CN111547111B - Autonomous guiding control method for virtual rail train - Google Patents

Autonomous guiding control method for virtual rail train Download PDF

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CN111547111B
CN111547111B CN202010439538.8A CN202010439538A CN111547111B CN 111547111 B CN111547111 B CN 111547111B CN 202010439538 A CN202010439538 A CN 202010439538A CN 111547111 B CN111547111 B CN 111547111B
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virtual rail
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CN111547111A (en
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张众华
杨蔡进
张卫华
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Southwest Jiaotong University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B61—RAILWAYS
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    • B61L27/00—Central railway traffic control systems; Trackside control; Communication systems specially adapted therefor
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Abstract

The invention provides an autonomous guiding control method of a virtual rail train, and belongs to the technical field of operation control of virtual rail trains. Firstly, dispersing a virtual rail train composed of three sections into M independent vehicles, and establishing a self-guiding virtual rail train decoupling dynamic model; establishing a discrete lateral dynamic model of each section of vehicle of the virtual rail train; calculating the first train steering control quantity of the self-guiding virtual rail train; calculating a lateral state prediction value of each section of vehicle in the virtual rail train marshalling; calculating the steering control quantity of the vehicle with the serial number 'i' larger than 1 behind the first train of the virtual rail train; and calculating the longitudinal reference speed of each vehicle of the self-guiding virtual rail train. The control input quantity required by each hub motor driving controller and steering action controller for realizing the autonomous guiding operation of the virtual rail train driven by the all-wheel to steer the all-wheel can be obtained. The invention can be completed by applying Matlab software for calculation.

Description

Autonomous guiding control method for virtual rail train
Technical Field
The invention belongs to the technical field of virtual rail train control.
Technical Field
The self-guiding virtual rail train runs under the public road right, and automatically guides to run along a virtual rail coated on the upper surface of a road, and is provided with medium-capacity urban rail transit trains. The multi-axle steering flexible marshalling vehicle adopts the technologies of rubber wheel bearing, all-wheel hub motor independent driving, bidirectional autonomous operation, multi-axle steering and flexible marshalling, and has the technical characteristics of redundant traction, steering and braking. Therefore, the carrying capacity, curve passing capacity and active safety capacity of the self-guided virtual rail train in a complex urban environment are greatly improved. The traction, steering and braking control and distribution technology is a key technology for realizing basic functions and guaranteeing operation safety of the self-guiding virtual rail train. The existing control method is mainly realized by adopting extended Ackermann steering geometry, rigid tire hypothesis and unified instant center, and has the advantages of simplicity, reliability, low cost, good real-time performance and the like, for example, the method is disclosed in a patent (CN 110244731A). In the process of traction, steering and braking of the self-guiding virtual rail train, the longitudinal and lateral adhesive force of tires, the interior of each vehicle and the vehicles have strong nonlinear coupling effect, and if no good coordination mechanism exists, the problems of lateral instability of the virtual rail train, folding of carriages in the braking process, overlarge hinge action force, reduction of self-guiding control precision and the like can be caused. Since the above coupling involves vehicle dynamics response and control, conventional coordinated control methods do not take into account vehicle dynamics.
Disclosure of Invention
The invention aims to provide an autonomous guiding control method for a virtual rail train, which can effectively solve the technical problem of distributing the control quantity of each hub motor and a steering actuator in the autonomous guiding operation process of the virtual rail train.
A virtual rail train autonomous guiding control method comprises the following steps:
step one, establishing a decoupling dynamic model of a self-guided virtual rail train:
the virtual rail train realizes all-wheel drive or all-wheel steering by controlling the hub motor and the steering actuator, and when the virtual rail train is in self-steering steady-state operation in an ideal state, the hinge acting force between the two trains is very small; based on this, the virtual rail train composed of M vehicles is discretized into M independent vehicles, the coupling force between the vehicles is an internal force for the train, and can be an external disturbance for each vehicle, and the disturbance is bounded, and the relationship of the coupling force can be expressed as:
Figure GDA0002964268700000011
wherein, assuming that the virtual rail train is located on a horizontal road surface,
Figure GDA0002964268700000012
and
Figure GDA0002964268700000013
the longitudinal force, the lateral force and the yaw moment of the 2 vehicles acting on the 1 vehicle in the plane are shown;
Figure GDA0002964268700000014
and
Figure GDA0002964268700000015
shows the longitudinal force applied to the 2 cars by the 1 car in the plane,Lateral force and yaw moment;
the decoupled two-degree-of-freedom 2DOF vehicle dynamics model between two adjacent vehicles of the virtual rail train is represented by a state space as follows:
Figure GDA0002964268700000016
wherein i is a train number of the virtual rail train formed by the M trains, and i is 1,2,3 … M; v. ofiRepresenting the amount of external disturbances caused by the coupling between two vehicles; hiRepresenting a perturbation gain matrix; definition of
Figure GDA00029642687000000213
Is xiFirst derivative of (a), xiAnd (3) representing the state variable array of the ith vehicle, and represented as:
Figure GDA0002964268700000021
Figure GDA0002964268700000022
respectively representing the center of the front and rear axles of the i-th vehicle in the ith vehicle coordinate system xioiyiDownward lateral displacement;
Figure GDA0002964268700000023
indicating the heading angle of the ith vehicle;
Figure GDA0002964268700000024
representing the lateral velocity and yaw rate of the vehicle; t represents matrix transposition;
Φiis a state transition matrix, represented as:
Figure GDA0002964268700000025
Figure GDA0002964268700000026
respectively representing the distances from the mass center of the ith vehicle to the center of the front axle and the center of the rear axle;
Figure GDA0002964268700000027
respectively representing the cornering stiffness of a front equivalent tire and a rear equivalent tire in a 2DOF vehicle model; m isi、
Figure GDA0002964268700000028
Respectively representing the total mass and the yaw moment of inertia of the ith section of the vehicle;
Figure GDA0002964268700000029
the longitudinal speed of the mass center of the ith section of vehicle is represented and is measured by a sensor, and the longitudinal speed is assumed to be constant in a prediction time domain; gamma-shapediTo control the gain matrix, it is expressed as:
Figure GDA00029642687000000210
uithe steering control input for the ith vehicle lateral dynamics model is expressed as:
Figure GDA00029642687000000211
in the formula (I), the compound is shown in the specification,
Figure GDA00029642687000000212
respectively representing the deflection angles of front and rear equivalent wheels in the ith section 2DOF vehicle model;
step two, establishing a discrete lateral dynamics model of each section of vehicle of the virtual rail train:
according to equation (2), the discrete vehicle lateral dynamics model is represented as:
xi(k+1)＝Ai(k)xi(k)+Bi(k)ui(k)+Hi(k)vi(k) (7)
wherein N represents the number of discrete moments in the prediction time domain; k denotes the kth time in the prediction time domain, k is 0,1,2 … N-1;
defining the state transition matrix of the discrete lateral dynamics model as Ai(k) Expressed as:
Figure GDA0002964268700000031
defining I as an identity matrix of 5 x 5 dimensions;
Figure GDA0002964268700000032
the length of the prediction time domain is in seconds;
defining the control gain matrix of the discrete lateral dynamics model as Bi(k) Expressed as:
Figure GDA0002964268700000033
defining a predicted value of an output variable of a vehicle control model as yi(k +1), expressed as:
yi(k+1)＝Cxi(k+1) (10)
wherein, C is a gain matrix for predicting vehicle pose output at the k +1 th moment, and is expressed as:
Figure GDA0002964268700000034
step three, calculating the first train steering control quantity of the self-guiding virtual rail train:
the method comprises the steps of taking a virtual track line of a road surface as a tracking target, adopting a special camera for real-time identification, obtaining a point cloud coordinate sequence described in a first vehicle coordinate system, and calculating target lateral displacement of the first vehicle for tracking the virtual track in a prediction time domain through point cloud coordinates
Figure GDA0002964268700000035
Angle displacement with course
Figure GDA0002964268700000036
The value of the superscript "i" is 1, which represents the first car; "i" is greater than 1 and represents a vehicle behind the lead, and subscript "des" represents a tracking target;
establishing a quadratic objective function of the first vehicle tracking virtual track, which is expressed as:
Figure GDA0002964268700000037
wherein x isi 0Is an initial state variable in a prediction time domain; q represents a tracking error weight matrix; r represents a control input weight matrix; solving a quadratic programming problem containing equality constraint by using the formula (12), and calculating the control input u of the first vehicle tracking virtual track of the virtual track traini(k) Calculating the control input quantity of the steering actuator of the front axle and the rear axle of the ith vehicle through proportional gain, and inputting the control input quantity into a steering action controller;
step four, calculating the lateral state prediction value of each section of vehicle in the virtual rail train marshalling:
coupled equation (10), state variable x of vehicle at k-th timei(k) And controlling the input ui(k) And disturbance estimate Hi(k)vi(k) Calculating the state variable x of the first vehicle at the k +1 th timei(k +1), calculating the predicted value of the state variable of the vehicle at the predicted time domain terminal through iterative calculation, and further calculating the predicted value of the lateral state of the vehicle, wherein the predicted value is expressed as:
Figure GDA0002964268700000038
wherein the subscript "pre" represents the prediction; e is a vehicle lateral state output coefficient matrix defined as
Figure GDA0002964268700000039
Step five, calculating the steering control quantity of the vehicle with the serial number 'i' larger than 1 behind the first train of the virtual rail train:
when the first train of the virtual rail train tracks strictly, the projection of the central point of the rear axle of the first train on the road surface is superposed with the virtual rail; based on the method, except the first train, other vehicles participating in marshalling track the lateral displacement and the course angle of the central point of the rear axle of the front train in a prediction time domain, and finally the state prediction and the self-steering motion following of the virtual rail train are realized;
defining the lateral distance and the heading angle of the center of the rear axle of the ith vehicle at the (k +1) th moment as
Figure GDA0002964268700000041
Figure GDA0002964268700000042
The calculation formula is as follows by taking the tracking target of the (i +1) th section of vehicle (i is more than or equal to M-1):
Figure GDA0002964268700000043
d is a gain matrix for predicting the central pose of the rear axle of the ith vehicle;
Figure GDA0002964268700000044
required lateral displacement is followed in each section of vehicle self-steering motion after virtual rail train first train
Figure GDA0002964268700000045
And vehicle heading angle
Figure GDA0002964268700000046
Is calculated as follows:
Figure GDA0002964268700000047
combining the formula (12) and the formula (15), namely calculating the steering actuation control quantity of each vehicle behind the first train, converting the steering actuation control quantity into the control quantity of a steering actuator through proportional gain, and realizing the steering actuation of each vehicle behind the first train of the virtual railway train;
step six, calculating the longitudinal reference speed of each section of vehicle of the self-guided virtual rail train:
when the self-guiding virtual rail train runs on different road sections, different target running speeds need to be tracked, and the longitudinal target speed of each section of vehicle is calculated according to the following method:
Figure GDA0002964268700000048
wherein the content of the first and second substances,
Figure GDA0002964268700000049
the working condition is traction;
Figure GDA00029642687000000410
the traction and braking are unified into an expression (18) under the braking condition;
step seven, calculating the traction control quantity of each section of the self-guiding virtual rail train:
assuming that the vehicle body is a rigid body, the velocity component at the wheel center is calculated according to the predicted values of the longitudinal velocity, the lateral velocity and the yaw velocity of the vehicle centroid by the basic theory of rigid body plane motion, and is expressed as:
Figure GDA00029642687000000411
wherein the content of the first and second substances,
Figure GDA00029642687000000412
the jth wheel center of the ith vehicle is positioned on the vehicle seatA coordinate component along the x-axis and a coordinate component along the y-axis in the coordinate system; with the vehicle running direction as a reference, fl, fr, rl, rr respectively represent position marks of a front left wheel, a front right wheel, a rear left wheel and a rear right wheel;
calculating the wheel speed deflection angle of the four-wheel steering hub motor driven vehicle:
Figure GDA00029642687000000413
calculating the tire slip angle of the four-wheel steering hub motor driven vehicle:
Figure GDA0002964268700000051
wherein the content of the first and second substances,
Figure GDA0002964268700000052
a wheel deflection angle of an actual vehicle;
calculating wheel rotating speed predicted values of all sections of vehicles of the virtual rail train:
calculating the speed component of the wheel center in the tire symmetry plane according to the tire slip angle and the speed component of the wheel center in the vehicle coordinate system, and expressing the speed component as follows:
Figure GDA0002964268700000053
the calculation formula of the predicted value of the rotating speed when the wheel performs pure rolling is as follows:
Figure GDA0002964268700000054
wherein r issRepresents the tire rolling radius;
in summary, the steering control input u of the self-guided virtual rail train decoupling control model for the M-track train consist is first calculated by the equations (2) to (23)iCalculating the steering actuation of each shaft by proportional gainThe control input quantity of the steering controller is sent to the steering action controller; then calculating the predicted value of the rotating speed of each hub motor during forward driving or reverse driving
Figure GDA0002964268700000055
And sent to the corresponding in-wheel motor drive controller.
Drawings
FIG. 1 is a schematic view of the all-wheel drive all-wheel steering of a virtual rail train according to the present invention
FIG. 2 is a schematic diagram of decoupling between virtual rail train vehicles of the present invention
FIG. 3 is a schematic diagram of a rear car and a front car of the virtual rail train according to the present invention
FIG. 4 is a schematic diagram illustrating the prediction of the rotation speed of the front left wheel of the virtual rail train according to the present invention
FIG. 5 speed curves for each wheel of a virtual rail train of the present invention
FIG. 6 is a deflection angle curve for each wheel of a virtual rail train according to the present invention
FIG. 7 is a centroid trace plot for each vehicle of a virtual rail train of the present invention
FIG. 8 is a flow chart of a virtual rail train traction steering cooperative control algorithm of the present invention
Detailed Description
An autonomous guiding control method of a virtual rail train comprises the steps that three sections of vehicles are used as vehicle groups of the virtual rail train, the virtual rail train is dispersed into M independent vehicles, wherein M is 3 in the example, as shown in figures 1,2,3 and 4, the vehicles in the figures are all driven by hub motors, a steering shaft 1 of a first vehicle 4, a hinge joint 2 between the two vehicles and wheels 3 of the virtual rail train are arranged on the front end of the first vehicle; a second-section marshalling vehicle 5 and a third-section marshalling vehicle 6. The road forms a virtual track 7 by marking; the virtual track point cloud coordinate sequence 8 of the first vehicle 4. A point cloud coordinate sequence prediction value 9 of a vehicle rear axle central point in a second vehicle coordinate system; the first vehicle rear axle center point 10; a point cloud coordinate sequence prediction value 11 of a first vehicle rear axle center point in a third vehicle coordinate system after the first vehicle; first rear axle center point 12 after the first vehicle. Establishing a self-guiding virtual rail train decoupling dynamic model; establishing a discrete lateral dynamic model of each section of vehicle of the virtual rail train; calculating the first train steering control quantity of the self-guiding virtual rail train; calculating a lateral state prediction value of each section of vehicle in the virtual rail train marshalling; calculating the steering control quantity of the vehicle with the serial number 'i' larger than 1 behind the first train of the virtual rail train; and calculating the longitudinal reference speed of each section of vehicle of the virtual rail train. The control input quantity required by each hub motor driving controller and steering action controller for realizing the autonomous guiding operation of the virtual rail train driven by the all-wheel to steer the all-wheel can be obtained. The formula shown in the invention can be calculated by running (Matlab) software.

Claims (1)

1. A virtual rail train autonomous guiding control method comprises the following steps:
step one, establishing a decoupling dynamic model of a self-guided virtual rail train:
the virtual rail train realizes all-wheel drive or all-wheel steering by controlling the hub motor and the steering actuator, and when the virtual rail train is in self-steering steady-state operation in an ideal state, the hinge acting force between the two trains is very small; based on this, the virtual rail train composed of M vehicles is discretized into M independent vehicles, the coupling force between the vehicles is an internal force for the train, and can be an external disturbance for each vehicle, and the disturbance is bounded, and the relationship of the coupling force can be expressed as:
Figure FDA0002964268690000011
wherein, assuming that the virtual rail train is located on a horizontal road surface,
Figure FDA0002964268690000012
and
Figure FDA0002964268690000013
the longitudinal force, the lateral force and the yaw moment of the 2 vehicles acting on the 1 vehicle in the plane are shown;
Figure FDA0002964268690000014
and
Figure FDA0002964268690000015
the longitudinal force, the lateral force and the yaw moment of the 1 vehicle acting on the 2 vehicles in the plane are shown;
the decoupled two-degree-of-freedom 2DOF vehicle dynamics model between two adjacent vehicles of the virtual rail train is represented by a state space as follows:
Figure FDA0002964268690000016
wherein i is a train number of the virtual rail train formed by the M trains, and i is 1,2,3 … M; v. ofiRepresenting the amount of external disturbances caused by the coupling between two vehicles; hiRepresenting a perturbation gain matrix; definition of
Figure FDA0002964268690000017
Is xiFirst derivative of (a), xiAnd (3) representing the state variable array of the ith vehicle, and represented as:
Figure FDA0002964268690000018
Figure FDA0002964268690000019
respectively representing the center of the front and rear axles of the i-th vehicle in the ith vehicle coordinate system xioiyiDownward lateral displacement;
Figure FDA00029642686900000110
indicating the heading angle of the ith vehicle;
Figure FDA00029642686900000111
representing the lateral velocity and yaw rate of the vehicle; t represents matrix transposition;
Φiis a state transition matrix, represented as:
Figure FDA00029642686900000112
Figure FDA00029642686900000113
respectively representing the distances from the mass center of the ith vehicle to the center of the front axle and the center of the rear axle;
Figure FDA00029642686900000114
respectively representing the cornering stiffness of a front equivalent tire and a rear equivalent tire in a 2DOF vehicle model; m isi、
Figure FDA00029642686900000115
Respectively representing the total mass and the yaw moment of inertia of the ith section of the vehicle;
Figure FDA00029642686900000116
the longitudinal speed of the mass center of the ith section of vehicle is represented and is measured by a sensor, and the longitudinal speed is assumed to be constant in a prediction time domain; gamma-shapediTo control the gain matrix, it is expressed as:
Figure FDA0002964268690000021
uithe steering control input for the ith vehicle lateral dynamics model is expressed as:
Figure FDA0002964268690000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002964268690000023
respectively representing the deflection angles of front and rear equivalent wheels in the ith section 2DOF vehicle model;
step two, establishing a discrete lateral dynamics model of each section of vehicle of the virtual rail train:
according to equation (2), the discrete vehicle lateral dynamics model is represented as:
xi(k+1)＝Ai(k)xi(k)+Bi(k)ui(k)+Hi(k)vi(k) (7)
wherein N represents the number of discrete moments in the prediction time domain; k denotes the kth time in the prediction time domain, k is 0,1,2 … N-1;
defining the state transition matrix of the discrete lateral dynamics model as Ai(k) Expressed as:
Figure FDA0002964268690000024
defining I as an identity matrix of 5 x 5 dimensions;
Figure FDA0002964268690000025
the length of the prediction time domain is in seconds;
defining the control gain matrix of the discrete lateral dynamics model as Bi(k) Expressed as:
Figure FDA0002964268690000026
defining a predicted value of an output variable of a vehicle control model as yi(k +1), expressed as:
yi(k+1)＝Cxi(k+1) (10)
wherein, C is a gain matrix for predicting vehicle pose output at the k +1 th moment, and is expressed as:
Figure FDA0002964268690000027
step three, calculating the first train steering control quantity of the self-guiding virtual rail train:
the method comprises the steps of taking a virtual track line of a road surface as a tracking target, adopting a special camera for real-time identification, obtaining a point cloud coordinate sequence described in a first vehicle coordinate system, and calculating target lateral displacement of the first vehicle for tracking the virtual track in a prediction time domain through point cloud coordinates
Figure FDA0002964268690000028
Angle displacement with course
Figure FDA0002964268690000029
The value of the superscript "i" is 1, which represents the first car; "i" is greater than 1 and represents a vehicle behind the lead, and subscript "des" represents a tracking target;
establishing a quadratic objective function of the first vehicle tracking virtual track, which is expressed as:
Figure FDA0002964268690000031
s.t.xi(k+1)＝Ai(k)xi(k)+Bi(k)ui(k)+Hi(k)vi(k),xi(0)＝xi 0
wherein x isi 0Is an initial state variable in a prediction time domain; q represents a tracking error weight matrix; r represents a control input weight matrix; solving a quadratic programming problem containing equality constraint by using the formula (12), and calculating the control input u of the first vehicle tracking virtual track of the virtual track traini(k) Calculating the control input quantity of the steering actuator of the front axle and the rear axle of the ith vehicle through proportional gain, and inputting the control input quantity into a steering action controller;
step four, calculating the lateral state prediction value of each section of vehicle in the virtual rail train marshalling:
coupled equation (10), state variable x of vehicle at k-th timei(k) And controlling the input ui(k) And disturbance estimate Hi(k)vi(k) Calculating the state variable x of the first vehicle at the k +1 th timei(k +1), calculating the predicted value of the state variable of the vehicle at the predicted time domain terminal through iterative calculation, and further calculating the predicted value of the lateral state of the vehicle, wherein the predicted value is expressed as:
Figure FDA0002964268690000032
wherein the subscript "pre" represents the prediction; e is a vehicle lateral state output coefficient matrix defined as
Figure FDA0002964268690000033
Step five, calculating the steering control quantity of the vehicle with the serial number 'i' larger than 1 behind the first train of the virtual rail train:
when the first train of the virtual rail train tracks strictly, the projection of the central point of the rear axle of the first train on the road surface is superposed with the virtual rail; based on the method, except the first train, other vehicles participating in marshalling track the lateral displacement and the course angle of the central point of the rear axle of the front train in a prediction time domain, and finally the state prediction and the self-steering motion following of the virtual rail train are realized;
defining the lateral distance and the heading angle of the center of the rear axle of the ith vehicle at the (k +1) th moment as
Figure FDA0002964268690000034
Figure FDA0002964268690000035
The calculation formula is as follows by taking the tracking target of the (i +1) th section of vehicle (i is more than or equal to M-1):
Figure FDA0002964268690000036
d is a gain matrix for predicting the central pose of the rear axle of the ith vehicle;
Figure FDA0002964268690000037
required lateral displacement is followed in each section of vehicle self-steering motion after virtual rail train first train
Figure FDA0002964268690000038
And vehicle heading angle
Figure FDA0002964268690000039
Is calculated as follows:
Figure FDA00029642686900000310
combining the formula (12) and the formula (15), namely calculating the steering actuation control quantity of each vehicle behind the first train, converting the steering actuation control quantity into the control quantity of a steering actuator through proportional gain, and realizing the steering actuation of each vehicle behind the first train of the virtual railway train;
step six, calculating the longitudinal reference speed of each section of vehicle of the self-guided virtual rail train:
when the self-guiding virtual rail train runs on different road sections, different target running speeds need to be tracked, and the longitudinal target speed of each section of vehicle is calculated according to the following method:
Figure FDA0002964268690000041
wherein the content of the first and second substances,
Figure FDA0002964268690000042
the working condition is traction;
Figure FDA0002964268690000043
the traction and braking are unified into an expression (18) under the braking condition;
step seven, calculating the traction control quantity of each section of the self-guiding virtual rail train:
assuming that the vehicle body is a rigid body, the velocity component at the wheel center is calculated according to the predicted values of the longitudinal velocity, the lateral velocity and the yaw velocity of the vehicle centroid by the basic theory of rigid body plane motion, and is expressed as:
Figure FDA0002964268690000044
wherein the content of the first and second substances,
Figure FDA0002964268690000045
a coordinate component along an x-axis and a coordinate component along a y-axis of a jth wheel center of the ith vehicle in a vehicle coordinate system respectively; with the vehicle running direction as a reference, fl, fr, rl, rr respectively represent position marks of a front left wheel, a front right wheel, a rear left wheel and a rear right wheel;
calculating the wheel speed deflection angle of the four-wheel steering hub motor driven vehicle:
Figure FDA0002964268690000046
calculating the tire slip angle of the four-wheel steering hub motor driven vehicle:
Figure FDA0002964268690000047
wherein the content of the first and second substances,
Figure FDA0002964268690000048
a wheel deflection angle of an actual vehicle;
calculating wheel rotating speed predicted values of all sections of vehicles of the virtual rail train:
calculating the speed component of the wheel center in the tire symmetry plane according to the tire slip angle and the speed component of the wheel center in the vehicle coordinate system, and expressing the speed component as follows:
Figure FDA0002964268690000049
the calculation formula of the predicted value of the rotating speed when the wheel performs pure rolling is as follows:
Figure FDA00029642686900000410
wherein r issRepresents the tire rolling radius;
in summary, the steering control input u of the self-guided virtual rail train decoupling control model for the M-track train consist is first calculated by the equations (2) to (23)iCalculating the control input quantity of each shaft steering actuator through proportional gain and sending the control input quantity to a steering actuator controller; then calculating the predicted value of the rotating speed of each hub motor during forward driving or reverse driving
Figure FDA00029642686900000411
And sent to the corresponding in-wheel motor drive controller.
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