CN116627036A - Intelligent automobile parking planning control method based on intelligent tire technology - Google Patents
Intelligent automobile parking planning control method based on intelligent tire technology Download PDFInfo
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Abstract
The invention discloses an intelligent automobile parking planning control method based on an intelligent tire technology, which realizes track tracking by a horizontal and vertical integrated control method. The transverse and longitudinal controllers are composed of a transverse controller and a longitudinal controller, the transverse controller is based on a two-degree-of-freedom dynamic model, and the robustness of the system is improved by combining a self-adaptive pre-aiming method with a second-order sliding mode control method. The adaptive pre-aiming model is used for adaptively adjusting the pre-aiming time by designing an objective function based on the transverse deviation, the road boundary and the motion response characteristic of the whole vehicle, so that the ideal yaw rate is obtained, and then the steering wheel angle is calculated. Meanwhile, the low-pass filter is combined with the sliding mode control, so that the buffeting phenomenon caused by sliding mode surface switching can be effectively restrained, and the smoothness after filtering is 9.35% of that before filtering. The longitudinal control adopts layered control, wherein the upper layer control adopts model predictive control to calculate the expected acceleration, and the lower layer control adopts a P controller to obtain the control quantity in the driving mode and the braking mode.
Description
Technical Field
The invention relates to an intelligent automobile parking planning control method based on an intelligent tire technology.
Background
The automatic driving automobile bears the future world prospect of human beings, aggregates intelligent crystals in various large-area technologies, integrates environment perception technology, planning decision technology and control execution technology, and is a subject cross-fusion intensive. The intelligent parking system gradually becomes a research hotspot and is widely focused by related staff such as high-tech enterprises, scientific research institutions and the like at home and abroad.
Conventional tires are simple execution modules that cannot feed back road conditions in real time to the overall vehicle control system and are therefore considered "passive elements". However, the intelligent tire with the sensor inside can provide tire-road surface contact information timely and accurately, and the intelligent tire is an important sensor for identifying the environment outside the vehicle by intelligent driving of the vehicle like a camera and a laser radar, so that a two-degree-of-freedom vehicle dynamics model is established for solving the problems of difficult parallel parking and overlong parking time, and a parallel parking path is planned and controlled.
Disclosure of Invention
The invention provides an intelligent automobile parking planning control method based on an intelligent tire technology, aiming at solving the problems existing in the prior art.
The invention adopts the technical scheme that:
an intelligent automobile parking planning control method based on intelligent tire technology comprises the following steps:
step one: planning a track of parallel parking by using a tangent circle method;
step two: and the transverse controller design is used for analyzing and establishing a dynamics model from transverse dynamics characteristics and tire cornering characteristics of the vehicle based on theoretical mechanics related knowledge and combining the motion rule of the vehicle. The two-degree-of-freedom state space equation of the vehicle about the yaw rate and the centroid slip angle of the vehicle can be obtained through the law of acceleration of the object, the law of rotation of the rigid body and the characteristic of the tire slip, the precision of a vehicle model can be basically ensured, and a simple and effective vehicle model is provided for ensuring the calculation efficiency of a controller, and the model describes the state of the vehicle based on the yaw rate and the centroid slip angle;
step three: the method comprises the steps of designing a transverse controller, establishing a self-adaptive pre-aiming model for optimizing pre-aiming time based on a driver pre-aiming theory, and selecting optimal pre-aiming time by integrating three factors including tracking error, safety coefficient of a vehicle and a road boundary and vehicle steering response time characteristic. Then establishing a single-point optimal curvature pre-aiming model based on steady-state yaw rate assumption, and solving an ideal yaw rate based on self-adaptive pre-aiming time, wherein the self-adaptive pre-aiming model can solve the ideal yaw rate of parking;
step four: the method comprises the steps of designing a transverse controller, namely designing a Super-twist-based second-order slip-form controller according to an ideal yaw rate obtained by solving a two-degree-of-freedom vehicle dynamics model and a self-adaptive pre-aiming model obtained in the second step and the third step, and combining a Super-twist second-order slip-form control algorithm, wherein the controller takes a difference value between the ideal yaw rate and the current actual yaw rate in the vehicle parking process as input, takes the current steering wheel angle control quantity in the vehicle parking process as output quantity, and performs stability demonstration through a Lyapunov function;
the two-degree-of-freedom dynamics model, the self-adaptive pre-aiming model and the second-order sliding mode controller jointly form a transverse controller.
Step five: setting a longitudinal controller, wherein the longitudinal controller is a double-layer controller and comprises an upper MPC controller and a lower P controller, firstly setting a vehicle longitudinal speed model, obtaining a prediction model according to the speed model, secondly designing an objective function to convert a solving problem into a quadratic programming problem, secondly designing constraint conditions according to control quantity constraint and control increment constraint, and finally solving expected acceleration in a rolling optimization mode, namely solving the expected vehicle acceleration according to the current speed in the parking process of a reference vehicle by the upper MPC controller, transmitting the expected vehicle acceleration to the lower P controller, and driving or braking the vehicle in real time by the lower P controller;
step six: and (3) combining the second-order sliding mode controller in the fourth step and the longitudinal controller in the fifth step to design a transverse-longitudinal controller, obtaining control amounts of steering wheel rotation angle, throttle opening and braking pressure, realizing control over steering, driving and braking of the vehicle, and controlling and tracking the tangential circle parking track planned in the first step.
Further, the parking track planning process by using the tangent circle method comprises the following steps: during parking, the vehicle is first parked by O 1 As the center of a circle, with the minimum turning radius R of the trolley min For turning the radius, after reaching the switching point C, the vehicle turns reversely to O 2 As the center of a circle, also with the minimum steering radius R of the vehicle min Steering for radius until parking operation is completed, the switching point C is represented by O 1 Circle with circle center being O 2 The tangent point of the circle which is the center of the circle.
Further, the step of establishing the two-degree-of-freedom dynamics model is as follows:
the following modeling environment is assumed:
(1) neglecting the influence of friction and damping in a steering system, and assuming that the left and right tires in the vehicle have the same steering angle and rotation speed at any moment, taking the rotation angles of the left and right wheels as input;
(2) assuming that the motion and steering of the vehicle are driven by the front wheels;
(3) assuming that both the body and the suspension system are rigid;
(4) neglecting the transfer of front and rear axle loads;
based on the assumption, a two-degree-of-freedom dynamics model is established, and the two-degree-of-freedom dynamics model is specifically as follows:
1) Is provided with
Wherein m is the mass of the vehicle,is the lateral acceleration of the vehicle, v x Is the longitudinal speed of the vehicle, ω is the yaw rate of the vehicle, I z Is the moment of inertia of the vehicle at the centre of mass, +.>Is the yaw acceleration of the vehicle, a is the distance from the front axis to the centroid, b is the distance from the rear axis to the centroid, F yf Is the lateral force of the front axle, F yr Is the lateral force of the rear axle;
2) Under the assumption of small rotation angles, the relationship among cornering force, cornering angle and cornering stiffness of the tire in a linear region is as follows:
F yf ＝C f α f
F yr ＝C r α r
in the formula ,Cf 、C r Respectively the front wheel cornering stiffness and the rear wheel cornering stiffness, alpha f 、α r The front wheel slip angle and the rear wheel slip angle are respectively;
the front and rear wheel slip angles of the vehicle are related to the motion parameters thereof, assuming that the speeds of the front and rear axles of the vehicle are v x 、v y The centroid side deflection angle is
3) The included angle between the front wheel speed direction and the x axis is θ, which can be expressed as:
4) The slip angle of the front and rear wheels of the automobile is expressed as:
5) A vehicle state space equation about the vehicle yaw angle ω and the centroid slip angle β is obtained:
further, the step of establishing the adaptive pre-aiming model is as follows:
1) Ideal yaw rate omega based on steady-state single-point pre-aiming model d The method comprises the following steps:
in the formula ,vx Is the vehicle speed, Δf is the lateral deviation, t p Is pre-aiming time;
2) Designing a multi-objective optimization function integrating lateral deviation, road boundary and response characteristics of steering motion of the whole vehicle:
J＝min(ω 1 J 1 +ω 2 J 2 +ω 3 J 3 )
in the formula ,ω1 、ω 2 、ω 3 For the weight coefficients, the weights are set in relation to the object achieved, ω 1 Related to the accuracy of the trajectory tracking; omega 2 Related to the distance between the vehicle and the road boundary; omega 3 Related to the response characteristics of the whole vehicle;
3) Designing an objective function J based on the lateral offset of the current centroid 1 ：
J 1 ＝∫ 0 t L_Drv_2 2 dx
Where L_Drv_2 is the centroid lateral offset and t is the model prediction time;
4) Designing an objective function J based on the distance between the current centroid and the boundary 2 ：
J 2 ＝∫ 0 t gdx
Wherein g is a safety function, and delta is the distance from the center line of the road to the boundary as the vehicle position approaches the boundary;
5) Design objective function J based on response characteristic of whole vehicle 3 ：
J 3 ＝(t p -T) 2
Where T is a time associated with the vehicle steering response characteristic.
Further, the specific method of the fourth step is as follows:
1) In order to filter the signal input by the second-order sliding mode controller, the buffeting signal is weakened, and the second-order sliding mode controller is connected with the buffeting signalFilterAnd (3) designing:
where ζ is the cut-off frequency, δ sw Is the signal before the filtering,is the filtered signal;
2) Design of second-order sliding mode controller
(a) For a system that is uncertain and requires consideration of internal parameter perturbation and external disturbance, the system state equation can be further expressed as:
in the formula ,
(b) The equations of the controlled system can be expressed as the following state equations:
(c) The uncertainty of the controlled system and the applied disturbance are denoted by E (t), and can be expressed as:
E(t)＝ΔA 3 B+ΔA 4 ω r +ΔB 2 δ+(d+Δd)f
(d) The equations of the controlled system can be transformed into the following state equations:
(e) Selecting the actual yaw rate omega r And an ideal yaw rate omega d As the tracking error of the system:
e＝ω r -ω d
(f) The switching function is designed as follows:
s＝e+λ∫ 0 t e(τ)dτ(λ>0)
(g) The derivative of the switching function is obtained:
(h) Super-twist algorithm general form:
substitution into the above formula can be obtained:
the control amount of the front wheel rotation angle can be obtained:
(i) For systems that meet the existence uncertainty, when k 1 >0，k 2 >At 0, the system state can be stably converged and reach the origin (0, 0) in a limited time, and at this time, the system
(j) Order the
Due to k 1 >0，k 2 >0, then this matrix is Hurwitz, for any positive definite matrix P that satisfies the Lyapunov function:
D T P+PD＝-Q
(k) Definition of Lyapunov function V 0 (Λ)＝Λ T PΛ，V 0 (Λ) is a continuous positive function except that s=0 is differentiable, and thus can be derived using the chained approach:
(l) Deriving the above formula can obtain:
(m) for V 0 (Λ) the following formula can be derived:
in the formula ,
(n) vs V 0 Derivative can be obtained by:
therefore, when->When Λ may tend to stabilize for a finite period of time;
3) Obtaining the final steering wheel angle delta sw ：
in the formula ,isw Is the angular transmission ratio of steering wheel angle to wheel angle.
Further, the specific method of the fifth step is as follows:
1) Firstly, designing an upper MPC controller, wherein the upper MPC controller adopts model predictive control, and adopts a first-order inertia system to express dynamic change of the longitudinal speed of the vehicle:
wherein, K=1 is the gain or amplification factor of the inertial link; t is t d The time constant of the inertia link;
the continuous system state equation of motion in the longitudinal direction of the vehicle can be expressed as:
wherein x= [ va ]] T U=a, which is the state vector of the upper MPC controller e Is the input quantity of the upper MPC controller;
discretizing a continuous system state equation of the longitudinal motion of the vehicle by adopting a forward Euler method to obtain a discrete system state equation:
wherein k is the current sampling time; k+1 is the next sampling time, T s Is the sampling period;
setting the longitudinal speed of the vehicle as the system output, the output equation can be expressed as:
y(t)＝Cx(k)
the vehicle performance evaluation function is defined as:
wherein t-1 is the last sampling time, N p Is the prediction time domain, N c Is the control time domain, y p (k+i|k) is a predicted value of the control output, y ref (k+i|k) is a reference value of the control output, (k+i|k) represents prediction of information at k+i time using information at k sampling time, where i=1, 2, …, N p U (k+i) and Δu (k+i) are the k+i time control input and control increment and control quantity weight system matrices, respectively;
in the process of designing the upper MPC controller, constraint conditions are designed for restraining the acceleration and the change rate of the acceleration, and the constraint conditions are expressed as the following constraint formula:
u min ≤u(k+i)≤u max ,i＝0,1,…N c -1
Δu min ≤Δu(k+i)≤Δu max ,i＝0,1,…N c -1
in the formula ,umin and umax Is the minimum and maximum acceleration, deltau min and Δumax Is the minimum and maximum value of the acceleration increment;
the MPC solution problem needs to be converted into a quadratic programming problem, and a new state vector is constructed aiming at a discrete state equation of the vehicle motion in the longitudinal direction in the longitudinal motion process of the vehicle:
a new state space expression can be obtained:
defining an output equation:
predictions about vehicle conditions may be made and state quantities within the prediction time domain may be obtained:
the output of the new state space equation is available:
the clear relation between the state quantity and the output quantity can be obtained by integrating the formulas, and the output at the future moment can be obtained by expressing the output in a matrix form:
Y＝ψξ(k)+ΘΔU
in the formula, the state quantity and the output quantity in the prediction time domain can be clearly understood and obtained through calculation of the current state quantity xi (k) and the control increment delta U in the control time domain, and the prediction function in the model prediction control algorithm can be led out; defining the output of the system to obtain a reference value Y r For Y r And (3) carrying out an initialization operation:
the method can obtain:
Y-Y r ＝ψξ(k)+ΘΔU-Y r
definition e=ψζ (k), becomes:
Y-Y r ＝E+ΘΔU
substituting the optimization objective function can obtain:
wherein , represents the Kroneck product;
is partially constant and can be ignored in optimizing solutionThe performance evaluation function can be abbreviated as:
let h=Θ T Q Q Θ+R R ，g＝Θ T Q Q (E-Y r ) Then it can be transformed into:
the optimization solution can be further abbreviated as:
constraint condition design of the upper MPC controller is needed, and the constraint design is as follows:
u(k)＝u(k-1)+Δu(k)
u(k+1)＝u(k)+Δu(k+1)＝u(k-1)+Δu(k)+Δu(k+1)
…
u(k+N c -1)＝u(k+N c -2)+Δu(k+N c -1)＝u(k-1)+Δu(k)+Δu(k+1)+…Δu(k+N c -1)
the formula is rewritten as follows:
it can be seen that:
the control quantity constraint sum is as follows:
U min ≤U t +A I ΔU t ≤U max
control increment constraint:
ΔU min ≤ΔU≤ΔU max
the objective function may be designed as:
wherein epsilon is a relaxation factor and is used for preventing the situation of no solution when calculating the optimal solution;
2) The design of the lower layer P controller is performed by first determining the switching logic for driving and braking:
in the formula atdes and pbdes A desired throttle opening and a desired brake pressure, respectively;
the magnitude of the desired throttle opening may be calculated from the following equation:
a tdes ＝K throttle *a des
in order to prevent the desired throttle opening from overflowing, a limit needs to be made to the value of the throttle opening, with the following conditions:
the magnitude of the desired brake pressure may be calculated from the following equation:
P bdes ＝K brake *a des
to prevent the desired brake master cylinder pressure from overflowing, a limit needs to be placed on the value of the brake master cylinder pressure, with the following conditions:
the invention has the following beneficial effects:
from the simulation result of the parking track, the STMPC transverse and longitudinal integrated controller can integrate the advantages of the transverse controller and the longitudinal controller, can realize better tracking effect, better steering stability, good transverse stability and certain anti-interference capability, and has certain adaptability to different road surfaces.
Drawings
FIG. 1 is a schematic view of a parallel parking path of the present invention;
FIG. 2 is a two degree of freedom dynamics model of the vehicle of the present invention;
FIG. 3 is a steady-state yaw rate single point pre-sighting model of the present invention;
FIG. 4 is a block diagram of a second order sliding mode transversal controller based on a low pass filter of the present invention;
FIG. 5 is a cross-machine direction controller architecture diagram of the present invention;
FIG. 6 is a vehicle model and tire moment of inertia parameter configuration diagram of the present invention;
fig. 7 is a pre-aiming point setting diagram of the present invention.
Fig. 8 is a comparison chart of parking parameters.
Detailed Description
The technical scheme of the invention is further described in detail below with reference to the accompanying drawings:
vehicles typically include three steps when parking in parallel. Firstly, acquiring vehicle running information through an intelligent tire technology, wherein the vehicle runs along a direction parallel to a parking space until the vehicle reaches an initial point of a turning track; a second section that controls the turning angle of the vehicle and starts steering until the vehicle reaches a steering direction switching point; and thirdly, controlling the turning angle of the vehicle, starting to turn in the other direction, and reaching a final parking point to finish parking.
The parallel parking path can form an S-shaped curve traveling path by two tangent circles with equal radius, the movement track point of the whole vehicle is represented by the vehicle mass center, and the parking control of the whole vehicle is realized by inputting the planned parking track point into the transverse and longitudinal controllers.
In actual parkingIn the journey, the vehicle is firstly represented by O 1 As the center of a circle, with the minimum turning radius R of the trolley min Steering movement is performed for the radius. After reaching the switching point C, the vehicle turns reversely to O 2 As the center of a circle, also with the minimum steering radius R of the vehicle min Steering movement is performed for the radius until the parking operation is completed. Minimum steering radius R of vehicle min Measuring distance d between vehicle and parking end point x The starting and ending point distance d of the vehicle can be obtained y . As shown in fig. 1, a schematic view of a path of parallel parking can be seen, the vehicle being parked from a starting point P 1 To the target point P 2 Displacement d along the x, y axes during movement of (c) x 、d y Can be expressed as:
the method can be characterized by comprising the following steps:
the specific method of the second step is as follows:
the following assumptions are based on fig. 2: (1) neglecting the influence of friction and damping in a steering system, and taking the rotation angles of left and right wheels as input on the assumption that the left and right tires have the same steering angle and rotation speed at any moment; (2) assuming that the motion and steering of the vehicle are driven by the front wheels; (3) assuming that both the body and the suspension system are rigid systems; (4) neglecting the transfer of front and rear axle loads creates a two-degree-of-freedom dynamics model and simplifies into a bicycle model:
wherein m is the mass of the vehicle,is the lateral acceleration of the vehicle, v x Is the longitudinal speed of the vehicle, ω is the yaw rate of the vehicle, I z Is the moment of inertia of the vehicle at the centre of mass, +.>Is the yaw acceleration of the vehicle, a is the distance from the front axis to the centroid, b is the distance from the rear axis to the centroid, F yf Is the lateral force of the front axle, F yr Is the lateral force of the rear axle.
Under the assumption of small rotation angles, the relationship among cornering force, cornering angle and cornering stiffness of the tire in a linear region is as follows:
F yf ＝C f α f
F yr ＝C r α r
in the formula ,Cf 、C r Respectively the front wheel cornering stiffness and the rear wheel cornering stiffness, alpha f 、α r The front wheel slip angle and the rear wheel slip angle are respectively. The front and rear wheel slip angles of the vehicle are related to the motion parameters thereof, assuming that the speeds of the front and rear axles of the vehicle are v x 、v y The centroid side deflection angle is
The angle between the front wheel speed direction and the x-axis is expressed as θ:
the slip angle of the front and rear wheels of the vehicle can be expressed as:
the vehicle state space equation for the yaw angle ω and the centroid slip angle β can be derived:
the specific method of the third step is as follows:
the ideal steering wheel angle is determined by an expected method: referring to FIG. 3, the ideal yaw rate ω is obtained based on a steady-state single-point pretightening model and combined with simulation experience based on a constant yaw rate assumption d The method comprises the following steps:
in the formula ,vx Is the vehicle speed, Δf is the lateral deviation, t p Is the pre-aiming time.
Designing a multi-objective optimization function integrating lateral deviation, road boundary and response characteristics of steering motion of the whole vehicle:
J＝min(ω 1 J 1 +ω 2 J 2 +ω 3 J 3 )
in the formula ,ω1 、ω 2 、ω 3 For the weight coefficients, the weights are set in relation to the object achieved, ω 1 Related to the accuracy of the trajectory tracking; omega 2 Related to the distance between the vehicle and the road boundary; omega 3 Related to the response characteristics of the whole vehicle.
Designing an objective function J based on the lateral offset of the current centroid 1 ：
Where l_drv_2 is the centroid lateral offset and t is the model prediction time.
Designing an objective function J based on the distance between the current centroid and the boundary 2 ：
J 2 ＝∫ 0 t gdx
Where g is a safety function, and Δ is the distance from the road centerline to the boundary as the vehicle position approaches the boundary.
Design objective function J based on response characteristic of whole vehicle 3 ：
J 3 ＝(t p -T) 2
Where T is a time related to the steering response characteristic of the vehicle, and may be 1s or less when the speed is high and may be appropriately increased when the speed is low.
The specific method of the fourth step is as follows:
in order to combine the second order sliding mode lateral control with the filter as shown in fig. 4, the control input signal is filtered, the buffeting signal is filtered, and the low-pass filter needs to be designed first:
where ζ is the cut-off frequency, δ sw Is the signal before the filtering,is the filtered signal.
Design of a second-order sliding mode transverse controller: for a system that is uncertain and requires consideration of internal parameter perturbation and external disturbance, the system state equation can be further expressed as:
in the formula ,
the equations of the controlled system can be expressed as the following state equations:
/>
the uncertainty of the system and the applied disturbance are denoted by E (t), and can be expressed as:
E(t)＝ΔA 3 β+ΔA 4 ω r +ΔB 2 δ+(d+Δd)f
the equations of the controlled system can be transformed into the following state equations:
selecting the actual yaw rate omega r And an ideal yaw rate omega d As the tracking error of the system:
e＝ω r -ω d
the switching function is designed as follows:
the switching function is derived
Super-twist algorithm general form:
substitution into the above formula can be obtained:
the control amount of the front wheel rotation angle can be obtained:
obtaining the final steering wheel angle delta sw ：
in the formula ,isw Is the angular transmission ratio of steering wheel angle to wheel angle.
For systems that meet the existence uncertainty, when k 1 ＞0，k 2 At > 0, the system state can converge steadily and reach the origin (0, 0) in a finite time, when the system
Order the
Due to k 1 ＞0，k 2 > 0, then this matrix is Hurwitz, for any positive definite matrix P that satisfies the Lyapunov function:
D T P+PD＝-Q
definition of Lyapunov function V 0 (Λ)＝Λ T PΛ，V 0 (Λ) is a continuous positive function except that s=0 is differentiable, and thus can be derived using the chained approach:
deriving the above formula can obtain:
for V 0 (Λ) the following formula can be derived:
in the formula ,
for V 0 Derivative can be obtained by:
therefore, when V 0 (Λ)＝Λ T PΛ≥0，When Λ may tend to stabilize for a finite period of time. A class of systems that satisfies the above equation can converge steadily to 0 over a finite period of time. Through Lyapunov function verification, the controller meets the stability requirement.
The specific method of the fifth step is as follows:
firstly, designing an upper MPC controller, wherein the upper MPC controller adopts model predictive control, and adopts a first-order inertial system to express dynamic change of the longitudinal speed of the vehicle:
wherein, k=1 is the gain or amplification factor of the inertia link; t is t d Is the time constant of the inertial link.
The continuous system state equation of motion in the longitudinal direction of the vehicle can be expressed as:
wherein x= [ v a ]] T U=a for the state vector of the MPC longitudinal control system e Is the input of the MPC longitudinal control system.
Discretizing a continuous system state equation of the longitudinal motion of the vehicle by adopting a forward Euler method to obtain a discrete system state equation:
wherein k is the current sampling time; k+1 is the next sampling time, T s Is the sampling period.
Setting the longitudinal speed of the vehicle as the system output, the output equation can be expressed as:
y(t)＝Cx(k)
the system control objective is to define the performance evaluation function as:
wherein t-1 is the last sampling time, N p Is the prediction time domain, N c Is the control time domain, y p (k+i|k) is a predicted value of the control output, y ref (k+i|k) is a reference value of the control output, (k+i|k) represents prediction of information at k+i time using information at k sampling time, where i=1, 2, …, N p U (k+i) and Δu (k+i) are the k+i time control input and control increment and control quantity weight system matrices, respectively. Wherein the first half reflects the ability of the evaluation function to track following performance and the second half reflects the requirement of evaluation ambiguity on smooth change of control quantity, so that the designed evaluation function can make the control system as fast and smooth as possible in the wholeThe desired trajectory is tracked.
In the process of designing the upper-layer MPC controller, in order to restrict the control quantity, namely the acceleration and the change rate thereof, design constraint conditions are required, and are expressed as the following constraint formula:
u min ≤u(k+i)≤u max ,i＝0,1,…N c -1
Δu min ≤Δu(k+i)≤Δu max ,i＝0,1,…N c -1
in the formula umin and umax Is the minimum and maximum acceleration, deltau min and Δumax Is the minimum and maximum value of the acceleration increment.
The MPC solution problem needs to be converted into a quadratic programming problem, and a new state vector is constructed aiming at a discrete state equation of the vehicle motion in the longitudinal direction in the longitudinal motion process of the vehicle:
a new state space expression can be obtained:
defining an output equation:
predictions about vehicle conditions may be made and state quantities within the prediction time domain may be obtained:
the system output of the new state space equation is available:
the clear relation between state quantity and output quantity can be obtained by integrating the above formulas, and the output of the system at the future time can be obtained by expressing the output in a matrix form:
Y＝ψξ(k)+ΘΔU
in the formula, it can be clearly understood that the state quantity and the output quantity in the prediction time domain can be obtained by calculating the current state quantity xi (k) of the system and the control increment delta U in the control time domain, which can lead out the prediction function in the model prediction control algorithm, and define the output quantity of the system to obtain the reference value Y r For Y r And (3) carrying out an initialization operation:
/>
the method can obtain:
Y-Y r ＝ψξ(k)+ΘΔU-Y r
definition e=ψζ (k), becomes:
Y-Y r ＝E+ΘΔU
substituting the optimization objective function can obtain:
wherein , representing the Kroneck product. />The part is constant, and the part can be ignored when optimizing and solving, so the performance evaluation function can be abbreviated as:
let h=Θ T Q Q Θ+R R ，g＝Θ T Q Q (E-Y r ) The method can be converted into:
the optimization solution can be further abbreviated as:
the MPC algorithm constraint design is required, and the constraint is designed to constrain the control quantity and control increment, such as acceleration and acceleration increment. The constraint design is as follows:
u(k)＝u(k-1)+Δu(k)
u(k+1)＝u(k)+Δu(k+1)＝u(k-1)+Δu(k)+Δu(k+1)
…
u(k+N c -1)＝u(k+N c -2)+Δu(k+N c -1)＝u(k-1)+Δu(k)+Δu(k+1)+…Δu(k+N c -1)
the formula is rewritten as follows:
it can be seen that:
the control quantity constraint sum is as follows:
U min ≤U t +A I ΔU t ≤U max
control increment constraint:
ΔU min ≤ΔU≤ΔU max
the objective function may be designed as:
where ε is a relaxation factor that is used to prevent the case of no solution when calculating the optimal solution.
Secondly, the design of the lower P controller is carried out, and firstly, the switching logic of driving and braking needs to be determined:
in the formula atdes and pbdes The throttle opening and the brake pressure are obtained by the expected acceleration solved in the upper control. The lower-layer P controller adopted by the invention is P control, the throttle opening and the braking pressure respectively required in a driving mode and a braking mode are obtained by utilizing the P control mode, and the upper limit and the lower limit of the throttle opening are determined to be [0, throttle_max ]]Throttle_max=1, and the upper and lower limits of the brake pressure are [0, brake_max ]]The lower layer P controller adopts a P controller, with brake_max=15.
The magnitude of the desired throttle opening may be calculated from the following equation:
a tdes ＝K throttle *a des
in order to prevent the desired throttle opening from overflowing, a limit needs to be made to the value of the throttle opening, with the following conditions:
the magnitude of the desired brake master cylinder pressure may be calculated from the following equation:
P bdes ＝K brake *a des
to prevent the desired brake master cylinder pressure from overflowing, a limit needs to be placed on the value of the brake master cylinder pressure, with the following conditions:
the specific method in the step six is as follows:
the horizontal and vertical control architecture is obtained by combining the horizontal and vertical controllers, the track under the parallel parking scene is planned, track points are imported, as shown in fig. 5, a MATLAB/Simulink and Carsim combined simulation model is built, and input and output are set: setting a vehicle model and tire moment of inertia as in fig. 6, and setting a vehicle speed and a road adhesion coefficient; the vehicle pre-sight point (associated with the centroid) is set as in fig. 7.
Example 1
The road scene selects a parallel parking road, the road adhesion coefficient is set to be 0.9, performance verification simulation is carried out for verifying the designed transverse and longitudinal controllers, a corresponding vehicle model and a test road scene are established in the Carsim, and a control algorithm is designed in Matlab/Simulink. And comparing the joint simulation results of the parameters under the working condition with those of FIG. 8, the designed transverse and longitudinal controllers have good tracking effect on the step reference track. The tracking error of the reference track is smaller than 0.17m, so that reasonable track tracking can be realized. The steering wheel angle and transverse acceleration curves are smooth and have no severe buffeting, so that the stable running of the vehicle can be ensured, and the riding comfort can be improved. The foregoing is merely a preferred embodiment of the invention, and it should be noted that modifications could be made by those skilled in the art without departing from the principles of the invention, which modifications would also be considered to be within the scope of the invention.
Claims (6)
1. An intelligent automobile parking planning control method based on an intelligent tire technology is characterized in that: the method comprises the following steps:
step one: planning a track of parallel parking by using a tangent circle method;
step two: establishing a two-degree-of-freedom dynamics model about the yaw rate and the centroid slip angle of the vehicle in the process of parking the vehicle;
step three: establishing a self-adaptive pre-aiming model, obtaining pre-aiming time in the vehicle parking process through the self-adaptive pre-aiming model, and obtaining ideal yaw rate of parking based on the pre-aiming time and the current parking speed of the vehicle;
step four: according to the two-degree-of-freedom vehicle dynamics model and the self-adaptive pre-aiming model, solving together to obtain an ideal yaw rate, establishing a second-order sliding mode controller by combining a Super-twist second-order sliding mode control algorithm, taking the difference between the ideal yaw rate and the current actual yaw rate in the vehicle parking process as input through the second-order sliding mode controller, taking the current steering wheel rotation angle control quantity in the vehicle parking process as output quantity, and performing stability demonstration through a Lyapunov function;
step five: the method comprises the steps that a longitudinal controller is arranged, the longitudinal controller is a double-layer controller and comprises an upper MPC controller and a lower P controller, the upper MPC controller solves the expected vehicle acceleration according to the current speed in the parking process of a reference vehicle and transmits the expected vehicle acceleration to the lower P controller, and the real-time driving or braking control quantity of the vehicle is controlled through the lower P controller;
step six: and (3) combining the second-order sliding mode controller in the fourth step and the longitudinal controller in the fifth step to design a transverse-longitudinal controller, so as to control steering, driving and braking of the vehicle, and controlling and tracking the tangential circle parking track planned in the first step.
2. The intelligent vehicle parking planning control method based on intelligent tire technology as set forth in claim 1, wherein: method for planning parking track by utilizing tangent circlesThe process is as follows: during parking, the vehicle is first parked by O 1 As the center of a circle, with the minimum turning radius R of the trolley min For turning the radius, after reaching the switching point C, the vehicle turns reversely to O 2 As the center of a circle, also with the minimum steering radius R of the vehicle min Steering for radius until parking operation is completed, the switching point C is represented by O 1 Circle with circle center being O 2 The tangent point of the circle which is the center of the circle.
3. The intelligent vehicle parking planning control method based on the intelligent tire technology as claimed in claim 1, wherein: the steps for establishing the two-degree-of-freedom dynamics model are as follows:
the following modeling environment is assumed:
(1) neglecting the influence of friction and damping in a steering system, and assuming that the left and right tires in the vehicle have the same steering angle and rotation speed at any moment, taking the rotation angles of the left and right wheels as input;
(2) assuming that the motion and steering of the vehicle are driven by the front wheels;
(3) assuming that both the body and the suspension system are rigid;
(4) neglecting the transfer of front and rear axle loads;
based on the assumption, a two-degree-of-freedom dynamics model is established, and the two-degree-of-freedom dynamics model is specifically as follows:
1) Is provided with
Wherein m is the mass of the vehicle,is the lateral acceleration of the vehicle, v x Is the longitudinal speed of the vehicle, ω is the yaw rate of the vehicle, I z Is the moment of inertia of the vehicle at the centre of mass, +.>Is the yaw acceleration of the vehicle, a is the distance from the front axis to the centroid, b is the distance from the rear axis to the centroid, F yf Is the lateral force of the front axle, F yr Is the lateral force of the rear axle;
2) Under the assumption of small rotation angle of the front wheel rotation angle, the relation among the cornering force, the cornering angle and the cornering stiffness of the tire in a linear region is as follows:
F yf ＝C f α f
F yr ＝C r α r
in the formula ,Cf 、C r Respectively the front wheel cornering stiffness and the rear wheel cornering stiffness, alpha f 、α r The front wheel slip angle and the rear wheel slip angle are respectively;
the front and rear wheel slip angles of the vehicle are related to the motion parameters thereof, assuming that the speeds of the front and rear axles of the vehicle are v x 、v y The centroid side deflection angle is
3) The included angle between the front wheel speed direction and the x axis is θ, which can be expressed as:
4) The slip angle of the front and rear wheels of the automobile is expressed as:
5) A vehicle state space equation about the vehicle yaw angle ω and the centroid slip angle β is obtained:
4. the intelligent automobile parking planning control method based on the intelligent tire technology as claimed in claim 1, wherein: the step of establishing the self-adaptive pre-aiming model is as follows:
1) Ideal yaw rate omega based on steady-state single-point pre-aiming model d The method comprises the following steps:
in the formula ,vx Is the vehicle speed, Δf is the lateral deviation, t p Is pre-aiming time;
2) Designing a multi-objective optimization function integrating lateral deviation, road boundary and response characteristics of steering motion of the whole vehicle:
J＝min(ω 1 J 1 +ω 2 J 2 +ω 3 J 3 )
in the formula ,ω1 、ω 2 、ω 3 For the weight coefficients, the weights are set in relation to the object achieved, ω 1 Related to the accuracy of the trajectory tracking; omega 2 Related to the distance between the vehicle and the road boundary; omega 3 Related to the response characteristics of the whole vehicle;
3) Designing an objective function J based on the lateral offset of the current centroid 1 ：
J 1 ＝∫ 0 t L_Drv_2 2 dx
Where L_Drv_2 is the centroid lateral offset and t is the model prediction time;
4) Designing an objective function J based on the distance between the current centroid and the boundary 2 ：
J 2 ＝∫ 0 t gdx
Wherein g is a safety function, and delta is the distance from the center line of the road to the boundary as the vehicle position approaches the boundary;
5) Design objective function J based on response characteristic of whole vehicle 3 ：
J 3 ＝(t p -T) 2
Where T is a time associated with the vehicle steering response characteristic.
5. The intelligent automobile parking planning control method based on the intelligent tire technology as claimed in claim 1, wherein: the specific method of the fourth step is as follows:
1) In order to perform filtering processing on signals input by the second-order sliding mode controller, buffeting signals are weakened, and a filter connected with the second-order sliding mode controller needs to be designed firstly:
where ζ is the cut-off frequency, δ sw Is the signal before the filtering,is the filtered signal;
2) Design of second-order sliding mode controller
(a) For a system that is uncertain and requires consideration of internal parameter perturbation and external disturbance, the system state equation can be further expressed as:
in the formula ,
(b) The equations of the controlled system can be expressed as the following state equations:
(c) The uncertainty of the controlled system and the applied disturbance are denoted by E (t), and can be expressed as:
E(t)＝ΔA 3 β+ΔA 4 ω r +ΔB 2 δ+(d+Δd)f
(d) The equations of the controlled system can be transformed into the following state equations:
(e) Selecting the actual yaw rate omega r And an ideal yaw rate omega d As the tracking error of the system: e=ω r -ω d
(f) The switching function is designed as follows:
s＝e+λ∫ 0 t e(τ)dτ(λ>0)
(g) The derivative of the switching function is obtained:
(h) Super-twist algorithm general form:
substitution into the above formula can be obtained:
the control amount of the front wheel rotation angle can be obtained:
(i) For systems that meet the existence uncertainty, when k 1 >0，k 2 >At 0, the system state can be stably converged and reach the origin (0, 0) in a limited time, and at this time, the system
(j) Order the
Due to k 1 >0，k 2 >0, then this matrix is Hurwitz, for any positive definite matrix P that satisfies the Lyapunov function:
D T P+PD＝-Q
(k) Definition of Lyapunov function V 0 (Λ)＝A T PΛ，V 0 (Λ) is a continuous positive function except that s=0 is differentiable, and thus can be derived using the chained approach:
(1) Deriving the above formula can obtain:
(m) for V 0 (Λ) the following formula can be derived:
in the formula ,
(n) vs V 0 Derivative can be obtained by:
therefore, when V 0 (Λ)＝A T PA≥0，/>When Λ may tend to stabilize for a finite period of time;
3) Obtaining the final steering wheel angle delta sw ：
in the formula ,isw Is the angular transmission ratio of steering wheel angle to wheel angle.
6. The intelligent automobile parking planning control method based on the intelligent tire technology as claimed in claim 1, wherein: the specific method of the fifth step is as follows:
1) Firstly, designing an upper MPC controller, wherein the upper MPC controller adopts model predictive control, and adopts a first-order inertia system to express dynamic change of the longitudinal speed of the vehicle:
wherein, k=1 is the gain or amplification factor of the inertia link; t is t d The time constant of the inertia link;
the continuous system state equation of motion in the longitudinal direction of the vehicle can be expressed as:
wherein x= [ v a ]] T U=a, which is the state vector of the upper MPC controller e Is the input quantity of the upper MPC controller;
discretizing a continuous system state equation of the longitudinal motion of the vehicle by adopting a forward Euler method to obtain a discrete system state equation:
wherein k is the current sampling time; k+1 is the next sampling time, T s Is the sampling period;
setting the longitudinal speed of the vehicle as the system output, the output equation can be expressed as:
y(t)＝Cx(k)
the vehicle performance evaluation function is defined as:
wherein t-1 is the last sampling time, N p Is the prediction time domain, N c Is the control time domain, y p (k+i|k) is a predicted value of the control output, y ref (k+i|k) is a reference value of the control output, (k+i|k) represents prediction of information at k+i time using information at k sampling time, where i=1, 2, …, N p U (k+i) and Δu (k+i) are the k+i time control input and control increment and control quantity weight system matrices, respectively;
in the process of designing the upper MPC controller, constraint conditions are designed for restraining the acceleration and the change rate of the acceleration, and the constraint conditions are expressed as the following constraint formula:
u min ≤u(k+i)≤u max ，i＝0，1，...N c -1
Δu min ≤Δu(k+i)≤Δu max ，i＝0，1，...N c -1
in the formula ,umin and umax Is the minimum and maximum acceleration, deltau min and Δumax Is the minimum and maximum value of the acceleration increment;
the MPC solution problem needs to be converted into a quadratic programming problem, and a new state vector is constructed aiming at a discrete state equation of the vehicle motion in the longitudinal direction in the longitudinal motion process of the vehicle:
a new state space expression can be obtained:
defining an output equation:
predictions about vehicle conditions may be made and state quantities within the prediction time domain may be obtained:
the output of the new state space equation is available:
the clear relation between the state quantity and the output quantity can be obtained by integrating the formulas, and the output at the future moment can be obtained by expressing the output in a matrix form:
Y＝ψξ(k)+ΘΔU
in the formula, the state quantity and the output quantity in the prediction time domain can be clearly understood and obtained through calculation of the current state quantity xi (k) and the control increment delta U in the control time domain, and the prediction function in the model prediction control algorithm can be led out; defining the output of the system to obtain a reference value Y r For Y r And (3) carrying out an initialization operation:
the method can obtain:
Y-Y r ＝ψξ(k)+ΘΔU-Y r
definition e=ψζ (k), becomes:
Y-Y r ＝E+ΘΔU
substituting the optimization objective function can obtain:
wherein , represents the Kroneck product;
the part is constant, and the part can be ignored when optimizing and solving, so the performance evaluation function can be abbreviated as:
let h=Θ T Q Q Θ+R R ，g＝Θ T Q Q (E-Y r ) Then it can be transformed into:
the optimization solution can be further abbreviated as:
constraint condition design of the upper MPC controller is needed, and the constraint design is as follows:
u(k)＝u(k-1)+Δu(k)
u(k+1)＝u(k)+Δu(k+1)＝u(k-1)+Δu(k)+Δu(k+1)
…
u(k+N c -1)＝u(k+N c -2)+Δu(k+N c -1)＝
u(k-1)+Δu(k)+Δu(k+1)+…Δu(k+N c -1)
the formula is rewritten as follows:
it can be seen that:
the control quantity constraint sum is as follows:
U min ≤U t +A I ΔU t ≤U max
control increment constraint:
ΔU min ≤ΔU≤ΔU max
the objective function may be designed as:
wherein epsilon is a relaxation factor and is used for preventing the situation of no solution when calculating the optimal solution;
2) The design of the lower layer P controller is performed by first determining the switching logic for driving and braking:
in the formula atdes and pbdes A desired throttle opening and a desired brake pressure, respectively;
the magnitude of the desired throttle opening may be calculated from the following equation:
a tdes ＝K throttle *a des
in order to prevent the desired throttle opening from overflowing, a limit needs to be made to the value of the throttle opening, with the following conditions:
the magnitude of the desired brake pressure may be calculated from the following equation:
P bdes ＝K brake *a des
to prevent the desired brake master cylinder pressure from overflowing, a limit needs to be placed on the value of the brake master cylinder pressure, with the following conditions:
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