A cooperative control method for four-wheel independent drive and steering electric vehicle

Abstract

The application relates to a kind of four-wheel independent drive and steering electric vehicle's collaborative control method, comprising the following steps: according to steering wheel angle and current vehicle speed, the expected yaw angular velocity is calculated, and the expected value of yaw angular velocity is limited according to current road adhesion condition, and the final yaw angular velocity expected value is generated;According to the current vehicle motion state and yaw angular velocity expected value, an optimization problem is constructed, the optimization problem is solved, and the expected active rear wheel angle control amount and the expected additional yaw torque control amount are obtained;According to the expected additional yaw torque control amount, the additional torque of each tire is calculated, and the expected active rear wheel angle is obtained according to the expected lateral force control amount, then the additional torque of each tire and the expected active rear wheel angle are sent into the actuator of vehicle for collaborative control.Compared with the prior art, the application avoids the conflict of multiple control quantities, reduces the model cumulative error and greatly improves the solving speed.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electric vehicle control, in particular to a cooperative control method for four-wheel independent driving and steering electric vehicle. BACKGROUND

[0002] Four-wheel independent driving and steering vehicle is a special vehicle that can independently adjust the torque of four tires and the steering angle of front and rear axles by installing distributed driving motors and front and rear axle independent steering motors. Through active steering, the tire side slip angle of the vehicle can be directly controlled, and the tire lateral force of the vehicle can be controlled. It can be seen that the introduction of active steering increases a control variable for the control of the vehicle, which can greatly improve the flexibility and safety of the vehicle control. At the same time, the introduction of distributed driving motors also enables the four-wheel torque to be directly adjusted. Therefore, compared with traditional vehicles, four-wheel independent driving and steering vehicles can greatly improve safety in extreme conditions and have a broad application prospect. However, since the vehicle itself is a complex nonlinear system, especially in extreme conditions, the tire force tends to be saturated, and the nonlinear characteristics of the vehicle are more pronounced. On the other hand, due to the increase of control variables, the complexity of the vehicle model is further increased, and the coupling relationship between each control variable and state variable is more complex. Therefore, when designing the controller, the complex nonlinearities and coupling characteristics of the vehicle, as well as the coordination problem under the action of multiple control variables, should be fully considered. In extreme conditions, since the stable region of the vehicle is small, the state of the vehicle in the future period of time needs to be reasonably predicted to find potential safety risks to prevent the vehicle from losing stability. Therefore, in the whole process, the strong nonlinearities and strong coupling characteristics of the vehicle system, as well as the safety constraints and control constraints of the vehicle itself, need to be considered. In order to solve the above problems, predictive cooperative control is a relatively ideal method. Through this method, the original control problem is converted into a nonlinear optimization problem under constraints, and is solved by nonlinear programming. However, under the current technical conditions, the computing power of the vehicle-mounted controller is limited, and it may not be able to solve the solution of the optimization problem in time. And the vehicle is a typical fast-changing system, if the corresponding control variable cannot be solved in a short time, it may cause the vehicle to lose stability. In summary, the current predictive cooperative control for four-wheel independent driving and steering vehicles in extreme conditions mainly has the following problems:

[0003] 1. Compared with general conditions, the nonlinear characteristics of the vehicle in extreme conditions are more prominent, and in order to improve the control performance, a nonlinear model is generally used to model the action of the control variable. However, in extreme conditions, the nonlinear model will still introduce modeling errors, thereby affecting the further improvement of the control performance.

[0004] 2. The traditional method does not consider the coupling of multiple control variables of the four-wheel independent drive and steering vehicle. In extreme working conditions, if the coordination and conflict between multiple control variables are not considered, the control effect may be affected, and the vehicle may even lose stability.

[0005] 3. Since a nonlinear vehicle model is used to improve the accuracy of the model, the optimization problem to be solved is also a nonlinear optimization problem. If a conventional direct optimization method (such as sequential quadratic programming SQP and interior point method IPOPT) is used, the required solving time will greatly exceed the control period of the vehicle, thereby causing the optimal control variable to be unable to be solved in time and unable to be applied on the vehicle-mounted controller.

[0006] Chinese patent CN202011114070.1 discloses a fast real-time rear wheel active steering predictive control method. In order to facilitate solving, a linear tire model is used for the rear wheel tire model of the vehicle. In fact, the tire force of the vehicle is longitudinally and laterally coupled, and the controller of the scheme directly optimizes the rear wheel steering angle. However, since a linear tire model is used, the model error is large, and therefore the control effect of this method is poor. Moreover, a simplex-based optimization algorithm is used to solve the optimization problem. However, this method is prone to local optimal solution in use, and the exploratory ability for global optimal solution is poor. SUMMARY

[0007] The purpose of the present application is to overcome the defects of the prior art and provide a predictive coordination control method for four-wheel independent drive and steering vehicles in extreme working conditions.

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

[0009] A coordination control method for four-wheel independent drive and steering electric vehicles, the method comprising the following steps:

[0010] calculating a desired yaw angular velocity according to a steering wheel steering angle and a current vehicle speed;

[0011] constructing an original optimization problem according to a current vehicle motion state and the desired yaw angular velocity, the objective function of the original optimization problem being used to track the yaw angular velocity, suppress the center of mass side slip angle, and coordinate adjustment of the active rear wheel steering angle and the additional yaw moment control variable;

[0012] solving the original optimization problem to obtain a desired active rear wheel steering angle control variable and a desired additional yaw moment control variable;

[0013] calculating additional torques of each tire according to the desired additional yaw moment control variable;

[0014] The expected active rear wheel rotation angle is obtained according to the expected lateral force control amount;

[0015] The additional rotation torque of each tire and the expected active rear wheel rotation angle are sent to the actuators of the vehicle for cooperative control; the fast solving step of the original optimization problem is as follows:

[0016] The to-be-optimized problem is converted into a display solving problem based on the Pontryagin extremum principle;

[0017] The optimal cooperative state variable initial value is found in a particle swarm optimization manner;

[0018] The original optimization problem is indirectly solved based on the optimal cooperative state variable initial value.

[0019] Further, the expected yaw rate is generated by using a second-order reference model, and the front wheel rotation angle δ f is a transfer function of the expected yaw rate γ ref , and can be expressed as:

[0020]

[0021] Wherein, ω n , ζ, K γ and τ γ respectively represent a natural oscillation frequency, a damping coefficient, a yaw rate gain and a differential coefficient of the yaw rate, and are calculated in the following manner:

[0022]

[0023]

[0024]

[0025]

[0026] Wherein, K = -m (C f L f -C r L r ) / 2C f C r L is defined as an insufficient steering gradient, L = L f + L r , and L f and L r respectively represent the distance from the front and rear axles to the center of mass of the vehicle, V represents the longitudinal speed of the vehicle, L, m is the mass of the vehicle, I z is the rotational inertia of the vehicle around the center of mass, C f and C r are the front and rear tire cornering stiffnesses respectively;

[0027] The upper limit value of the yaw rate is defined as The desired yaw rate satisfies the constraint |γ ref ≤γ up .

[0028] Further, the original optimization problem includes:

[0029] a target function for tracking the yaw rate, suppressing the side slip angle of the mass center, and cooperatively adjusting the active rear wheel steering angle and the additional yaw moment control amount;

[0030] establishing a target function constraint according to the safety constraint of the vehicle, the actuator constraint, and the real-time driving state;

[0031] The optimization problem is expressed as follows:

[0032]

[0033] s.t.-1≤x1(k i )≤1

[0034] ΔF yr,min ≤u1(k i )≤ΔF yr,max

[0035] -1≤u2(k i )≤1

[0036] In the formula, L1(k i ), L2(k i ) represent the target function sub-items of the yaw rate and the side slip angle of the mass center tracking item at time k i , L3(k i ), L4(k i ) represent the target function sub-items of the active rear wheel steering angle control amount u1 and the additional yaw moment control amount u2 at time k i , Γ γ and Γ β represent the weight coefficients of the yaw rate tracking item and the side slip angle of the mass center tracking item, respectively, Γ u1 and Γ u2 represent the weight coefficients of the additional yaw moment control amount u1 and the additional yaw moment control amount u2, respectively, x1(k i ) represents the side slip angle of the mass center tracking item of the vehicle, u1(k i ) and u2(k i ) represent the additional yaw moment control amount and the additional yaw moment control amount, respectively, ΔF yr,min , ΔF yr,max represent the minimum value and the maximum value of the additional part of the lateral force of the rear wheel tire, respectively.

[0037] Further, each k+1≤k i ≤k+N+1,

[0038] The objective function subterm of tracking the side slip angle and the yaw rate is:

[0039] L1(k i )=(x2(k i )-γ ref / γ up ) 2

[0040] L2(k i )=(x1(k i )-β ref / β up ) 2

[0041] Wherein, N represents the size of the prediction horizon, x1(k i ), x2(k i ) respectively represent the side slip angle tracking term and the yaw rate tracking term of the vehicle; the upper limit of the yaw rate is defined as The expected yaw rate satisfies the constraint |γ ref |≤γ up , the expected side slip angle is defined as β ref =0, and the upper limit of the side slip angle is defined as: The side slip angle satisfies the constraint |β|≤β up ;

[0042] The objective function subterm of the additional yaw moment control amount u1 and the additional yaw moment control amount u2 is:

[0043] L3(k i )=u1(k i -1) 2

[0044] L4(k i )=u2(k i -1) 2 .

[0045] Further, the side slip angle tracking term x1(k i ) and the yaw rate tracking term x2(k i ) of the vehicle are obtained based on the discrete two-degree-of-freedom bicycle model of the vehicle, and the steps are as follows:

[0046] Define the state vector of the system as x=[x1,x2] T =[β / β up ,γ / γ up ] Twhere β and γ represent the vehicle's sideslip angle and yaw rate, respectively up , β up represent the upper limit values of the yaw rate and the sideslip angle, respectively

[0047] The control input of the system is defined in a normalized form u = [u1, u2] T = [ΔF yr , ΔM z / ΔM max ] T where ΔF yr represents the additional portion of the lateral force of the rear wheel, ΔM z is the additional yaw moment, and ΔM max represents the maximum value of the additional yaw moment

[0048] The discrete-time two-degree-of-freedom bicycle model of the vehicle is obtained as follows:

[0049]

[0050]

[0051] where T s represents the discrete time of the system, u1(k) represents the additional yaw moment control amount, 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 moment of inertia of the vehicle about the center of mass, and V represents the longitudinal speed of the vehicle; the lateral force F yf of the front wheel and the standard portion of the lateral force of the rear wheel are calculated from a nonlinear tire model.

[0052] Further, the nonlinear tire model uses a nonlinear Fiala tire model, tan(α) is approximated as α, and the nonlinear tire model is expressed as follows:

[0053]

[0054] where μ is the road adhesion coefficient, F z is the vertical load, C α is the tire cornering stiffness, and α is the tire cornering angle, which is divided into the front wheel cornering angle α f and the rear wheel cornering angle α r , and is calculated from the following equations:

[0055]

[0056]

[0057] ​where β and γ represent the vehicle's centroid side slip angle and yaw rate, respectively, L f and L r represent the distance from the front and rear axles to the vehicle's centroid, V represents the vehicle's longitudinal speed, δ f and δ r represent the vehicle's front and rear wheel steering angles, respectively.

[0058] Further, the specific steps for solving the optimization problem include:

[0059] introducing a relaxation factor to transform the state constraint transformation;

[0060] constructing a corresponding Hamilton function according to the objective function and the vehicle system state space equation;

[0061] deriving an explicit optimal control expression according to the minimum value principle of a binary function, and then deriving an iterative relationship of the Hamilton equation and a terminal condition according to the extreme value principle;

[0062] finding an optimal co-state variable initial value, and then obtaining an optimal control input sequence through an explicit iterative method based on the optimal initial value.

[0063] Further, the optimal co-state variable initial value is found through a particle swarm optimization method, and the steps include:

[0064] population initialization: given the position of an initial point; generate a plurality of initial population particles near the initial point and set the speed of the initial point; according to the analytical solution of the explicit optimal control quantity, calculate the convergence value of the particles in the initial population through the iterative relationship of the Hamilton equation, and find the optimal point and the worst point in the entire population of particles after the calculation is completed, and record the corresponding convergence values; set the historical optimal point of each particle as the current initial position point, and define the current iteration number as 0;

[0065] particle population update: update the speed and position of the historical optimal point of the entire particle population according to the historical optimal point of each particle;

[0066] particle population convergence value update: the updated particle population is re-calculated for the convergence value, and in the calculation process, if the convergence value of the i-th particle is less than the current optimal value of the i-th particle, the position of the historical optimal point of the particle is updated to the current particle position, otherwise the position of the historical optimal point of the particle remains unchanged; after the convergence value calculation of all particles is completed, the group optimal point is updated to the position of the particle with the smallest convergence value among the current all particles, the group worst point is updated to the position of the particle with the largest convergence value among the current all particles, and the current iteration number is increased by one;

[0067] termination condition judgment: the termination conditions include:

[0068] λ(P w,g ) > λ(P b,g ) + ε and I c < I max

[0069] I c < I min

[0070] where λ(P b,g ) and λ(P w,g ) represent the final convergence value calculated by convergence value calculation when the group optimal point and the group worst point are taken as the initial value of the Lagrange multiplier, ε represents the tolerance, I c represents the iteration number, I max and I min represent the maximum iteration number and the minimum iteration number set respectively.

[0071] After the particle population is updated, the termination conditions are judged, if one of the conditions is met, it means that the search process is not completed, and the particle population is returned to continue iteration; if the two conditions are not met, the search is completed, and the current group optimal point is output as the optimal Lagrange multiplier initial value.

[0072] Further, the additional yaw moment is generated in an average distribution manner, and the optimal additional yaw moment control quantity obtained by solving the optimization problem is input to obtain the additional torque distributed to each tire:

[0073]

[0074]

[0075] where ΔT cfl and ΔT crl represent the additional torques of the left front wheel and the rear wheel respectively, ΔT cfr and ΔT crr represent the additional torques of the right front wheel and the rear wheel respectively, ΔM max represents the maximum value of the additional yaw moment, R e represents the effective rolling radius of the tire, and d represents the vehicle body width.

[0076] Further, the step of obtaining the desired active rear wheel steering angle according to the desired side force control quantity comprises:

[0077] A tire side force MAP table is constructed according to the tire model, and the three axes of the MAP table are the tire side force, the tire slip angle and the vertical load respectively.

[0078] The tire side slip angle corresponding to the vertical load of the tire and the desired tire lateral force is obtained by table lookup method;

[0079] The desired active rear wheel steering angle is obtained:

[0080]

[0081] Wherein, β represents the vehicle's mass center side slip angle, L r represents the distance from the rear axle to the vehicle's mass center, V represents the vehicle's longitudinal speed, γ represents the vehicle's yaw rate, α r,ref is the desired rear wheel side slip angle obtained by table lookup.

[0082] Compared with the prior art, the present application has the following beneficial effects:

[0083] 1) The present application is based on the extremum principle to transform the original optimization problem, and transforms the traditional direct solving method of optimal optimization variables into an indirect solving method of optimal control variables through the coordination variable, and simultaneously designs a search method for the initial value of the optimal coordination variable based on the particle swarm optimization (PSO) principle. Compared with the traditional direct solving method, the optimization ability of the global optimal solution is strong, the control performance is further improved, and the solving speed is greatly improved.

[0084] 2) Under the limit condition, the nonlinear characteristics of the vehicle are significant, in order to improve the control performance and avoid the adverse effects of the modeling error of the control variable on the control effect as much as possible, the tire lateral force is directly optimized in the present application, and a high-precision MAP table of the tire lateral force is established for finding the active rear wheel steering angle corresponding to the desired tire lateral force. Through this method, the model cumulative error in the prediction process can be effectively reduced, and the control effect can be improved.

[0085] 3) Compared with the traditional vehicle, the coupling relationship between multiple control variables and states of the four-wheel independent drive and steering automobile is more complex. In order to coordinate multiple control variables and avoid conflicts between control variables, the present application optimizes the tracking yaw rate, the suppression of the mass center side slip angle, and the simultaneous adjustment of the active rear wheel steering angle and the additional yaw moment control variable in the objective function, and adjusts the constraints in real time according to the driving state of the vehicle, effectively avoids the conflict problem of multiple control variables, and can more effectively coordinate and adjust multiple control variables. BRIEF DESCRIPTION OF DRAWINGS

[0086] Figure 1 is the flow chart of the cooperative control method designed in the present application;

[0087] Figure 2 is a schematic diagram of a vehicle model;

[0088] Figure 3is a high-precision tire lateral force MAP diagram;

[0089] Figure 4 is a schematic diagram of a relaxation function value changing with a state;

[0090] Figure 5 is a schematic diagram of an iterative relationship;

[0091] Figure 6 is a comparison diagram of calculation time of a direct solution method based on an interior point method under different prediction time domains;

[0092] Figure 7 is a comparison diagram of calculation time of a fast solution algorithm proposed by the application under different prediction time domains;

[0093] Figure 8 is a comparison diagram of average solution time of two algorithms in an embodiment of the application under different prediction time domains;

[0094] Figure 9 is a schematic diagram of vehicle state simulation results of two algorithms in an embodiment of the application and when the controller is closed, (a) is a schematic diagram of vehicle state simulation results of an IPOPT algorithm, (b) is a schematic diagram of vehicle state simulation results of a PMP algorithm, and (c) is a comparison diagram of control effects when the two algorithms and the controller are closed. DETAILED DESCRIPTION

[0095] The application will be described in detail below with reference to the drawings and specific embodiments. The embodiments are implemented on the premise of the technical scheme of the application, and detailed implementation modes and specific operation processes are given, but the protection scope of the application is not limited to the following embodiments.

[0096] The cooperative control method architecture designed in the application is as shown in Figure 1 The driver will give a certain steering wheel angle according to the current vehicle state. In the reference value generation module, the expected yaw rate is calculated according to the steering wheel angle punched by the driver and the current vehicle speed, and the expected value is also limited according to the current road adhesion condition to meet the maximum friction condition, and then the final yaw rate expected value is sent to the predictive controller. In the predictive controller, the original optimization problem is constructed according to the current vehicle motion state and the yaw rate expected value calculated by the reference value generation module, and then the optimization problem is solved to obtain two expected control amounts, and the expected control amounts are sent to the control action generation module. In the control action generation module, the additional torques of each tire are calculated according to the expected additional yaw moment, and the expected active rear wheel angle is obtained by looking up the table according to the expected lateral force, and then the additional torques of each tire and the active rear wheel angle are sent to the vehicle actuator.

[0097] The embodiment provides implementation steps of a cooperative control method of a four-wheel independent driving and steering electric vehicle and performs simulation test on the cooperative control method, and comprises the following parts:

[0098] I. Predictive control:

[0099] 1) Establish a vehicle dynamics model considering multiple control variables;

[0100] 2) Establish a tire force map table according to the tire model in CarSim, which is used for looking up the expected rear wheel active steering angle;

[0101] 3) Establish a reference model of the expected yaw rate according to a linear two-degree-of-freedom model;

[0102] 4) Establish a target function for tracking the yaw rate, suppressing the mass side slip angle, and cooperatively adjusting the active rear wheel steering angle and the additional yaw moment;

[0103] 5) Establish the constraints of the target function according to the safety constraints of the vehicle, the actuator constraints and the real-time driving state.

[0104] II. Design of a fast real-time solution method for a nonlinear optimization problem

[0105] 1) Introduce a relaxation factor, and the optimization problem under the original state constraints is converted into an unconstrained optimization problem;

[0106] 2) Construct the corresponding Hamilton function according to the target function and the system state space equation;

[0107] 3) Derive the explicit optimal control variable expression according to the minimum value principle of a binary function, and then derive the iteration relationship of the Hamilton equation and the terminal condition according to the extreme value principle;

[0108] 4) Design an optimal initial value search algorithm for the covariant according to the principle of the PSO optimization algorithm.

[0109] III. Modeling and simulation of the four-wheel independent driving and steering electric vehicle under extreme conditions: select a corresponding vehicle model in the CarSim software, and then replace the rear axle system of the vehicle with an active steering rear axle system. Finally, configure the simulation conditions on the basis of the model, to simulate the motion state of the vehicle under extreme conditions; and verify the effectiveness and rapidity of the designed algorithm.

[0110] The specific implementation and simulation steps are as follows:

[0111] The controlled object of the present application is a rear wheel active steering vehicle running on low adhesion road, so the control target is to calculate the required rear wheel steering angle and additional yaw moment according to the current vehicle state information and the current reference value, and to improve the stability of the vehicle. The main design process is described as follows. First, the lateral and yaw motions of the rear wheel active steering vehicle are modeled, and a suitable mathematical model is established.

[0112] 1) Two degree of freedom bicycle model of vehicle

[0113] In the present application, the lateral and yaw motions of the vehicle are mainly considered, and the longitudinal motion of the vehicle is not considered, so the widely used two degree of freedom bicycle model of vehicle is adopted to describe the lateral and yaw motions. In this model, it is first assumed that the longitudinal speed of the vehicle remains unchanged in a short time region, and then the model can be expressed in the following form:

[0114]

[0115] wherein, and respectively represent the derivative of the lateral angle of the mass center of the vehicle and the derivative of the yaw angular velocity of the vehicle, V represents the longitudinal speed of the vehicle, F yf and F yr respectively represent the lateral force of the front and rear tires, L f and L r respectively represent the distance from the front and rear axles to the mass center of the vehicle, m is the mass of the vehicle, I z is the rotational inertia of the vehicle rotating around the mass center, and ΔM z is the additional yaw moment. In the present application, the lateral force of the rear tire is divided into two parts, i.e. wherein, the definition of the standard lateral force is caused by the lateral angle of the tire. And the other part ΔF yr is defined as the additional part, which is the lateral force caused by the active rear wheel steering angle δ r . The control input of the system is defined as the additional yaw moment ΔM z generated by the longitudinal force of the tire and the additional rear wheel lateral force ΔF yr generated by the active rear wheel.

[0116] 2) Nonlinear tire model

[0117] Under extreme conditions, the non-linear characteristics of the vehicle are more prominent and must be considered in the model. In this embodiment, a non-linear Fiala tire model is used to describe the tire characteristics of the vehicle under extreme conditions. Since the side slip angle α of the vehicle tire is small, tan(α) is assumed to be equal to α, under which the original tire model can be expressed as follows:

[0118]

[0119] where μ is the road adhesion coefficient, F z is the vertical load, C α is the tire side slip stiffness. The tire side slip angle α in the equation is divided into the front wheel side slip angle α f and the rear wheel side slip angle α r , which can be calculated by the following equations, respectively:

[0120]

[0121] where δ f and δ r represent the front wheel steering angle and the rear wheel steering angle of the vehicle, respectively, and β and γ represent the vehicle's center of mass side slip angle and yaw rate, respectively.

[0122] 3) Vehicle reference model establishment

[0123] Under extreme conditions, considering the non-linear characteristics of the system, a second-order reference model is used to generate the expected yaw rate. The transfer function of the front wheel steering angle δ f to the expected yaw rate γ ref can be expressed as

[0124]

[0125] where ω n , ζ, K γ and τ γ represent the natural oscillation frequency, the damping coefficient, the yaw rate gain and the derivative coefficient of the yaw rate, respectively. They can be calculated by the following method:

[0126]

[0127] K = -m(C f L f - C r L r ) / 2C f C r L in the above equation is defined as the understeering gradient, and L = L f + L r is defined as the wheelbase of the vehicle.

[0128] On the basis of the above-mentioned reference model, the desired yaw rate of the vehicle can be obtained according to the front wheel steering angle input by the driver. However, due to the limited adhesion of the vehicle tires in extreme working conditions, an excessively large yaw rate can cause the vehicle to be unstable. Based on the above-mentioned consideration, the desired yaw rate generated by the reference model should be limited according to the adhesion condition of the driving surface. Herein, the upper limit value of the yaw rate is defined as The constraint that the actual value of the yaw rate should satisfy thereafter is |γ ref |≤γ up . Since the main purpose of the control method designed in the present application is to track the desired yaw rate value of the vehicle while also trying to suppress the vehicle's center of mass side slip angle β as much as possible, the desired value of the center of mass side slip angle is defined as β ref = 0. In addition, since an excessively large center of mass side slip angle can greatly deteriorate the stability and maneuverability of the vehicle in extreme working conditions, the center of mass side slip angle should also be limited within a safe region. Herein, the upper limit value of the center of mass side slip angle is defined as:

[0129]

[0130] Similarly to the yaw rate of the vehicle, the constraint that the center of mass side slip angle should satisfy is |β|≤β up .

[0131] 4) Control optimization problem design

[0132] In the control optimization problem design, since multiple parameters need to be adjusted and calibrated, in order to simplify the calibration process, the state vector of the system is first defined as x = [x1, x2] T = [β / β up , γ / γ up ] T . Correspondingly, the control input of the system can also be defined in a normalized form u = [u1, u2] T = [ΔF yr , ΔM z / ΔM max ] T , wherein ΔM max represents the maximum value of the additional yaw moment. Thereafter, in combination with the discretized system equation, the vehicle model for the predictive controller design can be obtained as:

[0133]

[0134] wherein T s represents the discrete time of the system. In extreme working conditions, in order to improve the accuracy of the model, the lateral force F yf of the front wheel and the standard part of the lateral force of the rear wheel are defined as are calculated by the nonlinear tire model in equation (2).

[0135] The main purpose of this invention is to improve the driving safety performance of the vehicle in extreme working conditions. In addition, the driving stability of the vehicle should also be considered. Therefore, the vehicle's side slip angle should be limited and constrained. Based on the above considerations, the target function subterm of the tracking yaw rate and the tracking side slip angle at each time k+1≤k i ≤k+N+1 is defined as:

[0136]

[0137] where N represents the size of the prediction horizon, and the expected value of the side slip angle is defined as β ref = 0. When the vehicle has a large side slip angle that exceeds the upper limit β up , the vehicle will lose stability. Therefore, the vehicle's side slip angle must be constrained within a safe range to ensure the driving safety of the vehicle. Based on the above reasons, a mandatory state constraint |x1(k i )|≤1 should be added. In addition, the interaction of the control action in the whole process should also be considered. In order to guarantee the yaw rate tracking performance, the energy consumption in the control process should be minimized. At the same time, in order to avoid the saturation of the tire lateral force, the additional lateral force of the rear wheel should also be minimized as much as possible. Considering the above two requirements, the target function subterm of the control amount can be defined as:

[0138]

[0139] Considering the limited execution capability of the actuator, the amplitude of the control input should also be limited within the physical limits of the actuator.

[0140] For the additional yaw moment of the vehicle, the main limitation is the longitudinal force of the tire and the torque of the motor, so the additional yaw moment should satisfy the constraint |ΔM z |≤ΔM max . For the lateral force of the rear wheel, the total lateral force F yr of the tire must satisfy the physical friction limit, so the constraint of the additional rear wheel lateral force can be defined as:

[0141]

[0142] Through the constraint definition of the control amount u1, it can be known that the upper and lower limits of this control amount are dynamically changed by the current motion state of the vehicle. Then, by combining the definition of the target function and the constraint, the optimization problem of the predictive cooperative control strategy can be obtained as:

[0143]

[0144] Γ γ and Γ β represent the weight coefficient of the yaw rate tracking term and the weight coefficient of the center side slip angle tracking term, respectively, Γ u1 and Γ u2 represent the weight coefficient of the control amount u1 and u2, respectively. After the optimization problem is constructed, the optimal control input can be obtained by solving the optimization problem.

[0145] 5) Control action generation

[0146] In the present application, two actuators are used to generate the control action and execute the control input. The in-wheel motor is used to generate the additional yaw moment, and the active rear wheel steering angle is used to generate the additional rear wheel lateral force. In the torque distribution, an average distribution method is used to generate the additional yaw moment. According to the optimal control input obtained by solving the optimization problem the torque distributed to each motor can be obtained as follows:

[0147]

[0148] where ΔT cfl , ΔT crl represent the additional torque of the left front wheel and the rear wheel, respectively, ΔT cfr , ΔT crr represent the additional torque of the right front wheel and the rear wheel, respectively, R e represents the effective rolling radius of the tire, and d represents the vehicle body width.

[0149] In the predictive cooperative control method designed in the present application, the second control quantity is the additional rear wheel lateral force, which needs to be converted into the active steering angle of the rear wheel of the vehicle. Therefore, in the present application, a high-precision tire lateral force MAP table is first constructed. The tire lateral force is not only related to the steering angle of the vehicle, but also related to the state of the vehicle, such as the yaw rate and the center side slip angle. In order to simplify the modeling process and reduce the model error, the tire side slip angle is selected as an intermediate variable to obtain the corresponding active rear wheel steering angle in the present application. As shown in Figure 3 the three axes of the MAP table are the tire lateral force, the tire side slip angle, and the vertical load. The tire model selected in the present embodiment is the tire model of 255-15R17. Once the vertical load of the tire and the desired tire lateral force are determined, the corresponding tire side slip angle can be obtained by the table lookup method. In the present application, the desired tire lateral force is first defined as the sum of the standard part and the additional part, i.e. and then combined with the vertical load of the tire, the desired active rear wheel steering angle can be obtained as follows:

[0150]

[0151] β represents the vehicle's centroid side slip angle, L r represents the distance from the rear axle to the vehicle's centroid, V represents the vehicle's longitudinal speed, γ represents the vehicle's yaw rate, α r,ref is the expected rear wheel side slip angle obtained by table lookup.

[0152] 6) Fast solution algorithm based on the principle of extremum

[0153] From the above process, it can be seen that the optimal control input can be obtained by solving a nonlinear programming problem. Generally, the nonlinear programming problem can be solved by some commonly used direct iteration methods, such as SQP and IPOPT methods. However, these methods cannot be applied in a vehicle environment due to the heavy computational burden. In order to solve this problem, an indirect iteration method based on the principle of extremum is designed in the present invention to improve the real-time performance of the solution algorithm.

[0154] In the process of vehicle driving, in order to ensure safety, the centroid side slip angle needs to be constrained. However, since the principle of extremum cannot directly handle the state constraints of the system, the state constraints need to be appropriately transformed, and a relaxation function is introduced as follows:

[0155]

[0156] Where κ represents the sensitivity of the relaxation function, ν represents the convergence value of the relaxation function, and is a large number to ensure that the state is constrained within the boundary. As Figure 4 shown, when the state of the system is far from its constraint boundary, the value of the relaxation function can be ignored, and when the state of the system is close to the constraint boundary, the value of the relaxation function will increase sharply. After introducing the relaxation function, the redefined objective function subterm is obtained as follows:

[0157] L′2(k i )=L2(k i )+ζ(k i ) (15)

[0158] After the above transformation, the original optimization problem under the constraint can be converted into a new unconstrained optimization problem, which can be represented as follows:

[0159]

[0160] On the basis of the above process, combined with the system equation in equation (1), the Hamiltonian function at time k+1≤k i ≤k+N+1 can be obtained as follows:

[0161]

[0162] where the subitem F1(x(k i )) and F2(x(k i )) are defined as:

[0163]

[0164] λ(k i ) = [λ1(k i ), λ2(k i )] T represents the Lagrange multiplier at the k i th time. According to the canonical equation the necessary condition for optimality is:

[0165]

[0166] According to the definition in equation (16), the optimization problem can be divided into the optimal control problem with fixed terminal time and free terminal state, so the terminal condition is:

[0167] λ(k+N+1) = 0 (20)

[0168] If the optimal control input u * (k i ) exists, it must be able to minimize the Hamiltonian function at each time, that is, under the action of the optimal control input u * (k i ), the Hamiltonian function must satisfy:

[0169]

[0170] In order to find the optimal control input according to the known Lagrange multiplier λ(k i ) and the initial state x(k i ) of the system, the Hamiltonian function is rewritten as follows:

[0171] H(x(k i ), u(k i )) = p1u1(k i ) 2 + p2(k i )u1(k i ) + q1u2(k i ) 2 + q2(k i )u2(k i ) + g(x(k i )) (22) where the coefficients are defined as:

[0172]

[0173] The constant residual equation can be expressed as:

[0174]

[0175] From the definition of the Hamiltonian function, it can be seen that the function can be regarded as a binary quadratic function with u1 and u2 as independent variables, and at this time the problem in equation (21) can be equivalent to finding the minimum value of the quadratic function.

[0176] In order to find the minimum value of the binary quadratic function, the coefficients are defined as follows:

[0177]

[0178] In the optimization problem, all weight coefficients are greater than zero. According to the extremum theorem of binary function, when B 2 -4AC=-16Γ u1 Γ u2 <0, and A>0, the binary function takes the minimum value at its stationary point. Therefore, it can be proved that the Hamiltonian function takes the minimum value at its stationary point . In addition, the constraints of the vehicle actuators are also considered, so the explicit optimal control input at each time can be expressed as:

[0179]

[0180] 7) Optimal Lagrange multiplier search algorithm based on particle swarm optimization

[0181] From the above analysis, the optimal control input solving problem at each time can be converted into an extremum solving problem of a polynomial function under the known initial conditions λ(k i ) and x(k i ). Then, if the optimal Lagrange multiplier initial value λ * (k) can be found and it satisfies the terminal condition:

[0182]

[0183] The optimal control input sequence (u * (k),...,u * (k+N)) can be obtained through explicit iteration. In order to find the optimal Lagrange multiplier initial value that satisfies the above condition, a search method based on particle swarm optimization is used in the present application, and the algorithm parameters are as follows: the number of particles n=10, the maximum number of iterations I max =20, the minimum number of iterations I min =5, the inertia factor C i =0.5, and the individual learning factor C s= 2, population learning factor C g = 2, tolerance ε = 0.5. The search process can be expressed as:

[0184] (1) Population initialization

[0185] First, the position of the initial point is given. If it is the first run of the control algorithm, the initial point position is given as (0, 0), otherwise the optimal value of the last iteration is inherited as the initial point. Then 10 initial population particles are generated around the initial point, the particle position P i (i = 1,...,n) is uniformly distributed in the range [-0.5, 0.5] of the initial point. For the velocity of the initial point, the particle velocity V i (i = 1,...,n) is uniformly distributed in [-5, 5]. Then according to the iterative calculation process shown in Figure 5 , the optimal control input solution is obtained from the analytical solution of the state at time k i by equations (23)-(26), and the convergence value of the particles in the initial population is calculated by the iterative relationship shown in equations (7), (17)-(19). After the calculation is completed, the optimal point P b,g and the worst point P w,g in the whole population of particles are found, and the corresponding convergence values are recorded. In addition, in the initialization process, the historical optimal point P b,i (i = 1,...,n) of each particle is set as the current initial position point. At the same time, the current iteration number I c = 0 is defined.

[0186] (2) Particle population update

[0187] The velocity and position are updated according to the historical optimal point of each particle and the historical optimal point of the whole particle population. The update process can be expressed as:

[0188]

[0189] Where random(0, 1) represents a random number between (0, 1).

[0190] (3) Particle population convergence value update

[0191] The updated particle population is calculated again according to the iterative process shown in Figure 5 . In the calculation process, if the convergence value of the i-th particle is less than the current optimal value of the i-th particle, the position of P b,i (i = 1,...,n) is updated to the current particle position, otherwise the position of P b,i (i = 1,...,n) remains unchanged. After the convergence value of all particles is calculated, the group optimal point P b,gUpdate the worst-case P of the population by finding the position of the particle with the smallest convergence value among all particles. w,g This represents the position of the particle with the largest convergence value among all current particles. Increment the current iteration count by one, i.e., I. c =I c +1.

[0192] (4) Termination condition judgment

[0193] To ensure the algorithm's effectiveness and avoid getting stuck in an infinite loop, the following two termination conditions are set:

[0194]

[0195] Where λ(P) b,g ) and λ(P w,g The numbers ) represent the initial values ​​of the Lagrange multipliers when the optimal and worst points of the population are used as the initial values, respectively, according to... Figure 5 The final convergence value obtained through iteration. After step (3), the above two conditions are judged. If one of the conditions is met, it means that the search process is not completed, and the process returns to step (2) to continue iterating; if neither of the above two conditions is met, it means that the search ends, and the current population optimum P is output. b,g As the optimal initial values ​​for the Lagrange multipliers.

[0196] 8) Simulation experiment verification and comparison

[0197] In this embodiment, the effectiveness of the proposed cooperative control method is verified using MATLAB / CarSim co-simulation. The vehicle parameters are shown in Table 1.

[0198] Table 1: Vehicle Model Parameters

[0199] Symbol Description Value Unit m Vehicle kerb mass 1270 [kg] I z ]]> Vehicle moment of inertia about the centre of mass 1536.7 [[kg·m 2 ]]]> [[ L f ]]> Vehicle front half axle track 1.05 [m] [[ L r ]]> Vehicle rear half axle track 1.895 [m] C f ]]> Front wheel cornering stiffness 135000 [N / rad] [C r ]]> Rear wheel cornering stiffness 85000 [N / rad] [R e ]]> Tire rolling radius 0.325 [m] μ Road surface friction coefficient 0.35 /

[0200] In the predictive control optimization problem, the weight parameters are set as follows: Γ γ =1.55, Γ β =0.63, Γ u1 =0.13, Γ u2 =0.18, and its value is set as ΔM in the control constraint. max =800Nm, sampling time is T s =0.01s, the prediction time domain is N=15.

[0201] Double line shifting test

[0202] In the simulation experiment, the double lane change condition was selected, and the vehicle speed was 80km / h and remained constant throughout the entire condition.

[0203] Firstly, the solving time of the traditional direct solving method based on IPOPT and the fast solving algorithm based on PMP proposed in the present application is compared. The solving time of the IPOPT algorithm and the PMP algorithm is given in Figure 6 and Figure 7 respectively. It can be seen from the figure that the solving time of both will increase with the increase of the prediction horizon. However, under the same prediction horizon, the solving time of the fast solving algorithm based on PMP designed in the present application is much smaller than that of the traditional IPOPT algorithm. In addition, when the optimization problem is more complex, for example, during the 4th to 11th second, the solving time of the fast real-time solving algorithm designed in the present application can be about ten times faster than that of the IPOPT algorithm. The average calculation time of the above two algorithms is given in Figure 8 . It can be seen that the average solving time based on the IPOPT algorithm increases exponentially and sharply with the increase of the prediction horizon, while the solving algorithm based on PMP proposed in the present application increases linearly with the increase of the prediction horizon. From the transient and average solving time, it can be seen that the fast solving algorithm based on PMP proposed in the present application has better real-time performance, can solve the control quantity in time in the vehicle-mounted environment, and can greatly improve the driving safety of the vehicle.

[0204] The yaw angular velocity tracking effect of the vehicle and the suppression effect of the center of mass side slip angle are given in Figure 9 . It can be seen that the control scheme proposed in the present application can accurately track the expected yaw angular velocity of the vehicle, and can greatly improve the driving safety of the vehicle under extreme working conditions. When the control method is turned off, a large center of mass side slip angle appears, and under the action of the center of mass side slip angle, the vehicle will lose stability and further cause accidents. From the control effect of the simulation experiment, it is proved that the fast solving algorithm designed in the present application can be comparable to the traditional IPOPT in solving effect, and it is proved that the solving algorithm has high effectiveness.

[0205] In summary, through the simulation experiment, firstly, it is proved that compared with the traditional solving algorithm, the fast solving algorithm designed in the present application can greatly improve the solving speed, making it possible to apply the nonlinear predictive cooperative control algorithm in the vehicle-mounted controller. On the other hand, through the simulation, it is proved that the predictive cooperative control method of the four-wheel independent drive and steering vehicle under extreme working conditions designed in the present application is effective, which can effectively improve the safety of the vehicle under extreme working conditions and ensure the driving safety of the vehicle.

[0206] The preferred embodiments of the present application have been described above in detail. It should be understood that modifications and variations to the preferred embodiments could be made by those skilled in the art in light of the teachings above. It is therefore contemplated that the application can encompass other variations and modifications that fall within the scope of the claims.

Claims

1. A cooperative control method of a four-wheel independent drive and steering electric vehicle, characterized by, The method comprises the following steps: calculating a desired yaw rate according to a steering wheel angle and a current vehicle speed; constructing an original optimization problem according to a current vehicle motion state and the desired yaw rate, the objective function of the original optimization problem being used for tracking a yaw rate, suppressing a mass side slip angle, and coordinately adjusting a desired active rear wheel steering angle and a desired additional yaw moment control amount; solving the original optimization problem to obtain the desired active rear wheel steering angle control amount and the desired additional yaw moment control amount; calculating additional torques of each tire according to the desired additional yaw moment control amount; obtaining the desired active rear wheel steering angle according to the desired lateral force control amount; sending the additional torques of each tire and the desired active rear wheel steering angle to an actuator of the vehicle for coordinately controlling; the original optimization problem is solved quickly in the following steps: translating the optimization problem into a displayed solving problem based on the Pontryagin extremum principle; finding an optimal initial value of a Lagrange multiplier by means of particle swarm optimization; indirectly solving the original optimization problem based on the optimal initial value of the Lagrange multiplier.

2. The cooperative control method of a four-wheel independent drive and steering electric vehicle according to claim 1, characterized by, The desired yaw rate is generated using a second order reference model to the desired yaw rate The transfer function of the desired yaw rate to the front wheel steering angle can be expressed as: wherein s is a complex frequency variable; and respectively represent a natural oscillation frequency, a damping coefficient, a yaw angular velocity gain, and a differential coefficient of the yaw angular velocity, and are calculated in the following manner: wherein, is defined as the understeering gradient, is defined as the front and rear wheelbase of the vehicle, and denote the distance from the front and rear axles to the center of mass of the vehicle, denotes the longitudinal velocity of the vehicle, is the mass of the vehicle, is the moment of inertia of the vehicle about the center of mass, , are the front and rear tire cornering stiffnesses, respectively; An upper limit value of the yaw angular velocity is defined as , and it is desired that the yaw angular velocity satisfies the constraint ; wherein is the road surface adhesion coefficient, and is the gravitational acceleration.

3. The method of claim 2, wherein the method further comprises: The original optimization problem comprises: an objective function used for tracking a yaw rate, suppressing a mass side slip angle, and coordinately adjusting a desired active rear wheel steering angle and a desired additional yaw moment control amount; establishing the objective function constraint according to a safety constraint of the vehicle, an actuator constraint, and a real-time driving state; the original optimization problem is expressed as follows: In the formula, N denotes the size of the prediction horizon; , denote the target function sub-items of the yaw rate and the center of mass side slip angle tracking items at time t, , denote the target function sub-items of the active rear wheel steering angle control amount and the additional yaw moment control amount at time t, and denote the weight coefficients of the yaw rate tracking item and the center of mass side slip angle tracking item, and denote the weight coefficients of the active rear wheel steering angle control amount and the additional yaw moment control amount , denotes the center of mass side slip angle tracking item of the vehicle, and denote the additional yaw moment control amount and the additional yaw moment control amount, , denote the minimum and maximum values of the additional part of the lateral force of the rear wheel tire.​​ 4. The cooperative control method of four-wheel independent drive and steering electric vehicle according to claim 3, characterized in that, each at the moment, The The target function subterm of the time instant yaw angular velocity and the mass center side slip angle tracking term is: wherein, denotes the size of the prediction horizon, , denote the vehicle's center of mass side slip angle tracking term and yaw rate tracking term, respectively; the yaw rate upper limit value is defined as , the desired yaw rate satisfies the constraint , the desired center of mass side slip angle is defined as , the center of mass side slip angle upper limit value is defined as , the constraint that the center of mass side slip angle satisfies is ; the active rear wheel steering angle control amount and the additional yaw moment control amount the target function subterm is: 。 5. The method of claim 4, wherein the method further comprises: A side slip angle tracking term for the center of mass of the vehicle A yaw rate tracking term Based on a discrete two-degree-of-freedom bicycle model of the vehicle, the steps are as follows: The state vector of the system is defined as wherein and denote the vehicle's yaw rate and the vehicle's side slip angle at the center of mass, respectively, , denote the yaw rate upper limit value and the side slip angle upper limit value at the center of mass, respectively; The control input of the system is defined in normalized form wherein denotes the additional lateral force of the rear tire, is the additional yaw moment, denotes the maximum value of the additional yaw moment; obtained from a discretized two-degree-of-freedom bicycle model of the vehicle: wherein, denotes the discrete time of the system, denotes an additional yaw moment control quantity, and denote the distances of the front and rear axles to the vehicle's center of mass, is the mass of the vehicle, is the moment of inertia of the vehicle rotating around the center of mass, denotes the longitudinal velocity of the vehicle; the lateral force of the front wheel and the standard part of the rear wheel lateral force are calculated by a non-linear tire model of the form 6. The cooperative control method of a four-wheel independent drive and steering electric vehicle according to claim 5, wherein The nonlinear tire model employs a nonlinear Fiala tire model, such that The nonlinear tire model is expressed in the following form: wherein, is the lateral force on the tire, is the road adhesion coefficient, is the vertical load, is the tire cornering stiffness, is the tire cornering angle divided into a front tire cornering angle and a rear tire cornering angle respectively calculated by the following equations: wherein, and respectively denote a vehicle's mass center side slip angle and yaw rate, and respectively denote the distance of the front and rear axles to the vehicle's mass center, denotes the vehicle's longitudinal speed, and respectively denote the front and rear wheel steering angles of the vehicle.

7. The method of claim 1, wherein the method further comprises: the specific steps for solving the optimization problem comprise: introducing a relaxation factor to convert the state constraint; constructing a corresponding Hamilton function according to the objective function and a state space equation of the vehicle system; deriving an explicit optimal control amount expression according to a binary function minimum value principle, and then deriving an iterative relationship of the Hamilton equation and a terminal condition according to the extremum principle; finding an optimal initial value of a Lagrange multiplier, and then obtaining an optimal control input sequence by means of an explicit iterative method based on the optimal initial value.

8. The method of claim 1, wherein the method is characterized by: The optimal initial value of the Lagrange multiplier is found by means of particle swarm optimization, and the steps comprise: population initialization: given a position of an initial point, a plurality of initial population particles are generated around the initial point, and a speed of the initial point is set; the convergence values of the particles in the initial population are calculated through the iterative relationship of the Hamilton equation according to the analytical solution of the explicit optimal control amount, and the optimal point and the worst point in the whole population of particles are found and the corresponding convergence values are recorded; the historical optimal point of each particle is set as the current initial position point, and the current iteration number is defined as 0; particle population updating: the historical optimal point of the whole particle population is updated in speed and position according to the historical optimal point of each particle; Particle swarm convergence value update: The updated particle swarm convergence value is recalculated. During the calculation process, if the first... The convergence value of the i-th particle is less than that of the j-th particle. If the current optimal value of a particle is calculated, the position of the particle's historical optimal value is updated to the current particle position; otherwise, the position of the particle's historical optimal value remains unchanged. After all particle convergence values ​​have been calculated, the swarm optimal value is updated to the position of the particle with the smallest current particle convergence value, and the swarm worst value is updated to the position of the particle with the largest current particle convergence value. The current iteration count is then increased by one. termination condition judgment: the termination conditions include: wherein and respectively represent the final convergence value obtained by performing convergence value calculation when the group optimum point and the group worst point are set as the initial value of the Lagrange multiplier, represents the tolerance, represents the number of iterations, , respectively represent the maximum number of iterations and the minimum number of iterations set after the particle population updating is completed, the above termination conditions are judged, if one of the conditions is met, it indicates that the search process is not completed, and the particle population updating is returned for continuous iteration; if neither of the two conditions is met, the search is completed, and the current population optimal point is output as the optimal initial value of the Lagrange multiplier.

9. The method of claim 1, wherein, The additional yaw moment is generated in a way that the average distribution is applied, according to the optimal additional yaw moment control quantity input obtained by solving an optimization problem The additional torque distributed to each tire is obtained as wherein, respectively represent the additional torques of the left front and rear wheels, respectively represent the additional torques of the right front and rear wheels, represents the maximum value of the additional yaw moment, represents the effective rolling radius of the tire, represents the vehicle body width.

10. The method of claim 1, wherein, The step of obtaining the desired active rear wheel steering angle according to the desired lateral force control amount comprises: According to the tire model, a tire lateral force MAP table is constructed, three axes of the MAP table being a tire lateral force, a tire side slip angle, and a vertical load, respectively; A corresponding tire side slip angle is obtained by a table lookup method from a vertical load of the tire and a desired tire lateral force; A desired active rear wheel turning angle is obtained: wherein, denotes a vehicle's mass center side slip angle, denotes a distance from the rear axle to the vehicle's mass center, denotes a vehicle's longitudinal speed, denotes a vehicle's yaw rate, is a desired rear wheel side slip angle obtained by a look-up table.

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