CN112677992B - Path tracking optimization control method for distributed driving unmanned vehicle - Google Patents
Path tracking optimization control method for distributed driving unmanned vehicle Download PDFInfo
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Abstract
The invention discloses a path tracking optimization control method for a distributed driving unmanned vehicle, which comprises the steps of firstly constraining longitudinal vehicle speed according to the side-turning and side-slipping conditions of the vehicle, determining parameters of environment, road conditions, historical accidents and running years, and then designing an active speed-limiting activation condition based on vehicle speed distribution intervals, thereby obtaining expected longitudinal resultant force of the vehicle in different speed distribution intervals; then determining a multi-constraint optimal objective function, providing weight coefficient adjustment methods of different motor failures and failure forms, and obtaining the driving and braking torques of the motors through an active set algorithm; and finally, providing an objective function of vehicle track tracking according to a vehicle dynamics model, wherein the objective function mainly comprises lateral path tracking deviation, vehicle system state variables, the change rate of steering wheel corners, acceleration tracking deviation, the change rate of acceleration derivatives and safety factor items, and the optimal path tracking of the vehicle is realized on the premise of meeting the requirements of vehicle control stability and active safety.
Description
Technical Field
The invention belongs to the technical field of unmanned vehicle control, and particularly relates to a path tracking optimization control method for a distributed driving unmanned vehicle.
Background
The electromotion, intellectualization, networking and sharing of the vehicle are the future development trend of the intelligent networking vehicle industry, and the distributed drive unmanned vehicle has a full-line control chassis layout, and particularly has a wide development prospect as an intelligent mobile machine in a specific scene. Much of the current research is focused on single distributed drive vehicles or single unmanned vehicles, while less research is being conducted on distributed drive unmanned vehicles. The distributed driving unmanned vehicle is used as an overdrive system and has an independently controllable driving system and an independently controllable steering system, and great potential is brought to the improvement of the dynamic performance of the vehicle through chassis control. However, path tracking of the distributed drive unmanned vehicle needs to fully and comprehensively consider the active safety of the vehicle, optimize energy conservation, motor failure, smoothness and other multi-objective tasks.
The primary objective of active safety control of a vehicle is to prevent the vehicle from sideslipping and rolling over, because safety accidents of the vehicle are mostly caused by the sideslip of wheels and the rolling over of the vehicle body during the driving and steering process of the vehicle. Excessive vehicle sideslip marks an excessive heading bias that can cause the vehicle to deviate from the intended travel path. As for the vehicle rollover, once the vehicle rollover occurs, the safety accident of the vehicle rollover safety system is more serious, and the vehicle rollover safety system often leads to the death of passengers or serious economic loss. The most common control method for preventing the vehicle from sideslip/rollover at present is active speed limit control, and the core idea of the active speed limit control is to set the allowable vehicle running speed upper limit under different running conditions (steering angle and road adhesion coefficient) so as to prevent the vehicle from sideslip and rollover caused by the fact that the actual vehicle running speed exceeds the allowable speed upper limit. However, the unmanned vehicle has complex and variable running conditions, dynamically changes the surrounding environment, has different learning capabilities, and has different running speeds, so that the adaptability of the unmanned vehicle to the environment, the working conditions and the self-capability needs to be improved.
A common energy-saving method is to set different driving modes (for example, 4 × 2 or 4 × 4) according to a target force requirement required by the vehicle, so that a single motor works in a high-efficiency region, or each motor works in the high-efficiency region based on an optimized objective function, thereby achieving the purpose of saving energy for the motor. However, the motor torque energy-saving distribution needs to fully consider the influence of an efficiency map of the motor on the output torque of the motor, the effect of load transfer of the vehicle during acceleration and braking on the vehicle dynamic property and the capacity of distributing the motor torque by different failure types and failure forms of the motor.
The sensor can detect the environment around the vehicle, the prediction information can be obtained in a perceiving mode in unmanned driving, the vehicle path planner can generate vehicle motion information for several seconds in the future, and the model prediction control is considered to be the most effective control method for path tracking. Several different model predictive control methods have been applied to vehicle steering and stability control and trajectory tracking. However, in the optimization target, the problems of how to coordinate the trajectory tracking capability of the vehicle and the steering stability of the vehicle and how to ensure the smoothness of the unmanned vehicle are lacked.
Disclosure of Invention
In view of this, the present invention provides a path tracking optimization control method for a distributed-driving unmanned vehicle, which can improve the path tracking and safety capabilities of the unmanned vehicle.
The technical scheme for realizing the invention is as follows:
a path-tracking optimization control method for a distributed drive unmanned vehicle, comprising the steps of:
step 1, measuring the position (X, Y), the heading angle psi and the longitudinal acceleration of the vehicle by using the GPS/INS
Lateral acceleration
And yaw rate
Obtaining the rotating speed n of the motor in real time through the motor controller mij And motor output torque T ij ；
Step 2, obtaining the longitudinal speed of the vehicle based on the step 1
Vehicle limiting using vehicle dynamics theorySafe running speed of vehicle
Including preventing rollover velocity
Constraining and anti-sideslip speed
Constraining;
step 3, based on the safe driving speed in step 2
Correcting the vehicle speed to obtain a corrected value of the safe driving vehicle speed
And determines the environment k c Road condition k d Historical Accident k m And the travel age k n A coefficient;
step 4, correcting value based on safe running speed in step 3
Setting the activation conditions of the active speed limit control in different distribution intervals of the vehicle speed, and determining the activation condition values under different vehicle speed classifications
The vehicle speed is controlled based on a nonlinear algorithm, and the total driving force T in the longitudinal direction of the vehicle is obtained according to different activation conditions des (ii) a According to the optimal objective function under multiple constraints
Solving for τ r ∈[τ r0 ,1]Medium optimal torque distribution coefficient
Obtaining the optimal torque driving braking torque of the motor
Step 5, based on discrete vehicle nonlinear dynamic model x (T) k+1 )＝F(x(T k ),u(T k ) Establish a cost function under nonlinear constraints
The cost function mainly comprises lateral path tracking deviation, vehicle system state variables, the change rate of steering wheel corners, acceleration tracking deviation, the change rate of acceleration derivatives and safety factor items; the constraint conditions give wheel rotation angle constraint, vehicle state constraint and acceleration constraint, and then the front wheel rotation angle of the vehicle is obtained.
Further, in step 3, the correction value of the safe running vehicle speed
Comprises the following steps:
the environment k is fully considered in the vehicle self-adaptive parameter adjustment strategy of environment and driving identification c Road condition k d History of accidents k m And age of travel k n And correcting the upper limit vehicle speed of the unmanned vehicle by using four different factors which mainly influence the safety of the vehicle, wherein the adjustment parameters are shown in a table 1.
TABLE 1 Environment k c Road condition k d Historical Accident k m And the travel age k n Coefficient of performance
Further, the step 4 specifically includes the activation conditions of the active speed limit control in the different distribution intervals of the vehicle speed:
designing the vehicle active speed limit based on sliding mode control, defining a sliding mode surface according to the speed limit:
in order to effectively weaken high-frequency jitter caused by frequent crossing of a sliding mode surface, an approximation law of a saturation function is constructed:
wherein, K x ,
Respectively representing the gain of the sliding mode and the boundary thickness of the sliding mode surface;
the vehicle longitudinal motion equation is:
wherein, F x Is the resultant force acting in the longitudinal direction of the vehicle; through a simultaneous upper formula, the expected longitudinal resultant force of the vehicle obtained by the active speed limiting control based on the sliding mode control is as follows:
in order to coordinate the vehicle with desired speed control and active speed limit control, the activation conditions of longitudinal motion control are designed:
and classifying according to the current vehicle speed distribution interval of the vehicle so as to determine the activation condition of the active speed limit control, wherein the vehicle classification comprises five conditions of high speed, medium-high speed, medium-low speed and low speed, and is shown in table 2.
TABLE 2 activation condition values for different vehicle speeds
Further, in step 4, the optimal objective function under multiple constraints
Is composed of
Wherein, the adaptive weight adjustment coefficient pi η ,Π τ ,Π θ Respectively an energy weight coefficient, a load transfer weight coefficient and a motor failure form weight coefficient; eta m As a function of the operating efficiency of the machine, τ r Distributing a proportional coefficient for the torque of the rear axle wheel; t is i Driving and braking torque of each motor; through an active set algorithm, the optimal torque distribution coefficient between the shafts can be solved
Further, the optimal driving and braking torque of the motor can be obtained
Threshold factor τ r0 The values of (a) are defined as:
in order to equalize the effect of the braking force on the individual wheels, the mechanical braking force is equally distributed over four wheels:
vehicle basic driving and braking torque T obtained by path tracking ij_b Can be expressed as:
in the path tracking control of the distributed drive vehicle, the torque average distribution of the left wheel and the right wheel is adopted to define the minimum value of the maximum torque of the coaxial wheels
m is formed by { d, b }, wherein m is d, and m is b respectively represents the driving torque or the braking torque of the motor;
wherein the content of the first and second substances,
indicating the speed n with the motor mij A varying outer characteristic curve; according to the difference between the driving condition and the braking condition, the generalized maximum constraint of the total required torque of the driving motor can be expressed as follows:
wherein, T b_max Representing the maximum braking torque that each wheel can generate;
assuming a rear axle torque distribution coefficient of τ r Then the torque distribution of the individual motors can be obtained:
the motor works in a driving working condition and a braking working condition which are differentWorking efficiency eta of the same working condition m Can be respectively expressed as:
wherein eta is d (n wij ,T ij ),η b (n wij ,T ij ) Respectively representing three-dimensional efficiency distribution diagrams under the motor driving and braking conditions;
from the longitudinal direction acceleration obtained by inertial navigation, the load transfer of the front and rear axes is expressed as follows:
if the motor fails and has different failure forms, the original distribution method is not applicable any more, and in order to improve the adaptability and robustness of the distributed driving vehicle to the motor failure, the weight coefficient adjustment methods of the different motor failures and the failure forms are determined, as shown in table 3.
TABLE 3 weight coefficient adjustment method for different motor failures and failure modes
Further, the cost function in step 5
Comprises the following steps:
for each sampling instant (k 0,1, …, N) c ) Nonlinear model predictive control in a specified future prediction horizon
In the interior of said container body,
is a reference track point (X) on the planned path ref ,Y ref ) Reference yaw rate psi ref And a reference speed
The first term, the second term, the third term, the fourth term and the fifth term of the cost function are respectively defined by dimensions
The semipositive definite weighting matrix W punishs the tracking deviation and has the dimension of
The semi-positive definite weighting matrix Q penalizes the system state variable, and the dimension is one-dimensional
Is used to penalize acceleration by a semi-positive definite weighting matrix R with one dimension
Penalizing the acceleration derivatives da by a semi-positive definite weighting matrix theta x And a safety factor with a parameter ρ;
in the first term and the second term of the objective function, the path constraint in the nonlinear model predictive control problem formula comprises the geometric constraint and the physical constraint of the system; path constraints include front wheel steering, longitudinal speed and yaw rate constraints:
-δ f_max -δ f_Δ ≤δ f ≤δ f_max +δ f_Δ
wherein, delta f_max ,
Limit constraints, δ, representing front wheel steering angle, longitudinal vehicle speed and yaw rate, respectively f_Δ ,
Soft constraints respectively representing the corner of a front wheel, the longitudinal speed and the yaw angular speed;
the acceleration constraint condition is constrained according to different running conditions of the vehicle, the basic idea is that when the running condition of the vehicle is severe, the acceleration of the vehicle is limited in a smaller range, when the vehicle is in a low-speed good working condition, the acceleration of the vehicle can be relaxed, and different constraint value ranges are set for the acceleration of the vehicle according to three types of severe working conditions, general working conditions and good working conditions, as shown in table 4.
TABLE 4 vehicle acceleration setting different constraint value ranges
| Class of operating conditions | Severe operating conditions | General operating conditions | Good working condition |
| a x | -1<a x <1 | -2<a x <2 | -4<a x <4 |
Has the advantages that:
the invention uses the distributed driving unmanned vehicle path tracking method, can realize that the vehicle can meet the minimum path error in the lateral tracking under the premise of limiting the active safety of the sideslip and the side rollover of the vehicle, ensures the safety of the vehicle, and simultaneously, firstly ensures the safety of the vehicle under the condition of the instability trend of the safety of the vehicle and under the condition of properly sacrificing the lateral tracking deviation of the vehicle, and comprehensively improves the path tracking and safety performance of the unmanned vehicle.
Drawings
FIG. 1 is a schematic diagram of a method for controlling and tracking longitudinal motion of a vehicle according to the present invention
FIG. 2 is a schematic diagram of a vehicle path tracking method provided in accordance with the present invention
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a path tracking optimization control method for a distributed driving unmanned vehicle, which specifically comprises the following steps as shown in fig. 2:
step 1, measuring the position (X, Y), the heading angle psi and the longitudinal acceleration of the vehicle by using the GPS/INS
Lateral acceleration
And yaw angular velocity
Obtaining the rotating speed n of the motor in real time through a motor controller mij And motor output torque T ij 。
Step 2,Vehicle longitudinal speed obtained based on step 1
Method for limiting safe driving speed of vehicle by using vehicle dynamics theory
Including preventing rollover velocity
Constraining and anti-sideslip speed
And (5) restraining.
Step 3, based on the safe driving speed in step 2
And corrects it. In order to improve the adaptability of the unmanned vehicle to environment, working conditions and self capacity, a vehicle adaptive parameter adjustment strategy based on environment and driving recognition is provided, and an environment k is determined c Road condition k d Historical Accident k m And the travel age k n And (4) the coefficient.
Step 4, correcting value based on safe running speed in step 3
Designing an activation condition of active speed limit control in different distribution intervals of vehicle speed, and determining activation condition values under different vehicle speed classifications
The vehicle speed is controlled based on a nonlinear algorithm, and the total driving force T in the longitudinal direction of the vehicle is obtained according to different activation conditions des . Providing an optimal objective function under new multi-constraints
The function is based on the braking efficiency of the motor, the failure mode of the motor andload transfer influence multi-target in vehicle acceleration and deceleration process, and solving tau r ∈[τ r0 ,1]Medium optimum torque distribution coefficient
Obtaining the optimal torque driving and braking torque of the motor
Step 5, based on discrete vehicle nonlinear dynamic model x (T) k+1 )＝F(x(T k ),u(T k ) Establish a cost function under nonlinear constraints
The cost function mainly comprises lateral path tracking deviation, vehicle system state variables, change rate of steering wheel turning angle, acceleration tracking deviation, acceleration derivative change rate and safety factor items. The constraint conditions give wheel corner constraint, vehicle state constraint and acceleration constraint, and the front wheel corner of the vehicle is obtained by a rapid method.
The safe driving speed in the step 2
The method specifically comprises the following steps:
the active safety and the operation stability of the vehicle need to prevent the sideslip and the rollover problems of the vehicle in the steering process, and the sideslip and the rollover problems are closely related to the speed of the vehicle.
To prevent the vehicle from skidding due to insufficient tire lateral force, the vehicle's lateral inertial force cannot exceed the maximum tire adhesion limit provided by the ground:
wherein m represents the mass of the vehicle, a y Which is indicative of the lateral acceleration of the vehicle,
respectively, the road adhesion coefficient and the gradient estimated by the algorithm.
The lateral acceleration of the vehicle is:
wherein R is T Is the turning radius. At steady state steering
The steering radius is a function of steering angle and tire slip angle:
wherein l f And l r Respectively, the distance of the front and rear wheels of the vehicle to the center of mass of the vehicle.
The velocity constraint relationship for preventing vehicle sideslip may be expressed as
Wherein S is slip The safety coefficient of the vehicle sideslip is high.
Lateral acceleration of the vehicle causes vertical load transfer between the left and right wheels of the vehicle as the vehicle turns. The sign of the rollover behavior of the vehicle is that the wheels on a certain side of the vehicle lose adhesion capability due to undersize vertical loads of the wheels caused by the rolling motion or the transverse motion, so that the rollover of the vehicle is prevented, namely, the excessive transfer among the loads of the wheels is limited by setting a safe upper limit of the vehicle speed. The rollover-preventing speed limit should be such that the road surface provides sufficient traction to overcome the vehicle's driving resistance when the wheel torque is evenly distributed.
When the vehicle is transversely accelerated, the side with less vertical load of the wheels can overcome the running resistance F of the vehicle due to the load transfer of the vehicle w ：
Where ρ, C d A represents air density, air resistance coefficient and frontal area, respectively, f r Representing the wheel rolling resistance coefficient.
The rollover constraint may be expressed as:
wherein H b Representing the height of the center of mass of the vehicle. d represents the distance of the vehicle's left or right wheel from the vehicle's center of mass, and assumes equal wheelbase.
The vehicle rollover speed constraint is expressed as:
wherein S is over And the safety factor of the vehicle rollover is high.
In summary, the upper limit of vehicle longitudinal speed is determined by vehicle side-slip limit and vehicle rollover limit constraints
Wherein the content of the first and second substances,
is the maximum travel speed allowed by the vehicle.
The vehicle adaptive parameter adjustment strategy based on environment and driving identification in step 3 specifically comprises:
in order to improve the adaptability of the unmanned vehicle to the environment, the working condition and the self capacity, a vehicle self-adaptive parameter adjusting strategy based on the environment and the driving identification is provided:
the environment k is fully considered in the vehicle self-adaptive parameter adjustment strategy of environment and driving identification c Road condition k d Historical Accident k m And age of travel k n And correcting the upper limit vehicle speed of the unmanned vehicle by using four different factors which mainly influence the safety of the vehicle, wherein the adjustment parameters are shown in a table 1.
TABLE 1 Environment k c Road condition k d Historical Accident k m And the travel age k n Coefficient of performance
And carrying out online adjustment on the vehicle speed safety threshold value through the weight coefficient according to environment and road condition identification. The active speed limit control can intervene on the speed of the vehicle, so that the driving safety of the vehicle is ensured. And if the expected vehicle speed on the time-varying planned path is higher than the upper limit of the safe vehicle speed, the active speed limit control is activated, and intervention is applied to the vehicle speed to prevent vehicle instability caused by overhigh vehicle speed.
As shown in fig. 1, the step 4 of activating the active speed limit control in different distribution intervals of the vehicle speed and the optimal objective function under multiple constraints specifically includes:
designing the vehicle active speed limit based on sliding mode control, defining a sliding mode surface according to the speed limit:
in order to effectively weaken high-frequency jitter caused by frequent crossing of a sliding mode surface, an approximation law of a saturation function is constructed:
wherein, K x ,
Respectively representing the gain of the slip form and the boundary thickness of the slip form surface, K x If too small, the convergence rate is slow; too large, easily causing high frequency oscillation, and requiring reasonable value selection.
The vehicle longitudinal motion equation is:
wherein, F x Is the resultant force acting in the longitudinal direction of the vehicle. Through the simultaneous upper formula, the expected longitudinal resultant force of the vehicle obtained by the active speed-limiting control based on the sliding mode control is as follows:
in order to coordinate the vehicle with desired speed control and active speed limit control, the activation conditions of longitudinal motion control are designed:
and classifying according to the current vehicle speed distribution interval of the vehicle so as to determine the activation condition of the active speed limit control, wherein the vehicle classification comprises five conditions of high speed, medium-high speed, medium-low speed and low speed, and is shown in table 2.
TABLE 2 activation condition values for different vehicle speeds
When the vehicle active speed limiting control is activated, the above type active control is adoptedDesired longitudinal resultant force of vehicle obtained by speed limit control
Solving the expected resultant moment of the vehicle; otherwise, the sliding mode control is adopted to obtain the expected longitudinal resultant force F of the vehicle x,d To make the actual vehicle speed track the reference vehicle speed
Wherein, K x2 ,
The gain of the slip form and the thickness of the slip form face boundary are shown separately.
The longitudinal movement of the vehicle then corrects the total desired torque T des Comprises the following steps:
corrected total desired moment T of longitudinal movement of the vehicle des It needs to be reasonably distributed to each drive wheel, which is a typical overdrive configuration. Comprehensively considering the driving and braking efficiency of the motor, the failure mode of the motor and the load transfer in the vehicle acceleration and deceleration process, an optimal objective function under multiple constraints is provided
The torque of the wheels is optimally distributed, so that the energy consumption is the lowest on the premise that the vehicle meets the active safety.
Wherein, the intelligent adaptive weight adjustment coefficient pi η ,Π τ ,Π θ The energy weight coefficient, the load transfer weight coefficient and the motor failure form weight coefficient are respectively. Eta m As a function of the operating efficiency of the machine, τ r A proportionality coefficient is allocated to the torque of the rear axle wheels. T is a unit of i The driving and braking torque of each motor. Through an active set algorithm, the optimal torque distribution coefficient between the shafts can be solved
Further, the optimal driving and braking torque of the motor can be obtained
The optimal objective function will be further explained and illustrated.
Considering that symmetry may exist in the distribution of the two-side motor system, rear wheel drive braking is preferentially used in order to prevent torque distribution jump in the distribution, and rear axle vehicle torque distribution coefficient tau is selected mainly considering that the front wheels are driving wheels and if the front wheels are preferentially distributed, the output of lateral force in the vehicle steering process can be influenced r ∈[τ r0 ,1]. Wherein the threshold factor τ r0 The value of (b) is defined as:
the braking condition is slightly different from the driving condition because mechanical braking also exists in the braking condition. In order to equalize the effect of the braking force on the individual wheels, the mechanical braking force is distributed equally over the four wheels.
Vehicle basic driving and braking torque T obtained by path tracking ij_b Can be expressed as:
in the path tracking control of the distributed drive vehicle, the torque average distribution of the left wheel and the right wheel is adopted to define the minimum value of the maximum torque of the coaxial wheels
m ∈ { d, b }, where m ═ d and m ═ b denote the drive torque or the braking torque of the electric machine, respectively.
Wherein the content of the first and second substances,
indicating the speed n with the motor mij A varying outer characteristic. According to the difference between the driving condition and the braking condition, the generalized maximum constraint of the total required torque of the driving motor can be expressed as follows:
wherein, T b_max Indicating the maximum braking torque that each wheel is capable of generating.
Assuming a rear axle torque distribution coefficient of τ r Then the torque distribution of the individual motors can be obtained:
the motor works in a driving working condition and a braking working condition, and the working efficiency eta of the two different working conditions m Can be respectively expressed as:
wherein eta is d (n wij ,T ij ),η b (n wij ,T ij ) Respectively showing motor drives andand (4) a three-dimensional efficiency distribution map under the braking condition.
When the load of the front axle and the rear axle is transferred, the vertical load of each tire can be influenced, so that the adhesion limit of each tire can be greatly changed, and in order to consider the safety of the vehicle, the wheel with larger vertical force is divided into larger driving torque, and conversely, the wheel with smaller vertical force is required to output smaller driving and braking torque. From the longitudinal direction acceleration obtained by inertial navigation, the load transfer of the front and rear axes is expressed as follows:
if the motor fails and different failure modes occur, the original distribution method is not applicable any more, and in order to improve the adaptability and robustness of the distributed driving vehicle to the motor failure, a weight coefficient adjusting method aiming at different motor failures and failure modes is provided, as shown in table 3.
TABLE 3 weight coefficient adjustment method for different motor failures and failure modes
The method for tracking the path of the distributed driving unmanned vehicle in the step 5 specifically comprises the following steps:
the objective of active front wheel control is to design a control strategy such that the vehicle follows a time-dependent, real-time generated reference trajectory, and the uncertainty behavior caused by vehicle model errors or environmental disturbances is guaranteed by setting the soft constraints of the cost function. Given time
Noiseless time-continuous distributed drive unmanned vehicleThe kinetic model is expressed as:
wherein the content of the first and second substances,
n x ＝length(x),n u length (u) is an analytic vector mapping function, and u (t) is the system control input, including front wheel rotation δ f And x (t) is the state vector of the system, including the longitudinal vehicle speed
Lateral speed
And yaw rate
With discrete instantaneous time T 0 <T 1 <T 2 <…, at a given sampling period
And adopt the time of day
By the above equation, the euler discrete model of perturbation can be defined as:
wherein the discrete function F is obtained based on numerical integration analysis or implicit expression. Further, assume control input u (T) k ) At a time interval [ T k ,T k+1 ]Above are piecewise constants, and for simplicity of representation, define x k :＝x(T k ),u k :＝u(T k )。
With vehicle seatLongitudinal speed of vehicle under mark
Lateral speed
And yaw rate
As a state, the dual rail model can be represented by:
wherein, F xij ,F yij I ∈ { f, r }, j ∈ { l, r } represent the longitudinal and lateral forces of the respective tires in the vehicle coordinate system. m represents the mass of the vehicle, I zz Representing the moment of inertia of the vehicle about the z-axis in the vehicle coordinate system. The vehicle position (X, Y) in absolute coordinates can be obtained from the kinematic equation:
the tire force in the vehicle coordinate system can be obtained by the tire force in the tire coordinate system:
wherein, F wxij ,F wyij Respectively, a tire longitudinal force and a wheel lateral force in a tire coordinate system. The vehicle tire model describes the calculation of tire forces. Nominal tire longitudinal force F of each tire under pure longitudinal/lateral cornering conditions wxij,n And nominal tire side force F wxij,n Can be represented by the magic formula tire model:
F wxij,n ＝μ xij F zij sin(C xij arctan(B xij (1-E xij )s ij +E xij arctan(B xij s ij )))
F wyij,n ＝μ yij F zij sin(C yij arctan(B yij (1-E yij )α ij +E xij arctan(B yij α ij )))
wherein s is ij ,α ij ,F zij I belongs to { f, r }, j belongs to { l, r } and respectively represents the slip rate, the slip angle and the vertical force of each tire; mu.s hij H ∈ { x, y }, i ∈ { f, r }, j ∈ { l, r } represents a road surface friction coefficient, B hij ,C hij ,E hij H belongs to { x, y }, i belongs to { f, r }, j belongs to { l, r }, and represent a tire stiffness factor, a shape factor and a curvature factor respectively.
In a combined condition, i.e. where both the tire slip ratio and the slip angle are not zero, the coupling of the tire longitudinal force and the tire lateral force can be expressed as a friction circle:
although the above equation does not establish a direct relationship between tire lateral force and tire slip angle, the friction ellipse model is used to calculate tire lateral force under combined conditions because of its simplicity and sufficient accuracy.
The tire slip angle represents the angle between the tire longitudinal direction and the tire vehicle speed direction, and can be expressed as:
wherein v is wxij ,v wyij Respectively, the longitudinal speed and the lateral speed of the wheel center in the tire coordinate system, which can be calculated by the following equation:
wherein v is xij ,v yij Respectively, the longitudinal speed and the lateral speed at each wheel center in the vehicle coordinate system, which can be calculated by the following formula:
the calculation of the tire slip rate under the driving working condition and the braking working condition is slightly different, and the tire slip rate s is different according to the driving and braking working conditions ij Can be obtained by the following formula:
wherein, ω is wij Indicating wheel angular velocity, R we Indicating the effective rolling radius of the wheel.
Since lateral or side-to-side acceleration/deceleration movements of a vehicle can cause load transfer to the left and right or front and rear wheels of the vehicle, the vertical force of a tire is expressed as follows:
wherein, K φf ，K φr Roll stiffness of the front and rear suspensions, respectively. h is a total of rf ,h rr Respectively, the roll centers of the front and rear suspensions.
Wheel dynamics may establish an equation between wheel driving braking torque and wheel longitudinal force:
wherein, I w Representing moment of inertia of the wheel, b w Representing the wheel damping coefficient.
In fact, this distributed drive unmanned vehicle has only the front steering wheels that are controllable, and assumes that the steering angles of the front left and right wheels are the same, i.e.: delta fl ＝δ fl ＝δ f ，δ rl ＝δ rr ＝0。
Using cost functions
The actual driving path of the vehicle can be tracked to the expected path, and the smoothness and the safety of path tracking are guaranteed. The cost function mainly comprises lateral path tracking deviation, vehicle system state variables, change rate of steering wheel turning angle, acceleration tracking deviation, acceleration derivative change rate and safety factor items.
For each sampling instant (k 0,1, …, N) c ) Nonlinear model predictive control in a specified future prediction horizon
In the interior of the container body,
is a reference track point (X) on the planned path ref ,Y ref ) Reference yaw rate psi ref And a reference speed
The first term, the second term, the third term, the fourth term and the fifth term of the cost function are respectively defined by dimensions
The semipositive definite weighting matrix W punishs the tracking deviation and has the dimension of
The system state variable is punished by a semi-positive definite weighting matrix Q, and the dimension is one-dimensional
Is used to penalize acceleration by a semi-positive definite weighting matrix R with one dimension
Penalizing the acceleration derivative da by the semi-positive definite weighting matrix theta x And a safety factor with a parameter p.
In the first term and the second term of the objective function, the path constraint in the nonlinear model predictive control problem formula comprises the geometrical constraint and the physical constraint of the system. In fact, the robustness in the control of the objective function is improved by considering the uncertainty caused by unknown interference and modeling errors, and the constraint condition is set as soft constraint through a relaxation factor. Path constraints include front wheel steering, longitudinal speed and yaw rate constraints:
-δ f_max -δ f_Δ ≤δ f ≤δ f_max +δ f_Δ
wherein, delta f_max ,
Limit constraints, delta, representing front wheel steering angle, longitudinal vehicle speed and yaw rate, respectively f_Δ ,
Soft constraints representing front wheel steering, longitudinal vehicle speed and yaw rate, respectively.
In the third item of the objective function, in order to prevent the jump and unreasonable change of the expected front wheel corner caused in the mathematical solving process in the lateral path tracking of the unmanned vehicle, the objective is to accord with the actual engineering application when the lateral expected track is tracked by controlling the front wheel corner, and ensure the stable change of the front wheel corner.
The acceleration constraint condition is constrained according to different running conditions of the vehicle, the basic idea is that when the running conditions of the vehicle are severe, such as rain, snow and foggy days, the acceleration of the vehicle is limited in a smaller range, when the vehicle is in a low-speed good working condition, the acceleration of the vehicle can be relaxed, and different constraint value ranges are set for the acceleration of the vehicle according to three types, namely a severe working condition, a general working condition and a good working condition, as shown in a table.
TABLE 4 vehicle acceleration setting different constraint value ranges
| Class of operating conditions | Severe operating conditions | General operating conditions | Good working condition |
| a x | -1<a x <1 | -2<a x <2 | -4<a x <4 |
In order to solve the problem of optimization solution of nonlinear constraint, the infinite dimension constraint optimization problem is converted into nonlinear programming based on a direct multi-shooting method, and the control input under each control time step is solved through sequential quadratic programming of a real-time iteration method. One iteration is performed for each time control time step and a continuous state hot start and control trajectory from one time step to the next is used. Under reasonable assumptions, when errors and external interference exist, the stability of the obtained closed-loop system can be correspondingly ensured. It does not seem appropriate to solve the nonlinear programming problem if the solution is not a local optimization problem, however, for unmanned vehicle systems, model predictive control tracks the path generated by the motion planning controller as a reference for linearization, e.g., constrained perception of motion feasible. Therefore, the scheme is suitable for nonlinear control optimization solution. The block structure decomposition technology with low-rank updating is applied to an iterative solver in an original active set algorithm with a customized initialization method, so that a simple, efficient and reliable solver suitable for embedded control hardware is generated.
In order to compensate for the time delay T caused by the vehicle network communication and the actuator interface at the time T d Handle bar
Is defined as a predicted state value
It is estimated from the current state
And the past input signal u stored in the buffer. Such skew compensation is important to maintain robustness and high control performance. The real-time solver algorithm is shown as a table.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. A path-following optimization control method for a distributed drive unmanned vehicle, comprising the steps of:
step 1, measuring the position (X, Y), the heading angle psi and the longitudinal acceleration of the vehicle by using the GPS/INS
Lateral acceleration
And yaw rate
Obtaining the rotating speed n of the motor in real time through the motor controller mij And motor output torque T ij ；
Step 2, obtaining the longitudinal speed of the vehicle based on the step 1
Method for limiting safe driving speed of vehicle by using vehicle dynamics theory
Including preventing rollover velocity
Constraining and anti-sideslip speed
Constraining;
step 3, based on the safe driving speed in step 2
Correcting the vehicle speed to obtain a corrected value of the safe driving vehicle speed
And determines the environment k c Road condition k d Historical Accident k m And the travel age k n A coefficient;
step 4, correcting value based on safe running speed in step 3
Setting the activation conditions of the active speed limit control in different distribution intervals of the vehicle speed, and determining the activation condition values under different vehicle speed classifications
The vehicle speed is controlled based on a nonlinear algorithm, and the total driving force T in the longitudinal direction of the vehicle is obtained according to different activation conditions des (ii) a According to the optimal objective function under multiple constraints
Solving for τ r ∈[τ r0 ,1]Medium optimal torque distribution coefficient
Obtaining the optimal torque driving braking torque of the motor
Step 5, based on discrete vehicle nonlinear dynamic model x (T) k+1 )＝F(x(T k ),u(T k ) Establish a cost function under nonlinear constraints
The cost function mainly comprises lateral path tracking deviation, vehicle system state variables, the change rate of steering wheel corners, acceleration tracking deviation, the change rate of acceleration derivatives and safety factor items; the constraint conditions give wheel rotation angle constraint, vehicle state constraint and acceleration constraint, and then the front wheel rotation angle of the vehicle is obtained.
2. The path-tracing optimization control method for the distributed drive unmanned vehicle according to claim 1, wherein in step 3, the correction value of the safe-running vehicle speed
Comprises the following steps:
the environment k is fully considered in the vehicle self-adaptive parameter adjustment strategy of environment and driving identification c Road condition k d Historical Accident k m And the travel age k n Four different factors mainly influencing the safety of the vehicle are used for correcting the upper limit speed of the unmanned vehicle, and the adjustment parameters are shown in the table 1.
TABLE 1 Environment k c Road condition k d Historical Accident k m And age of travel k n Coefficient of performance
3. The path tracking optimization control method for the distributed drive unmanned vehicle as claimed in claim 1, wherein the activation conditions of the active speed limit control in the different distribution intervals of the vehicle speed in step 4 specifically include:
designing the vehicle active speed limit based on sliding mode control, defining a sliding mode surface according to the speed limit:
in order to effectively weaken high-frequency jitter caused by frequent crossing of a sliding mode surface, an approximation law of a saturation function is constructed:
wherein, the first and the second end of the pipe are connected with each other,
respectively representing the gain of the sliding mode and the boundary thickness of the sliding mode surface;
the vehicle longitudinal motion equation is:
wherein, F x Is the resultant force acting in the longitudinal direction of the vehicle; through a simultaneous upper formula, the expected longitudinal resultant force of the vehicle obtained by the active speed limiting control based on the sliding mode control is as follows:
in order to coordinate the vehicle with desired speed control and active speed limit control, the activation conditions of longitudinal motion control are designed:
and classifying according to the current vehicle speed distribution interval of the vehicle so as to determine the activation condition of the active speed limit control, wherein the vehicle classification comprises five conditions of high speed, medium-high speed, medium-low speed and low speed, and is shown in table 2.
TABLE 2 activation condition values for different vehicle speeds
4. A path-tracking optimization control method for a distributed drive unmanned vehicle as claimed in claim 1, wherein in step 4, the optimal objective function under multiple constraints
Is composed of
s.t.
τ r ∈[τ r0 ,1]
Wherein, the adaptive weight adjustment coefficient pi η ,Π τ ,Π θ Respectively an energy weight coefficient, a load transfer weight coefficient and a motor failure form weight coefficient; eta m As a function of the operating efficiency of the machine, τ r Distributing a proportion coefficient for the torque of the rear axle wheel; t is i Driving and braking torque of each motor; through an active set algorithm, the optimal torque distribution coefficient between the shafts can be solved
Further, the optimal driving and braking torque of the motor is obtained
Threshold factor τ r0 The values of (a) are defined as:
in order to equalize the effect of the braking force on the individual wheels, the mechanical braking force is equally distributed over four wheels:
vehicle basic driving and braking torque T obtained by path tracking ij_b Expressed as:
in the path tracking control of the distributed drive vehicle, the torque average distribution of the left wheel and the right wheel is adopted to define the minimum value of the maximum torque of the coaxial wheels
Wherein, m ═ d, m ═ b respectively represent the driving torque or braking torque of the electrical machinery;
wherein the content of the first and second substances,
indicating the speed n with the motor mij A varying outer characteristic; according to drivingThe difference between the dynamic working condition and the braking working condition, the generalized maximum constraint of the total required torque of the driving motor is expressed as follows:
wherein, T b_max Representing the maximum braking torque that each wheel can generate;
assuming a rear axle torque distribution coefficient of τ r Then the torque distribution of the individual motors can be obtained:
the motor works in a driving working condition and a braking working condition, and the working efficiency eta of the two different working conditions m Respectively expressed as:
wherein eta is d (n wij ,T ij ),η b (n wij ,T ij ) Respectively representing three-dimensional efficiency distribution diagrams under the motor driving and braking conditions;
from the longitudinal direction acceleration obtained by inertial navigation, the load transfer of the front and rear axes is expressed as follows:
if the motor fails and has different failure forms, the original distribution method is not applicable any more, and in order to improve the adaptability and robustness of the distributed driving vehicle to the motor failure, the weight coefficient adjustment methods of the different motor failures and the failure forms are determined, as shown in table 3.
TABLE 3 weight coefficient adjustment method for different motor failures and failure modes
5. A path-following optimization control method for a distributed drive unmanned vehicle as claimed in claim 1, wherein the cost function in step 5
Comprises the following steps:
for each sampling instant (k 0,1, …, N) c ) Nonlinear model predictive control in a specified future prediction horizon
In the interior of said container body,
is a reference track point (X) on the planned path ref ,Y ref ) Reference yaw rate psi ref And a reference speed
The first term, the second term, the third term, the fourth term and the fifth term of the cost function are respectively defined by dimensions
The semipositive definite weighting matrix W punishs the tracking deviation and has the dimension of
The semi-positive definite weighting matrix Q penalizes the system state variable, and the dimension is one-dimensional
Is used to penalize the acceleration by a semi-positive definite weighting matrix R, the dimension is one-dimensional
Penalizing the acceleration derivatives da by a semi-positive definite weighting matrix theta x And a safety factor with a parameter ρ;
in the first term and the second term of the objective function, the path constraint in the nonlinear model predictive control problem formula comprises the geometric constraint and the physical constraint of the system; path constraints include front wheel steering, longitudinal speed and yaw rate constraints:
-δ f_max -δ f_Δ ≤δ f ≤δ f_max +δ f_Δ
wherein the content of the first and second substances,
limit constraints representing the front wheel steering angle, the longitudinal vehicle speed and the yaw rate, respectively,
respectively representing the soft constraints of the corner of a front wheel, the longitudinal speed and the yaw angular speed;
the acceleration constraint condition is constrained according to different running conditions of the vehicle, the basic idea is that when the running condition of the vehicle is severe, the acceleration of the vehicle is limited in a smaller range, when the vehicle is in a low-speed good working condition, the acceleration of the vehicle is relaxed and constrained, and different constraint value ranges are set for the acceleration of the vehicle according to three categories of severe working conditions, general working conditions and good working conditions, as shown in table 4.
TABLE 4 vehicle acceleration setting different constraint value ranges
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