle,For the second-order differential of yaw angle ψ, FyfFor vehicle front-wheel lateral force, FyrFor vehicle
Rear-wheel lateral force seeks vehicle front-wheel and rear-wheel lateral force by formula (3);
Fyf=2Cfαf,Fyf=-2Crαr (3)
Wherein, CfFor the cornering stiffness of vehicle front-wheel, CrFor the cornering stiffness of vehicle rear wheel, αfFor vehicle front-wheel side drift angle, αrFor
Vehicle rear wheel side drift angle;
C) side velocity of vehicle is defined For the first differential of y, vehicle front-wheel side drift angle is calculated by formula (4)
αfWith vehicle rear wheel side drift angle αr;
Wherein, δfFor the steering angle of vehicle front-wheel, the lateral dynamical equation of vehicle is established by formula (5);
Wherein, T is matrix transposition,ForFirst differential,
D) e is chosen1, e2And e1, e2First differential be state variable, establish as formula (6) Trajectory Tracking Control model;
Wherein,For yrFirst differential,For ψrFirst differential,For ψrSecond-order differential,
E) the wheel steering rigidity for assuming vehicle is time-varying, establishes the multiplying property perturbation equation such as formula (7);
Cf=(1+ λf)Cf0,Cr=(1+ λr)Cr0 (7)
Wherein, λf, λrFor time-varying parameter, and meet condition | λi|≤1, i=f, r, Cf0, Cr0Respectively Cf, CrNominal value, lead to
It crosses formula (8) and establishes system parameter matrix;
A=A0+ Δ A, B=B0+ΔB (8)
Wherein, A0, B0The nominal value of respectively A, B, and Δ A, Δ B represent A, the variable quantity of B is established uncertain by formula (9)
Parameter matrix;
[Δ A Δ B]=H Λ [E1 E2] (9)
Wherein, the certainty matrix that H is 4 × 9, the uncertain parameters diagonal matrix that Λ is 9 × 9, E1, E2Respectively 9 × 4,9
× 1 constant matrices, when front and back wheel pavement friction is consistent, λf=λr, it is based on uncertain parameter expression matrix (9), establishes
Such as the Trajectory Tracking Control model of formula (10);
Wherein,For the first differential of x;
F) network delay and data packet-dropping model based on network control system, in each sampling period, sampling instant t are establishedk
When time delay be expressed as τk=τsc+τca, wherein τscFor sensor-controller time delay, τcaFor controller-actuator time delay, it is based on
The zeroth order retention property of control system, the data packet that controller receives by formula (11) indicate,
Wherein, h indicates the sampling period, and n (k) represents sampling instant tkWhen data packetloss number, the data packet that controller receives
It is indicated by formula (12);
Mark τ (t)=t- (tk-lh-τk), thenAs 0 < τ (t)≤τmaxWhen, pass through formula
(13) vehicle-state feedback controller is established;
Wherein, K is STATE FEEDBACK CONTROL gain matrix to be designed, τmaxFor be delayed the upper bound,It feeds back and controls for vehicle-state
Device processed is in sampling instant tkWhen the status signal that receives;
G) choosing controlled output isC is numbers matrix, establishes the vehicle such as formula (14)
Track following closed-loop system;
The Disturbance Rejection performance indicator γ of closed-loop system (14) is calculated by formula (15),
H) the positive definite matrix X > 0 for meeting the linear matrix inequality such as formula (16) is solved,General matrix Y,With quantity ∈ > 0;
Wherein, in formula (16) * be matrix symmetric element transposition,
Ξ15=XAT,
Ξ17=∈ H,Ξ19=XCT,
Ξ25=(B0Y)T,
Ξ28=(E2Y)T,
Ξ44=-γ2I,
Ξ57=∈ H,
Ξ77=-∈ I, Ξ88=-∈ I, Ξ99=-I
Vehicle-state feedback control gain matrix is sought by formula (17);
K=YX-1(17),
By solving the convex optimization problem such as formula (18),
2. autonomous driving vehicle Trajectory Tracking Control method according to claim 1, it is characterised in that: when vehicle network control
System signal transmission process processed is established Vehicle tracing by formula (19) in step g) and is closed without time delay and when data packetloss
Loop system,
Wherein, KndFor feedback control gain to be designed;
The positive definite matrix for meeting linear matrix inequality (20) is solved in step h)General matrixWith quantity ∈0
> 0,
Wherein,Controller gain matrix isFormula
Middle γ0Autonomous driving vehicle track and tracking and controlling method Disturbance Rejection performance indicator when for for time delay and data packetloss.
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CN110471277B (en) * | 2019-07-22 | 2020-06-16 | 清华大学 | Intelligent commercial vehicle automatic tracking control method based on output feedback gain programming |
CN110677428A (en) * | 2019-09-30 | 2020-01-10 | 上海智驾汽车科技有限公司 | Vehicle control method and device based on intelligent network connection |
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CN113791611B (en) * | 2021-08-16 | 2024-03-05 | 北京航空航天大学 | Real-time tracking iterative learning control system and method for vehicle under interference |
CN113625551B (en) * | 2021-08-16 | 2024-03-01 | 北京航空航天大学 | Real-time tracking iterative learning control system and method for time-varying vehicle system |
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