CN112677992B - Path tracking optimization control method for distributed driving unmanned vehicle - Google Patents

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

Path following optimization control method for distributed driving unmanned vehicles

technical field

The invention belongs to the technical field of unmanned vehicle control, and in particular relates to a path tracking optimization control method for distributed driving of unmanned vehicles.

Background technique

The electrification, intelligence, networking, and sharing of vehicles are the future development trends of the intelligent networked vehicle industry. Distributed-driven unmanned vehicles have a full-wire chassis layout, especially as 'smart mobile machines' in specific scenarios. Has broad prospects for development. The current research mostly focuses on a single distributed drive vehicle or a single unmanned vehicle, while the research on distributed drive unmanned vehicle is less. Distributed drive unmanned vehicle, as an overdrive system, has an independently controllable drive system and an independently controllable steering system, which brings great potential for chassis control to improve vehicle dynamics. However, the path tracking of distributed driving unmanned vehicles needs to fully consider the active safety of the vehicle, optimize energy saving, motor failure and smoothness and other multi-objective tasks.

The primary goal of vehicle active safety control is to prevent vehicle side slip and rollover, because vehicle safety accidents are mostly caused by wheel side slip and body rollover during vehicle steering. Excessive sideslip of the vehicle indicates an excessive heading deviation, which will cause the vehicle to deviate from the intended driving trajectory. As for the vehicle rollover, once it happens, its safety accident is more serious, and it often leads to the death of the occupant or serious economic loss. At present, the most commonly used vehicle anti-slip/rollover control method is active speed limit control. The core idea of active speed limit control is to set the upper limit of the allowable speed of the vehicle under different driving conditions (steering angle and road adhesion coefficient) to Prevent the vehicle from sliding and rolling over caused by the actual driving speed of the vehicle exceeding the upper limit of the allowable speed. However, the driving conditions of unmanned vehicles are complex and changeable, the surrounding environment changes dynamically, the learning ability is different, and the driving speed is in different ranges. Therefore, it is necessary to improve the adaptability of unmanned vehicles to the environment, working conditions and their own capabilities.

Distributed drive vehicles generally consist of two drive motors or multiple drive motors, and each motor has a coupling relationship when outputting driving force. A common energy-saving method is to set different driving modes (such as 4×2 Or 4×4), so that a single motor can work in the high-efficiency region, or each motor can work in the high-efficiency region based on the optimization objective function, so as to achieve the purpose of motor energy saving. However, the energy-saving distribution of motor torque needs to fully consider the influence of the efficiency map of the motor on the output torque of the motor, the effect of the load transfer of the vehicle during acceleration and braking on the dynamics of the vehicle, and how the different failure types and failure forms of the motor affect the motor. The ability of the motor to distribute torque.

Since the sensor can detect the environment around the vehicle, the prediction information is perceptually acquired in the driverless, and the vehicle path planner can generate the vehicle motion information in the next few seconds, the model predictive 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 goal, there is a lack of how to coordinate the trajectory tracking ability of the vehicle and the handling stability of the vehicle, and how to ensure the smoothness of the unmanned vehicle.

SUMMARY OF THE INVENTION

In view of this, the present invention provides a path tracking optimization control method for distributed driving of unmanned vehicles, which can improve the path tracking and safety capabilities of unmanned vehicles.

The technical scheme that realizes the present invention is as follows:

A path tracking optimization control method for distributed driving unmanned vehicles, including the following steps:

横向加速度

和横摆角速度

通过电机控制器实时获取电机的转速n_mij和电机输出转矩T_ij；Step 1. Use GPS/INS to measure vehicle position (X, Y), heading angle ψ, vehicle longitudinal acceleration

Lateral acceleration

and yaw rate

Obtain the speed n _mij of the motor and the output torque T _ij of the motor in real time through the motor controller;

利用车辆动力学理论限制车辆安全行驶车速

包括防侧翻速度

约束和防侧滑速度

约束；Step 2. Obtain the longitudinal speed of the vehicle based on Step 1

Using Vehicle Dynamics Theory to Limit the Safe Driving Speed of Vehicles

Including anti-rollover speed

Restraint and Anti-Slip Speed

constraint;

对其进行修正得到安全行驶车速的修正值

并确定环境k_c，路况k_d，历史事故k_m和行驶年限k_n系数；Step 3. Based on the safe driving speed in Step 2

Correct it to get the correction value of the safe driving speed

And determine the environment k _c , road condition k _d , historical accident _{km and driving years k n coefficient} ;

设定车速不同分布区间的主动限速控制的激活条件，并确定不同车速分类下的激活条件值

基于非线性算法对车辆车速控制，根据不同的激活条件获取车辆纵向方向的总驱动力T_des；根据多约束下的最优目标函数

求解τ_r∈[τ_r0,1]中最优转矩分配系数

获得电机最优转矩驱制动转矩

Step 4. Based on the corrected value of the safe driving speed in Step 3

Set the activation conditions of active speed limit control in different distribution intervals of vehicle speed, and determine 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 _des in the longitudinal direction of the vehicle is obtained according to different activation conditions; according to the optimal objective function under multiple constraints

Solve the optimal torque distribution coefficient in τ _r ∈[τ _r0 ,1]

Obtain the optimal torque of the motor to drive the braking torque

成本函数主要包括侧向路径跟踪偏差，车辆系统状态变量，方向盘转角的变化率，加速度跟踪偏差,加速度导数变化率和安全因数项；其中，约束条件给出了车轮转角约束，车辆状态约束以及加速度约束，进而获取车辆的前轮转角。Step 5. Based on the discrete vehicle nonlinear dynamics model x(T _k+1 )=F(x(T _k ), u(T _k )), establish a cost function under nonlinear constraints

The cost function mainly includes lateral path tracking deviation, vehicle system state variables, rate of change of steering wheel angle, acceleration tracking deviation, rate of change of acceleration derivative and safety factor term; among them, the constraints give wheel angle constraints, vehicle state constraints and acceleration constraints, and then obtain the front wheel angle of the vehicle.

为：Further, in step 3, the correction value of the safe driving speed

for:

The vehicle adaptive parameter adjustment strategy for environment and driving recognition fully considers four different factors that mainly affect vehicle safety, such as environment k _c , road conditions k _d , historical accidents k _m and driving years k _n . Make corrections and adjust the parameters as shown in Table 1.

Table 1. Environment k _c , road condition k _d , historical accident k _m and driving years k _n coefficients

Further, the activation conditions of the active speed limit control in the different distribution intervals of the vehicle speed in step 4 specifically include:

The active speed limit of the vehicle is designed based on the sliding mode control, and the sliding mode surface is defined according to the speed limit:

In order to effectively reduce the high-frequency jitter caused by frequent crossing of the sliding mode surface, the reaching law of the saturation function is constructed:

分别表示滑模的增益和滑模面边界厚度；Among them, K _x ,

represent the gain of the sliding mode and the thickness of the boundary of the sliding mode surface, respectively;

The equation of longitudinal motion of the vehicle is:

Among them, F _x is the resultant force acting in the longitudinal direction of the vehicle; by combining the above equations, the expected longitudinal resultant force of the vehicle obtained by the active speed limit control based on sliding mode control is:

In order to coordinate vehicle desired speed control and active speed limit control, the activation conditions of longitudinal motion control are designed:

According to the current speed distribution interval of the vehicle, the activation conditions of the active speed limit control are determined.

Table 2. Activation condition values at different vehicle speeds

为Further, in step 4, the optimal objective function under multiple constraints

for

进而可以求得电机最优的驱制动转矩

Among them, the adaptive weight adjustment coefficients Π _η , Π _τ , Π _θ are the energy weight coefficient, load transfer weight coefficient and motor failure form weight coefficient respectively; η _m is the working efficiency function of the motor, τ _r is the torque distribution of the rear axle wheels proportional coefficient; T _i is the driving and braking torque of each motor; through the effective set algorithm, the optimal torque distribution coefficient between shafts can be solved

Then, the optimal driving and braking torque of the motor can be obtained.

The value of the threshold factor τ _r0 is defined as:

In order to balance the effect of braking force on each wheel, the mechanical braking force is evenly distributed to four wheels:

The basic driving and braking torque T _{ij_b} of the vehicle obtained by path tracking can be expressed as:

m∈{d,b},其中，m＝d,m＝b分别表示电机的驱动力矩或制动力矩；In the path tracking control of the distributed drive vehicle, the torque of the left and right wheels is evenly distributed, and the maximum torque and minimum value of the coaxial wheels are defined.

m∈{d,b}, where m=d, m=b respectively represent the driving torque or braking torque of the motor;

表示随着电机转速n_mij变化的外特性曲线；根据驱动工况和制动工况的不同，广义的驱动电机总需求转矩最大约束可以表示为：in,

Represents the external characteristic curve that changes with the motor speed n _mij ; according to the different driving conditions and braking conditions, the generalized maximum constraint of the total demand torque of the driving motor can be expressed as:

Among them, T ^b_max represents the maximum braking torque that each wheel can generate;

Assuming that the torque distribution coefficient of the rear axle is τ _r , the torque distribution of each motor can be obtained:

The work of the motor is divided into driving condition and braking condition. The working efficiency η _m of the two different conditions can be expressed as:

Among them, η _d (n _wij , T _ij ), η _b (n _wij , T _ij ) represent the three-dimensional efficiency distribution map under the motor driving and braking conditions, respectively;

According to the acceleration in the longitudinal direction obtained by inertial navigation, the load transfer of the front and rear axles is expressed as follows:

If the motor fails and has different failure forms, the original allocation method will no longer be applicable. In order to improve the adaptability and robustness of the distributed drive vehicle to the motor failure, the weight coefficient adjustment method for different motor failures and failure forms is determined. as shown in Table 3.

Table 3. Weight coefficient adjustment methods for different motor failures and failure modes

为：Further, the cost function in step 5

for:

内，

是规划路径上的参考轨迹点(X_ref,Y_ref)，参考横摆角速度ψ_ref和参考速度

成本函数的第一项，第二项，第三项，第四项和第五项分别通过维数为

的半正定加权矩阵W惩罚跟踪偏差，维数为

的半正定加权矩阵Q来惩罚系统状态变量，维数为一维

的半正定加权矩阵R来惩罚加速度，维数为一维

的半正定加权矩阵Θ来惩罚加速度导数da_x以及参数为ρ的安全因子；For each sampling instant (k=0,1,...,N _c ), the nonlinear model prediction controls in the specified future prediction time domain

Inside,

are the reference trajectory points (X _ref , Y _ref ) on the planned path, the reference yaw angular velocity ψ _ref and the reference velocity

The first, second, third, fourth, and fifth terms of the cost function pass through the dimensions of

The positive semi-definite weighting matrix W penalizes tracking bias with dimension

The positive semi-definite weighting matrix Q is used to penalize the state variables of the system, and the dimension is one-dimensional

The positive semi-definite weighting matrix R to penalize the acceleration, with one dimension

The positive semi-definite weighting matrix Θ to penalize the acceleration derivative da _x and the safety factor with parameter ρ;

In the first and second terms of the objective function, the path constraints in the nonlinear model predictive control problem formula include the geometric constraints and physical constraints of the system; the path constraints include the front wheel rotation angle, longitudinal speed and yaw rate constraints:

-δ _{f_max} -δ _{f_Δ} ≤δ _f ≤δ _{f_max} +δ _{f_Δ}

分别表示前轮转角，纵向车速和横摆角速度的极限约束，δ_{f_Δ},

分别表示前轮转角，纵向车速和横摆角速度的软约束；Among them, δ _{f_max} ,

respectively represent the limit constraints of front wheel angle, longitudinal vehicle speed and yaw rate, δ _{f_Δ} ,

respectively represent the soft constraints of the front wheel angle, longitudinal vehicle speed and yaw rate;

The acceleration constraint conditions are constrained according to the different driving conditions of the vehicle. The basic idea is that when the vehicle driving conditions are bad, the acceleration of the vehicle should be limited to a small range. When the vehicle is in a low speed and good condition, the acceleration of the vehicle The constraints can be relaxed, and different constraint value ranges are set for the vehicle acceleration according to the three categories of severe working conditions, general working conditions and excellent working conditions, as shown in Table 4.

Table.4 Vehicle Acceleration Setting Different Constraint Value Ranges

Working condition category Bad working conditions General working conditions Excellent working condition a_x -1<a_x<1 -2<a_x<2 -4<a_x<4

Beneficial effects:

The invention uses the distributed driving unmanned vehicle path tracking method, which can ensure the safety of the vehicle while the side tracking of the vehicle can minimize the path error under the premise of limiting the active safety of vehicle side slip and rollover. At the same time, in the case of vehicle safety instability trend, and at the same time when the vehicle lateral tracking deviation is appropriately sacrificed, the safety of the vehicle is first ensured, and the path tracking and safety capabilities of the unmanned vehicle are comprehensively improved.

Description of drawings

1 is a schematic diagram of a vehicle longitudinal motion control tracking method provided by the present invention

Fig. 2 is a schematic diagram of a vehicle path tracking method provided by the present invention

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

The present invention provides a path tracking optimization control method for distributed driving of unmanned vehicles, as shown in FIG. 2 , which specifically includes the following steps:

横向加速度

和横摆角速度

通过电机控制器实时获取电机的转速n_mij和电机输出转矩T_ij。Step 1. Use GPS/INS to measure vehicle position (X, Y), heading angle ψ, vehicle longitudinal acceleration

Lateral acceleration

and yaw rate

The rotational speed n _mij of the motor and the output torque T _ij of the motor are acquired in real time through the motor controller.

利用车辆动力学理论限制车辆安全行驶车速

包括防侧翻速度

约束和防侧滑速度

约束。Step 2. Based on the longitudinal speed of the vehicle obtained in Step 1

Using Vehicle Dynamics Theory to Limit the Safe Driving Speed of Vehicles

Including anti-rollover speed

Restraint and Anti-Slip Speed

constraint.

并对其进行修正。为了提高无人驾驶车辆对环境、工况和自身能力的适应性，提出了一种基于环境和驾驶识别的车辆自适应参数调整策略，并确定了环境k_c，路况k_d，历史事故k_m和行驶年限k_n系数。Step 3. Based on the safe driving speed in Step 2

and amend it. In order to improve the adaptability of unmanned vehicles to the environment, working conditions and their own capabilities, a vehicle adaptive parameter adjustment strategy based on environment and driving recognition is proposed, and the environment k _c , road conditions k _d , and historical accident km _m are determined. and driving years k _n coefficient.

设计一种车速不同分布区间的主动限速控制的激活条件，并确定了不同车速分类下的激活条件值

基于非线性算法对车辆车速控制，根据不同的激活条件获取车辆纵向方向的总驱动力T_des。提出一种新得多约束下的最优目标函数

该函数以电机的驱制动效率，电机的失效形式以及车辆加减速过程中的载荷转移影响多目标，求解τ_r∈[τ_r0,1]中最优转矩分配系数

获得电机最优转矩驱制动转矩

Step 4. Based on the corrected value of the safe driving speed in Step 3

An activation condition of active speed limit control with different speed distribution intervals is designed, and the activation condition values under different vehicle speed classifications are determined

The vehicle speed is controlled based on a nonlinear algorithm, and the total driving force T _des in the longitudinal direction of the vehicle is obtained according to different activation conditions. Propose a new optimal objective function under many constraints

This function calculates the optimal torque distribution coefficient in τ _r ∈[τ _r0 ,1] based on the drive efficiency of the motor, the failure form of the motor and the load transfer during the acceleration and deceleration of the vehicle.

Obtain the optimal torque of the motor to drive the braking torque

成本函数主要包括侧向路径跟踪偏差，车辆系统状态变量，方向盘转角的变化率，加速度跟踪偏差,加速度导数变化率和安全因数项。其中，约束条件给出了车轮转角约束，车辆状态约束以及加速度约束，利用一种快速的方法获取车辆的前轮转角。Step 5. Based on the discrete vehicle nonlinear dynamics model x(T _k+1 )=F(x(T _k ), u(T _k )), establish a cost function under nonlinear constraints

The cost function mainly includes lateral path tracking bias, vehicle system state variables, rate of change of steering wheel angle, acceleration tracking bias, rate of change of acceleration derivative and safety factor term. Among them, the constraint conditions give the wheel angle constraint, vehicle state constraint and acceleration constraint, and a fast method is used to obtain the front wheel angle of the vehicle.

具体包括：Safe driving speed as described in step 2

Specifically include:

The active safety and handling stability of the vehicle need to prevent the side slip and rollover problems caused by the vehicle during the steering process, and it is closely related to the speed of the vehicle.

In order to prevent the vehicle from slipping due to insufficient lateral tire force, the lateral inertial force of the vehicle cannot exceed the maximum tire adhesion limit provided by the ground:

分别为通过算法估计出来的路面附着系数和坡度。where m is the mass of the vehicle, a _y is the lateral acceleration of the vehicle,

are the road adhesion coefficient and slope estimated by the algorithm, respectively.

The lateral acceleration of the vehicle is:

转向半径为转向角和轮胎侧偏角的函数：where _RT is the turning radius. Steady state steering

Steering radius is a function of steering angle and tire slip angle:

Among them, l _f and l _r represent the distance from the front and rear wheels of the vehicle to the center of mass of the vehicle, respectively.

The speed constraint relationship of vehicle anti-skid can be expressed as

Among them, S _slip is the safety factor of vehicle sideslip.

When the vehicle is turning, the lateral acceleration of the vehicle causes a vertical load transfer between the left and right wheels of the vehicle. The sign of the vehicle rolling over is that the vertical load of the wheel on one side of the vehicle is too small due to the rolling movement or lateral movement, and the wheel loses its ability to adhere. excessive transfer between. The anti-rollover speed limit should be satisfied when the wheel torque is evenly distributed, and the road surface can provide enough adhesion to overcome the driving resistance of the vehicle.

When the vehicle accelerates laterally, the side with less vertical wheel load can overcome the vehicle's running resistance F _w due to the transfer of the vehicle load:

Among them, ρ, C _d , and A represent air density, air resistance coefficient and windward area, respectively, and _fr represent wheel rolling resistance coefficient.

The rollover constraint can be expressed as:

Among them, H _b represents the height of the center of mass of the vehicle. d represents the distance from the left or right wheel of the vehicle to the center of mass of the vehicle, and assumes that the front and rear wheel tracks are equal.

The vehicle rollover speed constraint is expressed as:

Among them, S _over is the safety factor of vehicle rollover.

In summary, the upper limit of the vehicle's longitudinal speed is determined by the vehicle side slip limit and the vehicle rollover limit constraint

是车辆容许的最大行驶车速。in,

is the maximum speed allowed by the vehicle.

A vehicle adaptive parameter adjustment strategy based on environment and driving recognition described in step 3 specifically includes:

In order to improve the adaptability of unmanned vehicles to the environment, working conditions and their own capabilities, a vehicle adaptive parameter adjustment strategy based on environment and driving recognition is proposed:

The vehicle adaptive parameter adjustment strategy for environment and driving recognition fully considers the environment k _c , road conditions k _d , historical accidents k _m and driving years k _n four different factors that mainly affect vehicle safety. Make corrections and adjust the parameters as shown in Table 1.

Table 1. Environment k _c , road condition k _d , historical accident k _m and driving years k _n coefficients

According to the identification of the environment and road conditions, the vehicle speed safety threshold is adjusted online through the weight coefficient. Active speed limit control can intervene in the speed of the vehicle to ensure the driving safety of the vehicle. 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 to intervene in the vehicle speed to prevent the vehicle from becoming unstable due to the high vehicle speed.

As shown in Figure 1, in step 4, the activation conditions of active speed limit control in different distribution intervals of vehicle speed and the optimal objective function under multiple constraints include:

The active speed limit of the vehicle is designed based on the sliding mode control, and the sliding mode surface is defined according to the speed limit:

In order to effectively reduce the high-frequency jitter caused by frequent crossing of the sliding mode surface, the reaching law of the saturation function is constructed:

分别表示滑模的增益和滑模面边界厚度，K_x过小，则收敛速度慢；过大，容易导致高频振荡，需要合理的选值。Among them, K _x ,

Respectively represent the gain of the sliding mode and the thickness of the boundary of the sliding mode surface. If K _x is too small, the convergence speed will be slow; if it is too large, it is easy to cause high-frequency oscillation, and a reasonable value should be selected.

The equation of longitudinal motion of the vehicle is:

Among them, F _x is the resultant force acting in the longitudinal direction of the vehicle. By combining the above equations, the expected longitudinal resultant force of the vehicle obtained by the active speed limit control based on sliding mode control is:

In order to coordinate vehicle desired speed control and active speed limit control, the activation conditions of longitudinal motion control are designed:

According to the current speed distribution interval of the vehicle, the activation conditions of the active speed limit control are determined.

Table 2. Activation condition values at different vehicle speeds

求解车辆希望合力矩；否则，采用滑模控制获得车辆期望纵向合力F_x,d，使实际车速跟踪参考车速

When the active speed limit control of the vehicle is activated, the desired longitudinal resultant force of the vehicle obtained by the above-mentioned active speed limit control

Solve the desired resultant moment of the vehicle; otherwise, use sliding mode control to obtain the desired longitudinal resultant force F _x,d of the vehicle, so that the actual vehicle speed tracks the reference vehicle speed

分别表示滑模的增益和滑模面边界厚度。Among them, K _x2 ,

are the gain of the sliding mode and the thickness of the boundary of the sliding mode surface, respectively.

Then, the vehicle longitudinal motion correction total expected torque T _des is:

优化分配车轮的转矩，使得车辆满足主动安全性的前提下，能量消耗最低。The corrected total desired torque T _des of the longitudinal motion of the vehicle needs to be reasonably distributed to each driving wheel, which is a typical overdrive structure. Considering the driving efficiency of the motor, the failure mode of the motor and the load transfer during the acceleration and deceleration of the vehicle, an optimal objective function under multiple constraints is proposed

The torque of the wheels is optimally distributed, so that the energy consumption is the lowest under the premise of satisfying the active safety of the vehicle.

进而可以求得电机最优的驱制动转矩

最优目标函数将进一步地进行解释和阐述。Among them, the intelligent adaptive weight adjustment coefficients Π _η , Π _τ , Π _θ are the energy weight coefficient, the load transfer weight coefficient and the motor failure form weight coefficient, respectively. η _m is the working efficiency function of the motor, and τ _r is the torque distribution proportional coefficient of the rear axle wheels. T _i is the driving torque of each motor. Through the effective set algorithm, the optimal torque distribution coefficient between shafts can be solved

Then, the optimal driving and braking torque of the motor can be obtained.

The optimal objective function will be further explained and elaborated.

Considering that there may be symmetry in the distribution of the motor systems on both sides, in order to prevent the jump in torque distribution during distribution, the rear-wheel-drive braking is given priority, mainly considering that the front wheels are the driving wheels. It affects the output of the lateral force during the steering process of the vehicle, so the rear axle wheel torque distribution coefficient τ _r ∈ [τ _r0 ,1] is selected. Among them, the value of the threshold factor τ _r0 is defined as:

The braking condition is slightly different from the driving condition, because in the braking condition, there is also mechanical braking. In order to balance the effect of braking force on each wheel, the mechanical braking force is evenly distributed to the four wheels.

The basic driving and braking torque T _{ij_b} of the vehicle obtained by path tracking can be expressed as:

m∈{d,b},其中，m＝d,m＝b分别表示电机的驱动力矩或制动力矩。In the path tracking control of the distributed drive vehicle, the torque of the left and right wheels is evenly distributed, and the maximum torque and minimum value of the coaxial wheels are defined.

m∈{d,b}, where m=d and m=b respectively represent the driving torque or braking torque of the motor.

表示随着电机转速n_mij变化的外特性曲线。根据驱动工况和制动工况的不同，广义的驱动电机总需求转矩最大约束可以表示为：in,

Represents the external characteristic curve that varies with the motor speed n _mij . According to the different driving conditions and braking conditions, the generalized maximum constraint on the total demand torque of the drive motor can be expressed as:

Among them, T ^b_max represents the maximum braking torque that each wheel can generate.

Assuming that the torque distribution coefficient of the rear axle is τ _r , the torque distribution of each motor can be obtained:

The work of the motor is divided into driving condition and braking condition. The working efficiency η _m of the two different conditions can be expressed as:

Among them, η _d (n _wij , T _ij ), η _b (n _wij , T _ij ) represent the three-dimensional efficiency distribution map under the motor driving and braking conditions, respectively.

When the load of the front and rear axles is transferred, it will affect the vertical load change of each tire, so the adhesion limit of each tire will change greatly. In order to consider the safety of the vehicle, the wheel with larger vertical force should be divided Greater drive torque, on the contrary, the wheel with less vertical force should output less drive torque. According to the acceleration in the longitudinal direction obtained by inertial navigation, the load transfer of the front and rear axles is expressed as follows:

If the motor fails and has different failure forms, the original allocation method will no longer be applicable. In order to improve the adaptability and robustness of the distributed drive vehicle to motor failure, a weight coefficient adjustment for different motor failures and failure forms is proposed. method, as shown in Table 3.

Table 3. Weight coefficient adjustment methods for different motor failures and failure modes

The distributed driving unmanned vehicle path tracking method described in step 5 specifically includes:

无噪声时间连续的分布式驱动无人驾驶车辆动力学模型表示为：The goal of active front-wheel control is to design a control strategy such that the vehicle follows a time-dependent, real-time generated reference trajectory that guarantees uncertain behavior caused by vehicle model errors or environmental disturbances by setting soft constraints on the cost function. given time

The noise-free time-continuous distributed driving unmanned vehicle dynamics model is expressed as:

n_x＝length(x),n_u＝length(u)为解析向量映射函数，u(t)是系统控制输入，包括前轮转角δ_f，x(t)是系统的状态向量，其中包括车辆纵向车速

侧向车速

和横摆角速度

in,

n _x =length(x),n _u =length(u) is the analytic vector mapping function, u(t) is the system control input, including the front wheel angle δ _f , x(t) is the state vector of the system, including the vehicle longitudinal speed

lateral speed

and yaw rate

和采用时刻

通过上式，扰动的欧拉离散模型可以被定义为：With discrete instantaneous times T ₀ <T ₁ <T ₂ <…, at a given sampling period

and adoption moment

Through the above formula, the perturbed Euler discrete model can be defined as:

Among them, the discrete function F is obtained analytically or implicitly based on numerical integration. Furthermore, assuming that the control input u(T _k ) is a piecewise constant over the time interval [T _k , T _k+1 ], to simplify the representation, define x _k :=x(T _k ),u _k :=u(T _k ).

侧向车速

和横摆角速度

作为状态，双轨模型可以由下式表示：The longitudinal speed of the vehicle in the vehicle coordinate system

lateral speed

and yaw rate

As states, the two-track model can be represented by:

Among them, F _xij , F _yij , i∈{f,r}, j∈{l,r} represent the longitudinal force and lateral force of each tire in the vehicle coordinate system. m represents the mass of the vehicle, and _Izz represents the moment of inertia of the vehicle around the z-axis in the vehicle coordinate system. The vehicle position (X, Y) in the absolute coordinate system can be obtained by the kinematic equation:

The tire force in the vehicle coordinate system can be obtained from the tire force in the tire coordinate system:

Among them, F _wxij , F _wyij represent the tire longitudinal force and the wheel lateral force in the tire coordinate system, respectively. The vehicle tire model describes the calculation of tire forces. Under pure longitudinal/sideways conditions, the nominal tire longitudinal force F _wxij,n and nominal tire lateral force F _wxij,n of each tire 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 )))

Among them, s _ij , α _ij , F _zij , i∈{f,r}, j∈{l,r} represent the slip ratio, slip angle and vertical force of each tire respectively; μ hij , _h∈ {x ,y},i∈{f,r},j∈{l,r} represents the road friction coefficient, B _hij ,C _hij ,E hij , _h∈ {x,y},i∈{f,r},j ∈{l,r}, denote tire stiffness factor, shape factor and curvature factor, respectively.

In the joint condition, that is, when the tire slip rate and slip angle are not zero, the coupling between the tire longitudinal force and the tire lateral force can be represented by the friction circle:

Although the above formula does not establish a direct relationship between the tire lateral force and the tire slip angle, the friction ellipse model is used to calculate the tire lateral force under combined conditions because of its simplicity and sufficient accuracy.

The tire slip angle represents the angle between the longitudinal direction of the tire and the direction of the tire speed, and it can be expressed as:

Among them, v _wxij , v _wyij represent the longitudinal speed and lateral speed of the wheel center in the tire coordinate system, respectively, and they can be calculated by the following formulas:

Among them, v _xij , v _yij respectively represent the longitudinal speed and lateral speed at each wheel center in the vehicle coordinate system, and they can be calculated by the following formulas:

The tire slip rate is calculated slightly differently under driving conditions and braking conditions. According to the different driving conditions, the tire slip rate s _ij can be obtained by the following formula:

Among them, ω _wij represents the wheel angular velocity, and R _we represents the effective rolling radius of the wheel.

Since the lateral or lateral acceleration/deceleration motion of the vehicle will cause the load transfer between the left and right or front and rear wheels of the vehicle, the vertical force of the tire is expressed as follows:

Among them, K _φf and K _φr are the roll stiffnesses of the front and rear suspensions, respectively. h _rf , h _rr are the roll centers of the front and rear suspensions, respectively.

Wheel dynamics establishes the equation between the wheel drive braking torque and the wheel longitudinal force:

Among them, I _w represents the moment of inertia of the wheel, and b _w represents the wheel damping coefficient.

In fact, only the front steering wheel is controllable in this distributed driving unmanned vehicle, and it is assumed that the steering angle of the front left wheel and the front right wheel are the same, namely: δ _fl =δ _fl =δ _f , δ _rl =δ _rr =0.

使得车辆实际行驶路径能够跟踪到期望路径，同时保证路径跟踪的平顺性和安全性。成本函数主要包括侧向路径跟踪偏差，车辆系统状态变量，方向盘转角的变化率，加速度跟踪偏差,加速度导数变化率和安全因数项。using a cost function

The actual driving path of the vehicle can be tracked to the desired path, while ensuring the smoothness and safety of path tracking. The cost function mainly includes lateral path tracking bias, vehicle system state variables, rate of change of steering wheel angle, acceleration tracking bias, rate of change of acceleration derivative and safety factor term.

内，

是规划路径上的参考轨迹点(X_ref,Y_ref)，参考横摆角速度ψ_ref和参考速度

成本函数的第一项，第二项，第三项，第四项和第五项分别通过维数为

的半正定加权矩阵W惩罚跟踪偏差，维数为

的半正定加权矩阵Q来惩罚系统状态变量，维数为一维

的半正定加权矩阵R来惩罚加速度，维数为一维

的半正定加权矩阵Θ来惩罚加速度导数da_x以及参数为ρ的安全因子。For each sampling instant (k=0,1,...,N _c ), the nonlinear model prediction controls in the specified future prediction time domain

Inside,

are the reference trajectory points (X _ref , Y _ref ) on the planned path, the reference yaw angular velocity ψ _ref and the reference velocity

The first, second, third, fourth, and fifth terms of the cost function pass through the dimensions of

The positive semi-definite weighting matrix W penalizes tracking bias with dimension

The positive semi-definite weighting matrix Q is used to penalize the state variables of the system, and the dimension is one-dimensional

The positive semi-definite weighting matrix R to penalize the acceleration, with one dimension

The positive semi-definite weighting matrix Θ to penalize the acceleration derivative da _x and a safety factor of parameter ρ.

In the first and second terms of the objective function, the path constraints in the formulation of the nonlinear model predictive control problem include the geometric constraints and physical constraints of the system. In fact, considering the uncertainty caused by unknown disturbances and modeling errors, to improve the robustness in objective function control, the constraints are set as soft constraints through relaxation factors. Path constraints include nose wheel angle, longitudinal velocity, and yaw velocity constraints:

-δ _{f_max} -δ _{f_Δ} ≤δ _f ≤δ _{f_max} +δ _{f_Δ}

分别表示前轮转角，纵向车速和横摆角速度的极限约束，δ_{f_Δ},

分别表示前轮转角，纵向车速和横摆角速度的软约束。Among them, δ _{f_max} ,

respectively represent the limit constraints of front wheel angle, longitudinal vehicle speed and yaw rate, δ _{f_Δ} ,

Soft constraints representing the front wheel angle, longitudinal vehicle speed and yaw rate, respectively.

In the third term of the objective function, in order to make the unmanned driving in the lateral path tracking, to prevent the jump and unreasonable changes of the expected front wheel angle due to the mathematical solution process, the purpose is to control the front wheel angle to track When the lateral desired trajectory is in line with the actual engineering application, it ensures the smooth change of the front wheel angle.

The acceleration constraints are constrained according to the different driving conditions of the vehicle. The basic idea is that when the vehicle is in bad driving conditions, such as rain, snow, and fog, the acceleration of the vehicle should be limited to a small range. Under the working conditions, the acceleration of the vehicle can be relaxed, and different constraint value ranges are set for the acceleration of the vehicle according to the three categories of severe working conditions, general working conditions and excellent working conditions, as shown in the table.

Table.4 Vehicle Acceleration Setting Different Constraint Value Ranges

Working condition category Bad working conditions General working conditions Excellent working condition a_x -1&lt;a_x&lt;1 -2&lt;a_x&lt;2 -4&lt;a_x&lt;4

In order to solve the optimization problem of nonlinear constraints, based on the direct multiple shooting method, the optimization problem of infinite dimension constraints has been transformed into a nonlinear programming, and the sequence quadratic programming of a real-time iterative method is used to solve the problem under each control time step. Control input. One iteration is performed for each time control time step, and the state warm-start and control trajectory from one time step to the next are used for continuity. Under reasonable assumptions, when there are errors and external disturbances, the stability of the obtained closed-loop system can also be guaranteed accordingly. It does not seem to be suitable for solving nonlinear programming problems 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. Motion feasible constraint perception. Therefore, this scheme is suitable for nonlinear control optimization solution. Applying the block-structure decomposition technique with low-rank updates to an iterative solver in the original active set algorithm with a custom initialization method yields a simple, efficient, and reliable solver suitable for embedded control hardware.

的值定义为预测的状态值

它由当前状态估计

和存储在缓冲器中的过去输入信号u计算。这种时滞补偿对于保持鲁棒性和高控制性能具有重要意义。其中，实时求解器算法如表所示。To compensate for the time delay Td caused by the vehicle network communication and the actuator interface at time _t , put

The value of is defined as the predicted state value

It is estimated by the current state

and the past input signal u stored in the buffer is calculated. This time-delay compensation is important for maintaining robustness and high control performance. Among them, the real-time solver algorithm is shown in the table.

To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within 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,

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,

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,

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

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

Images