CN114859733A - Differential steering unmanned vehicle trajectory tracking and attitude control method - Google Patents

Differential steering unmanned vehicle trajectory tracking and attitude control method Download PDF

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CN114859733A
CN114859733A CN202210561298.8A CN202210561298A CN114859733A CN 114859733 A CN114859733 A CN 114859733A CN 202210561298 A CN202210561298 A CN 202210561298A CN 114859733 A CN114859733 A CN 114859733A
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unmanned vehicle
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track
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田杰
周建兵
杨铭菲
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Nanjing Forestry University
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Abstract

The invention provides a track tracking and attitude control method for a differential steering unmanned vehicle. Firstly, a dynamics and kinematics model of the differential steering of the unmanned vehicle and an unmanned vehicle roll model are established, and a linear three-degree-of-freedom vehicle model is selected as a reference model to obtain an ideal vehicle body roll angle. A reference track is given, the model prediction controller is used for controlling the unmanned vehicle differential steering model to track the given reference track so as to obtain the required differential moment and the front wheel corner generated by the differential moment, the sliding mode controller is designed for controlling the unmanned vehicle roll model to track the ideal vehicle body roll angle and obtain the required roll moment, and simulation results show that the model prediction control and the sliding mode controller can enable the differential steering unmanned vehicle to realize track tracking and can also realize control of the vehicle body posture.

Description

Differential steering unmanned vehicle trajectory tracking and attitude control method
Technical Field
The invention relates to the field of track tracking and attitude control of a differential steering unmanned vehicle, in particular to a track tracking and attitude control method of a differential steering unmanned vehicle.
Background
The unmanned vehicle and the unmanned vehicle rescue system provided by the invention patent/invention patent of China (application number: CN202010998512.5) comprise a communication unit for receiving a rescue request signal, wherein the rescue request signal carries personal basic information and position information of a rescue object.
However, in the process of rescue or transportation, the existing unmanned vehicle is easy to turn over during steering, and meanwhile, the track tracking and the attitude control cannot be performed in the process of steering the unmanned vehicle, so that the track tracking and the attitude control method of the differential steering unmanned vehicle are improved.
Disclosure of Invention
The invention aims to: in order to solve the problems of the prior art, the invention provides the following technical scheme: the utility model provides a differential steering unmanned vehicles trajectory tracking and attitude control method to improve above-mentioned problem this application is specifically such: the method comprises the following steps:
s1, establishing three vehicle models including an unmanned vehicle differential steering model, an unmanned vehicle side-tipping vehicle model and a reference model; s11, the unmanned vehicle differential steering model comprises longitudinal, lateral and yaw dynamic models and kinematic models, and the longitudinal, lateral and yaw dynamic models and the kinematic models are used for tracking a specific track through model prediction control and acquiring required differential moment and a front wheel turning angle generated by the differential moment; s12, the unmanned vehicle roll model is used for tracking an ideal vehicle body roll angle through sliding mode control; s13, the reference model mainly provides an ideal vehicle body roll angle for attitude control of the differential steering unmanned vehicle; s2 establishing a reference trajectory for generating a specific travel trajectory; s3 realizes differential steering by model prediction controller, and obtains required differential torque M by controlling unmanned vehicle to track specific driving track z (ii) a S4, controlling the differential steering unmanned vehicle to track an ideal vehicle body roll angle through a sliding mode controller, namely a vehicle body inward-inclining controller, and reducing the shaking of the system through the control of an exponential approaching law; s5 simulates the vehicle model, and analyzes the result of the simulation.
As a preferred technical solution of the present application, in step S1, the unmanned vehicle differential steering model, XOY is an inertial coordinate system, XOY is a vehicle body coordinate system fixed to the vehicle center of mass, and according to newton' S second law, the stress balance equations along the x-axis, the y-axis, and around the z-axis are respectively:
Figure BDA0003656690300000021
F yfl ＝F yfr ＝k f α f ,F yrl ＝F yrr ＝k r α r ,F xfl ＝F xfr ＝k lf s f ,F xrl ＝F xrr ＝k lr s r ，
Figure BDA0003656690300000022
wherein m is the total mass of the vehicle, a y Is the inertial acceleration at the mass center of the vehicle in the y-axis direction,
Figure BDA0003656690300000023
and
Figure BDA0003656690300000024
for lateral velocity and acceleration along the y-axis,
Figure BDA0003656690300000025
and
Figure BDA0003656690300000026
for longitudinal velocity and acceleration along the x-axis,
Figure BDA0003656690300000027
and
Figure BDA0003656690300000028
yaw rate and angular acceleration of the vehicle, F yfl 、F yfr 、F yrl And F yrr The lateral forces of the front, rear, left and right wheels, respectively, F xfl 、F xfr 、F xrl And F xrr Longitudinal forces of four wheels, front, rear, left and right, respectively, I z Is the yaw moment of inertia of the vehicle, /) f And l r Respectively, the distance from the center of mass to the front and rear axes,/ s Is half of the track, k f And k r Respectively front and rear wheel side deflection stiffness, alpha f And alpha r Respectively front and rear wheel side slip angles, k lf And k lr Longitudinal stiffness of the front and rear wheels, s f And s r Respectively the slip rates of the front wheel and the rear wheel;
from established kinematic equations of
Figure BDA0003656690300000031
The structure of the distributed direct-drive unmanned vehicle is shown in figure 2, when the intention of a driver is provided to the electric control unit through a steering wheel, the electric control unit respectively gives an instruction to the hub motors of the left front wheel and the right front wheel to generate two driving forces F with different magnitudes xfl And F xfr Due to offset distance r of the kingpin σ Respectively, which generate a moment τ about the respective kingpin deflecting the wheel towards the longitudinal centerline of the vehicle dr And τ dl When the two torques are in phase, the automobile moves straight; when tau is dr ≠τ dl When the steering ladder mechanism is used, the two wheels can deflect to one side with small moment under the action of the steering ladder mechanism, so that differential steering is realized;
the dynamic equation of the differential steering system is expressed as
Figure BDA0003656690300000032
τ α ＝τ αr +τ αl ＝2k f α f l 2 /3，M z ＝T fl -T fr ＝(F xfl -F xfr )r，
Wherein, J e And b e Effective moment of inertia and damping coefficient, τ, of the steering system, respectively αl And τ αr Aligning moment, τ, of the front wheels, left and right, respectively a Is the total aligning moment, T, of the front wheel fl And T fr Driving torque of the left and right front wheels, F xfl And F xfr Longitudinal forces of the left and right front wheels, M z Is the differential torque between the right and left front wheels, r is the rolling radius of the tire, τ f The friction force of a steering system is represented by l, which is half of the contact patch of the front wheel tire;
the differential steering mathematical model of the unmanned vehicle obtained by integrating (1) to (3) is
Figure BDA0003656690300000041
Taking the state variable as
Figure BDA0003656690300000042
u(t)＝M z Then equation (4) can be expressed as
Figure BDA0003656690300000043
As a preferred technical solution of the present application, in step S1, the unmanned vehicle roll model, considering that when the vehicle travels in a curve, the vehicle body on the suspension tilts outward to cause a sharp decrease in the vertical load of the inner wheels, when the vehicle occurs on the front wheels, there is a failure that can directly cause differential steering, and in severe cases, even rollover of the vehicle may be caused, and the vehicle body is actively tilted inward to an optimal angle by the active suspension to balance the gravity component and the centrifugal force, so that the effectiveness of the differential steering and the stability during steering of the vehicle can be effectively ensured, and the roll kinetic equation established is:
Figure BDA0003656690300000044
wherein, I x For rolling of vehiclesInertia phi v 、
Figure BDA0003656690300000045
And
Figure BDA0003656690300000046
respectively roll angle, angular velocity and angular acceleration, h is the distance from the height of the roll center at the centroid position to the height of the roll center of the axle, m s Is the sprung mass of the vehicle, g is the acceleration of gravity, c v And k v Roll damping coefficient and roll stiffness coefficient for suspension, M x Roll moment provided for the active suspension;
the first equation in (1) is substituted to obtain
Figure BDA0003656690300000051
As a preferred embodiment of the present invention, the model predictive controller of step S1 is configured to control the unmanned vehicle differential steering model to track a specific driving track to obtain the required differential torque M z Thus, the linear equation of (5) is obtained by the following method,
Figure BDA0003656690300000052
Figure BDA0003656690300000053
Figure BDA0003656690300000054
discretizing (7) by a first-order difference quotient method to obtain a discrete state space expression,
χ(k+1)＝A(k)χ(k)+B(k)u(k)， (8)
wherein, a (k) ═ I + ta (t), b (k) ═ tb (t),
build a newState variable ξ (k) ═ χ (k) u (k)] T Then (8) can be represented as
Figure BDA0003656690300000055
Figure BDA0003656690300000056
The predicted output equation of the system can be expressed as
Y(k+1|t)＝ψξ(k|t)+ΘΔU(k|t) (9)
Figure BDA0003656690300000061
Figure BDA0003656690300000062
Wherein N is p To predict the time domain, N c To control the time domain.
As the preferable technical scheme of the application, the method also comprises a sliding mode controller module, wherein sliding mode control in the sliding mode controller module is a control method with strong robustness and has the advantages of quick response and insensitivity to external variation disturbance, the jitter of the system is reduced through control of an exponential approach law, the vehicle body inward inclination controller is designed based on the sliding mode control theory, the tracking error of the vehicle body side inclination angle and the ideal vehicle body side inclination angle is set as e according to the established unmanned vehicle side inclination model and the reference model,
e＝φ vref -φ v (10)
the following switching function is selected for controlling the roll angle of the vehicle body:
Figure BDA0003656690300000063
wherein c is a controller parameter required to satisfy the Hurwitz condition, and the value is larger than zero,
get
Figure BDA0003656690300000064
Namely, it is
Figure BDA0003656690300000065
Substituting the unmanned vehicle roll dynamics equation in the step (6) into a step (12) to obtain the equivalent control of the vehicle body inward roll:
Figure BDA0003656690300000071
to ensure that the conditions for arrival of the slip-form are fulfilled, i.e.
Figure BDA0003656690300000072
The switching control of the inward inclination of the vehicle body is designed as follows:
M xsw ＝I x (k+η)sgn(s) (14)
wherein k is a controller parameter, the value of which is greater than zero,
the sliding mode control law of the inward inclination of the vehicle body consists of an equivalent control item and a switching control item, namely
M x ＝M xeq +M xsw 。
As a preferred technical scheme of the application, the objective function is converted into the following standard quadratic form
J(ξ(t),u(t-1),ΔU(t))＝[ΔU(t) T ,ε] T H[ΔU(t) T ,ε]+G[ΔU(t) T ,ε]
Wherein the content of the first and second substances,
Figure BDA0003656690300000073
e 1 to predict the tracking error in the time domain, the constraint is designed as
Figure BDA0003656690300000074
Objective function and its approximationSolving the quadratic programming problem through a quadprog function of matlab under the beam condition to obtain a differential moment M required by the tracking reference track of the differential steering unmanned vehicle z 。
As a preferred embodiment of the present invention, in step S3, the model predictive controller performs differential steering, and the unmanned vehicle is controlled to follow a specific travel path to obtain a required differential torque M z And the unmanned vehicle is expected to track the upper expected track quickly and stably, and the set objective function is as follows:
Figure BDA0003656690300000081
where Δ η (k + i | t) is the tracking error between the actual system and the reference system state, Δ U (k + i | t) is the control increment of the differential moment, Q, R and ρ are both weight coefficients, and ε is the relaxation factor.
As a preferred embodiment of the present invention, step S2 is to establish a reference trajectory for deriving the lateral position X from the unmanned vehicle differential steering model in generating the specific driving trajectory to obtain a reference trajectory Y required for the model predictive control objective function ref And
Figure BDA0003656690300000082
and simultaneously providing related state variables χ for constraint conditions, namely obtaining differential moment M required by the differential steering unmanned vehicle to track a specific driving track through optimization solution z Further, the unmanned vehicle model of the rolling vehicle shown in (7) is made to have exactly the same vehicle body inclination angle as the reference model by the sliding mode controller, and thereby the rolling moment M required for controlling the vehicle is obtained x Differential moment M to be obtained z And roll moment M x Respectively input into the unmanned vehicle differential steering model and the unmanned vehicle side-tipping vehicle model to obtain state variables chi and front wheel steering angle delta f And vehicle body inclination angle phi v Wherein the front wheel steering angle is used to provide a reference model to obtain an ideal vehicle body inclination angle phi vref Inner inclination of vehicle body phi v Then the angle phi is inclined to the ideal vehicle body inner inclination angle vref For generatingAnd (3) a tracking error e required by sliding mode control, so that a closed-loop control system can be formed.
Step S13, the reference model is to provide a required ideal vehicle body roll angle for subsequent control strategy research, and requires that the model is not too complex, so a linear three-degree-of-freedom vehicle model is adopted as the reference model, that is, the steering system influence and the suspension action are ignored, only the lateral, lateral and roll motions of the vehicle are considered, and meanwhile, the tire linearization process is performed:
let the state space variable be
Figure BDA0003656690300000083
The system input is the front wheel turning angle delta f I.e. u 2 (t)＝δ f Then the reference model is represented as:
Figure BDA0003656690300000091
Figure BDA0003656690300000092
Figure BDA0003656690300000093
wherein, beta d And gamma d Ideal centroid slip angle and yaw angular velocity;
the torque produced by the centrifugal force of steering is
Figure BDA0003656690300000094
The roll moment generated by gravity is
M G ＝m s ghsinφ v (17)
By M S ＝M G The ideal roll angle of the vehicle body which is actively leaned inwards is obtained
Figure BDA0003656690300000095
Thus, the ideal yaw rate and the vehicle body roll angle are obtained based on the reference models (15) and (18),
the active camber effect of a vehicle body is evaluated by adopting two indexes of lateral acceleration sensed by passengers and transverse load transfer rate LTR, wherein the lateral acceleration sensed by the passengers has certain influence on the riding comfort of the vehicle and mainly comprises three parts [48], namely lateral acceleration, components of gravity acceleration and vehicle body roll acceleration, which are expressed as:
Figure BDA0003656690300000101
the lateral load transfer rate is a commonly used indicator for predicting non-stumbled rollover of a vehicle and is expressed as
Figure BDA0003656690300000102
S2, establishing a reference track for generating a specific driving track, wherein the reference track adopts a double-shift-line reference track as a tracking track of the differential steering unmanned vehicle, and the specific expression is as follows:
Figure BDA0003656690300000103
Figure BDA0003656690300000104
d x1 ＝25，d x2 ＝21.95，d y1 ＝4.05，d y2 ＝4.05；
the reference track is defined by a reference transverse position Y ref And a reference yaw angle
Figure BDA0003656690300000105
In which Y is ref And
Figure BDA0003656690300000106
are represented as a non-linear function with respect to the lateral position X.
Compared with the prior art, the invention has the beneficial effects that: in the scheme of the application: the method comprises the steps of firstly establishing a dynamics and kinematics model of the differentially steered unmanned vehicle and an unmanned vehicle roll model, selecting a linear three-degree-of-freedom vehicle model as a reference model to obtain an ideal vehicle roll angle, giving a reference track, the model predictive controller controls the unmanned vehicle differential steering model to track a given reference track so as to obtain the required differential moment and the front wheel corner generated by the differential moment, the sliding mode controller is designed to control the unmanned vehicle roll model to track an ideal vehicle body roll angle, and the required roll moment is obtained, and simulation results show that the model prediction control and the sliding mode controller can realize the track tracking of the differential steering unmanned vehicle and the control of the posture of the vehicle body.
Description of the drawings:
FIG. 1 is a control block diagram provided herein;
FIG. 2 is a diagram of a differential steering unmanned vehicle dynamics model provided herein;
FIG. 3 is a differential turn diagram provided herein;
FIG. 4 is a diagram of a model of unmanned vehicle roll dynamics provided herein;
FIG. 5 is a comparative graph of a differentially steered unmanned vehicle and reference trajectory as provided herein;
FIG. 6 is a differential torque graph provided herein;
FIG. 7 is a graph of front wheel steering angle as provided herein;
FIG. 8 is a graph comparing the roll angle of a differentially steered unmanned vehicle with or without roll control and an ideal vehicle body provided by the present application;
FIG. 9 is a roll moment graph as provided herein;
FIG. 10 is a comparison graph of lateral acceleration sensed by the unmanned vehicle without lateral tilt control and differential steering according to the present application;
fig. 11 is a comparison graph of lateral load transfer rate of the differential steering unmanned vehicle with or without roll control according to the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings. It is clear that the described embodiment is a specific implementation of the invention and is not limited to all embodiments.
Example (b): referring to fig. 1-11, a method for tracking a track and controlling an attitude of a differential steering unmanned vehicle includes the following steps: s1, establishing three vehicle models including an unmanned vehicle differential steering model, an unmanned vehicle roll model and a reference model; s11, the unmanned vehicle differential steering model comprises longitudinal, lateral and yaw dynamic models and kinematic models, and the longitudinal, lateral and yaw dynamic models and the kinematic models are used for tracking a specific track through model prediction control and acquiring required differential moment and a front wheel turning angle generated by the differential moment; s12, the unmanned vehicle roll model is used for tracking an ideal vehicle body roll angle through sliding mode control; s13, the reference model mainly provides an ideal vehicle body roll angle for attitude control of the differential steering unmanned vehicle; s2 establishing a reference trajectory for generating a specific travel trajectory; s3 realizes differential steering by model prediction controller, and obtains required differential torque M by controlling unmanned vehicle to track specific driving track z (ii) a S4, controlling the differential steering unmanned vehicle to track the ideal vehicle body roll angle through a sliding mode controller, namely a vehicle body roll controller, and reducing the shaking of the system through the control of an exponential approximation law; s5 simulates the vehicle model, and analyzes the result of the simulation.
As a preferred technical solution of the present application, in step S1, the unmanned vehicle differential steering model, XOY is an inertial coordinate system, XOY is a vehicle body coordinate system fixed to the vehicle center of mass, and according to newton' S second law, the stress balance equations along the x-axis, the y-axis, and around the z-axis are respectively:
Figure BDA0003656690300000121
F yfl ＝F yfr ＝k f α f ,F yrl ＝F yrr ＝k r α r ,F xfl ＝F xfr ＝k lf s f ,F xrl ＝F xrr ＝k lr s r ，
Figure BDA0003656690300000131
wherein m is the total mass of the vehicle, a y Is the inertial acceleration at the mass center of the vehicle in the y-axis direction,
Figure BDA0003656690300000132
and
Figure BDA0003656690300000133
for lateral velocity and acceleration along the y-axis,
Figure BDA0003656690300000134
and
Figure BDA0003656690300000135
for longitudinal velocity and acceleration along the x-axis,
Figure BDA0003656690300000136
and
Figure BDA0003656690300000137
yaw rate and angular acceleration of the vehicle, F yfl 、F yfr 、F yrl And F yrr The lateral forces of the front, rear, left and right wheels, respectively, F xfl 、F xfr 、F xrl And F xrr Longitudinal forces of four wheels, front, rear, left and right, respectively, I z Is the yaw moment of inertia of the vehicle, /) f And l r Respectively, the distance from the center of mass to the front and rear axes,/ s Is half of the track, k f And k r Respectively, front and rear wheel side yaw stiffness, alpha f And alpha r Respectively front and rear wheel side slip angles, k lf And k lr Longitudinal stiffness of the front and rear wheels, s f And s r Respectively the slip rates of the front wheel and the rear wheel,
from established kinematic equations of
Figure BDA0003656690300000138
The structure of the distributed direct-drive unmanned vehicle is shown in figure 2, when the intention of a driver is provided to the electric control unit through a steering wheel, the electric control unit respectively gives an instruction to the hub motors of the left front wheel and the right front wheel to generate two driving forces F with different magnitudes xfl And F xfr Due to offset distance r of the kingpin σ Respectively, which generate a moment τ about the respective kingpin deflecting the wheel towards the longitudinal centerline of the vehicle dr And τ dl When the two torques are in phase, the automobile moves straight; when tau is dr ≠τ dl When the steering ladder mechanism is used, the two wheels can deflect to one side with small moment under the action of the steering ladder mechanism, so that differential steering is realized;
the dynamic equation of the differential steering system is expressed as
Figure BDA0003656690300000139
τ α ＝τ αr +τ αl ＝2k f α f l 2 /3，M z ＝T fl -T fr ＝(F xfl -F xfr )r，
Wherein, J e And b e Effective moment of inertia and damping coefficient, tau, of the steering system, respectively αl And τ αr Aligning moments, τ, of the left and right front wheels, respectively a Is the total aligning moment, T, of the front wheel fl And T fr Driving forces of left and right front wheels, respectivelyMoment, F xfl And F xfr Longitudinal forces of the left and right front wheels, M z Is the differential torque between the right and left front wheels, r is the rolling radius of the tire, τ f Is the friction force of a steering system, is half of the contact patch of the front wheel tire,
the differential steering mathematical model of the unmanned vehicle obtained by integrating (1) to (3) is
Figure BDA0003656690300000141
Taking the state variable as
Figure BDA0003656690300000142
u(t)＝M z Then equation (4) can be expressed as
Figure BDA0003656690300000143
Step S1 is an unmanned vehicle roll model, considering that when a vehicle travels in a curved line, a vertical load of an inner wheel is sharply reduced due to outward tilting of a vehicle body on a suspension, and when the vehicle body is on a front wheel, failure of differential steering can be directly caused, and even roll of the vehicle can be caused in a severe case, the vehicle body is actively tilted inward to an optimal angle through an active suspension so that a gravity component and a centrifugal force are balanced, so that the effectiveness of differential steering and the stability during steering of the vehicle can be effectively ensured, and an established roll dynamics equation is as follows:
Figure BDA0003656690300000151
wherein, I x Is the rolling moment of inertia of the vehicle, phi v 、
Figure BDA0003656690300000152
And
Figure BDA0003656690300000153
respectively, roll angle, angular velocity and angular sumSpeed, h is the distance from the height of the roll center at the centroid position to the height of the roll center of the axle, m s Is the sprung mass of the vehicle, g is the acceleration of gravity, c v And k v Roll damping coefficient and roll stiffness coefficient for suspension, M x The roll moment provided for the active suspension,
the first equation in (1) is substituted to obtain
Figure BDA0003656690300000154
As a preferred embodiment of the present invention, the model predictive controller of step S1 is used for controlling the differentially steered unmanned vehicle to track a specific travel path to obtain a required differential torque M z Thus, the linear equation of (5) is obtained by the following method,
Figure BDA0003656690300000155
Figure BDA0003656690300000156
Figure BDA0003656690300000157
discretizing (7) by adopting a first-order difference quotient method to obtain a discrete state space expression
χ(k+1)＝A(k)χ(k)+B(k)u(k)， (8)
Wherein, a (k) ═ I + ta (t), b (k) ═ tb (t),
construction of a New State variable ξ (k) ═ χ (k) u (k)] T Then (8) can be represented as
Figure BDA0003656690300000161
Figure BDA0003656690300000162
The predicted output equation of the system can be expressed as
Y(k+1|t)＝ψξ(k|t)+ΘΔU(k|t) (9)
Figure BDA0003656690300000163
Figure BDA0003656690300000164
Wherein N is p To predict the time domain, N c To control the time domain.
The method is characterized by further comprising a sliding mode controller module, wherein sliding mode control in the sliding mode controller module is a control method with strong robustness and has the advantages of fast response and insensitivity to external change disturbance, the jitter of a system is reduced through control of an exponential approach law, a vehicle body inward inclination controller is designed based on a sliding mode control theory, the tracking error of a vehicle body side inclination angle and an ideal vehicle body side inclination angle is set to be e according to an established unmanned vehicle side inclination model and a reference model,
e＝φ vref -φ v (10)
the following switching functions are selected for controlling the camber angle of the vehicle body:
Figure BDA0003656690300000171
wherein c is a controller parameter required to satisfy the Hurwitz condition, and the value is larger than zero,
get the
Figure BDA0003656690300000172
Namely, it is
Figure BDA0003656690300000173
Substituting the unmanned vehicle roll dynamics equation in the step (6) into the step (12) to obtain the equivalent control of the vehicle body roll:
Figure BDA0003656690300000174
to ensure that the conditions for arrival of the slip-form are fulfilled, i.e.
Figure BDA0003656690300000175
The switching control of the vehicle body roll is designed as follows:
M xsw ＝I x (k+η)sgn(s) (14)
wherein k is a controller parameter, the value of which is greater than zero,
the sliding mode control law of the body roll consists of an equivalent control term and a switching control term, i.e.
M x ＝M xeq +M xsw 。
As a preferred technical scheme of the application, the objective function is converted into the following standard quadratic form
J(ξ(t),u(t-1),ΔU(t))＝[ΔU(t) T ,ε] T H[ΔU(t) T ,ε]+G[ΔU(t) T ,ε]
Wherein the content of the first and second substances,
Figure BDA0003656690300000176
e 1 to predict the tracking error in the time domain, the constraint is designed as
Figure BDA0003656690300000181
Solving of a quadratic programming problem is completed through a quadprog function of matlab to obtain a differential moment M required by the tracking reference track of the differential steering unmanned vehicle according to the target function and the constraint condition z 。
Step S3 is to realize differential steering through model prediction controller, control unmanned vehicle to track specific driving track to obtain required differential moment M z Expecting the unmanned vehicle to quickly and smoothly followThe desired trajectory on the track sets an objective function:
Figure BDA0003656690300000182
where Δ η (k + i | t) is the tracking error between the actual system and the reference system state, Δ U (k + i | t) is the control increment of the differential moment, Q, R and ρ are both weight coefficients, and ε is the relaxation factor.
Step S2 is to establish a reference trajectory for deriving the lateral position X from the unmanned vehicle differential steering model in generating a specific travel trajectory to obtain a reference trajectory Y required for the model predictive control objective function ref And
Figure BDA0003656690300000183
and simultaneously providing related state variables χ for constraint conditions, namely obtaining differential moment M required by the differential steering unmanned vehicle to track a specific driving track through optimization solution z Further, the unmanned vehicle model of the rolling vehicle shown in (7) is made to have exactly the same vehicle body inclination angle as the reference model by the sliding mode controller, and thereby the rolling moment M required for controlling the vehicle is obtained x Differential moment M to be obtained z And roll moment M x Respectively input into the unmanned vehicle differential steering model and the unmanned vehicle side-tipping vehicle model to obtain state variables chi and front wheel steering angle delta f And vehicle body inclination angle phi v Wherein the front wheel steering angle is used to provide a reference model to obtain an ideal vehicle body inclination angle phi vref Inner inclination of vehicle body phi v Then the angle phi is inclined to the ideal vehicle body inner inclination angle vref And generating a tracking error e required by sliding mode control, thus forming a closed-loop control system.
The reference model in step S13 is to provide a required ideal vehicle body roll angle for subsequent control strategy research, and requires that the model is not too complex, so a linear three-degree-of-freedom vehicle model is used as the reference model, that is, the steering system influence and the suspension action are ignored, only the lateral, roll and roll motions of the vehicle are considered, and meanwhile, the tire is linearized:
let the state space variable be
Figure BDA0003656690300000191
The system input is the front wheel turning angle delta f I.e. u 2 (t)＝δ f Then the reference model is represented as:
Figure BDA0003656690300000192
Figure BDA0003656690300000193
Figure BDA0003656690300000194
wherein, beta d And gamma d Ideal centroid slip angle and yaw angular velocity;
the torque produced by the centrifugal force of steering is
Figure BDA0003656690300000195
The roll moment generated by gravity is
M G ＝m s ghsinφ v (17)
By M S ＝M G The ideal roll angle of the vehicle body for active inward inclination is
Figure BDA0003656690300000201
According to the reference models (15) and (18), ideal yaw rate and body roll angle are obtained,
the active camber effect of a vehicle body is evaluated by adopting two indexes of lateral acceleration sensed by passengers and transverse load transfer rate LTR, wherein the lateral acceleration sensed by the passengers has certain influence on the riding comfort of the vehicle and mainly comprises three parts [48], namely lateral acceleration, components of gravity acceleration and vehicle body roll acceleration, which are expressed as:
Figure BDA0003656690300000202
the lateral load transfer rate is a commonly used indicator for predicting non-stumbled rollover of a vehicle and is expressed as
Figure BDA0003656690300000203
S2, establishing a reference track for generating a specific driving track, wherein the reference track adopts a double-shift-line reference track as a tracking track of the differential steering unmanned vehicle, and the specific expression is as follows:
Figure BDA0003656690300000204
Figure BDA0003656690300000205
d x1 ＝25，d x2 ＝21.95，d y1 ＝4.05，d y2 ＝4.05；
the reference track is defined by a reference transverse position Y ref And a reference yaw angle
Figure BDA0003656690300000206
In which Y is ref And
Figure BDA0003656690300000207
are represented as a non-linear function with respect to the lateral position X.
The above embodiments are only used for illustrating the invention and not for limiting the technical solutions described in the invention, and although the present invention has been described in detail in the present specification with reference to the above embodiments, the present invention is not limited to the above embodiments, and therefore, any modification or equivalent replacement of the present invention is made; all such modifications and variations are intended to be included herein within the scope of this disclosure and the appended claims.

Claims (10)

1. A differential steering unmanned vehicle trajectory tracking and attitude control method is characterized by comprising the following steps:
s1, establishing three vehicle models including an unmanned vehicle differential steering model, an unmanned vehicle roll model and a reference model;
s11, the unmanned vehicle differential steering model comprises longitudinal, lateral and yaw dynamic models and kinematic models, and the longitudinal, lateral and yaw dynamic models and the kinematic models are used for tracking a specific track through model prediction control and acquiring required differential moment and a front wheel turning angle generated by the differential moment;
s12, the unmanned vehicle roll model is used for tracking an ideal vehicle body roll angle through sliding mode control;
s13, the reference model mainly provides an ideal vehicle body roll angle for attitude control of the differential steering unmanned vehicle;
s2 establishing a reference trajectory for generating a specific travel trajectory;
s3 realizes differential steering by model prediction controller, and obtains required differential torque M by controlling unmanned vehicle to track specific driving track z ；
S4, controlling the unmanned vehicle roll model to track the ideal vehicle roll angle through a sliding mode controller, namely a vehicle body inward-inclining controller, and reducing the shaking of the system through the control of an exponential approximation law;
s5 simulates the vehicle model, and analyzes the result of the simulation.
2. The method of claim 1, wherein step S1 is a differential steering model of the unmanned vehicle, XOY is an inertial coordinate system, XOY is a body coordinate system fixed at the centroid of the vehicle, and the stress balance equations along the x-axis, the y-axis and the z-axis are respectively obtained according to newton' S second law as follows:
Figure FDA0003656690290000021
F yfl ＝F yfr ＝k f α f ,F yrl ＝F yrr ＝k r α r ,F xfl ＝F xfr ＝k lf s f ,F xrl ＝F xrr ＝k lr s r ，
Figure FDA0003656690290000022
wherein m is the total mass of the vehicle, a y Is the inertial acceleration at the mass center of the vehicle in the y-axis direction,
Figure FDA0003656690290000023
and
Figure FDA0003656690290000024
for lateral velocity and acceleration along the y-axis,
Figure FDA0003656690290000025
and
Figure FDA0003656690290000026
for longitudinal velocity and acceleration along the x-axis,
Figure FDA0003656690290000027
and
Figure FDA0003656690290000028
yaw rate and angular acceleration of the vehicle, F yfl 、F yfr 、F yrl And F yrr The lateral forces of the front, rear, left and right wheels, respectively, F xfl 、F xfr 、F xrl And F xrr Longitudinal forces of four wheels, front, rear, left and right, respectively, I z Is the yaw moment of inertia of the vehicle, /) f And l r Are respectively provided withIs the distance of the centroid to the anterior-posterior axis, l s Is half of the track, k f And k r Respectively front and rear wheel side deflection stiffness, alpha f And alpha r Respectively front and rear wheel side slip angles, k lf And k lr Longitudinal stiffness of the front and rear wheels, s f And s r Respectively the front and rear wheel slip rates.
From established kinematic equations of
Figure FDA0003656690290000029
The hub motors are arranged in four wheels of the distributed direct-drive unmanned vehicle, the two front hub motors can realize differential steering, the differential steering is realized by the driving torque difference of the coaxial left and right wheels, and when the intention of a driver is provided to the electric control unit through a steering wheel, the electric control unit respectively gives an instruction to the hub motors of the left and right front wheels to generate two driving forces F with different magnitudes xfl And F xfr Due to offset distance r of the kingpin σ Respectively, which generate a moment τ about the respective kingpin deflecting the wheel towards the longitudinal centerline of the vehicle dr And τ dl When the two moments are in phase, the automobile moves straight; when tau is dr ≠τ dl When the steering mechanism is used, the two wheels can deflect to one side with small moment under the action of the steering trapezoidal mechanism, so that differential steering is realized;
the dynamic equation of the differential steering system is expressed as
Figure FDA0003656690290000031
τ α ＝τ αr +τ αl ＝2k f α f l 2 /3，M z ＝T fl -T fr ＝(F xfl -F xfr ) r ，
Wherein, J e And b e Effective moment of inertia and damping coefficient, τ, of the steering system, respectively αl And τ αr Aligning moment, τ, of the front wheels, left and right, respectively a Is the total aligning moment, T, of the front wheel fl And T fr Driving torque of the left and right front wheels, F xfl And F xfr Longitudinal forces of the left and right front wheels, M z Is the differential torque between the right and left front wheels, r is the rolling radius of the tire, τ f The friction force of a steering system is represented by l, which is half of the contact patch of the front wheel tire;
the differential steering mathematical model of the unmanned vehicle obtained by integrating (1) to (3) is
Figure FDA0003656690290000032
Taking the state variable as
Figure FDA0003656690290000033
u(t)＝M z Then equation (4) can be expressed as
Figure FDA0003656690290000041
3. The method for tracking and controlling the attitude of the unmanned vehicle with differential steering according to claim 1, wherein the unmanned vehicle roll model of step S1 is characterized in that, considering that the vehicle body on the suspension tilts outward to cause the vertical load of the inner wheels to decrease sharply when the vehicle travels in a curve, when the vehicle body occurs on the front wheels, the unmanned vehicle can directly cause the failure of the differential steering, and even cause the rollover of the vehicle in serious cases, and the active suspension tilts the vehicle body inward to an optimal angle to balance the gravity component and the centrifugal force, so as to effectively ensure the effectiveness of the differential steering and the stability of the vehicle during steering, and the mechanical equations for the roll of the unmanned vehicle are established as follows:
Figure FDA0003656690290000042
wherein, I x Is the rolling moment of inertia of the vehicle, phi v 、
Figure FDA0003656690290000043
And
Figure FDA0003656690290000044
respectively roll angle, angular velocity and angular acceleration, h is the distance from the roll center height at the centroid position to the roll center height of the axle, m s Is the sprung mass of the vehicle, g is the acceleration of gravity, c v And k v Roll damping coefficient and roll stiffness coefficient for suspension, M x Roll moment provided for the active suspension;
the first equation in (1) is substituted to obtain
Figure FDA0003656690290000045
4. The method as claimed in claim 1, wherein the step S1 is a step for controlling the model predictive controller to control the unmanned vehicle differential steering model to track a specific driving track to obtain the required differential torque M z Thus, the linear equation of (5) is obtained by the following method,
Figure FDA0003656690290000051
Figure FDA0003656690290000052
Figure FDA0003656690290000053
discretizing (7) by adopting a first-order difference quotient method to obtain a discrete state space expression
χ(k+1)＝A(k)χ(k)+B(k)u(k)， (8)
Wherein, a (k) ═ I + ta (t), b (k) ═ tb (t),
construction of a New State variable ξ (k) ═ χ (k) u (k)] T Then (8) can be expressed as
Figure FDA0003656690290000054
Figure FDA0003656690290000055
The predicted output equation of the system can be expressed as
Y(k+1|t)＝ψξ(k|t)+ΘΔU(k|t) (9)
Figure FDA0003656690290000061
Figure FDA0003656690290000062
Wherein N is p To predict the time domain, N c To control the time domain.
5. The method for track tracking and attitude control of a differentially steered unmanned vehicle according to claim 1, further comprising a sliding mode controller module, wherein sliding mode control in the sliding mode controller module is a control method with strong robustness, and has the advantages of fast response and insensitivity to disturbance of external change, the jitter of the system is reduced through control of exponential approximation law, the vehicle body inward-inclination controller is designed based on sliding mode control theory, the tracking error of the vehicle body camber angle and the ideal vehicle body camber angle is set as e according to the established unmanned vehicle roll model and the reference model,
e＝φ vref -φ v (10)
the following switching functions are selected for controlling the camber angle of the vehicle body:
Figure FDA0003656690290000063
wherein c is a controller parameter required to satisfy the Hurwitz condition, and the value is larger than zero,
get
Figure FDA0003656690290000071
Namely, it is
Figure FDA0003656690290000072
Substituting the unmanned vehicle roll dynamics equation in the step (6) into the step (12) to obtain the equivalent control of the vehicle body roll:
Figure FDA0003656690290000073
to ensure that the conditions for arrival of the slip-forms are fulfilled, i.e.
Figure FDA0003656690290000074
The switching control of the vehicle body roll is designed as follows:
M xsw ＝I x (k+η)sgn(s) (14)
wherein k is a controller parameter, the value of which is greater than zero,
the sliding mode control law of the body roll consists of an equivalent control term and a switching control term, i.e.
M x ＝M xeq +M xsw 。
6. The method for track following and attitude control of a differentially steered unmanned vehicle as claimed in claim 5, wherein the objective function is transformed into a standard quadratic form
J(ξ(t),u(t-1),ΔU(t))＝[ΔU(t) T ,ε] T H[ΔU(t) T ,ε]+G[ΔU(t) T ,ε]
Wherein the content of the first and second substances,
Figure FDA0003656690290000075
e 1 in order to predict the tracking error in the time domain,
the constraint condition is designed as
Figure FDA0003656690290000081
Solving of a quadratic programming problem is completed through a quadprog function of matlab to obtain a differential moment M required by the tracking reference track of the differential steering unmanned vehicle according to the target function and the constraint condition z 。
7. The method of claim 1, wherein the model predictive controller controls the drone differential steering model to track a specific travel path to obtain a desired differential torque M z Expecting unmanned vehicle to track quickly and smoothly
The objective function is set as:
Figure FDA0003656690290000082
where Δ η (k + i | t) is the tracking error between the actual system and the reference system state, Δ U (k + i ] t) is the control increment of the differential moment, Q, R and ρ are both weight coefficients, and ε is the relaxation factor.
8. The method for tracking and controlling the attitude of the unmanned vehicle with differential steering according to claim 3, wherein step S2 is to establish a reference trajectory for deriving the lateral position X from the unmanned vehicle differential steering model in generating the specific driving trajectory to obtain the model pre-predictionReference trajectory Y required for measuring and controlling objective function ref And
Figure FDA0003656690290000083
and simultaneously providing related state variables χ for constraint conditions, namely obtaining differential moment M required by the differential steering unmanned vehicle to track a specific driving track through optimization solution z Further, the unmanned vehicle model of the rolling vehicle shown in (7) is made to have exactly the same vehicle body inclination angle as the reference model by the sliding mode controller, and thereby the rolling moment M required for controlling the vehicle is obtained x Differential moment M to be obtained z And roll moment M x Respectively input into the unmanned vehicle differential steering model and the unmanned vehicle side-tipping vehicle model to obtain state variables chi and front wheel steering angle delta f And vehicle body inclination angle phi v Wherein the front wheel steering angle is used to provide a reference model to obtain an ideal vehicle body inclination angle phi vref Inner inclination of vehicle body phi v Then the angle phi is inclined to the ideal vehicle body inner inclination angle vref And generating a tracking error e required by sliding mode control, thus forming a closed-loop control system.
9. A method for tracking and attitude control of a differentially steered unmanned vehicle according to claim 1, wherein the reference model of step S13 is to provide the required ideal vehicle body roll angle for subsequent control strategy study, and the model is not too complex, so a linear three-degree-of-freedom vehicle model is adopted as the reference model, namely, the steering system influence and suspension action are ignored, only the lateral, transverse and roll motions of the vehicle are considered, and simultaneously the tires are linearized:
let the state space variable be
Figure FDA0003656690290000091
The system input is the front wheel turning angle delta f I.e. u 2 (t)＝δ f Then the reference model is represented as:
Figure FDA0003656690290000092
Figure FDA0003656690290000093
Figure FDA0003656690290000101
wherein, beta d And gamma d Ideal centroid slip angle and yaw angular velocity;
the torque produced by the centrifugal force of steering is
Figure FDA0003656690290000102
The roll moment generated by gravity is
M G ＝m s ghsinφ v (17)
By M S ＝M G The ideal roll angle of the vehicle body which is actively leaned inwards is obtained
Figure FDA0003656690290000103
According to reference models (15) and (18), two indexes of ideal yaw velocity and vehicle body roll angle, lateral acceleration and transverse load transfer rate LTR are obtained to evaluate the active inner-inclining effect of the vehicle body, wherein the index is mainly composed of three parts, namely lateral acceleration, a gravity acceleration component and vehicle body roll acceleration, and the index is expressed as:
Figure FDA0003656690290000104
the lateral load transfer rate is a commonly used indicator for predicting non-stumbled rollover of a vehicle and is expressed as
Figure FDA0003656690290000111
10. The method for track following and attitude control of a differentially steered unmanned vehicle according to claim 1, further comprising step S2 of establishing a reference track for generating a specific driving track, wherein the reference track adopts a double-shift reference track as the following track of the differentially steered unmanned vehicle, and the specific expression is as follows:
Figure FDA0003656690290000112
Figure FDA0003656690290000113
d x1 ＝25，d x2 ＝21.95，d y1 ＝4.05，d y2 ＝4.05；
the reference track is defined by a reference transverse position Y ref And a reference yaw angle
Figure FDA0003656690290000114
In which Y is ref And
Figure FDA0003656690290000115
are represented as a non-linear function with respect to the lateral position X.
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