CN110696793B - Intelligent vehicle layered control method combining four-wheel steering and differential braking - Google Patents
Intelligent vehicle layered control method combining four-wheel steering and differential braking Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60T—VEHICLE BRAKE CONTROL SYSTEMS OR PARTS THEREOF; BRAKE CONTROL SYSTEMS OR PARTS THEREOF, IN GENERAL; ARRANGEMENT OF BRAKING ELEMENTS ON VEHICLES IN GENERAL; PORTABLE DEVICES FOR PREVENTING UNWANTED MOVEMENT OF VEHICLES; VEHICLE MODIFICATIONS TO FACILITATE COOLING OF BRAKES
- B60T8/00—Arrangements for adjusting wheel-braking force to meet varying vehicular or ground-surface conditions, e.g. limiting or varying distribution of braking force
- B60T8/17—Using electrical or electronic regulation means to control braking
- B60T8/172—Determining control parameters used in the regulation, e.g. by calculations involving measured or detected parameters
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60T—VEHICLE BRAKE CONTROL SYSTEMS OR PARTS THEREOF; BRAKE CONTROL SYSTEMS OR PARTS THEREOF, IN GENERAL; ARRANGEMENT OF BRAKING ELEMENTS ON VEHICLES IN GENERAL; PORTABLE DEVICES FOR PREVENTING UNWANTED MOVEMENT OF VEHICLES; VEHICLE MODIFICATIONS TO FACILITATE COOLING OF BRAKES
- B60T8/00—Arrangements for adjusting wheel-braking force to meet varying vehicular or ground-surface conditions, e.g. limiting or varying distribution of braking force
- B60T8/17—Using electrical or electronic regulation means to control braking
- B60T8/1755—Brake regulation specially adapted to control the stability of the vehicle, e.g. taking into account yaw rate or transverse acceleration in a curve
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Abstract
The invention discloses a four-wheel steering and differential braking combined unmanned vehicle hierarchical control method, which designs a combined controller by a nonlinear Model Prediction (MPC) algorithm to control four-wheel steering and differential braking of a vehicle. The method has a three-layer control structure, the upper layer is a track planning layer, so that the longitudinal, transverse and yaw angle tracking of the vehicle is realized, and an ideal yaw angular speed and a centroid side drift angle are output; the middle layer is an MPC centralized control layer to realize the control of the rear wheel steering angle and the control of the additional yaw moment of the vehicle; the lower layer is a braking force distributor which is converted into braking control on a single wheel through the calculation of an additional yaw moment; finally, the MPC is combined with the four-wheel corner and the differential braking force output by the controller to act on the whole vehicle, so as to realize the stability tracking of the target path. The method utilizes the rolling optimization characteristic of the MPC control method, realizes the combined control of four-wheel steering and differential braking on the basis of improving the tracking precision, and improves the stability of intelligent automobile track tracking under the condition of high-speed automobiles.
Description
Technical Field
The invention relates to the field of intelligent vehicle control, in particular to a track tracking layered control method for an unmanned vehicle with four-wheel steering combined differential braking.
Background
The existing path tracking control of the unmanned vehicle mostly carries out transverse tracking control through front wheel steering, because the strong nonlinearity of a vehicle model causes that the stability of the vehicle cannot be ensured only by the front wheel steering control when the vehicle is under a high-speed working condition, and the design and application difficulty of an over-integrated control algorithm is too high, the comprehensive consideration of the four-wheel steering combined differential braking hierarchical control is an effective way for solving the path tracking stability of the unmanned vehicle.
Disclosure of Invention
In order to solve the problems of unmanned vehicle path tracking control precision and vehicle stability, the invention provides a layered control method of four-wheel steering combined differential braking, which aims to: a combined controller is designed by a nonlinear Model Prediction (MPC) algorithm, four-wheel steering and differential braking control is carried out on the vehicle, and stable tracking of an expected path under a high-speed vehicle condition is realized.
In order to achieve the purpose, the invention adopts the technical scheme that:
a layered control method for four-wheel steering combined differential braking has a three-layer control structure, and specifically comprises the following steps:
and (3) upper layer: the track planning layer is used for tracking the longitudinal direction, the transverse direction and the yaw angle of the vehicle and outputting an ideal yaw angular speed and a centroid side slip angle;
an intermediate layer: the MPC centralized control layer realizes the control of the rear wheel steering angle and the control of the additional yaw moment of the vehicle;
the lower layer: the braking force distributor is used for converting the calculation of the additional yaw moment into braking control on a single wheel;
finally, the MPC is combined with the four-wheel corner and the differential braking force output by the controller to act on the whole vehicle, so as to realize the stability tracking of the target path.
Specifically, the method comprises the following steps:
a first layer: kinematics based MPC control
1 establishing an MPC controller of an upper track planning layer to realize front wheel steering control
1.1 according to a vehicle single-track model, a vehicle kinematic model is established and written into a state space expression form as follows:
wherein the state quantities are:
in the formula: x is the longitudinal displacement of the vehicle, Y is the transverse displacement of the vehicle,
is the vehicle yaw angle;
the control quantity is selected as follows:
u＝[v,δ f ] T
in the formula: v is the central speed of the rear axle of the vehicle, delta f For deflecting the angle of the front wheel
1.2, carrying out linear processing on the vehicle kinematic nonlinear model shown by the formula to obtain a linear time-varying system as follows:
1.3 discretizing the formula by a first-order difference quotient method to obtain a discrete state space expression:
wherein: a. the k ＝I+A*T；B k ＝I+B*T；
1.4, setting a certain moment in the vehicle track tracking process as a moment t, and establishing the following objective function for solving the front wheel rotation angle at the moment t:
in the formula: n is a radical of P Is a prediction time domain; n is a radical of c Is a control time domain; rho is a weight coefficient; epsilon is a relaxation factor 1.5 formula, and the system is controlled by replacing a control quantity with a control increment, so that the formula is rewritten into a state space equation of the control increment formula:
wherein:
1.6, the control quantity and the control increment in the control process are restrained:
u min (k+1)<u<u max (k+1)
Δu min (k+1)<Δu<Δu max (k+1)
1.7 solving the objective function to obtain a series of control input increments in the control time domain
Applying the first element in the control sequence at time t as a control input increment to the system, namely:
u(t)＝u(t-1)+Δu(t)
1.8 repeating the steps at the moment t +1 to complete the tracking of the expected track and obtain a series of control quantities v, delta f
A second layer: ideal following model
2. Establishing an ideal vehicle following model, and calculating an ideal mass center slip angle and a yaw angular velocity under trajectory tracking
2.1 ideal barycenter side deviation angle model of vehicle
The ideal centroid slip angle at vehicle steady state is:
in the formula: l is the wheelbase; l. the f Is the centroid to front wheel distance; l r Is the distance from the center of mass to the rear wheel; k is a radical of r The centroid slip angle under the maximum adhesion limit of the tire with the rear wheel side slip stiffness is as follows:
in the formula: μ is the adhesion rate; g is the acceleration of gravity
The ideal vehicle centroid slip angle is:
β d ＝min(|β ideal |,|β max |)·sgn(β ideal )
2.2 model of ideal yaw rate of vehicle
The maximum yaw acceleration at the tire adhesion limit is:
the ideal vehicle yaw rate is:
r d ＝min(|r ideal |,|r max |)·sgn(r ideal )
and a third layer: middle control layer
3. An intermediate-layer MPC controller is established, an additional yaw moment generated by braking force is calculated, and rear wheel steering angle control is realized
3.1, establishing a vehicle four-wheel steering and differential braking combined dynamic model, and rewriting the model into a state space expression form:
wherein the state quantities are:
x＝[β,r] T
in the formula: beta is the vehicle mass center slip angle, r is the vehicle yaw rate,
a front wheel deflection angle;
the control quantity is selected as follows:
u＝[δ r ,M s ] T
in the formula: m s Additional yaw moment, delta, generated for braking r For deflecting the angle of the rear wheel
3.2, carrying out linear processing on the vehicle kinematic nonlinear model shown by the formula to obtain a linear time-varying system as follows:
3.3 discretizing the formula by a first-order difference quotient method to obtain a discrete state space expression:
wherein: a. the k ＝I+A*T；B k ＝I+B*T；
3.4, setting a certain moment in the vehicle track tracking process as a moment t, and establishing the following objective function for solving the front wheel rotation angle at the moment t:
in the formula: n is a radical of hydrogen P Is a prediction time domain; n is a radical of c Is a control time domain; rho is a weight coefficient; epsilon is a relaxation factor;
and 3.5, replacing the control quantity with the control increment to carry out system control by adopting a control increment formula, and therefore rewriting the formula into a state space equation of the control increment formula:
wherein:
3.6, the control quantity and the control increment in the control process are restrained:
u min (k+1)<u<u max (k+1)
Δu min (k+1)<Δu<Δu max (k+1)
3.7 solving the objective function to obtain a series of control input increments in the control time domain
Applying the first element in the control sequence at time t as a control input increment to the system, namely:
u(t)＝u(t-1)+Δu(t)
3.8 repeating the steps at the moment t +1 to complete the tracking of the expected track and obtain a series of control quantities M s ,δ r A fourth layer: braking force distribution layer
4.1 vehicle steering Condition discrimination
In the formula:
when K is 1 ＝0，
Neutral steering: k is equal to 0, and K is equal to 0,
is the median value;
and (3) oversteering: k<0，
Increasing;
understeer: k>0，
Decrease;
4.1 Single-wheel brake pressure calculation
4.2 brake application decisions
Compared with the prior art, the invention has the following beneficial effects:
1. the invention designs an intelligent vehicle track tracking layered control method of four-wheel steering combined differential braking considering vehicle stability, which tracks an expected path through an upper track planning layer, optimally calculates a rear wheel corner and an additional yaw moment control quantity by using a front wheel corner, an expected yaw velocity and a mass center sideslip angle planned by the upper layer through an intermediate layer, and distributes braking force through a lower layer controller, thereby realizing the active adjustment of four-wheel corners and differential braking of an unmanned vehicle and improving the stability of vehicle track tracking.
2. The invention brings the four-wheel steering control into the control algorithm, and improves the maneuverability and the stability of the vehicle under the high-speed working condition.
3. The invention realizes the differential braking control of the track tracking, and can actively adjust the steering angle and the braking moment of the rear wheel of the automobile, thereby optimizing the mass center slip angle, the yaw velocity and the lateral displacement of the automobile and improving the track tracking stability of the intelligent vehicle under the high-speed working condition.
4. The method adopts the model prediction controller as a control algorithm, carries out real-time prediction and rolling optimization on the control target, processes the multi-constraint optimization problem, and greatly improves the stability of trajectory tracking.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a diagram of a vehicle kinematic model according to the present invention;
FIG. 2 is a frame diagram of a hierarchical control algorithm of an intelligent vehicle with four-wheel steering combined with differential braking according to the present invention;
FIG. 3 is a control strategy simulation diagram of the present invention;
FIG. 4 is a diagram of a trace-tracking simulation result of the present invention;
FIG. 5 is a diagram of a simulation result of four wheel turning angles according to the present invention;
FIG. 6 is a diagram of the simulation result of four wheel longitudinal force according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1-5, the invention relates to a four-wheel steering combined differential braking unmanned vehicle layered control method, which has a three-layer control structure. The upper layer is a track planning layer, so that the longitudinal, transverse and yaw angles of the vehicle are tracked, and an ideal yaw velocity and a centroid side slip angle are output. The middle layer is an MPC centralized control layer, and the control of the rear wheel steering angle and the control of the additional yaw moment of the vehicle are realized. The lower layer is a braking force distributor which is converted into braking control of a single wheel through calculation of an additional yaw moment. And finally, the MPC is combined with four-wheel corners and differential braking force output by the controller to act on the whole vehicle, so that the stability tracking of the target path is realized.
A first layer: upper track following control layer
The design of the upper layer model predicted trajectory tracking controller is explained in detail below with reference to fig. 1:
1. vehicle kinematics modeling
In the formula: l is the vehicle wheel base; v is the vehicle rear axle center velocity; delta f For deflecting the angle of the front wheel
2. From the formula, it can be derived as a state space expression of:
wherein the state quantities are:
in the formula: x is the longitudinal displacement of the vehicle, Y is the transverse displacement of the vehicle,
is the vehicle yaw angle;
the control quantity is selected as follows:
u＝[v,δ f ] T
in the formula: v is the vehicle rear axle center speed, delta f For deflecting the angle of the front wheel
3. Establishing a linear error equation
3.1 because the vehicle model has the non-linear characteristic, the model needs to be linearized, because the expected input can not give the information of all state points, the invention adopts the approximate linearization method to linearize the model, applies the constant control quantity of a certain working point to the system, designs the control algorithm according to the deviation of the track and the actual state of the working point, considers that the certain working point of the system is [ x ] x 0 ,u 0 ],x 0 To always apply a control quantity of u 0 The system state quantity obtained later is
x 0 (k+1)＝f(x 0 (k),u 0 )
x 0 (0)＝x 0
By derivation, it can be obtained that:
in the formula:
3.2 discretizing the formula by a first-order difference quotient method to obtain a discrete state space expression:
y(k)＝C k x(k)
wherein:
3.3 the formula replaces the control quantity with the control increment to carry out the control of the system, so the formula is rewritten as a state space equation of the control increment formula:
wherein:
3.4 through derivation, a prediction output expression of the system can be obtained:
4. establishing rolling time domain optimization controller
4.1 for the trajectory tracking control problem, the following control objective function is established
In the formula: n is a radical of hydrogen P Is a prediction time domain; n is a radical of c Is a control time domain; rho is a weight coefficient; epsilon is a relaxation factor; q and R are weight matrixes.
4.2 in order to increase the smoothness of the track tracking, the control quantity and the control increment need to be restrained:
u min (t+k)≤u(t+k)≤u max (t+k)
Δu min (t+k)≤Δu(t+k)≤Δu max (t+k)
in the formula: Δ u is the control increment, u min For controlling incremental minimums, u max For controlling incremental maximum
The invention sets the control limit to u min ＝[-0.2 -0.6] T ，u max ＝[0.2 0.6] T ,Δu min ＝[-0.34 -0.02] T ，Δu max ＝[0.02] T Y max ＝[-3 -0.3] T ,Y min ＝[3 0.3] T
4.3 converting the objective function into a standard quadratic form and combining constraint conditions to solve the following optimization problems:
J(ξ(t),u(t-1),ΔU(t))＝[ΔU(t) T ,ε]H t [ΔU(t) T ,ε]+G t [ΔU(t) T ,ε]
in the formula:
e t for predicting tracking errors in the time domain
4.3 solving the objective function to obtain a series of control input increments in the control time domain
Applying the first element in the control sequence at time t as a control input increment to the system, namely:
u(t)＝u(t-1)+Δu(t)
repeating the steps at the moment of t +1 to complete the tracking of the expected track and obtain a series of control quantities v, delta f A second layer: ideal following model
2. Establishing an ideal vehicle following model, and calculating an ideal mass center slip angle and a yaw angular velocity under trajectory tracking
2.1 vehicle ideal centroid cornering angle model
The ideal centroid slip angle at vehicle steady state is:
in the formula: l is the wheelbase; l f Is the centroid to front wheel distance; l r Is the distance from the center of mass to the rear wheel; k is a radical of r The centroid slip angle under the maximum adhesion limit of the tire with the rear wheel side slip stiffness is as follows:
in the formula: μ is the adhesion rate; g is gravity acceleration
The ideal vehicle centroid slip angle is:
β d ＝min(|β ideal |,|β max |)·sgn(β ideal )
2.2 model of ideal yaw rate of vehicle
The maximum yaw acceleration at the tire adhesion limit is:
the ideal vehicle yaw rate is:
r d ＝min(|r ideal |,|r max |)·sgn(r ideal )
and a third layer: middle control layer
1. Vehicle kinematics modeling
In the formula: i is rotational inertia; l f ,l r Is the wheelbase; k is a radical of formula f ,k r For side deflection rigidity of front and rear wheels
2. From the formula, it can be derived as a state space expression of the form:
wherein the state quantities are:
x＝[β,r] T
in the formula: beta is the vehicle mass center slip angle, r is the vehicle yaw rate,
a front wheel deflection angle;
the control quantity is selected as follows:
u＝[δ r ,M s ] T
in the formula: m s Additional yaw moment, delta, generated for braking r For deflecting rear wheels
3. Establishing a linear error equation
3.1 because the vehicle model has the non-linear characteristic, the model needs to be linearized, because the expected input can not give the information of all state points, the invention adopts the approximate linearization method to linearize the model, applies the constant control quantity of a certain working point to the system, designs the control algorithm according to the deviation of the track and the actual state of the working point, considers that the certain working point of the system is [ x ] x 0 ,u 0 ],x 0 To always apply a control quantity of u 0 The system state quantity obtained later is
x 0 (k+1)＝f(x 0 (k),u 0 )
x 0 (0)＝x 0
By derivation, we can get:
in the formula:
3.2 discretizing the formula by a first-order difference quotient method to obtain a discrete state space expression:
wherein:
3.3 formula replaces the controlled variable with the control increment to control the system, so the formula is rewritten as a state space equation of the control increment formula:
wherein:
the formula replaces the control quantity with the control increment to carry out the control of the system, so the formula is rewritten into a state space equation of the control increment formula:
wherein:
3.4 through derivation, a prediction output expression of the system can be obtained:
4. establishing rolling time domain optimization controller
4.1 for the trajectory tracking control problem, the following control objective function is established
In the formula: n is a radical of P Is a prediction time domain; n is a radical of hydrogen c To control the time domain; rho is a weight coefficient; epsilon is a relaxation factor; q and R are weight matrixes.
4.2 in order to increase the smoothness of the track tracking, the control quantity and the control increment need to be restrained:
u min (t+k)≤u(t+k)≤u max (t+k)
Δu min (t+k)≤Δu(t+k)≤Δu max (t+k)
in the formula: Δ u is the control increment, u min For controlling incremental minimums, u max For controlling incremental maximum
The present invention sets the control amount limit to:
u min ＝[-0.6 -100] T ，u max ＝[0.2 100] T ,Δu min ＝[-0.34 -5] T ,Δu min ＝[0.34 5] T ,Y max ＝[-1.5 -10] T ,Y min ＝[1.5 10] T
4.3 converting the objective function into a standard quadratic form and combining constraint conditions to solve the following optimization problems:
J(ξ(t),u(t-1),ΔU(t))＝[ΔU(t) T ,ε]H t [ΔU(t) T ,ε]+G t [ΔU(t) T ,ε]
in the formula:
e t solving the objective function for predicting the tracking error 4.3 in the time domain to obtain a series of control input increments in the control time domain
Applying the first element in the control sequence at time t as a control input increment to the system, namely:
u(t)＝u(t-1)+Δu(t)
repeating the steps at the moment of t +1 to complete the tracking of the expected track and obtain a series of control quantities delta r ,M s A fourth layer: braking force distribution layer
4.1 vehicle steering Condition discrimination
In the formula:
when K is 1 ＝0，
Neutral steering: k is equal to 0, and K is equal to 0,
is the median value;
oversteer: k<0，
Increasing;
understeer: k>0，
Decreasing;
4.1 Single-wheel brake pressure calculation
4.2 brake application decisions
The technical means disclosed in the invention scheme are not limited to the technical means disclosed in the above embodiments, but also include the technical scheme formed by any combination of the above technical features. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
Claims (1)
1. A layered control method for four-wheel steering combined differential braking is characterized in that: the device has a three-layer control structure, which specifically comprises the following steps:
and (3) upper layer: the track planning layer is used for tracking the longitudinal direction, the transverse direction and the yaw angle of the vehicle and outputting an ideal yaw angular speed and a centroid side slip angle;
an intermediate layer: the MPC centralized control layer realizes the control of the rear wheel steering angle and the control of the additional yaw moment of the vehicle;
the lower layer: the braking force distributor is used for converting the calculation of the additional yaw moment into braking control on a single wheel;
finally, the MPC is combined with four-wheel corners and differential braking force output by the controller to act on the whole vehicle, so as to realize the stability tracking of the target path;
the specific control process of the upper track planning layer is as follows:
(1) an MPC controller of an upper track planning layer is established to realize front wheel steering control
(1.1) building a vehicle kinematic model according to a vehicle monorail model, and writing the vehicle kinematic model into a state space expression form:
in the formula: x is a state quantity, and u is a control quantity;
wherein the state quantities are:
in the formula: x is the longitudinal displacement of the vehicle, Y is the transverse displacement of the vehicle,
is the vehicle yaw angle, T is the time;
the control quantity is selected as follows:
u＝[v,δ f ] T
in the formula: v is the central speed of the rear axle of the vehicle, delta f A front wheel deflection angle;
(1.2) carrying out linear processing on the vehicle kinematic nonlinear model shown by the formula to obtain a linear time-varying system as follows:
(1.3) discretizing the formula by a first-order difference quotient method to obtain a discrete state space expression:
wherein: a. the k ＝I+A*T；B k ＝I+B*T；
(1.4) setting a certain moment in the vehicle track tracking process as a time t, and establishing the following objective function for solving the front wheel rotation angle at the time t:
in the formula: n is a radical of P Is a prediction time domain; n is a radical of c Is a control time domain; rho is a weight coefficient; epsilon is a relaxation factor;
(1.5) the formula replaces the control quantity with the control increment to control the system, so the formula is rewritten as a state space equation of the control increment formula:
wherein:
(1.6) constraining the control quantity and the control increment in the control process:
u min (k+1)<u<u max (k+1)
Δu min (k+1)<Δu<Δu max (k+1)
(1.7) solving the objective function to obtain a series of control input increments in the control time domain
Applying the first element in the control sequence at time t as a control input increment to the system, namely:
u(t)＝u(t-1)+Δu(t)
(1.8) repeating the steps at the time t +1 to complete the tracking of the expected track and obtain a series of control quantities v, delta f ；
(2) Establishing an ideal vehicle following model, and calculating an ideal mass center slip angle and a yaw angular velocity under trajectory tracking
(2.1) vehicle ideal centroid cornering angle model
The ideal centroid slip angle at vehicle steady state is:
in the formula: l is the wheelbase; l f Is the centroid to front wheel distance; l r Is the distance from the center of mass to the rear wheel; k is a radical of r Is rear wheel cornering stiffness;
the centroid slip angle at the maximum adhesion limit of the tire is:
in the formula: μ is the attachment rate; g is gravity acceleration;
the ideal vehicle centroid slip angle is:
β d ＝min(|β ideal |,|β max |)·sgn(β ideal )
(2.2) model of ideal yaw rate of vehicle
The maximum yaw acceleration at the tire adhesion limit is:
the ideal vehicle yaw rate is:
r d ＝min(|r ideal |,|r max |)·sgn(r ideal )；
the specific control process of the middle layer MPC centralized control layer is as follows: establishing an intermediate-layer MPC controller, calculating an additional yaw moment generated by braking force, and realizing rear wheel steering angle control;
(1) establishing a vehicle four-wheel steering and differential braking combined dynamic model, and rewriting the model into a state space expression form:
wherein the state quantities are:
x＝[β,r] T
in the formula: beta is the vehicle mass center slip angle, r is the vehicle yaw rate,
a front wheel deflection angle;
the control quantity is selected as follows:
u＝[δ r ,M s ] T
in the formula: m s Additional yaw moment, delta, generated for braking r A rear wheel deflection angle;
(2) the vehicle kinematics nonlinear model shown in the formula is subjected to linear processing to obtain a linear time-varying system as follows:
(3) discretizing the formula by a first-order difference quotient method to obtain a discrete state space expression:
wherein: a. the k ＝I+A*T；B k ＝I+B*T；
(4) Setting a certain moment in the vehicle track tracking process as a moment t, and establishing the following objective function for solving the front wheel rotation angle at the moment t:
in the formula: n is a radical of P Is a prediction time domain; n is a radical of c To control the time domain; rho is a weight coefficient; epsilon is a relaxation factor
(5) The formula replaces the control quantity with the control increment to carry out the control of the system, so the formula is rewritten into a state space equation of the control increment formula:
wherein:
(6) and (3) constraining the control quantity and the control increment in the control process:
u min (k+1)<u<u max (k+1)
Δu min (k+1)<Δu<Δu max (k+1)
(7) solving the objective function to obtain a series of control input increments in the control time domain
Applying the first element in the control sequence at time t as a control input increment to the system, namely:
u(t)＝u(t-1)+Δu(t)
(8) Repeating the steps at the moment of t +1 to complete the tracking of the expected track and obtain a series of control quantities M s ,δ r (ii) a The specific control process of the lower-layer braking force distributor is as follows:
(1) vehicle steering condition determination
When K is 1 ＝0，
Neutral steering: k is equal to 0, and K is equal to 0,
is the median value;
oversteer: k<0，
Enlarging;
understeer: k is>0，
Decrease;
(2) single wheel brake pressure calculation
(3) Brake application decision
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| CN108944866B (en) * | 2018-07-06 | 2021-06-01 | 长春工业大学 | Self-adaptive model prediction control algorithm for improving steering and braking cooperative control |
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| CN109017759B (en) * | 2018-07-31 | 2022-04-08 | 大连民族大学 | Desired path vehicle yaw control method |
| CN109017760B (en) * | 2018-07-31 | 2022-04-12 | 大连民族大学 | Vehicle expected trajectory tracking method and device and rolling time domain optimization algorithm |
| CN109795502B (en) * | 2018-09-27 | 2021-05-04 | 吉林大学 | Intelligent electric vehicle path tracking model prediction control method |
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