CN114859733B - Differential steering unmanned vehicle trajectory tracking and attitude control method - Google Patents
Differential steering unmanned vehicle trajectory tracking and attitude control method Download PDFInfo
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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 the control of the vehicle body posture.
Description
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: CN 202010998512.5) 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 differential steering model of the unmanned vehicle comprises a longitudinal dynamic model, a lateral dynamic model and a yaw dynamic model, and is used for predicting and controlling to track a specific track through a model and acquiring required differential moment and a front wheel corner generated by the differential torque; s12, the unmanned vehicle side-tipping model is used for tracking an ideal vehicle body side-tipping 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 track for generating a specific driving track; s3, realizing differential steering through a model prediction controller, and obtaining required differential moment M by controlling the unmanned vehicle to track a specific running 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 system jitter through the control of an exponential approaching law; and S5, simulating the vehicle model, and analyzing a simulation result.
As a preferred technical solution of the present application, in step S1, the differential steering model of the unmanned vehicle, 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 obtained as:
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 ，
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,
and
for lateral velocity and acceleration along the y-axis,
and
for longitudinal velocity and acceleration along the x-axis,
and
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 of the centroid to the front-rear axis, l 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
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, about the respective kingpin, a moment τ that deflects the wheel towards the longitudinal centre line of the vehicle dr And τ dl When the two moments are in phase, the automobile moves straight; when tau is measured 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
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 For the friction of the steering system, l is the front wheelHalf of the tire footprint;
the differential steering mathematical model of the unmanned vehicle obtained by integrating (1) to (3) is
Taking the state variable as
u(t)＝M z Then equation (4) can be expressed as
As a preferred technical solution of the present application, in step S1, considering that when a vehicle travels in a curved line, a vehicle body on a suspension tilts outward to cause a rapid decrease of a vertical load of an inner wheel, when a front wheel occurs, a failure that can directly cause differential steering occurs, and even a vehicle rolls over in a severe case, the vehicle body is actively tilted inward to an optimal angle by an active suspension to balance a gravity component and a centrifugal force, so that the effectiveness of the differential steering and the stability during steering of the vehicle can be effectively ensured, and an established roll kinetic equation is as follows:
wherein, I x Is the rolling moment of inertia of the vehicle, phi v 、
And
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, M, for a suspension x Roll moment provided for the active suspension;
substituting the first equation in (1) to obtain
As a preferred embodiment of the present invention, the step S1 model predictive controller is configured to control the unmanned vehicle differential steering model to track a specific travel path to obtain the required differential torque M z Therefore, the linear equation of (5) is obtained by the following method,
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),
construction of a New State variable ξ (k) = [ χ (k) u (k) ]] T Then (8) can be represented as
The predicted output equation of the system can be expressed as
Y(k+1|t)＝ψξ(k|t)+ΘΔU(k|t) (9)
Wherein, N 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:
wherein c is a controller parameter required to satisfy the Hurwitz condition, and the value thereof is larger than zero,
get the
Namely, it is
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:
to ensure that the conditions for arrival of the slip-form are fulfilled, i.e.
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,
e 1 to predict the tracking error in the time domain, constraints are designed
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 。
As a preferred embodiment of the present invention, step S3 is to implement differential steering by the model predictive controller, and to obtain the required differential torque M by controlling the unmanned vehicle to follow a specific travel track z And the unmanned vehicle is expected to track the upper expected track quickly and stably, and the set objective function is as follows:
wherein, 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 all weight coefficients, and ε is a relaxation factor.
As a preferable technical scheme of the application, step S2 is used for establishing a reference track for leading out a transverse position X from an unmanned vehicle differential steering model in generating a specific running track so as to obtain a reference track Y required by a model prediction control objective function ref And
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 the same body inclination as the reference model by the sliding mode controller, and thereby the roll 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 such as 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 The tracking error e required by sliding mode control is generated, and thus 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, influence of a steering system and a suspension effect are ignored, only lateral, roll and roll motions of the vehicle are considered, and meanwhile, tires are subjected to linearization:
let the state space variable be
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:
wherein, beta d And gamma d Ideal centroid slip angle and yaw angular velocity;
the torque produced by the centrifugal force of steering is
The gravity-generated roll moment 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
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:
the lateral load transfer rate is a commonly used indicator for predicting non-stumbled rollover of a vehicle and is expressed as
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:
the reference track is defined by a reference transverse position Y ref And a reference yaw angle
In which Y is ref And
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 differential steering 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 body roll angle, giving a reference track, controlling the unmanned vehicle differential steering model to track the given reference track through a model prediction controller to obtain a required differential moment and a front wheel corner generated by the required differential moment, designing a sliding mode controller to control the unmanned vehicle roll model to track the ideal vehicle body roll angle, and obtaining the required roll moment.
Description of the drawings:
FIG. 1 is a control block diagram provided herein;
FIG. 2 is a diagram of a model of a differentially steered unmanned vehicle dynamics;
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 trajectories provided herein;
FIG. 6 is a differential torque graph provided herein;
FIG. 7 is a graph of front wheel steering angle provided by the present application;
FIG. 8 is a graph comparing the roll angle of the differentially steered unmanned vehicle with or without roll control and the 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 clearly and completely described below 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 a posture of a differentially steered 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 differential steering model of the unmanned vehicle comprises a longitudinal dynamic model, a lateral dynamic model and a yaw dynamic model, and is used for tracking a specific track through model prediction control and acquiring required differential torque and a front wheel corner generated by the differential torque; s12, the unmanned vehicle side-tipping model is used for tracking an ideal vehicle body side-tipping 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 track for generating a specific driving track; s3, realizing differential steering through a model prediction controller, and obtaining required differential moment M by controlling the unmanned vehicle to track a specific running 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; and S5, simulating the vehicle model, and analyzing the simulation result.
As a preferred technical solution of the present application, in step S1, the differential steering model of the unmanned vehicle, 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 obtained as:
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 ，
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,
and
for lateral velocity and acceleration along the y-axis,
and
for longitudinal velocity and acceleration along the x-axis,
and
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 Are front and rear wheel side slip angles, k, respectively 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
Four of distributed direct-drive unmanned vehicleThe structure of the differential steering device is shown in figure 2, when the intention of a driver is provided to the electronic control unit through a steering wheel, the electronic 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
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 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 of the right and left front wheels, r is the rolling radius of the tire, tau 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
Taking the state variable as
u(t)＝M z Then equation (4) can be expressed as
The method comprises the following steps that S1, an unmanned vehicle side-tipping model is established, considering that when a vehicle runs in a curve, the vertical load of an inner side wheel is reduced sharply due to the fact that a vehicle body on a suspension inclines outwards, when the vehicle body on the suspension inclines outwards, the failure of differential steering can be caused directly, even the vehicle turns over when the vehicle is serious, the vehicle body is actively inwards tipped to an optimal angle through an active suspension, so that the gravity component and the centrifugal force are balanced, the effectiveness of the differential steering of the vehicle and the stability of the vehicle during steering can be effectively guaranteed, and the established side-tipping dynamic equation is as follows:
wherein, I x Is the rolling moment of inertia of the vehicle, phi v 、
And
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, M, for a suspension x The roll moment provided for the active suspension,
the first equation in (1) is substituted to obtain
As a preferred technical scheme of the application, the step S1 model prediction controller is used for controlling the differential steering unmanned vehicle to track a specific running track so as to obtain the required differential moment M z Thus, the linear equation of (5) is obtained by the following method,
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 novel State variable ξ (k) = [ χ (k) u (k) ]] T Then (8) can be represented as
The predicted output equation of the system can be expressed as
Y(k+1|t)＝ψξ(k|t)+ΘΔU(k|t) (9)
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:
wherein c is a controller parameter required to satisfy the Hurwitz condition, and the value is larger than zero,
get the
Namely that
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:
to ensure that the conditions for arrival of the slip-form are fulfilled, i.e.
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 vehicle body side inclination consists of an equivalent control term and a switching control term, 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,
e 1 to predict the tracking error in the time domain, the constraint is designed as
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, realizing differential steering through a model prediction controller, and controlling the unmanned vehicle to track a specific driving track to obtain required differential moment M z And expecting the unmanned vehicle to quickly and smoothly track the upper expected track to set an objective function:
wherein, 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 all weight coefficients, and ε is a relaxation factor.
Step (ii) ofS2, establishing a reference track for leading out a transverse position X from the unmanned vehicle differential steering model in the specific driving track to obtain a reference track Y required by a model predictive control objective function ref And
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 the same body inclination as the reference model by the sliding mode controller, and thereby the roll 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.
Step S13, the reference model is to provide a required ideal vehicle body roll angle for subsequent control strategy research, and the model is required to be not too complex, so a linear three-degree-of-freedom vehicle model is adopted as the reference model, that is, influence of a steering system and a suspension action are ignored, only lateral, lateral and roll motions of the vehicle are considered, and meanwhile, tire linearization is performed:
let the state space variable be
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:
wherein, beta d And gamma d Ideal centroid slip angle and yaw angular velocity;
the torque produced by the centrifugal force of steering is
The gravity-generated roll moment 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
Ideal yaw rate and vehicle body roll angle are obtained according to 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:
the lateral load transfer rate is a commonly used indicator for predicting non-stumbled rollover of a vehicle and is expressed as
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:
the reference track is defined by a reference transverse position Y ref And a reference yaw angle
In which Y is ref And
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 (8)
1. A track tracking and attitude control method for a differential steering unmanned vehicle 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 differential steering model of the unmanned vehicle comprises a longitudinal dynamic model, a lateral dynamic model and a yaw dynamic model, and is used for predicting and controlling to track a specific track through a model and acquiring required differential moment and a front wheel corner generated by the differential torque;
s12, the unmanned vehicle side-tipping model is used for tracking an ideal vehicle body side-tipping 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 track for generating a specific driving track;
s3, realizing differential steering through a model prediction controller, and obtaining required differential moment M by controlling the unmanned vehicle to track a specific running track z ；
S4, controlling an unmanned vehicle roll model to track an 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 index approaching law;
s5, simulating the vehicle model, and analyzing a simulation result;
step S1, an unmanned vehicle differential steering model is obtained, wherein XOY is an inertial coordinate system, XOY is a vehicle body coordinate system fixed on the mass center of a vehicle, and stress balance equations along an x axis, a y axis and a z axis are respectively obtained according to Newton' S second law as follows:
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 ，
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,
and
for lateral velocity and acceleration along the y-axis,
and
for longitudinal velocity and acceleration along the x-axis,
and
yaw rate and angular acceleration of the vehicle, F yfl 、F yfr 、F yfr 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
Distributed typeThe hub motors are arranged in four wheels of the 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 measured 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
τ a ＝τ ar +τ al ＝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 al And τ ar 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 torques of the right and left 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
Taking the state variable as
u(t)＝M z Then equation (4) can be expressed as
Step S1, an unmanned vehicle side-tipping model is obtained, when the vehicle runs in a curve, the vertical load of an inner side wheel is reduced sharply due to the fact that the vehicle body on a suspension tilts outwards, when the vehicle body on the suspension moves in the curve, the failure of differential steering can be caused directly, even the vehicle turns over when the vehicle body is serious, the vehicle body is actively tilted inwards to an optimal angle through an active suspension, so that the gravity component force and the centrifugal force are balanced, the effectiveness of the differential steering of the vehicle and the stability of the vehicle during steering can be effectively guaranteed, and the established unmanned vehicle side-tipping mechanical equation is as follows:
wherein, I x Is the rolling moment of inertia of the vehicle, phi v 、
And
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;
substituting the first equation in (1) to obtain
2. The method as claimed in claim 1, wherein the step S1 model predictive controller is used for controlling the unmanned vehicle differential steering model to track a specific driving track to obtain a required differential moment M z Thus, the linear equation of (5) is obtained by the following method,
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 novel State variable ξ (k) = [ χ (k) u (k) ]] T Then (8) can be expressed as
The predicted output equation of the system can be expressed as
Y(k+l|t)＝ψξ(k|t)+ΘΔu(k|t) (9)
Wherein N is p To predict the time domain, N c To control the time domain.
3. The method for track tracking and attitude control of the differential steering 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 asymptotic law, the vehicle body inward-inclination controller is designed based on sliding mode control theory, according to the established unmanned vehicle roll model and the reference model, the tracking error of the vehicle body camber angle and the ideal vehicle body camber angle is set as e,
e＝φ vref -φ v (10)
the following switching functions are selected for controlling the camber angle of the vehicle body:
wherein c is a controller parameter required to satisfy the Hurwitz condition, and the value thereof is larger than zero,
get
Namely that
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:
to ensure that the conditions for arrival of the slip-forms are fulfilled, i.e.
(η > 0), 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 xqe +M xsw 。
4. The method for track following and attitude control of a differentially steered unmanned vehicle as claimed in claim 3, 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,
e 1 in order to predict the tracking error in the time domain,
the constraint condition is designed as
Objective function and constraint, by matlThe quadratic programming problem is solved by the aid of ab quadrprog function to obtain differential moment M required by the tracking reference track of the differential steering unmanned vehicle z 。
5. 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:
wherein, 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 all weight coefficients, and ε is a relaxation factor.
6. The method for tracking and attitude control of a differentially steered unmanned vehicle as defined in claim 1, wherein step S2 comprises establishing a reference trajectory for deriving a lateral position X from the unmanned vehicle differential steering model in generating a specific driving trajectory to obtain a reference trajectory Y required by the model predictive control objective function ref And
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 the same body inclination as the reference model by the sliding mode controller, and thereby the roll moment M required for controlling the vehicle is obtained x Differential moment M to be obtained z And a roll moment M x Respectively input into the unmanned vehicle differential steering model and the unmanned vehicle side-tipping vehicle model to obtain the shapeAttitude variables χ, front wheel steering angle δ 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 inclined at an angle phi with the ideal vehicle body vref The tracking error e required by sliding mode control is generated, and thus a closed-loop control system can be formed.
7. A method for tracking and controlling the posture of a differentially steered unmanned vehicle according to claim 1, wherein the reference model in step S13 is to provide a desired vehicle body roll angle required for subsequent control strategy research, and the model is not too complex, so that a linear three-degree-of-freedom vehicle model is adopted as the reference model, namely, steering system influence and suspension action are ignored, only the lateral, cross-rolling and roll motions of the vehicle are considered, and meanwhile, the tires are linearized:
let a state space variable be
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:
wherein beta is d And gamma d Ideal centroid slip angle and yaw angular velocity;
the torque produced by the centrifugal force of the steering is
The gravity-generated roll moment 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
According to reference models (15) and (18), the ideal yaw velocity and two indexes of the vehicle body roll angle, the lateral acceleration and the transverse load transfer rate LTR are obtained to evaluate the active inward-tilting effect of the vehicle body, wherein the active inward-tilting effect mainly comprises three parts, namely the lateral acceleration, the component of the gravity acceleration and the vehicle body roll acceleration which are expressed as the lateral acceleration, the component of the gravity acceleration and the vehicle body roll acceleration
The lateral load transfer rate is a commonly used indicator for predicting non-stumbled rollover of a vehicle and is expressed as
8. The method for track tracking and attitude control of the differentially steered unmanned vehicle according to claim 1, further comprising the step S2 of establishing a reference track for generating a specific driving track, wherein the reference track adopts a double-shift-line reference track as the tracking track of the differentially steered unmanned vehicle, and the specific expression is as follows:
the reference track is defined by a reference transverse position Y ref And a reference yaw angle
In which Y is ref And
are represented as a non-linear function with respect to the lateral position X.
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