A vehicle longitudinal and lateral motion cooperative control method based on a fast solving algorithm

Abstract

The application relates to a vehicle longitudinal and lateral motion cooperative control method based on a fast solving algorithm, which comprises the following steps: calculating a desired yaw angular velocity according to a steering wheel turning angle and a current vehicle running speed; constructing a nonlinear optimization problem according to the desired yaw angular velocity and a current actual motion state of the vehicle, wherein an objective function of the nonlinear optimization problem is used to track the desired yaw angular velocity, and meanwhile, lateral speed and tire slip rate of the vehicle are inhibited; solving the nonlinear optimization problem to calculate desired slip rates of four tires; calculating additional torques of the tires according to actual slip rates and desired slip rates of the tires; and sending the additional torques of the tires into an executor of the vehicle for cooperative control. Compared with the prior art, the application can effectively inhibit the tire slip rate, avoid vehicle skidding, and the provided fast solving algorithm can greatly improve solving efficiency and improve real-time performance.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vehicle longitudinal and lateral motion cooperative control, and particularly relates to a vehicle longitudinal and lateral motion cooperative control method based on a model predictive control architecture. BACKGROUND

[0002] If the driver operates improperly during the driving process of a vehicle, such as emergency acceleration, deceleration, emergency steering and the like, the vehicle may deviate from a stable driving state, and if not controlled, the vehicle may further lose stability and cause an accident. Therefore, a corresponding controller needs to be designed to help the vehicle improve stability. Under extreme working conditions, the vehicle is a complex nonlinear system, and the longitudinal motion and lateral motion of the vehicle are coupled together. Therefore, when designing the controller, a high-precision vehicle dynamics model needs to be used to describe the state of the vehicle to meet the requirements of stability control. In addition, considering the limited execution capability of the vehicle actuator, the controller also needs to consider the constraints of the control amount of the vehicle. During the driving process of the vehicle, the state of the vehicle in the future needs to be predicted to find the risk of instability in time and pull the vehicle back to the normal driving state. In summary, the vehicle longitudinal and lateral motion cooperative control under extreme working conditions can be summarized as a multi-objective optimization problem with constraints, and therefore the model predictive control is a relatively ideal solution. On the other hand, the vehicle is a very typical fast-changing system, and therefore the stability control period of the vehicle is short and the frequency is high. However, due to cost or power consumption and the like, the existing vehicle-mounted controller often has very limited computing capability and cannot meet the real-time requirements. Therefore, in summary, the current vehicle longitudinal and lateral motion cooperative control based on model predictive control has the following problems:

[0003] 1. In the existing scheme, in order to simplify the design of the controller and reduce the complexity of the calculation, an approximate linear model is often used to describe the vehicle motion. However, the vehicle is actually a typical nonlinear time-varying system, and the approximate linear model will face problems such as reduced accuracy and reduced performance of the controller when the vehicle enters a highly nonlinear region. Therefore, it is necessary to use a high-precision nonlinear model to describe the motion state of the vehicle.

[0004] 2. In the existing vehicle stability control scheme, the coupling of the longitudinal and lateral motion of the vehicle is often not considered. However, in practice, the longitudinal and lateral tire forces of the vehicle have complex nonlinear coupling characteristics. If not considered, the vehicle may lose stability under certain extreme working conditions.

[0005] 3. In the control scheme based on model predictive control, a nonlinear constraint optimization problem needs to be solved, which has a large amount of calculation. The traditional solving algorithm (such as interior point method and sequential quadratic programming) needs a long solving time when solving the nonlinear optimization problem, and cannot meet the real-time requirements of vehicle-mounted applications. Therefore, the solving method needs to be improved to improve the solving speed so that it can meet the real-time requirements of vehicle-mounted applications.

[0006] Chinese patent CN202010020411.2 discloses a model predictive control fast solving method for vehicle-mounted applications. For the convenience of solving, the established system model is a low-order single control quantity system, the vehicle model only considers the lateral and yaw motion, and the longitudinal motion of the vehicle is not considered, and the tire model is a pure side slip tire model. In practice, the tire force of the vehicle is coupled with the longitudinal and lateral directions, and the vehicle model constructed by the scheme has poor accuracy. In the scheme, the controller directly generates an additional yaw moment and is distributed by the lower layer average distribution strategy, without considering the slip of the tire in the real situation, and cannot inhibit it. SUMMARY

[0007] The present application is directed to the problem of vehicle longitudinal and lateral stability control under extreme driving conditions, and a controller based on the principle of model predictive control is designed.

[0008] The object of the present application can be achieved by the following technical solutions:

[0009] A vehicle longitudinal and lateral motion cooperative control method based on a fast solving algorithm, the method comprising the following steps:

[0010] According to the steering wheel angle and the current vehicle speed, the expected yaw angular velocity is calculated;

[0011] According to the expected yaw angular velocity and the current actual motion state of the vehicle, a nonlinear optimization problem is constructed, and the objective function of the nonlinear optimization problem is used to track the expected yaw angular velocity, while also inhibiting the lateral velocity and tire slip rate of the vehicle;

[0012] The expected slip rate of the four tires is calculated by solving the nonlinear optimization problem;

[0013] According to the actual slip rate and the expected slip rate of the tire, the additional torque of each tire is calculated;

[0014] The additional torque of each tire is sent to the actuator of the vehicle for cooperative control;

[0015] The nonlinear optimization problem is quickly solved based on the Pontryagin minimum principle, including the following processes:

[0016] A relaxation factor is introduced to transform the state constraints of the system;

[0017] Defining the Hamiltonian function within the prediction horizon The argument of the Hamiltonian function is four tire desired slip ratios u(k i ) = [u1(k i ), u2(k i ), u3(k i ), u4(k i )] T ;

[0018] Discretizing the regular equation of the nonlinear optimization problem to obtain the necessary conditions for the optimal control, and according to the extreme value principle, obtaining the terminal conditions of the nonlinear optimization problem;

[0019] The original Hamiltonian function is Taylor expanded, and the Hamiltonian function is converted into a multivariate quadratic function about the argument u(k i ) = [u1(k i ), u2(k i ), u3(k i ), u4(k i )] T ;

[0020] Let Solve the multivariate quadratic function to obtain the stationary point P s of the Hamiltonian function;

[0021] The stationary point P s is the minimum point of the Hamiltonian function , and the explicit optimal control amount at each time is obtained, that is, the desired slip ratio of each tire.

[0022] Further, the desired yaw rate of the vehicle is calculated using a second-order reference model, and the transfer function between the front wheel angle δ f of the vehicle and the desired yaw rate γ ref can be expressed as:

[0023]

[0024] Wherein, the stability factor of the vehicle is defined as The distance between the front and rear axles is defined as L = L f + L r ; The natural oscillation frequency of the second-order reference model system is defined as The damping coefficient of the second-order reference model system is The yaw rate steady-state gain is The yaw rate differential coefficient is defined as m is the mass of the vehicle, I zis the moment of inertia of the vehicle rotating around the center of mass, V x is the longitudinal velocity of the vehicle, L f and L r are the front and rear half-axle lengths, C f and C r are the front and rear axle tire stiffnesses.

[0025] Further, the upper limit value of the desired yaw rate is defined as the desired yaw rate γ ref satisfies the constraint |γ ref |≤γ up , where μ denotes the friction coefficient of the road, g represents the gravity coefficient, V x is the longitudinal velocity of the vehicle.

[0026] Further, the nonlinear optimization problem is expressed as:

[0027]

[0028] s.t.-V y,up ≤x2(k i )≤V y,up

[0029] -u up ≤u(k i )≤u up

[0030] In the formula, L1(k i ), L2(k i ), L3(k i ) and L4(k i ) are the objective function sub-items of the tracked yaw rate, the tracked side velocity, the control amount and the control amount rate of change, respectively, Γ1, Γ2, Γ3 and Γ4 are the yaw rate tracking weight coefficient, the side velocity tracking weight coefficient, the control amount weight coefficient and the control amount rate of change weight coefficient, respectively, V y,up and u up are the upper limit value of the side velocity and the upper limit value of the control amount, respectively.

[0031] Further, the center of mass side slip angle constraint of the vehicle is defined as:

[0032]

[0033] According to the relationship between the side velocity and the center of mass side slip angle, the corresponding upper limit value of the side velocity is V y,up =tan(β up )V x , and the vehicle side velocity constraint is |V y |≤V y,up;

[0034] where μ denotes the friction coefficient of the road, g represents the gravity coefficient, V x denotes the longitudinal speed of the vehicle, L f and L r denote the front and rear half shaft lengths, L represents the distance between the front and rear axles, C r denotes the stiffness of the rear axle tires, and m denotes the mass of the vehicle.

[0035] Further, at each time instant k i (k+1≤k i ≤k+N),

[0036] the objective function sub-items for tracking the desired yaw rate γ ref and the desired lateral speed V y,ref are expressed as:

[0037] L1(k i )=[x3(k i )-γ ref ] 2

[0038] L2(k i )=[x2(k i )-V y,ref ] 2

[0039] where N denotes the prediction horizon, the desired lateral speed is set to V y,ref =0, and the lateral speed of the vehicle is constrained within a safety range, i.e., |x2(k i )|≤V y,up

[0040] the objective function sub-items for the control variable and the rate of change of the wheel control variable are expressed as:

[0041] L3(k i ) = u(k i -1) 2

[0042] L4(k i ) = Δu(k i -1) 2

[0043] the control variable input is constrained as |u(k i )|≤u up , where u up denotes the upper limit value of the control variable.

[0044] Further, the objective function sub-items are obtained according to a vehicle dynamics model, and the specific steps are as follows:

[0045] The state vector of the vehicle system is defined as x = [x1, x2, x3] T = [V x , V y , γ] T , V x , V y and γ represent the longitudinal velocity, lateral velocity and yaw rate of the vehicle;

[0046] The control vector of the vehicle system is defined as represent the desired slip ratios of the four tires;

[0047] The Euler discretization method is adopted to discretize the vehicle dynamics model, and the discretization sampling time is T s The discretized vehicle dynamics model is obtained as follows:

[0048]

[0049]

[0050]

[0051] where F xi and F yi represent the longitudinal force and lateral force of the front tire respectively, and the subscript i = 1, 2, 3, 4 represents the left front wheel, right front wheel, left rear wheel and right rear wheel of the vehicle respectively, L f and L r represent the distances from the front and rear axles to the center of mass of the vehicle, m is the mass of the vehicle, I z is the rotational inertia of the vehicle around the center of mass, δ f represents the front wheel steering angle, and d represents the wheelbase of the vehicle.

[0052] Further, the longitudinal force and lateral force of the vehicle tire are described by using a composite slip nonlinear tire model, which is represented as follows:

[0053]

[0054] where μ represents the friction coefficient of the road, F z represents the vertical load of the tire, C represents the stiffness of the tire force, σ sl = (3μF z / C) represents the threshold value of the tire composite slip amount, and σ represents the size of the tire composite slip amount, which is calculated as follows:

[0055]

[0056] where σ x and σy respectively represent the longitudinal and lateral slip amount of the tire, which are calculated by:

[0057]

[0058] wherein κ represents the longitudinal slip ratio of the tire, which can be calculated by the current longitudinal velocity of the vehicle and V x The rotation speed ω of the tire is calculated by:

[0059]

[0060] wherein Re represents the effective rolling radius of the tire, and α represents the side slip angle of the tire, which is calculated by:

[0061]

[0062]

[0063] wherein δ f represents the front wheel rotation angle of the vehicle, and α f represents the side slip angle of the two tires of the front axle, and α r represents the two tires of the rear axle, which are calculated by:

[0064]

[0065] Further, after the nonlinear optimization problem is quickly solved based on the Pontryagin Minimum Principle, the nonlinear optimization problem is converted to finding the optimal Lagrange multiplier initial value, which can satisfy the terminal condition along the optimal necessary condition;

[0066] The optimal Lagrange multiplier initial value is obtained by optimization search using the Nelder-Mead simplex search algorithm, and the specific steps are as follows:

[0067] The Nelder-Mead simplex search algorithm outputs the initial value for iteration;

[0068] The initial value is iterated to obtain the terminal value based on the discretized vehicle dynamics model, the Hamilton function, and the optimal control amount expression obtained by quick solving;

[0069] The terminal value is subjected to terminal condition judgment, and if it does not satisfy, the Nelder-Mead simplex search algorithm is returned to continue searching;

[0070] When the Nelder-Mead simplex search algorithm reaches the maximum number of iterations or satisfies the terminal condition, the optimal Lagrange multiplier initial value is output.

[0071] Further, the additional torque of each tire is calculated using PID control, and the expression is:

[0072]

[0073] Wherein, the subscript i = 1, 2, 3, 4 represents different tire numbers, ΔT i represents the additional torque of each tire, K P and K I respectively represent the proportional coefficient and the integral coefficient, κ i and respectively represent the actual slip ratio at the current time and the expected slip ratio of each tire obtained by the upper controller.

[0074] Compared with the prior art, the present application has the following beneficial effects:

[0075] 1) In the present application, the vehicle system dimension is expanded to three dimensions, and the control quantity dimension is expanded to four dimensions. In order to improve the solving speed and meet the real-time requirements of vehicle application, a fast solving algorithm based on the extremum principle is proposed. In the present application, the extremum principle is extended to high-order multi-control variable systems, and a solving method is provided to obtain the expression of the optimal control law of the high-order nonlinear optimization problem, and the method for the optimal control law to meet the sufficient and necessary conditions of the minimum point, so as to realize the fast solving of the high-order nonlinear problem. Compared with the traditional numerical optimization solving algorithm, the solving efficiency can be greatly improved under similar solving accuracy, and the real-time performance is improved.

[0076] 2) The present application designs a model predictive controller based on a nonlinear vehicle dynamics model for vehicle stability control under extreme conditions. The freedom degree of longitudinal motion of the vehicle is considered in the vehicle model, which greatly improves the model accuracy compared with the traditional linearized approximate model and the second-order model, and effectively improves the vehicle stability under extreme conditions. The coupling nonlinear characteristics of tire longitudinal and lateral forces are considered in the tire model, which further improves the tire force calculation accuracy and the prediction accuracy of the future state of the vehicle under extreme conditions compared with the traditional pure side slip tire model.

[0077] 3) In the lower controller of the present application, a PID controller is designed. The additional torque of the motor is calculated according to the expected tire slip ratio generated by the upper controller and the actual slip ratio of the vehicle at the current time, which can effectively suppress the tire slip ratio and avoid vehicle skidding while improving the vehicle stability. BRIEF DESCRIPTION OF DRAWINGS

[0078] Figure 1 The flow chart of the cooperative control method designed in the present application;

[0079] Figure 2is a schematic diagram of vehicle dynamics model;

[0080] Figure 3 is a schematic diagram of the iteration process based on the extremum principle and Nelder-Mead simplex search algorithm;

[0081] Figure 4 is a control effect diagram solved based on the traditional interior point method;

[0082] Figure 5 is a control effect diagram solved based on the extremum principle designed in the application;

[0083] Figure 6 is a control effect diagram when the controller is closed and no control is applied;

[0084] Figure 7 is a lateral speed comparison diagram in the process of double lane shift;

[0085] Figure 8 is a slip ratio comparison diagram of the four tires in the process of double lane shift; wherein a, b, c and d are the slip ratio diagrams of the four tires respectively;

[0086] Figure 9 is a comparison diagram of the average solving time of two solving algorithms under different prediction horizons;

[0087] Figure 10 is a comparison diagram of the instantaneous solving time of the traditional interior point method under different prediction horizons;

[0088] Figure 11 is a comparison diagram of the instantaneous solving time of the solving algorithm based on the extremum principle under different prediction horizons. DETAILED DESCRIPTION

[0089] The application will be described in detail below in combination with the drawings and specific embodiments. The embodiments are implemented on the premise of the technical solution of the application, and detailed implementation and specific operation processes are given, but the protection scope of the application is not limited to the following embodiments.

[0090] The controller block diagram based on the application is shown in Figure 1 When driving the vehicle, the driver will make the corresponding steering wheel angle, the reference model calculates the expected yaw rate according to the steering wheel angle, and the original expected yaw rate is limited according to the friction coefficient of the road, and then the expected yaw rate is sent to the controller. The controller calculates the corresponding control amount according to the expected yaw rate and the current actual motion state of the vehicle, and the control amount in the application is the expected slip ratio of the four tires. Since the expected slip ratio cannot be directly executed by the vehicle actuator, a PID controller is designed in the lower controller to calculate the additional torque of the tire to track the expected slip ratio.

[0091] In order to verify the model predictive controller and the fast solving algorithm designed in the application, the working condition of vehicle stability control under low adhesion road surface is selected for verification. Firstly, the dynamics model capable of considering the longitudinal and lateral motion of the vehicle is derived; secondly, the appropriate vehicle model is selected in CarSim and the corresponding parameters are obtained; then the simulation working condition is constructed under the low adhesion road surface; then the model predictive controller is designed according to the derived vehicle dynamics model and the objective function, and the fast solving algorithm is used to solve the control quantity; finally, the method described in the application is verified in the joint simulation experiment, and compared with the traditional IPOPT solving algorithm to illustrate the beneficial effects of the application.

[0092] The application specifically comprises the following steps:

[0093] Step one, controller design based on fast solving algorithm: the required control problem is described based on the model predictive control principle, which is described as a nonlinear optimization problem, and the constructed nonlinear optimization problem is solved in real time based on the fast solving algorithm described in the application.

[0094] The controlled object of the application is a four-wheel independent drive distributed drive electric vehicle, the driving road surface is a low friction coefficient road surface, and the control target is to calculate the additional torque of the four tires according to the current motion state of the vehicle, so that the vehicle can track the expected yaw rate, and also suppress the lateral velocity and tire slip rate. The main design process is described as follows. Firstly, a suitable mathematical model is established for the four-wheel independent drive distributed drive electric vehicle.

[0095] 1) Vehicle motion model

[0096] In the application, since the coupling nonlinear characteristics of the longitudinal and lateral motion of the vehicle need to be considered, a three-degree-of-freedom vehicle model capable of simultaneously considering the longitudinal, lateral and yaw motion of the vehicle is adopted. As shown in Figure 2 The dynamics model of the vehicle can be described by the following mathematical equations:

[0097]

[0098] wherein, and respectively represent the derivatives of the longitudinal speed, lateral speed and yaw angle speed of the vehicle, V x ,V y and γ represent the longitudinal speed, lateral speed and yaw angle speed of the vehicle, F xi and F yiThese represent the longitudinal force and lateral force of the front tires, respectively. The subscripts i = 1, 2, 3, 4 represent the left front tire, right front tire, left rear tire, and right rear tire, respectively. L f and L r Let m and I represent the distances from the front and rear axles to the vehicle's center of gravity, respectively, where m is the vehicle's mass, and I is the distance from the front and rear axles to the vehicle's center of gravity. z It is the moment of inertia of the vehicle rotating about its center of mass, δ f d represents the front wheel steering angle of the vehicle, and d represents the left and right wheel track of the vehicle.

[0099] 2) Establishment of the composite skid tire model

[0100] In this invention, to account for the coupled nonlinear characteristics of the longitudinal and lateral tire forces of the vehicle, a composite slip ratio nonlinear tire model is used to describe the longitudinal and lateral tire forces of the vehicle. This tire model can be expressed in the following form:

[0101]

[0102] Where μ represents the friction coefficient of the road surface, F z σ represents the vertical load on the tire, C represents the tire's force stiffness, and σ represents the vertical load on the tire. sl = (3μF) z / C) represents the threshold value of the tire's compound slip, and σ represents the magnitude of the tire's compound slip, which can be calculated as follows:

[0103]

[0104] Where σ x and σ y These represent the longitudinal and lateral slippage of the tire, respectively, and can be calculated as follows:

[0105]

[0106] In the formula, κ represents the longitudinal slip ratio of the tire, which can be obtained by considering the vehicle's current longitudinal speed and V. x The tire rotational speed ω is calculated as follows:

[0107]

[0108] Where Re represents the effective rolling radius of the tire. α represents the tire slip angle, which is divided into front and rear wheels, and their calculation methods are as follows:

[0109]

[0110] Where α f α represents the slip angle of the two tires on the front axle, specifically the tires with subscripts 1 and 2. rThe two tires of the rear axle, i.e. the two tires with subscripts 3 and 4. According to the above definition, the longitudinal side force of the tire can be calculated by:

[0111]

[0112] 3) Vehicle reference model establishment

[0113] In the present application, the main function of the controller is to control the vehicle to track the desired yaw rate while suppressing the lateral velocity and tire slip ratio of the vehicle, so the desired yaw rate needs to be calculated in real time according to the motion state of the vehicle, so the reference model of the vehicle is used here to calculate the desired yaw rate. In the present application, a second-order reference model is used to calculate the desired yaw rate of the vehicle, and the transfer function between the front wheel angle δ f and the desired yaw rate γ ref can be expressed as:

[0114]

[0115] where the stability factor of the vehicle is defined as the distance between the front and rear axles is defined as L = L f + L r . The natural oscillation frequency of the second-order reference model system is defined as the damping coefficient of the second-order reference model system is the yaw rate steady-state gain is the yaw rate differential coefficient is defined as C f and C r in the above expression represent the stiffness of the front and rear axle tires, respectively.

[0116] In this model, the preliminary desired yaw rate signal can be calculated. However, due to the limited adhesion of the road surface, the actual adhesion of the road surface needs to be considered. Here, the upper and lower limit values of the desired yaw rate need to be calculated according to the actual adhesion of the road surface. The upper limit value of the desired yaw rate is defined as and the constraint that the desired yaw rate γ ref should satisfy is |γ ref |≤ γ up . In addition, the stability constraint of the vehicle needs to be considered. Since the stability of the vehicle can be reflected by the lateral velocity, the lateral velocity of the vehicle needs to be constrained to be within a safe range, and here the vehicle's center of mass side slip angle constraint is defined as:

[0117]

[0118] On this basis, the upper limit value of the lateral velocity V y,up = tan(β up )V x , and the lateral velocity constraint |V y |≤V y,up .

[0119] 5) Controller design

[0120] According to the vehicle dynamics model, the longitudinal motion, lateral motion and yaw motion of the vehicle need to be considered in the controller. In order to facilitate the design of the controller, the state vector of the system is defined as x = [x1, x2, x3] T = [V x , V y , γ] T , and the control vector of the system is defined as , i.e. the expected slip ratio of the four tires. In order to facilitate the design of the controller and formula derivation, the vehicle dynamics model needs to be discretized first. In this invention, the Euler discretization method is used to discretize the vehicle dynamics model, and the discretization sampling time is T s , and the discretized vehicle dynamics model is obtained as follows:

[0121]

[0122] In this controller, the expected yaw rate γ ref and the expected lateral velocity V y,ref need to be tracked simultaneously, and the subterm of the objective function at each time k i (k+1≤k i ≤k+N) can be expressed as:

[0123]

[0124] where N represents the prediction horizon. In this invention, in order to improve the stability of the vehicle, the expected lateral velocity is set to V y,ref = 0, i.e. to suppress the magnitude of the lateral velocity as much as possible. In addition, for safety considerations, the lateral velocity of the vehicle should be constrained within the safety range throughout the prediction horizon, i.e. |x2(k i )|≤V y,up . Considering the control objectives, it is also necessary to consider the suppression of tire slip ratio and its rate of change, so the last two objective function subterms can be expressed as:

[0125]

[0126] For the purpose of preventing tire slip and making full use of limited motor torque, the control input must be constrained in a safe range, i.e. |u(k i )|≤u up , where u up represents the upper limit value of control amount. According to the above definition of the objective function sub-item and its constraint, the nonlinear optimization problem in this controller can be obtained as:

[0127]

[0128] In the above formula, Γ1, Γ2, Γ3 and Γ4 represent yaw rate tracking weight coefficient, side slip velocity tracking weight coefficient, control amount weight coefficient and control amount change rate weight coefficient respectively.

[0129] 6) Fast solution algorithm based on Pontryagin extremum principle

[0130] According to the definition of extremum principle, the extremum principle cannot directly deal with the state constraint of the system, so a relaxation factor is introduced here to transform the state constraint of the system:

[0131]

[0132] Where τ represents the relaxation degree of the relaxation factor, and v is set to a large positive number, and then it can be guaranteed that the state can be constrained in a safe range. After introducing the relaxation factor, the second sub-item of the original objective function becomes:

[0133] L′2(k i )=L2(k i )+ζ(k i ). (15) At this time, the new nonlinear optimization problem can be obtained as:

[0134]

[0135] At this time, it can be seen that the original optimization problem is converted to a state constraint-free optimization problem. On this basis, the Hamilton function in the prediction time domain k+1≤k i ≤k+N+1 is defined as:

[0136]

[0137] Where λ(k i )=[λ1(k i ),λ2(k i ),λ3(k i )] T represents the Lagrange multiplier, and is defined as:

[0138]

[0139]

[0140]

[0141] According to the extremum principle, the canonical equation of this problem is Similarly to the discretization process of the model, the canonical equation is also discretized, and the sampling time is also T s Then the necessary condition of the optimal control can be obtained as

[0142]

[0143] According to the extremum principle, the terminal condition of this problem is

[0144] λ(k+N+1)=0. (20) At each time, the Hamiltonian must take the minimum value under the optimal control:

[0145] H(u * (k i ),λ * (k i ))≤H(u(k i ),λ * (k i )). (21)

[0146] If the Lagrange multiplier at each time, the current system state and the control input at the last time are known, the optimal control input at the current time can be obtained. Then according to the definition of the Hamiltonian in equation (17), the Hamiltonian is a highly nonlinear function of the independent variable u(k i )=[u1(k i ),u2(k i ),u3(k i ),u4(k i )] T It is very difficult to solve the analytical solution of this function, and there is even no analytical solution. Therefore, in the present application, the original Hamiltonian is Taylor expanded, and the Hamiltonian after Taylor expansion is:

[0147]

[0148] Where

[0149]

[0150] In this Hamiltonian, a constant remainder can be expressed as:

[0151]

[0152] According to the above process, the Hamilton function is a quadratic function of the independent variable u(k i ) = [u1(k i ), u2(k i ), u3(k i ), u4(k i )] T . Therefore, the original optimization problem is transformed into the problem of finding the minimum point of the quadratic function. Let the equation be solved, and the stationary point P s of the Hamilton function can be obtained as

[0153]

[0154] The Hessian matrix of the Hamilton function at this stationary point is

[0155]

[0156] In model predictive control, the weight coefficients of all sub-terms in the objective function are greater than zero, so p1 in equation (23) is also greater than zero. Therefore, the Hessian matrix W(P s ) is a positive definite matrix at the stationary point. According to advanced mathematics, the stationary point P s is the minimum point of the Hamilton function . Therefore, the explicit optimal control amount at each time can be expressed as

[0157]

[0158] The subscript j = 1, 2, 3, 4 represents the number of different control amounts. Based on the optimal explicit control amount, the constraint of the control amount itself needs to be considered, so the optimal control amount after constraint can be expressed as

[0159]

[0160] After that, the expected slip ratio of each tire can be expressed as Through the above process, the original nonlinear optimization problem in model predictive control is transformed into finding the optimal Lagrange multiplier initial value, and the initial value can satisfy the terminal condition in equation (20) along the optimal necessary condition in equation (19). Therefore, the original optimal control problem, through the transformation of the extreme value principle, can be expressed as

[0161]

[0162] Once the optimal initial value can be found, the optimal control sequence can be obtained by iteration. For the search problem of the optimal initial value, the Nelder-Mead simplex optimization algorithm can be used for searching, and the iteration relationship has been given in Figure 3 The specific steps are as follows:

[0163] The Nelder-Mead simplex search algorithm outputs the initial value for iteration;

[0164] The initial value is iterated to obtain the terminal value based on the discretized vehicle dynamics model, Hamilton function and the optimal control expression obtained by fast solving;

[0165] The terminal condition is judged for the terminal value, and if it is not satisfied, the Nelder-Mead simplex search algorithm is returned to continue searching;

[0166] When the Nelder-Mead simplex search algorithm reaches the maximum number of iterations or satisfies the terminal condition, the optimal Lagrange multiplier initial value is output.

[0167] For the original optimal control problem, there are 4xN independent variables, and for the transformed problem, there are only 3 independent variables. It can be seen that the number of independent variables is greatly reduced, thereby the solving speed can be greatly improved and the solving time can be reduced.

[0168] 7) Lower torque distribution controller

[0169] From the above design process, it can be seen that the optimal control quantity obtained by the model predictive controller is actually the expected value of the tire slip ratio, and the control quantity cannot be directly executed by the motor. Therefore, it is necessary to design a lower torque distribution controller to calculate the additional torque of the motor according to the actual slip ratio and the expected slip ratio of the tire. In the present application, a widely used PID controller is used to design the lower torque distribution controller, and the additional torque of each tire can be represented as:

[0170]

[0171] Wherein the subscript i=1, 2, 3, 4 represents different tire numbers, ΔT i represents the additional torque of each tire, K P and K I represent the proportional coefficient and the integral coefficient, κ i and represent the actual slip ratio at the current time and the expected slip ratio of each tire obtained by the upper controller, respectively.

[0172] Vehicle simulation model building: The vehicle model simulates the controlled object, and the main function is to accurately simulate the longitudinal, lateral and yaw motion characteristics of the actual vehicle.

[0173] In the present application, since joint simulation is used, in CarSim, mainly used are vehicle model selection and simulation condition construction.

[0174] First, a typical passenger car model is selected, then the relevant parameters of the model are modified and obtained, and the vehicle model parameters are added to the Simulink simulation model. The main model parameters of the vehicle are vehicle mass, front and rear wheelbase tire cornering stiffness, etc. After selecting the corresponding vehicle model and parameters, the corresponding simulation conditions need to be constructed. In the simulation conditions, the vehicle driving route, driving environment and driver model can be selected. Since in the present application, only the stability of the vehicle is controlled by the additional torque of the four tires, the driver model in CarSim is selected, and the motion state parameters of the vehicle are read into Simulink, and the simulation conditions under low adhesion road are constructed based on the selected vehicle model.

[0175] Simulation experiment verification and comparison

[0176] In order to verify the effectiveness of the method described in the present application, a vehicle stability control simulation experiment on a low adhesion road with a road friction coefficient μ = 0.35 is used for comparison and verification. For the solving algorithm for solving the speed reference, the traditional interior point method IPOPT algorithm is used for comparison simulation experiment. In the simulation experiment, the vehicle parameters and controller parameters are shown in Tables 1 and 2, respectively.

[0177] Table 1: Vehicle parameter table

[0178] Symbol Physical Description Value / Unit m Vehicle Mass 1430 / kg [R e ]]> Wheel Radius 0.325 / m [[ L f ]]> Distance from Vehicle Center of Mass to Front Axle 1.05 / m [[ L r ]]> Distance from Vehicle Center of Mass to Rear Axle 1.61 / m d Left and Right Wheel Track 1.55 / m [C f ]]> Front Wheel Tire Cornering Stiffness 90700 / N·rad -1 ]] [C r ]]> Rear Wheel Tire Cornering Stiffness 109000 / N·rad -1 ]] I z ]] Vehicle Moment of Inertia about z-axis 2059.2 / kg-m -2 ]] I w ]] Wheel Moment of Inertia 1.68 / kg·m -2 ]]

[0179] Table 2: Controller parameter table

[0180]

[0181]

[0182] Double lane shift condition experiment:

[0183] In this group of simulations, the vehicle speed is maintained at 70 km / h, and uniform speed driving is maintained throughout the condition. Figure 4 and Figure 5 The control effect of the traditional interior point method and the control effect of the solving algorithm based on the extremum principle described in the present application are shown, respectively. From the figures, it can be seen that both solving algorithms can control the vehicle to track the expected yaw rate, and can effectively improve the maneuverability and stability of the vehicle. Figure 6The vehicle yaw rate tracking effect diagram when the controller is closed is given, and it can be seen that the vehicle cannot track the desired yaw rate at this time, and the vehicle will lose control due to the excessive yaw rate, and the vehicle will rotate uncontrollably. Figure 7 The lateral velocity comparison effect diagram of the vehicle in the double lane shift working condition is given in the middle, and it can be seen that under the action of the controller, the lateral velocity of the vehicle can be suppressed in a very small range, ensuring the stability of the vehicle. When the controller is closed, the vehicle will lose stability due to the large lateral velocity. In Figure 8 The slip ratio comparison diagram of the four tires in the entire double lane shift working condition is given in the middle. It can be seen that under the action of the controller, the tire slip ratio of the vehicle can be suppressed in a very small range, preventing the vehicle from losing stability due to tire slip. When the controller is closed, the tire slip ratio cannot be suppressed in a small range, and the vehicle will lose stability due to the excessive slip ratio. In summary, with the help of the controller designed in the present application, the vehicle can maintain driving stability in the entire double lane shift working condition, and the tire slip ratio can also be suppressed in a very small range. The above results prove the effectiveness of the controller and the fast solving algorithm designed in the present application.

[0184] Figure 9 The average calculation time of the two solving algorithms under different prediction horizons is given in the middle. It can be seen from the figure that under the same prediction horizon, the average solving time of the fast solving algorithm designed in the present application is much smaller than that of the traditional interior point method, that is, the optimization problem can be solved at a faster speed. And with the increase of the prediction horizon, the average solving time of the traditional interior point method will increase exponentially with the increase of the prediction horizon. First of all, the average solving time of the fast solving algorithm designed in the present application increases linearly with the increase of the prediction horizon. Figure 10 and Figure 11 The instantaneous solving time of the fast solving algorithm designed in the present application and the traditional interior point method under different prediction horizons is given respectively. It can be seen that under the same prediction horizon, the solving speed of the fast solving algorithm designed in the present application is about 10 times faster than that of the traditional interior point method. From the above results, it can be seen that the fast solving algorithm designed in the present application can solve the optimization problem at a faster speed, which fully embodies the superiority of the fast solving algorithm designed in the present application.

[0185] The above detailed the preferred embodiments of the present application. It should be understood that those skilled in the art can make many modifications and changes without creative labor based on the concept of the present application. Therefore, any technical solution obtained by logical analysis, reasoning or limited experiment based on the prior art according to the concept of the present application shall be within the protection scope determined by the claims.

Claims

1. A vehicle longitudinal and lateral motion cooperative control method based on a fast solving algorithm, characterized in that, The method comprises the following steps: calculating a desired yaw rate according to a steering wheel angle and a current vehicle speed; constructing a nonlinear optimization problem according to the desired yaw rate and a current actual motion state of the vehicle, the nonlinear optimization problem having an objective function for tracking the desired yaw rate while also suppressing a lateral speed and a tire slip ratio of the vehicle; solving the nonlinear optimization problem to calculate desired slip ratios of four tires; calculating additional torques of the tires according to actual slip ratios and the desired slip ratios of the tires; sending the additional torques of the tires to actuators of the vehicle for cooperative control; The nonlinear optimization problem is quickly solved based on a Pontryagin minimum principle, comprising the following processes: introducing a relaxation factor to transform a state constraint of the system; Defining a hamiltonian function within a prediction horizon , the argument of which is the four-tire desired slip ratio ; discretizing a regular equation of the nonlinear optimization problem to obtain necessary conditions for optimal control, and obtaining a terminal condition of the nonlinear optimization problem according to an extremum principle; The original Hamiltonian function is Taylor expanded into a multivariate quadratic function with respect to the independent variables ​​ Let , solve the multivariate quadratic function to obtain the stationary point of the Hamilton function ; stationary point is a minimum point of the hamiltonian function The explicit optimal control at each time instant, i.e. the desired slip ratio of each tire, is obtained.

2. The vehicle longitudinal and lateral motion cooperative control method based on a fast solving algorithm according to claim 1, characterized in that, The desired yaw rate of the vehicle is calculated using a second-order reference model, based on the front wheel steering angle. To the desired yaw rate The transfer function between them can be expressed as: wherein the stability factor of the vehicle is defined as , the distance between the front and rear axles is defined as ; the natural oscillation frequency of the second order reference model system is defined as , the damping coefficient of the second order reference model system is , the yaw rate steady state gain is , the yaw rate derivative coefficient is defined as , is the mass of the vehicle, is the moment of inertia of the vehicle rotating around the center of mass, denotes the longitudinal speed of the vehicle, and denote the front and rear half axle length, respectively, and denote the stiffness of the front and rear axle tires, respectively.

3. The vehicle longitudinal and lateral motion cooperative control method based on fast solving algorithm according to claim 1, characterized in that, The upper limit value of the desired yaw rate is defined as , the desired yaw rate satisfies the constraint , wherein denotes the friction coefficient of the road surface, represents the gravitational coefficient, denotes the longitudinal speed of the vehicle.

4. The vehicle longitudinal and lateral motion cooperative control method based on a fast solving algorithm according to claim 1, characterized in that, The nonlinear optimization problem is expressed as: In the formula, denotes the distance between the front and rear axles; denotes the lateral velocity of the vehicle at the time t; denotes the lateral velocity of the vehicle at the time t; , , and denote the target function sub-items of the tracking yaw rate, the tracking lateral velocity, the control variable and the control variable rate, respectively, and denote the yaw rate tracking weight coefficient, the lateral velocity tracking weight coefficient, the control variable weight coefficient and the control variable rate weight coefficient, respectively, and denote the upper limit value of the lateral velocity and the upper limit value of the control variable, respectively.

5. The vehicle longitudinal and lateral motion coordinated control method based on fast solving algorithm according to claim 4, characterized in that, The center side slip angle constraint of the vehicle is defined as: According to the relationship between the lateral velocity and the side slip angle of the center of mass, the upper limit value of the corresponding lateral velocity is , and the vehicle lateral velocity constraint is ; wherein, denotes the friction coefficient of the road, denotes the gravity coefficient, denotes the longitudinal speed of the vehicle, and denote the front and rear half shaft lengths, respectively, denotes the distance between the front and rear axles, denotes the stiffness of the rear axle tires, denotes the mass of the vehicle.

6. The vehicle longitudinal and lateral motion coordinated control method based on fast solving algorithm according to claim 4, characterized in that, At each time instant , The target function subterm of tracking the desired yaw rate and the target function subterm of tracking the desired lateral velocity are represented as: wherein, denotes the prediction horizon, denotes the yaw rate of the vehicle at the time instant; the desired lateral velocity is set to , the lateral velocity of the vehicle is constrained to be within a safety range, i.e. ​ The objective function subitems of the control variables and the wheel control variable change rates are expressed as: The control quantity input is constrained to where denotes an upper limit value of the control quantity.

7. The vehicle longitudinal and lateral motion coordinated control method based on fast solving algorithm according to claim 6, characterized in that, The objective function subitems are obtained according to a vehicle dynamics model, and the specific steps are as follows: The state vector of the vehicle system is defined as , and denote the longitudinal, lateral and yaw velocities of the vehicle. The control vector of the vehicle system is defined as , representing the desired slip ratio of the four tires; The Euler discrete method is used to discretize the vehicle dynamics model, and the discretization sampling time is , and the discretized vehicle dynamics model is obtained as follows: wherein, and Fxfand Fyfdenote the longitudinal and lateral forces of the front tires, respectively, and the subscripts L, R, R, and R denote the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel of the vehicle, respectively, and L and L denote the distances from the front and rear axles to the center of mass of the vehicle, respectively, m is the mass of the vehicle, J is the moment of inertia of the vehicle about the center of mass, denotes the front wheel steering angle of the vehicle, denotes the track of the vehicle.

8. The vehicle longitudinal and lateral motion cooperative control method based on a fast solving algorithm according to claim 7, characterized in that, Longitudinal forces and lateral forces of the vehicle tires are described by using a composite slip ratio nonlinear tire model, and are expressed in the following form: wherein, represents the friction coefficient of the road surface, represents the vertical load of the tire, represents the stiffness of the tire force, represents a threshold value of the tire compound slip amount, represents the magnitude of the tire compound slip amount, calculated by: wherein, and respectively indicate the longitudinal and lateral slip amounts of the tire, calculated by the following way: wherein, represents the longitudinal slip ratio of the tire, which can be calculated by the current longitudinal speed of the vehicle and the rotational speed of the tire is calculated as: wherein, represents the effective rolling radius of the tire, represents the side slip angle of the tire, divided into front and rear wheels, represents the longitudinal velocity, represents the rotational speed of the tire, which are calculated in the following way, respectively: a wherein denotes the front wheel angle of the vehicle, denotes the side slip angle of the two front tires of the front axle, denotes the two tires of the rear axle, denotes the lateral velocity of the vehicle; denotes the yaw rate of the vehicle, calculated by 。 9. The vehicle longitudinal and lateral motion coordinated control method based on fast solving algorithm according to claim 1, characterized in that, After the nonlinear optimization problem is quickly solved based on the Pontryagin minimum principle, the nonlinear optimization problem is transformed into searching for an optimal Lagrange multiplier initial value, which can satisfy the terminal condition along the optimal necessary condition; The optimal Lagrange multiplier initial value is obtained by optimizing and searching by using a Nelder-Mead simplex search algorithm, and the specific steps are as follows: The Nelder-Mead simplex search algorithm outputs an initial value for iteration; The initial value is iterated to obtain a terminal value based on a discretized vehicle dynamics model, a Hamilton function and an optimal control variable expression obtained by quick solving; The terminal value is subjected to terminal condition judgment, and if the terminal condition is not satisfied, the Nelder-Mead simplex search algorithm is returned to continue searching; When the Nelder-Mead simplex search algorithm reaches a maximum iteration number or satisfies the terminal condition, the optimal Lagrange multiplier initial value is output.

10. The vehicle longitudinal and lateral motion cooperative control method based on a fast solving algorithm according to claim 1, characterized in that, The additional torques of the tires are calculated by using PID control, and the expression is as follows: wherein the subscripts denote different tire numbers, denote additional torques of the respective tires, and denote a proportional coefficient and an integral coefficient, respectively, and denote the actual slip ratio at the current time and the desired slip ratio of the respective tires obtained by the upper controller, respectively.

Images