CN107856733A

CN107856733A - It is a kind of to hide dynamic barrier control method towards man-machine harmonious automobile

Info

Publication number: CN107856733A
Application number: CN201711081091.6A
Authority: CN
Inventors: 李绍松; 郭陆平; 于志新; 张袅娜; 卢晓晖; 郑顺航; 李政; 王国栋; 李增
Original assignee: Changchun University of Technology
Current assignee: Changchun University of Technology
Priority date: 2017-11-07
Filing date: 2017-11-07
Publication date: 2018-03-30
Anticipated expiration: 2037-11-07
Also published as: CN107856733B

Abstract

Hide dynamic barrier control method towards man-machine harmonious automobile the present invention relates to a kind of, it is characterised in that this method is：Passage path Dynamic Programming module is according to the obstacle information, coordinate of ground point, motoring condition information gathered in real time, real-time optimization draws lateral displacement reference value, yaw angle reference value, yaw velocity reference value, the longitudinal velocity reference value of desired trajectory, it is input to path following control module, passage path tracing control module gathers current motoring condition information simultaneously, real-time optimization draws front wheel angle and four wheel slips, and control automobile realizes collision avoidance；During collision avoidance is controlled, pass through electric power steering（Electric Power Steering,EPS）Torque compensation module determines that torque compensation controls gain, steering wheel is mutated into Torque Control in the ideal range, realizes man-machine harmonious automobile emergency collision avoidance according to speed, front-wheel additional rotation angle.

Description

It is a kind of to hide dynamic barrier control method towards man-machine harmonious automobile

Technical field

The present invention relates to automobile assistant driving technical field, and in particular to a kind of to hide dynamic barrier towards man-machine harmonious automobile Hinder thing control method.

Background technology

It is convenient with quick that automobile can be brought, and its driving safety turns into global social concern.In order to enter One step improves traffic safety, helps driver to reduce faulty operation, in recent years with advanced drive assist system (Advanced Driver Assistance Systems, ADAS) is that the intelligent automobile safe practice of representative is gradually paid attention to And development.Automobile emergency anti-collision system the movement locus of auxiliary driver's adjustment automobile, is realized by the pro-active intervention of actuator Collision avoidance.It can save the life of driver in clutch, there is good market prospects.

Plan in real time and track the key that a collisionless optimal path is automobile emergency collision avoidance control.Automotive correlation prevention controls Automobile is needed constantly to plan desired path, and assist simultaneously on the premise of vehicle condition information and road information is obtained Driver completes to turn to and braking Optimum Operation, realizes the safe collision avoidance of automobile.Therefore, it is necessary to the row of real-time optimization automobile Sail track and corresponding control input.In recent years, with the Model Predictive Control (Model optimized based on real-time mathematical Predictive Control, MPC) theoretical breakthrough, from chemical industry etc., process industry is rapidly spread to aviation boat to MPC at a slow speed My god, the fast acting control system such as robot, automobile.But under urgent collision avoidance, due to the complexity of model, thus automobile be difficult Ensure to meet requirement of real-time on the premise of accurate control, this is also always the principal element of limitation MPC applications.

The existing many achievements in research of automobile emergency collision avoidance control aspect, can preferably solve collision avoidance control problem, but this A little achievements in research are mainly for stationary obstruction.Considering the automobile emergency collision avoidance control aspect of moving obstacle, document [Ackermann C,Isermann R,Min S,et al.Collision avoidance with automatic braking and swerving[J].IFAC Proceedings Volumes,2014,47(3):10694-10699.] consider Barrier lengthwise movement situation, detects the speed difference of automobile and moving obstacle, and whether decision-making goes out the steering opportunity of collision avoidance, i.e., may be used To carry out steering collision avoidance, but the dynamic change of dyskinesia object location is not accounted for during collision avoidance, and do not account for hindering Hinder thing lateral movement situation.Publication No. CN105539586A Chinese patent discloses a kind of automobile for autonomous driving and hided The unified motion planning method of moving obstacle is kept away, this method considers longitudinal direction and the lateral movement situation of barrier, but only uses Come steering opportunity and collision avoidance path that decision-making goes out collision avoidance, also without the dynamic that dyskinesia object location is considered during collision avoidance Change.

Automobile emergency collision avoidance control be unable to do without the pro-active intervention of steering.The existing rules and regulations steering wheel in Europe is with turning to There must be mechanical connection between wheel, so active front steering system (Active Front Steering, AFS) is as modern The transitional product of wire-controlled steering system (Steering-by-wire, SBW) arises at the historic moment afterwards.Document [Sumio Sugita, Masayoshi Tomizuka.Cancellation of Unnatural Reaction Torque in Variable- Gear-Ratio[J].Journal of Dynamic Systems Measurement&Control,2012,134(2): 021019.] and [Atsushi Oshima, Xu Chen, Sumio Sugita, Masayoshi Tomizuka.Control design for cancellation of unnatural reaction torque and vibrations in variable-gear-ratio steering system[C].ASME 2013Dynamic Systems and Control Conference.American Society of Mechanical Engineers,2013-3797,V001T11A003: 10pages.] AFS is mentioned while system displacement transmission characteristic is changed, the force transfering characteristic of steering can be also influenceed, is drawn Play the mutation of hand-wheel torque.Excessive steering wheel mutation torque can aggravate the nervous psychology of driver, easily produce driver Raw maloperation, is unfavorable for driving safety.Appropriate steering wheel mutation torque is but advantageous to the attitudes vibration that driver perceives automobile, And play warning function.But the acceptable degree that driver is mutated torque to steering wheel varies with each individual.

The content of the invention

In order to solve that the dynamic of dyskinesia object location is not accounted for during collision avoidance existing for existing urgent collision avoidance method State changes and causes the unsafe technical problem of collision avoidance process, and steering wheel mutation torque existing for existing urgent collision avoidance method It is uncontrollable, easily cause the technical problem of driver's maloperation, the present invention provide it is a kind of hide towards man-machine harmonious automobile it is dynamic Barrier control method, driver can be aided in complete collision avoidance, save the life of driver and crew at the critical moment.

The technical solution adopted for solving the technical problem of the present invention is as follows：

It is a kind of to hide dynamic barrier control method towards man-machine harmonious automobile, it is characterised in that this method is：Pass through road Dynamic Programming module in footpath obtains according to the obstacle information, coordinate of ground point, motoring condition information gathered in real time, real-time optimization Go out lateral displacement reference value, yaw angle reference value, yaw velocity reference value, the longitudinal velocity reference value of desired trajectory, input To path following control module, while passage path tracing control module gathers current motoring condition information, real-time optimization Front wheel angle and four wheel slips are drawn, control automobile realizes collision avoidance；During collision avoidance is controlled, pass through electric boosted turn , according to speed, front-wheel additional rotation angle, torque compensation is determined to (Electric Power Steering, EPS) torque compensation module Gain is controlled, steering wheel is mutated Torque Control in the ideal range, realizes man-machine harmonious automobile emergency collision avoidance；This method bag Include following steps：

Step 1, path Dynamic Programming module are according to the obstacle information, coordinate of ground point, running car shape gathered in real time State information, real-time optimization draw the lateral displacement reference value of desired trajectory, yaw angle reference value, yaw velocity reference value, vertical To speed reference, it includes following sub-step：

Step 1.1, the performance indications design process of path Dynamic Programming include following sub-step：

Step 1.1.1, the terminal point coordinate and the two norms work of coordinate of ground point error for predicting time domain interior prediction track are utilized For tracking performance index, the track following characteristic of automobile is embodied, its expression formula is as follows：

Wherein, H_{P, h}For the prediction time domain of path Dynamic Programming module, (X_{T+Hp, h},Y_{T+Hp, h}) it is prediction time domain interior prediction rail The terminal point coordinate of mark, obtained by Mass Model iteration, the automobile coordinate of ground point (X to be reached during collision avoidance_g,Y_g)；

The Mass Model is：

Wherein,a_yFor automobile side angle acceleration；For automobile longitudinal acceleration；Respectively yaw angle and yaw angle Speed；The longitudinal velocity and side velocity of automobile barycenter respectively in earth coordinates；V is the longitudinal direction speed of current automobile Degree；

Step 1.1.2, by the use of two norms of side acceleration as the automotive safety index during collision avoidance, automobile is embodied Collision avoidance stability, establishing discrete quadratic form automotive safety index is：

Wherein, H_{C, h}For the control time domain of path Dynamic Programming module, t represents current time, a_yFor the lateral of Mass Model Acceleration, w₁For a_yWeight coefficient；

Step 1.2, the constrained designs process of path Dynamic Programming include following sub-step：

Step 1.2.1, set stability of automobile to constrain, ensure automobile avoidance safety；

Stability of automobile constraint, its mathematic(al) representation are obtained using the bound of linear inequality limit lateral acceleration For：

|a_yk,t| ＜ μ g k=t, t+1t+H_c,h-1 (3)

Wherein, μ is coefficient of road adhesion, and g is acceleration of gravity；

Step 1.2.2, set location constrains, and ensures to collide with barrier during collision avoidance；

The positional information of t barrier may be characterized as the set of N number of discrete point, and these information can be surveyed by radar sensor Amount obtains, wherein the coordinate representation of j-th of discrete point is (X_j,t,Y_j,t), the automobile center-of-mass coordinate of t is designated as (X_k,t,Y_k,t), It can be calculated by Vehicle dynamics, position constraint is set to

Wherein, a is distance of the automobile barycenter to headstock；B is distance of the automobile barycenter to the tailstock；C is the one of automobile overall width Half；For using t as the yaw angle for playing k moment automobiles in point prediction time domain；D_x,j,tIt is j-th of discrete point of barrier in vapour The fore-and-aft distance of automobile barycenter, D are arrived in car coordinate system_y,j,tAutomobile matter is arrived in vehicle axis system for j-th of discrete point of barrier The lateral separation of the heart；

It is assumed that barrier characterizes automobile and barrier along Y-direction with constant speed movement, formula (5) in prediction time domain The degree of closeness of N number of discrete point, l values are bigger, illustrate that the distance of automobile discrete point corresponding with barrier is closer, also more endanger Danger；It is the dangerous spot in current sample period to define the maximum barrier discrete point j of t l values, is designated as (X_j,t,Y_j,t), pre- Survey in time domain and barrier motion is predicted based on this dangerous spot, iterative relation is expressed as：

Wherein, (X_j,t-1,Y_j,t-1) it is coordinate of the dangerous spot at the t-1 moment；(X_j,k,Y_j,k) endangered for the k moment in prediction time domain The coordinate nearly put；

The discrete point coordinates of barrier by way of iteration in more new formula (5), by barrier in prediction time domain Change in location is integrated into the position constraint of Model Predictive Control Algorithm；

Step 1.3, build path Dynamic Programming Multiobjective Optimal Control Problems, Multiobjective Optimal Control Problems are solved, are entered And yaw velocity reference value, yaw angle reference value, lateral displacement reference value and longitudinal velocity reference value are obtained, it includes as follows Sub-step：

Step 1.3.1, obstacle information is obtained by radar sensor, automobile is obtained by vehicle speed sensor and gyroscope Running condition information, and the obstacle information of acquisition and motoring condition information are inputted into path Dynamic Programming module；

Step 1.3.2, tracking performance index and automotive safety index are converted into single index, structure using weigthed sums approach Road construction footpath Dynamic Programming Multiobjective Optimal Control Problems, the problem will meet stability of automobile constraint and position constraint simultaneously, and Ensure that path Dynamic Programming input and output meet Mass Model：

Submit to

I) Mass Model

Ii) constraints is formula (3)~(7)

Step 1.3.3, in path Dynamic Programming controller, genetic algorithm is called, solves Multiobjective Optimal Control Problems (9) optimal opened loop control a, is obtained_y ^*For：

Submit to

I) Mass Model

Ii) constraints is formula (3)~(7)

Step 1.3.4, current time optimal opened loop control a is utilized_y ^*(0) yaw velocity reference value, is obtainedYaw Angle reference valueLateral displacement reference value Y_ref, longitudinal velocity reference valueExpression is as follows：

Wherein, V is the longitudinal velocity of current automobile,For the reference value of automobile side angle speed,For path side velocity Reference value；

Step 2, path following control module receive the lateral displacement of the desired trajectory transmitted by path Dynamic Programming module Reference value, yaw angle reference value, yaw velocity reference value, longitudinal velocity reference value, while path following control module gathers Current motoring condition information, real-time optimization draw the front wheel angle and four wheel slips of automobile, control automobile reality Existing collision avoidance, it includes following sub-step：

Step 2.1, the performance indications design process of path following control include following sub-step：

Step 2.1.1, the lateral displacement reference value Y exported using path Dynamic Programming module_ref, yaw angle reference valueYaw velocity reference valueLongitudinal velocity reference valueWith two models of the error of actual motoring condition information Number is used as tracking performance indications, embodies the track following characteristic of automobile, its expression formula is as follows：

Wherein, η_k,tFor motoring condition information, obtained by Vehicle dynamics iteration, η_refk,tThe reference value provided for path Dynamic Programming module,H_{P, l}For path trace control The prediction time domain of molding block, w₂For weight coefficient；

The Vehicle dynamics：

F_xi=f_xicos(δ_i)-f_yisin(δ_i),i∈{1,2,3,4} (31)

F_yi=f_xisin(δ_i)+f_yicos(δ_i),i∈{1,2,3,4} (32)

Wherein, F_xi、F_yiLongitudinal component and cross component force of respectively four wheels along vehicle body coordinate direction；f_xi、f_yiPoint Not Wei component of four wheels along wheel coordinate direction, wherein f_xiFor four wheel slips and the function of analysis of wheel vertical load, f_yiFor front wheel angle and the function of analysis of wheel vertical load, concrete numerical value can be determined by magic formula；Respectively automobile longitudinal Speed and longitudinal acceleration；Respectively automobile side angle speed and side acceleration；Respectively automobile yaw Angle, yaw velocity and yaw angular acceleration；l_f、l_rRespectively automobile barycenter is to the distance of axle, l_sFor wheelspan size Half；J_zFor around the yaw rotation inertia of the vertical axis of automobile barycenter；M is car mass；X, Y is respectively vapour in earth coordinates The transverse and longitudinal coordinate of car centroid position；δ_iFor four wheel steering angles, automobile is front-wheel steer here, therefore δ₃=δ₄=0；

The parameter of the magic formula show that expression is as follows by experiment fitting：

Wherein, V is the longitudinal velocity of current automobile；α_f、α_rRespectively front-wheel side drift angle and trailing wheel side drift angle；F_z,f、F_z,rPoint Wei not automobile axle load；s_iFor four wheel slips of automobile；A_xi、B_xi、C_xi、D_xi、E_xiAnd A_yi、B_yi、C_yi、D_yi、E_yi To test fitting parameter, design parameter is as shown in following table：

The magic formula parameter of table 4

a₀	a₁	a₂	a₃	a₄	a₅	a₆
									1.75	0	1000	1289	7.11	0.0053	0.1925
b₀	b₁	b₂	b₃	b₄	b₅	b₆	b₇	b₈
									1.57	35	1200	60	300	0.17	0	0	0.2

Step 2.1.2, put down by the use of two norms of controlled quentity controlled variable rate of change as the braking in a turn of the actuator during collision avoidance Sliding index, embodies braking in a turn smoothness properties；Controlled quentity controlled variable u is four wheel slip s of vehicle front corner δ and automobile_ii∈ { 1,2,3,4 }, establishing the discrete smooth index of quadratic form braking in a turn is：

Wherein, H_{C, l}To control time domain, t represents current time, and Δ u is controlled quentity controlled variable rate of change；

Step 2.2, the constrained designs of path following control ensure automobile avoidance safety to set stability of automobile to constrain； The bound of front wheel angle and four wheel slips is limited using linear inequality, is turned to, the physics of brake actuator Constraint, its mathematic(al) representation are：

δ_min＜ δ_k,t＜ δ_maxK=t, t+1t+H_c,l-1 (24)

s_imin＜ s_ik,t＜ s_imaxI ∈ { 1,2,3,4 } k=t, t+1 ... t+H_c,l-1 (25)

Wherein, δ_minFor front wheel angle lower limit, δ_maxFor the front wheel angle upper limit, s_iminFor four wheel slip lower limits, s_imax For four wheel slip upper limits；

Step 2.3, build path tracing control Multiobjective Optimal Control Problems, Multiobjective Optimal Control Problems are solved, are obtained Go out the vehicle front corner and four wheel slips of real-time optimization, realize the automobile emergency collision avoidance control for considering moving obstacle System, it includes following sub-step：

Step 2.3.1, path following control module obtains the lateral displacement of desired trajectory from path Dynamic Programming module Reference value, yaw angle reference value, yaw velocity reference value and longitudinal velocity reference value；

Step 2.3.2, tracking performance indications and the smooth index of braking in a turn are converted into single finger using weigthed sums approach Mark, build path tracing control Multiobjective Optimal Control Problems, the problem will meet to turn to simultaneously, the physics of brake actuator about Beam, and ensure that path following control input and output meet Vehicle dynamics：

Submit to

I) Vehicle dynamics

Ii) constraints is formula (24)~(25)

Step 2.3.3, in path following control device, SQP algorithms are called, solve Multiobjective Optimal Control Problems (26), Obtain optimal opened loop control u^*For：

Submit to

I) Vehicle dynamics

Ii) constraints is formula (24)~(25)

Step 2.3.4, current time optimal opened loop control u is utilized^*(0) fed back, realize that closed-loop control realizes and examine Consider the automobile emergency collision avoidance control of moving obstacle.

Step 3, design are implanted with the EPS torque compensation modules of steering wheel mutation torque hommization regulation algorithm, and EPS torques are mended Module is repaid according to speed, front-wheel additional rotation angle, determines that torque compensation controls gain, steering wheel is mutated Torque Control in preferable model Enclose；Wherein, front-wheel additional rotation angle is front wheel angle and the driver of path Dynamic Programming and real-Time Tracking Control module optimization The difference of front wheel angle caused by input is turned to, is realized by AFS control system；Design process includes following sub-step：

Step 3.1, the design method of EPS torque compensation modules are：Choose several drivers and carry out real vehicle debugging, it is logical first Toning orders speed for a trial, determines torque compensation control gain under front-wheel additional rotation angle, and laboratory technician enters according to the subjective feeling of driver Row is debugged repeatedly, ensures that steering wheel mutation torque can be received by driver；

Step 3.2, change front-wheel additional rotation angle, laboratory technician, which debugs torque compensation control gain, makes different front-wheel additional rotation angles Steering wheel mutation torque under intervening can be received by driver, and then determine that the torque compensation under the speed controls gain；

Step 3.3, determine using identical method torque compensation under different speeds, different front-wheel additional rotation angle interventions Gain is controlled, the determination of speed, front-wheel additional rotation angle, torque compensation control gain three-dimensional MAP is completed, uses torque compensation control The dimension table of gain three processed carries out torque compensation control, and steering wheel is mutated into Torque Control in the ideal range, realizes that steering wheel is dashed forward The automobile emergency collision avoidance of torque-variable hommization regulation.

Step 3.4, EPS torque compensations are controlled in gain three-dimensional MAP implantation EPS controllers, the control of EPS controllers EPS assist motors reach the control effect of torque compensation.

The beneficial effects of the invention are as follows：By building the hierarchy optimization problem based on Model Predictive Control, upper strata uses matter Point model carries out path planning, and lower floor carries out path trace using high-precision Vehicle dynamics, solves urgent collision avoidance When path Dynamic Programming and real-time tracking problem, and consider the situation of dynamic barrier simultaneously, realize the optimal collision avoidance of safety.Should Method is broken the barriers the mode of changes in coordinates, and barrier motion conditions are converted into the dynamic of collision avoidance control Optimization Solution about Beam, solves the problems, such as the moving obstacle in avoidance obstacle.Steering wheel is mutated by this method by EPS torque compensation controllers Torque Control is entered in the acceptable scope of driver, this method using the mode of subjectivity evaluation and test to the control gain of EPS torque compensations Row is debugged repeatedly, realizes hommization mutation torque adjusting.

Brief description of the drawings

Fig. 1 is a kind of principle schematic for hiding dynamic barrier control method towards man-machine harmonious automobile of the present invention.

Fig. 2 is the relation schematic diagram of automobile and Obstacle Position.

Fig. 3 is automobile and barrier movement relation schematic diagram.

Fig. 4 is car model figure of the present invention.

Fig. 5 is the EPS torque compensation controller experiment flow schematic diagrames of the present invention.

Fig. 6 is EPS torque compensations control gain three-dimensional MAP of the present invention.

Embodiment

The present invention is described in further details with example below in conjunction with the accompanying drawings.

Hide dynamic barrier control method as shown in figure 1, the present invention is a kind of towards man-machine harmonious automobile and include following step Suddenly：Path Dynamic Programming module 1 is according to the obstacle information, coordinate of ground point, motoring condition information gathered in real time, in real time Optimization show that lateral displacement reference value, yaw angle reference value, yaw velocity reference value, the longitudinal velocity of desired trajectory refer to Value, is input to path following control module 2, while path following control module 2 gathers current motoring condition information, real Shi Youhua draws the front wheel angle and four wheel slips of automobile 3, and control automobile 3 aids in driver 5 to realize collision avoidance；Controlling During collision avoidance, EPS torque compensations module 4 determines that torque compensation controls gain, will turned to according to speed, front-wheel additional rotation angle Disk mutation Torque Control in the ideal range, realizes man-machine harmonious automobile emergency collision avoidance.Wherein, obstacle information includes obstacle The discrete point coordinates of thing appearance profile, measured and obtained by radar sensor；Motoring condition information include automobile longitudinal speed, Side velocity, yaw velocity, automobile longitudinal speed and side velocity are measured by vehicle speed sensor and obtained, automobile yaw velocity Measured and obtained by gyroscope.

Below using certain car as platform, method of the invention is illustrated, the major parameter for testing car is as shown in table 1：

Table 1 tests the major parameter of car

Path Dynamic Programming module 1 realizes following three parts function：1.1st, the performance indications design of path Dynamic Programming； 1.2nd, the constrained designs of path Dynamic Programming；1.3rd, path Dynamic Programming control law rolling time horizon solves.

In 1.1 parts, the performance indications design of path Dynamic Programming includes following two parts content：1.1.1, utilize prediction The terminal point coordinate of time domain interior prediction track and two norms of coordinate of ground point error embody the rail of automobile as tracking performance index Mark tracking characteristics；1.1.2, by the use of two norms of side acceleration as automotive safety index, automotive correlation prevention stability is embodied；

In 1.1.1 parts, tracking performance index is to predict that the terminal point coordinate of time domain interior prediction track and coordinate of ground point miss Two norms of difference are evaluation criterion, and expression formula is as follows：

Wherein, H_{P, h}For the prediction time domain of path Dynamic Programming module 1, (X_{T+Hp, h},Y_{T+Hp, h}) it is prediction time domain interior prediction rail The terminal point coordinate of mark, obtained by Vehicle dynamics iteration, the automobile coordinate of ground point (X to be reached during collision avoidance_g,Y_g), that is, hinder Hinder a point of safes at thing rear.

In 1.1.2 parts, the automotive correlation prevention stability during collision avoidance is described using two norms of side acceleration, is established Discrete quadratic form automotive safety index is：

Wherein, H_{C, h}For the control time domain of path Dynamic Programming module 1, t represents current time, a_yFor the side of Mass Model To acceleration, w₁For a_yWeight coefficient, Dynamic Programming 1 design parameter of module in path is as shown in table 2, wherein T_s1For path dynamic The sampling period of planning module 1.

The urgent collision avoidance controller design parameter of table 2

Controller parameter	Parameter value	Controller parameter	Parameter value
				H_{P, h}	5	H_{C, h}	2
w₁	0.5	T_s1	0.01s

In 1.2 parts, the constrained designs of path Dynamic Programming include two parts：1.2.1 set stability of automobile to constrain, protect Hinder automobile avoidance safety；1.2.2 set location constrains, and ensures to collide with barrier during collision avoidance.

In 1.2.1 parts, stability of automobile constraint is obtained using the bound of linear inequality limit lateral acceleration, its Mathematic(al) representation is：

|a_yk,t| ＜ μ g k=t, t+1t+H_c,h-1 (3)

Wherein, μ is coefficient of road adhesion, is obtained by estimator, and g is acceleration of gravity.

In 1.2.2 parts, as shown in Fig. 2 the positional information of t barrier may be characterized as the set of N number of discrete point, this A little information can be measured by radar sensor and obtained, wherein the coordinate representation of j-th of discrete point is (X_j,t,Y_j,t), the automobile of t Center-of-mass coordinate is designated as (X_k,t,Y_k,t), it can be calculated by Vehicle dynamics, position constraint is set to

Wherein, a is distance of the automobile barycenter to headstock；B is distance of the automobile barycenter to the tailstock；C is the one of automobile overall width Half；For using t as the yaw angle for playing k moment automobiles in point prediction time domain；D_x,j,tIt is j-th of discrete point of barrier in vapour The fore-and-aft distance of automobile barycenter, D are arrived in car coordinate system_y,j,tAutomobile matter is arrived in vehicle axis system for j-th of discrete point of barrier The lateral separation of the heart.

As shown in figure 3, in vehicle traveling process, barrier may occur suddenly in a manner of motion；Consider barrier along Y Direction motion conditions, it is assumed that barrier is with constant speed movement in prediction time domain.

Formula (5) characterizes the degree of closeness of automobile and the N number of discrete point of barrier, and l values are bigger, illustrate automobile and barrier The distance of corresponding discrete point is closer, also more dangerous.In order to ensure algorithm real-time, the maximum barrier of t l values is defined Discrete point j is the dangerous spot in current sample period, is designated as (X_j,t,Y_j,t), based on this dangerous spot to obstacle in prediction time domain Thing motion is predicted, and iterative relation is expressed as：

Wherein, (X_j,t-1,Y_j,t-1) it is coordinate of the dangerous spot at the t-1 moment；(X_j,k,Y_j,k) endangered for the k moment in prediction time domain The coordinate nearly put.

The discrete point coordinates of barrier by way of iteration in more new formula (5), by barrier in prediction time domain Change in location is integrated into the position constraint of Model Predictive Control Algorithm, the urgent collision avoidance problem under Optimization Solution moving obstacle.

In 1.3 parts, path Dynamic Programming control law rolling time horizon, which solves, to be comprised the following steps：

1.3.1 obstacle information, is obtained by radar sensor, running car is obtained by vehicle speed sensor and gyroscope Status information, and the obstacle information of acquisition and motoring condition information are inputted into path Dynamic Programming module 1；

1.3.2 tracking performance index and automotive safety index, are converted into single index using weigthed sums approach, build road Footpath Dynamic Programming Multiobjective Optimal Control Problems, the problem will meet stability of automobile constraint and position constraint simultaneously, and ensure Path Dynamic Programming input and output meet Mass Model：

Submit to

I) Mass Model

Ii) constraints is formula (3)~(7)

1.3.3, in path Dynamic Programming controller, genetic algorithm is called, solves Multiobjective Optimal Control Problems (9), Obtain optimal opened loop control a_y ^*For：

Obey

I) Mass Model

Ii) constraints is formula (3)~(7)

1.3.4 current time optimal opened loop control a, is utilized_y ^*(0) yaw velocity reference value, is obtainedYaw angle is joined Examine valueLateral displacement reference value Y_ref, longitudinal velocity reference valueExpression is as follows：

Wherein, V is the longitudinal velocity of current automobile,For the reference value of automobile side angle speed,For path side velocity Reference value.

The Mass Model is：

Wherein,a_yFor automobile side angle acceleration；For automobile longitudinal acceleration；Respectively yaw angle and yaw angle Speed；The longitudinal velocity and side velocity of automobile barycenter respectively in earth coordinates.

Path following control module 2 realizes following three parts function：2.1st, the performance indications design of path following control； 2.2nd, the constrained designs of path following control；2.3rd, path following control control law rolling time horizon solves.

In 2.1 parts, the performance indications design of path following control includes following two parts content：2.1.1, utilize path The lateral displacement reference value Y that Dynamic Programming module 1 exports_ref, yaw angle reference valueYaw velocity reference valueLongitudinal direction Speed referenceTwo norms with the error of actual motoring condition information embody automobile as tracking performance indications Track following characteristic；2.1.2, by the use of two norms of controlled quentity controlled variable rate of change as the smooth index of braking in a turn, braking in a turn is embodied Smoothness properties.

In 2.1.1 parts, tracking performance indications are with the reference value that path Dynamic Programming module 1 exports and actual running car Two norms of the error of status information are evaluation criterion, and expression formula is as follows：

Wherein, η_{K, t}For motoring condition information,η_{Refk, t}Carried for path Dynamic Programming module 1 The reference value of confession,H_{P, l}For the prediction time domain of path following control module 2, w₂For weight Coefficient.

In 2.1.2 parts, the braking in a turn of the actuator during collision avoidance is described using two norms of controlled quentity controlled variable rate of change Smoothness properties, wherein, controlled quentity controlled variable u is vehicle front corner δ and four wheel slip s_iI ∈ { 1,2,3,4 }, establish discrete two The secondary smooth index of type braking in a turn is：

Wherein, H_c,lTo control time domain, t represents current time, and Δ u is controlled quentity controlled variable rate of change, path following control module 2 Design parameter is as shown in table 3, wherein T_s2For the sampling period of path following control module 2.

The urgent collision avoidance controller design parameter of table 3

Controller parameter	Parameter value	Controller parameter	Parameter value
				H_p,l	4	δ_min	-6deg
w₂	0.5	δ_max	6deg
				T_s2	0.01s	s_imin	0
H_c,l	3	s_imax	0.25

In 2.2 parts, the constrained designs of path Dynamic Programming ensure automobile avoidance peace to set stability of automobile to constrain Entirely；The bound of front wheel angle and four wheel slips is limited using linear inequality, is turned to, the thing of brake actuator Reason constraint, its mathematic(al) representation are：

δ_min＜ δ_k,t＜ δ_maxK=t, t+1t+H_c,l-1 (24)

s_imin＜ s_ik,t＜ s_imaxI ∈ { 1,2,3,4 } k=t, t+1t+H_c,l-1 (25)

Wherein, δ_minFor front wheel angle lower limit, δ_maxFor the front wheel angle upper limit, s_iminFor four wheel slip lower limits, s_imax For four wheel slip upper limits.

In 2.3 parts, path following control control law rolling time horizon, which solves, to be comprised the following steps：

2.3.1 reference value, is obtained from path Dynamic Programming module 1, and enters information into path following control module 2；

2.3.2 tracking performance indications and the smooth index of braking in a turn, are converted into single index, structure using weigthed sums approach Path following control Multiobjective Optimal Control Problems are built, the problem will meet steering, the physical constraint of brake actuator simultaneously, and Ensure that path following control input and output meet Vehicle dynamics：

Submit to

I) Vehicle dynamics

Ii) constraints is formula (24)~(25)

2.3.3, in path following control device, genetic algorithm is called, Multiobjective Optimal Control Problems (26) is solved, obtains Optimal opened loop control u^*For：

Submit to

I) Vehicle dynamics

Ii) constraints is formula (24)~(25)

2.3.4 current time optimal opened loop control u, is utilized^*(0) fed back, realize closed-loop control；

As shown in figure 4, Vehicle dynamics of the present invention are：

F_xi=f_xicos(δ_i)-f_yisin(δ_i),i∈{1,2,3,4} (31)

F_yi=f_xisin(δ_i)+f_yicos(δ_i),i∈{1,2,3,4} (32)

The magic formula parameter of table 4

The design method of EPS torque compensations module 4 is：30 drivers are chosen, are divided into according to sex, qualification following Four classes：Skilled male driver, skilled female driver, unskilled male driver, unskilled female driver.Driver is according to advance point Class carries out real vehicle debugging respectively, as shown in figure 5, speed is set into 60km/h first, front-wheel additional rotation angle is set to debugging flow 3deg, laboratory technician are mutated the feedback information of torque acceptance level according to driver to steering wheel, debug torque compensation control repeatedly Gain, when driver's sensory papilla torque-variable is excessive, torque compensation is controlled gain reduction by laboratory technician, when driver feels to be mutated When torque is too small, laboratory technician then tunes up torque compensation control gain, final to ensure that steering wheel mutation torque be by driver Received, and record torque compensation control gain values now；Secondly, speed is still set to 60km/h, front-wheel additional rotation angle model Enclose and arrive 6deg for -6deg, at intervals of 2deg, the left and right sides is symmetrical, front-wheel additional rotation angle identical width during due to motor turning Steering wheel mutation torque is identical caused by the left and right sides in the case of value, therefore need to only adjust front-wheel additional rotation angle scope and be Torque compensation control gain under 0deg to 6deg.Laboratory technician connects according to driver to steering wheel mutation torque during experiment Torque compensation under by each corner intervention in the range of degree debugging 0deg to 6deg controls gain, does each front-wheel additional rotation angle Steering wheel mutation torque under pre- is received by driver, and then determines that the torque under speed 60km/h difference corner interventions is mended Control gain is repaid, and records the concrete numerical value of torque compensation control gain；Finally, different speeds are debugged out using identical method Torque compensation control gain under different corner interventions, vehicle speed range is 10km/h to 100km/h, speed at intervals of 20km/h, Final to determine speed, front-wheel additional rotation angle, three dimension tables of torque compensation control gain, Fig. 6 is EPS torque compensations of the present invention Control gain three-dimensional MAP.Finally EPS torque compensations are controlled in gain three-dimensional MAP implantation EPS controllers, EPS controllers Control EPS assist motors reach the control effect of torque compensation.

Claims

1. a kind of hide dynamic barrier control method towards man-machine harmonious automobile, it is characterised in that this method is：Passage path Dynamic Programming module is drawn according to the obstacle information, coordinate of ground point, motoring condition information gathered in real time, real-time optimization Lateral displacement reference value, yaw angle reference value, yaw velocity reference value, the longitudinal velocity reference value of desired trajectory, are input to Path following control module, while passage path tracing control module gathers current motoring condition information, real-time optimization obtains Go out front wheel angle and four wheel slips, control automobile realizes collision avoidance；During collision avoidance is controlled, pass through EPS torque compensations Module determines that torque compensation controls gain, steering wheel is mutated into Torque Control in ideal range according to speed, front-wheel additional rotation angle It is interior, realize man-machine harmonious automobile emergency collision avoidance；This method comprises the following steps：

Step 1, path Dynamic Programming module are believed according to the obstacle information, coordinate of ground point, motoring condition gathered in real time Breath, real-time optimization draw lateral displacement reference value, yaw angle reference value, yaw velocity reference value, the longitudinal direction speed of desired trajectory Reference value is spent, it includes following sub-step：

Step 1.1.1, by the use of predict the terminal point coordinate of time domain interior prediction track and two norms of coordinate of ground point error as with Track performance indications, embody the track following characteristic of automobile, and its expression formula is as follows：

Wherein, H_{P, h}For the prediction time domain of path Dynamic Programming module, (X_{T+Hp, h},Y_{T+Hp, h}) it is prediction time domain interior prediction track Terminal point coordinate, obtained by Mass Model iteration, the automobile coordinate of ground point (X to be reached during collision avoidance_g,Y_g)；

The Mass Model is：

<mrow> <mover> <mi>y</mi> <mo>&CenterDot;&CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>a</mi> <mi>y</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mover> <mi>x</mi> <mo>&CenterDot;&CenterDot;</mo> </mover> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>

Wherein,a_yFor automobile side angle acceleration；For automobile longitudinal acceleration；Respectively automobile yaw angle and yaw angle Speed；The longitudinal velocity and side velocity of automobile barycenter respectively in earth coordinates；V is the longitudinal direction speed of current automobile Degree；

Step 1.1.2, by the use of two norms of side acceleration as the automotive safety index during collision avoidance, automotive correlation prevention is embodied Stability, establishing discrete quadratic form automotive safety index is：

<mrow> <msub> <mi>w</mi> <mn>1</mn> </msub> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mi>t</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <msub> <mi>H</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>h</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <mo>|</mo> <msub> <mi>a</mi> <mrow> <mi>y</mi> <mi>k</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>|</mo> <msub> <mo>|</mo> <mn>2</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>

Wherein, H_{C, h}For the control time domain of path Dynamic Programming module, t represents current time, a_yFor the lateral acceleration of Mass Model Degree, w₁For a_yWeight coefficient；

Stability of automobile constraint is obtained using the bound of linear inequality limit lateral acceleration, its mathematic(al) representation is：

|a_yk,t| ＜ μ g k=t, t+1 ... t+H_c,h-1 (3)

The positional information of t barrier may be characterized as the set of N number of discrete point, and these information can be obtained by radar sensor measurement , wherein the coordinate representation of j-th of discrete point is (X_j,t,Y_j,t), the automobile center-of-mass coordinate of t is designated as (X_k,t,Y_k,t), can be by Vehicle dynamics are calculated, and position constraint is set to

Wherein, a is distance of the automobile barycenter to headstock；B is distance of the automobile barycenter to the tailstock；C is the half of automobile overall width； For using t as the yaw angle for playing k moment automobiles in point prediction time domain；D_x,j,tIt is j-th of discrete point of barrier in automobile coordinate The fore-and-aft distance of automobile barycenter, D are arrived in system_y,j,tThe horizontal stroke of automobile barycenter is arrived in vehicle axis system for j-th of discrete point of barrier To distance；

It is assumed that for barrier along Y-direction with constant speed movement, it is N number of with barrier that formula (5) characterizes automobile in prediction time domain The degree of closeness of discrete point,Value is bigger, illustrates that the distance of automobile discrete point corresponding with barrier is closer, also more dangerous；It is fixed Adopted tThe maximum barrier discrete point j of value is the dangerous spot in current sample period, is designated as (X_j,t,Y_j,t), in prediction Barrier motion is predicted based on this dangerous spot in domain, iterative relation is expressed as：

<mrow> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>Y</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>)</mo> <mo>=</mo> <mo>(</mo> <msub> <mi>X</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>Y</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mo>+</mo> <msub> <mi>&Delta;d</mi> <mi>t</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mi>k</mi> <mo>=</mo> <mi>t</mi> <mo>,</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>t</mi> <mo>+</mo> <msub> <mi>H</mi> <mi>p</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&Delta;d</mi> <mi>t</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>X</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>Y</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>X</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow></mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>

Wherein, (X_j,t-1,Y_j,t-1) it is coordinate of the dangerous spot at the t-1 moment；(X_j,k,Y_j,k) it is k moment dangerous spots in prediction time domain Coordinate；

The discrete point coordinates of barrier by way of iteration in more new formula (5), by the position of barrier in prediction time domain Change is integrated into the position constraint of Model Predictive Control Algorithm；

Step 1.3, build path Dynamic Programming Multiobjective Optimal Control Problems, solve Multiobjective Optimal Control Problems, Jin Erqiu Go out yaw velocity reference value, yaw angle reference value, lateral displacement reference value and longitudinal velocity reference value, it includes following sub-step Suddenly：

Step 1.3.1, obstacle information is obtained by radar sensor, running car is obtained by vehicle speed sensor and gyroscope Status information, and the obstacle information of acquisition and motoring condition information are inputted into path Dynamic Programming module；

Step 1.3.2, tracking performance index and automotive safety index are converted into single index using weigthed sums approach, build road Footpath Dynamic Programming Multiobjective Optimal Control Problems, the problem will meet stability of automobile constraint and position constraint simultaneously, and ensure Path Dynamic Programming input and output meet Mass Model：

<mrow> <munder> <mi>min</mi> <msub> <mi>a</mi> <mi>y</mi> </msub> </munder> <mo>{</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>g</mi> </msub> <mo>-</mo> <msub> <mi>X</mi> <mrow> <mi>t</mi> <mo>+</mo> <msub> <mi>H</mi> <mi>p</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>Y</mi> <mi>g</mi> </msub> <mo>-</mo> <msub> <mi>Y</mi> <mrow> <mi>t</mi> <mo>+</mo> <msub> <mi>H</mi> <mi>p</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>+</mo> <msub> <mi>w</mi> <mn>1</mn> </msub> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mi>t</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <msub> <mi>H</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>h</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <mo>|</mo> <msub> <mi>a</mi> <mrow> <mi>y</mi> <mi>k</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>|</mo> <msub> <mo>|</mo> <mn>2</mn> </msub> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>

Submit to

I) Mass Model

Ii) constraints is formula (3)~(7)

Step 1.3.3, in path Dynamic Programming controller, genetic algorithm is called, solves Multiobjective Optimal Control Problems (9), Obtain optimal opened loop control a_y ^*For：

<mrow> <msup> <msub> <mi>a</mi> <mi>y</mi> </msub> <mo>*</mo> </msup> <mo>=</mo> <mi>arg</mi> <munder> <mi>min</mi> <msub> <mi>a</mi> <mi>y</mi> </msub> </munder> <mo>{</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>g</mi> </msub> <mo>-</mo> <msub> <mi>X</mi> <mrow> <mi>t</mi> <mo>+</mo> <msub> <mi>H</mi> <mi>p</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>Y</mi> <mi>g</mi> </msub> <mo>-</mo> <msub> <mi>Y</mi> <mrow> <mi>t</mi> <mo>+</mo> <msub> <mi>H</mi> <mi>p</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>+</mo> <msub> <mi>w</mi> <mn>1</mn> </msub> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mi>t</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <msub> <mi>H</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>h</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <mo>|</mo> <msub> <mi>a</mi> <mrow> <mi>y</mi> <mi>k</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>|</mo> <msub> <mo>|</mo> <mn>2</mn> </msub> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>

Submit to

I) Mass Model

Ii) constraints is formula (3)~(7)

Step 1.3.4, current time optimal opened loop control a is utilized_y ^*(0) yaw velocity reference value, is obtainedYaw angle is joined Examine valueLateral displacement reference value Y_ref, longitudinal velocity reference valueExpression is as follows：

<mrow> <msub> <mover> <mi>y</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mo>&Integral;</mo> <msup> <msub> <mi>a</mi> <mi>y</mi> </msub> <mo>*</mo> </msup> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>Y</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mo>&Integral;</mo> <msub> <mover> <mi>Y</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mover> <mi>x</mi> <mo>&CenterDot;</mo> </mover> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mi>V</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>

Wherein, V is the longitudinal velocity of current automobile,For the reference value of automobile side angle speed,For the ginseng of path side velocity Examine value；

Step 2, path following control module receive to be referred to by the lateral displacement of the desired trajectory of path Dynamic Programming module output Value, yaw angle reference value, yaw velocity reference value, longitudinal velocity reference value, while the collection of path following control module is current Motoring condition information, real-time optimization draws the front wheel angle and four wheel slips of automobile, and control automobile, which is realized, to be kept away Hit, it includes following sub-step：

Step 2.1.1, the lateral displacement reference value Y exported using path Dynamic Programming module_ref, yaw angle reference valueIt is horizontal Pivot angle speed referenceLongitudinal velocity reference valueWith two norm conducts of the error of actual motoring condition information Tracking performance indications, embody the track following characteristic of automobile, and its expression formula is as follows：

<mrow> <msub> <mi>w</mi> <mn>2</mn> </msub> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mi>t</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <msub> <mi>H</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <mo>|</mo> <msub> <mi>&eta;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&eta;</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> <mi>k</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>|</mo> <msub> <mo>|</mo> <mn>2</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>22</mn> <mo>)</mo> </mrow> </mrow>

Wherein, η_k,tFor motoring condition information, obtained by Vehicle dynamics iteration,η_refk,t The reference value provided for path Dynamic Programming module,H_{P, l}For path following control module Prediction time domain, w₂For weight coefficient；

The Vehicle dynamics：

F_xi=f_xicos(δ_i)-f_yisin(δ_i),i∈{1,2,3,4} (31)

F_yi=f_xisin(δ_i)+f_yicos(δ_i),i∈{1,2,3,4} (32)

Wherein, F_xi、F_yiLongitudinal component and cross component force of respectively four wheels along vehicle body coordinate direction；f_xi、f_yiIt is respectively Component of four wheels along wheel coordinate direction, wherein f_xiFor four wheel slips and the function of analysis of wheel vertical load, f_yiFor The function of front wheel angle and analysis of wheel vertical load, concrete numerical value can be determined by magic formula；Respectively automobile longitudinal speed And longitudinal acceleration；Respectively automobile side angle speed and side acceleration；Respectively automobile yaw angle, horizontal stroke Pivot angle speed and yaw angular acceleration；l_f、l_rRespectively automobile barycenter is to the distance of axle, l_sFor the half of wheelspan size； J_zIt is the yaw rotation inertia around the vertical axis of automobile barycenter；M is car mass；X, Y is respectively automobile matter in earth coordinates The transverse and longitudinal coordinate of heart position；δ_iFor four wheel steering angles, automobile is front-wheel steer here, therefore δ₃=δ₄=0；

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>D</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mi>arctan</mi> <mo>(</mo> <mrow> <msub> <mi>A</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>E</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>A</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mi>arctan</mi> <mi> </mi> <msub> <mi>A</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>B</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>&CenterDot;</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>39</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>C</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>D</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <msup> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mo>;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>B</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>b</mi> <mn>3</mn> </msub> <msup> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>b</mi> <mn>4</mn> </msub> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>C</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <msub> <mi>D</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow> <msub> <mi>b</mi> <mn>5</mn> </msub> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> </mrow> </msup> </mrow> </mfrac> <mo>;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>6</mn> </msub> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>7</mn> </msub> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>8</mn> </msub> <mo>;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>40</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>D</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mi>arctan</mi> <mo>(</mo> <mrow> <msub> <mi>A</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>E</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>A</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>arctanA</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>B</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>&CenterDot;</mo> <msub> <mi>&alpha;</mi> <mi>f</mi> </msub> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>41</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>C</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>D</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msup> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mo>;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>B</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mn>3</mn> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>a</mi> <mi>r</mi> <mi>c</mi> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>a</mi> <mn>4</mn> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mrow> <msub> <mi>C</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <msub> <mi>D</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> <mo>;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mn>5</mn> </msub> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>6</mn> </msub> <mo>;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>42</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>D</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mi>arctan</mi> <mo>(</mo> <mrow> <msub> <mi>A</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>E</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>A</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>arctanA</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>B</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>&CenterDot;</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <mo>{</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>43</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>C</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>D</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <msup> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mo>;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>B</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>b</mi> <mn>3</mn> </msub> <msup> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>b</mi> <mn>4</mn> </msub> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>C</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <msub> <mi>D</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow> <msub> <mi>b</mi> <mn>5</mn> </msub> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> </mrow> </msup> </mrow> </mfrac> <mo>;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>6</mn> </msub> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>7</mn> </msub> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>8</mn> </msub> <mo>;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <mo>{</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>44</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>D</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mi>a</mi> <mi>r</mi> <mi>c</mi> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mo>(</mo> <mrow> <msub> <mi>A</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>E</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>A</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>arctanA</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>B</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>&CenterDot;</mo> <msub> <mi>&alpha;</mi> <mi>r</mi> </msub> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <mo>{</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>45</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>C</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>D</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msup> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mo>;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>B</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>a</mi> <mn>3</mn> </msub> <mi>sin</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>arctan</mi> <mo>(</mo> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>a</mi> <mn>4</mn> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mrow> <msub> <mi>C</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <msub> <mi>D</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> <mo>;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mn>5</mn> </msub> <msub> <mi>F</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>6</mn> </msub> <mo>;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <mo>{</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>46</mn> <mo>)</mo> </mrow> </mrow>

Wherein, V is the longitudinal velocity of current automobile；α_f、α_rRespectively front-wheel side drift angle and trailing wheel side drift angle；F_z,f、F_z,rRespectively Automobile axle load；s_iFor four wheel slips of automobile；A_xi、B_xi、C_xi、D_xi、E_xiAnd A_yi、B_yi、C_yi、D_yi、E_yiIt is examination Fitting parameter is tested, design parameter is as shown in following table：

The magic formula parameter of table 4

Step 2.1.2, smoothly referred to as the braking in a turn of the actuator during collision avoidance by the use of two norms of controlled quentity controlled variable rate of change Mark, embody braking in a turn smoothness properties；Controlled quentity controlled variable u is four wheel slip s of vehicle front corner δ and automobile_i i∈{1,2, 3,4 }, establishing the discrete smooth index of quadratic form braking in a turn is：

<mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mi>t</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <msub> <mi>H</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <mo>|</mo> <msub> <mi>&Delta;u</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>|</mo> <msub> <mo>|</mo> <mn>2</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </mrow>

Step 2.2, the constrained designs of path following control ensure automobile avoidance safety to set stability of automobile to constrain；Utilize Linear inequality limits the bound of front wheel angle and four wheel slips, is turned to, the physical constraint of brake actuator, Its mathematic(al) representation is：

δ_min＜ δ_k,t＜ δ_maxK=t, t+1 ... t+H_c,l-1 (24)

s_imin＜ s_ik,t＜ s_imaxI ∈ { 1,2,3,4 } k=t, t+1 ... t+H_c,l-1 (25)

Wherein, δ_minFor front wheel angle lower limit, δ_maxFor the front wheel angle upper limit, s_iminFor four wheel slip lower limits, s_imaxFor four The individual wheel slip upper limit；

Step 2.3, build path tracing control Multiobjective Optimal Control Problems, Multiobjective Optimal Control Problems are solved, draw reality Shi Youhua vehicle front corner and four wheel slips, the automobile emergency collision avoidance control for considering moving obstacle is realized, its Including following sub-step：

Step 2.3.1, path following control module obtains the lateral displacement reference of desired trajectory from path Dynamic Programming module Value, yaw angle reference value, yaw velocity reference value and longitudinal velocity reference value；

Step 2.3.2, tracking performance indications and the smooth index of braking in a turn are converted into single index, structure using weigthed sums approach Path following control Multiobjective Optimal Control Problems are built, the problem will meet steering, the physical constraint of brake actuator simultaneously, and Ensure that path following control input and output meet Vehicle dynamics：

<mrow> <munder> <mi>min</mi> <mi>u</mi> </munder> <mo>{</mo> <msub> <mi>w</mi> <mn>2</mn> </msub> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mi>t</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <msub> <mi>H</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <mo>|</mo> <msub> <mi>&eta;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&eta;</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> <mi>k</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>|</mo> <msub> <mo>|</mo> <mn>2</mn> </msub> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mi>t</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <msub> <mi>H</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <mo>|</mo> <msub> <mi>&Delta;u</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>|</mo> <msub> <mo>|</mo> <mn>2</mn> </msub> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>26</mn> <mo>)</mo> </mrow> </mrow>

Submit to

I) Vehicle dynamics

Ii) constraints is formula (24)~(25)

Step 2.3.3, in path following control device, SQP algorithms are called, Multiobjective Optimal Control Problems (26) is solved, obtains Optimal opened loop control u^*For：

<mrow> <msup> <mi>u</mi> <mo>*</mo> </msup> <mo>=</mo> <mi>arg</mi> <munder> <mi>min</mi> <mi>u</mi> </munder> <mo>{</mo> <msub> <mi>w</mi> <mn>2</mn> </msub> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mi>t</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <msub> <mi>H</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <mo>|</mo> <msub> <mi>&eta;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&eta;</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> <mi>k</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>|</mo> <msub> <mo>|</mo> <mn>2</mn> </msub> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mi>t</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <msub> <mi>H</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <mo>|</mo> <msub> <mi>&Delta;u</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>|</mo> <msub> <mo>|</mo> <mn>2</mn> </msub> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>27</mn> <mo>)</mo> </mrow> </mrow>

Submit to

I) Vehicle dynamics

Ii) constraints is formula (24)~(25)

Step 2.3.4, current time optimal opened loop control u is utilized^*(0) fed back, realize that closed-loop control realizes consideration motion The automobile emergency collision avoidance control of barrier.

Step 3, design are implanted with the EPS torque compensation modules of steering wheel mutation torque hommization regulation algorithm, EPS torque compensation moulds Root tuber determines that torque compensation controls gain, steering wheel mutation Torque Control can be connect in driver according to speed, front-wheel additional rotation angle The scope received；Design process includes following sub-step：

Step 3.1, the design method of EPS torque compensation modules are：Choose several drivers and carry out real vehicle debugging, pass through tune first The torque compensation for order speed for a trial, determining under front-wheel additional rotation angle controls gain, and laboratory technician carries out anti-according to the subjective feeling of driver Polyphony tries, and ensures that steering wheel mutation torque can be received by driver；

Step 3.2, change front-wheel additional rotation angle, laboratory technician, which debugs torque compensation control gain, makes different front-wheel additional rotation angle interventions Under steering wheel mutation torque can be received by driver, and then determine the torque compensation under the speed control gain；

Step 3.3, determine using identical method torque compensation control under different speeds, different front-wheel additional rotation angle interventions Gain, the determination of speed, front-wheel additional rotation angle, torque compensation control gain three-dimensional MAP is completed, is controlled and increased using torque compensation Beneficial three dimension tables carry out torque compensation control, and steering wheel is mutated into Torque Control in the ideal range, realize that steering wheel is mutated power The automobile emergency collision avoidance of square hommization regulation.

Step 3.4, EPS torque compensations are controlled in gain three-dimensional MAP implantation EPS controllers, EPS controllers control EPS is helped Force motor reaches the control effect of torque compensation.