Vehicle trajectory tracking control method suitable for soft road surface

Abstract

The invention relates to a vehicle trajectory tracking control method suitable for a soft road surface. The method comprises the following steps: establishing a vehicle dynamics model; establishing a state equation and a prediction equation; designing a target function; the method comprises the following steps: establishing a soft pavement simulation environment, establishing a more accurate vehicle dynamics model according to a special wheel-ground contact condition in a soft pavement, discretizing the vehicle dynamics model according to a model prediction control theory to obtain a state equation and a prediction equation, considering trajectory tracking precision and control energy consumption, and designing a reasonable objective function. And obtaining a vehicle trajectory tracking controller. According to the vehicle trajectory tracking control method considering the soft road surface, the influence of deformation of the soft road surface on vehicle dynamics is fully considered, the vehicle dynamics model suitable for the soft road surface is established, and on the basis, more accurate vehicle trajectory tracking under the soft road surface condition is achieved through a model prediction control algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle motion control, and in particular to a vehicle trajectory tracking control for off-road conditions. Background Art

[0002] Vehicle trajectory tracking control technology is the core to ensure the safe operation of autonomous driving and intelligent transportation systems. However, on soft roads, due to the low friction coefficient and easy deformation of the road surface, vehicle trajectory tracking control faces unprecedented challenges. The application of existing technologies on soft roads has many shortcomings, including insufficient adaptability of vehicle dynamics models, low accuracy of state estimation, and the control strategy may ignore energy consumption while pursuing accuracy. Summary of the invention

[0003] In order to overcome these defects, the present invention proposes a vehicle trajectory tracking control method suitable for soft roads. This method obtains the lateral and longitudinal forces exerted on the vehicle more accurately by establishing a special vehicle dynamics model that takes into account the wheel-ground contact relationship. Furthermore, the model is discretized to obtain state equations and prediction equations suitable for control. A control strategy is designed based on model predictive control theory. When designing the objective function, the accuracy of trajectory tracking and the energy consumption in the control process are fully considered, and the vehicle trajectory tracking control is optimized in many aspects. At present, model predictive control is widely used in vehicle trajectory tracking control. It is to achieve high-precision trajectory tracking of the vehicle by establishing an accurate vehicle model to accurately predict the future behavior of the vehicle and then make the optimal control at the current moment. The main problems of this method are the establishment of a high-precision vehicle model and experimental verification of atypical working conditions:

[0004] 1) High-precision vehicle model: For a vehicle, the tire is the part that directly interacts with the ground. Therefore, accurately obtaining the state of the tire is a necessary condition for establishing a high-precision vehicle model. In the vehicle dynamics model, tire force is particularly critical, which directly affects Newton's second law equation and determines whether the model can work properly.

[0005] 2) Experimental verification of atypical working conditions: Atypical working conditions will have additional environmental parameters. For example, the presence of soft road surface will bring about parameters such as soil cohesion, soil internal friction angle and wheel settlement. Since some parameters are extremely difficult to measure or cannot be measured at all, it is difficult to carry out actual vehicle experiments. How to test the designed algorithm to form a development closed loop is an issue that needs to be considered and explored.

[0006] Technical solution of the present invention:

[0007] A vehicle trajectory tracking control method suitable for soft roads comprises the following steps:

[0008] Step 1: Establish vehicle dynamics model;

[0009] Step 2: Establish the state equation and prediction equation;

[0010] According to the vehicle dynamics equation considering the influence of soft road surface obtained in step 1, the state quantity and control quantity are selected and discretized into a form suitable for real-time control tasks;

[0011] Step 3: Design the objective function;

[0012] Design the objective function based on the system state quantity, control quantity and prediction equation obtained in step 2;

[0013] Step 4: Apply to vehicle trajectory tracking control.

[0014] Beneficial Effects

[0015] The ground is the external environment that the vehicle directly contacts during driving, and the road conditions have a decisive influence on the vehicle's handling performance. Soft roads, as a common working condition for off-road vehicles, often cause tires to sink during driving due to their easy deformation. This sinking not only increases the complexity of tire forces, but may also cause the vehicle's driving trajectory to deviate, thus causing serious safety issues in off-road environments.

[0016] In response to this challenge, the present invention cleverly incorporates consideration of the easy deformation characteristics of soft roads into the design of the vehicle controller. The controller is endowed with the ability to keenly perceive tire sinking. When the tire sinks, the present invention can accurately adjust the steering angle of the vehicle's front wheels, so that the vehicle can achieve accurate trajectory tracking even in harsh off-road environments, effectively preventing the vehicle from deviating from the predetermined driving path, thereby improving driving safety.

[0017] This innovation of the present invention not only solves the safety problem of off-road vehicles when driving on soft roads, but also provides a new idea for the design of vehicle controllers, demonstrating the potential for optimizing vehicle handling performance under complex road conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 The following is a schematic diagram of the implementation process and logical structure of the method according to the embodiment of the present invention;

[0019] Figure 2 The soft road trajectory tracking experiment results of the embodiment;

[0020] Figure 3 is the trajectory tracking error of the embodiment. DETAILED DESCRIPTION

[0021] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0022] Example 1

[0023] The present invention fully considers the influence of deformable road surface on vehicle dynamics, combines Bekker model and linearized tire model, establishes a vehicle dynamics model suitable for soft road surface, and uses model predictive control theory to realize vehicle trajectory tracking control on soft road surface for off-road conditions with the goal of improving vehicle trajectory tracking capability. The present invention mainly includes the following steps:

[0024] Step 1: Build a vehicle dynamics model

[0025] First, the inherent parameters of the vehicle are measured, including size parameters, mass, center of mass height, etc., to obtain the parameters required for the dynamic model.

[0026] Before analyzing the vehicle dynamics, in order to simplify the complex motion and ensure the calculation speed of the control algorithm, the following assumptions are made:

[0027] Assumption 1: Ignoring axle load transfer and suspension deformation, it is assumed that the forces on the left and right wheels are the same, and the four-wheeled vehicle is regarded as the splicing of two bicycle models.

[0028] Assumption 2: All four tires operate in the linear region.

[0029] Assumption 3: Road conditions are the same everywhere and the slope is 0.

[0030] Here, only the longitudinal, lateral and yaw degrees of freedom of the vehicle are considered. In order to consider the effect of the sideslip angle of the center of mass, the conversion relationship between the vehicle coordinate system and the inertial coordinate system can be obtained by taking the center of mass of the vehicle as the reference point:

[0031]

[0032] According to Newton's second law, the dynamic equations under three degrees of freedom can be obtained:

[0033]

[0034] Among them, a and b are the vertical distances from the center of mass of the vehicle to the front and rear axles of the vehicle, m is the curb weight of the vehicle, and I z is the moment of inertia of the vehicle around the z-axis, and f and r represent the parameters of the front and rear wheels respectively. It is worth noting that since the vehicle moves in the body coordinate system in a plane, but rotates in the global coordinate system, the Coriolis force F is generated when the coordinate system is transformed. Cx and FCy According to theoretical mechanics, the Coriolis force can be calculated by the following formula:

[0035]

[0036] When a vehicle is driving on a soft road, it will inevitably cause the soil to sink, which will cause the tire to be subjected to additional soil resistance. Therefore, a more accurate tire force can be fitted by using the "linear tire model + correction term". Here, the Bekker model is used to calculate the correction term. In addition, due to its unique ground characteristics, soft ground will cause tire slip in most cases, resulting in the friction provided by the ground being less than that of ordinary roads. Therefore, the linear tire model can be changed proportionally to make it suitable for soft ground.

[0037] Combining Bekker theory and linearized tire model, the additional soil force on the tire when the vehicle is driving on a soft road can be expressed as follows:

[0038] τ max =c+σ max tanφ

[0039]

[0040] F yr =k yr C αr α r

[0041] F xr =k xr C sr ·S r

[0042] where τ max is the maximum shear stress on the contact surface, σ max is the maximum normal stress on the contact surface, c and φ are the soil cohesion and internal friction angle, respectively, and n, k are the soil inherent parameters. c and k φ are the subsidence index, soil cohesion coefficient and soil friction coefficient, determined by a plate sinking test. is the additional lateral and longitudinal soil resistance of the tire, k is the stress coefficient. The subscript f represents the parameters related to the front wheel, r represents the parameters related to the rear wheel, and k y , k x is the linearized tire model scale factor. Since the rear wheel will follow the rut of the front wheel in most cases during the movement, the additional soil resistance can be ignored.

[0043] Step 2: Establish the state equation and prediction equation

[0044] According to the vehicle dynamics equation considering the influence of soft road surface obtained in step 1, the state quantity and control quantity are selected and discretized into a form suitable for real-time control tasks.

[0045] 2.1 Model discretization

[0046] The dynamic equations of a vehicle on soft ground are:

[0047]

[0048] In this system, the state quantity is selected The control quantity is selected as u=[δ].

[0049] Assume that the operating point of the system at time t is [ξ0,u0], expand Taylor at the operating point, and perform forward Euler discretization to obtain the following formula:

[0050]

[0051] A k =I+A t T

[0052] B k =B t T

[0053] Among them, A k and B k is the Jacobian matrix of the dynamic equation for the state and control variables, and T is the discrete period.

[0054] Expand the above formula to get:

[0055] ξ(k+1)=A k ξ(k)+B k ξ(k)+ξ0(k+1)-A k ξ0(k)-B k ξ0(k)

[0056] Yaw angle and lateral displacement Y as output, the output matrix C can be obtained, and then the state equation and output equation can be obtained:

[0057]

[0058] in,

[0059] 2.2 Reconstructing the state vector

[0060] According to the discretization result of the model in step 2.1, it is necessary to further consider the influence of the control quantity at the previous moment on the current moment. Therefore, it is necessary to reconstruct the state vector and take the control quantity at the previous moment as one of the state quantities at the current moment, that is, The result is:

[0061]

[0062] in, C=[C k 0].

[0063] 2.3 Establishing the prediction equation

[0064] According to the discrete state equation and output equation obtained in step 2.2, the current state can be predicted with historical data. The following is the entire prediction process:

[0065]

[0066] Arranging the above recursive process, the prediction equation can be expressed as:

[0067]

[0068] Step 3: Design the objective function;

[0069] The objective function is designed based on the system state quantity, control quantity and prediction equation obtained in step 2.

[0070] First of all, the basic principle of MPC (model predictive control) is to solve a quadratic programming problem in each computing time domain, and use the optimal solution of the quadratic programming problem as the input of the next step, so as to predict and control the state quantity in multiple time steps in the future. In the vehicle control task, the designed objective function must ensure that the vehicle can smoothly and quickly keep up with the set desired trajectory. In order to reduce the control amount while ensuring high control accuracy, the following objective function is used:

[0071]

[0072] Among them, Q and R are weight matrices. The first term reflects the system's ability to track the reference trajectory, and the second term reflects the constraint on the change of the control quantity.

[0073] Since the objective function cannot limit the control increment within each sampling period and cannot avoid the sudden change of the control quantity of the controlled system, the control increment is used to replace the control quantity in the function and the relaxation factor is added to obtain the final objective function form:

[0074]

[0075] Among them, ρ is the weight coefficient, ε is the relaxation factor, N p is the prediction time domain, N c To control the time domain.

[0076] Let E = Ψξ-ΓΦ-Yref , we can get the matrix expression of the objective function:

[0077]

[0078] in f T =[2E T QΘ0].

[0079] Constraint settings:

[0080]

[0081] That is: U min ≤U t ≤U max

[0082] Step 4: Build a soft road simulation environment

[0083] Based on the vehicle dynamics equation established in step one, the state equation and prediction equation derived in step two, and the objective function designed in step three, a complete controller was obtained, and the simulation environment was built and experimentally verified.

[0084] Due to the special conditions of soft road surface, ground parameters such as cohesion and internal friction angle are difficult to measure. In order to obtain accurate model parameters and correct tire force reference values, this embodiment uses Chrono software to define the experimental environment, establish a Chrono-Simulink joint simulation environment, and control vehicle motion in real time. The specific process is as follows:

[0085] Conducting joint simulation experiments requires three major elements: experimental objects, experimental environment, and experimental methods.

[0086] 4.1 Defining the experimental object: vehicle parameters

[0087] Soft road surfaces are working conditions faced by off-road vehicles. To ensure the rationality of the experiment, this embodiment redefines key parameters such as the mass, wheelbase, track width, and tire cornering stiffness of the experimental vehicle.

[0088] 4.2 Defining the experimental environment: ground parameters

[0089] In order to provide the model with parameters that are difficult to measure, such as soil cohesion, internal friction angle, and settlement index, this embodiment needs to redefine the pavement parameters.

[0090] 4.3 Defining the experimental method: working conditions

[0091] Based on 4.1 and 4.2, define the experimental conditions.

[0092] Double lane change is a common working condition for evaluating vehicle driving performance. The process is that the vehicle moves from the original lane to the adjacent parallel lane within a certain distance through the driver's operation of the steering wheel, and then returns to the original lane. During this period, the vehicle should not exceed the lane boundary line.

[0093] In the actual simulation test, the center line of the road is always used as the reference trajectory. Since the standard specifies the relevant provisions of the vehicle speed, considering that the vehicle will not have an excessively high speed when driving on a soft road, this design takes the target vehicle speed v ref =40km / h, the vehicle passes through the test section at a constant speed.

[0094] 4.4 Conduct joint simulation experiments

[0095] According to the experimental conditions set up in steps 4.1, 4.2, and 4.3, a joint simulation experiment is conducted.

[0096] Due to the difficulty in measuring ground parameters, joint simulation experiments are the most feasible solution to verify the correctness of the algorithm. The final experimental results are as follows: Figure 2 , the trajectory tracking error is Figure 3 .

Claims

1. A vehicle trajectory tracking control method suitable for soft roads, characterized in that: The steps include: Step 1: Establish vehicle dynamics model; Step 2: Establish the state equation and prediction equation; According to the vehicle dynamics equation considering the influence of soft road surface obtained in step 1, the state quantity and control quantity are selected and discretized into a form suitable for real-time control tasks; Step 3: Design the objective function; Design the objective function based on the system state quantity, control quantity and prediction equation obtained in step 2; Step 4: Apply to vehicle trajectory tracking control.

2. A vehicle trajectory tracking control method suitable for soft roads according to claim 1, characterized in that: Step 1: Establishing a vehicle dynamics model First, the inherent parameters of the vehicle are measured, including size parameters, mass, and center of mass height, to obtain the parameters required for the dynamic model; Assumptions: Assumption 1: Ignoring axle load transfer and suspension deformation, the forces on the left and right wheels are assumed to be the same, and the four-wheeled vehicle is regarded as the splicing of two bicycle models; Assumption 2: All four tires operate in the linear region; Assumption 3: The road conditions are the same everywhere, and the slope is 0; Only the longitudinal, lateral and yaw degrees of freedom of the vehicle are considered; to consider the effect of the sideslip angle of the center of mass, the center of mass of the vehicle is taken as the reference point, and the conversion relationship between the vehicle coordinate system and the inertial coordinate system is obtained: According to Newton's second law, the dynamic equations under three degrees of freedom are obtained: Among them, a and b are the vertical distances from the center of mass of the vehicle to the front and rear axles of the vehicle, m is the curb weight of the vehicle, and I z is the moment of inertia of the vehicle around the z-axis, f and r represent the relevant parameters of the front and rear wheels respectively; Coriolis force F generated when coordinate system transformation is performed Cx and F Cy , calculated by the following formula: When the vehicle is driving on a soft road, the tire force is fitted using the "linear tire model + correction term" method. Here, the Bekker model is used to calculate the correction term; the linear tire model is changed proportionally to make it suitable for soft ground; Combining Bekker theory and linearized tire model, the additional soil force on the tire when the vehicle is driving on a soft road is expressed as follows: t max =c+σ max tanf F yr =k yr C αr ·a r F xr =k xr C sr ·S r where τ max is the maximum shear stress on the contact surface, σ max is the maximum normal stress on the contact surface, c and φ are the soil cohesion and internal friction angle, respectively, and n, k are the soil inherent parameters. c and k φ are the subsidence index, soil cohesion coefficient and soil friction coefficient, determined by a plate sinking test. is the additional lateral and longitudinal soil resistance of the tire, k is the stress coefficient; subscript f represents the relevant parameters of the front wheel, r represents the relevant parameters of the rear wheel, and k y , k x is the linearized tire model scale factor.

3. The vehicle trajectory tracking control method suitable for soft roads according to claim 1, characterized in that: The second step: establishing the state equation and the prediction equation includes: 2.1 Model discretization The dynamic equations of a vehicle on soft ground are: In the system, select the state quantity Select the control quantity as u = [δ]; Assume that the operating point of the system at time t is [ξ0,u0], expand Taylor at the operating point, and perform forward Euler discretization to obtain the following formula: A k =I+A t T B k =B t T Among them, A k and B k is the Jacobian matrix of the dynamic equation for the state and control quantities, and T is the discrete period; Expand the above formula to get: ξ(k+1)=A k ξ(k)+B k ξ(k)+ξ0(k+1)-A k ξ0(k)-B k ξ0(k) Yaw angle and lateral displacement Y as output, and the output matrix C is obtained, and then the state equation and output equation are obtained: Where, d(k)=ξ(k+1)-A k ξ(k)-B k ξ(k), 2.2 Reconstructing the state vector According to the discretization result of the model in step 2.1, the state vector is reconstructed, and the control quantity at the previous moment is used as one of the state quantities at the current moment, that is, The result is: in, C=[C k 0]; 2.3 Establishing the prediction equation According to the discrete state equation and output equation obtained in step 2.2, the current state is predicted with historical data. The following is the entire prediction process: Arranging the above recursive process, the prediction equation is expressed as: in 4. The vehicle trajectory tracking control method suitable for soft roads according to claim 1, characterized in that: Step 3: Design the objective function, including; In the vehicle control task, the designed objective function must ensure that the vehicle can smoothly and quickly keep up with the set desired trajectory. In order to reduce the control amount while ensuring high control accuracy, the following objective function is used: Among them, Q and R are weight matrices. The first term reflects the system's ability to track the reference trajectory, and the second term reflects the constraint on the change of the control quantity.

5. A vehicle trajectory tracking control method suitable for soft roads according to claim 4, characterized in that: In step 3, since the objective function cannot limit the control increment within each sampling period and cannot avoid the sudden change of the control quantity of the controlled system, the control increment is used to replace the control quantity in the function and the relaxation factor is added to obtain the final objective function form: Among them, ρ is the weight coefficient, ε is the relaxation factor, N p is the prediction time domain, N c To control the time domain; Let E = Ψξ-ΓΦ-Y ref , we get the matrix expression of the objective function: in f T =[2E T QΘ0]; Constraint settings: Immediately: U min ≤U t ≤U max .

6. The vehicle trajectory tracking control method suitable for soft roads according to claim 1, characterized in that: Step 4: Apply to vehicle trajectory tracking control; The established vehicle model can accurately predict the vehicle's future behavior and make optimal control at the current moment, thereby achieving high-precision trajectory tracking of the vehicle.

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