A Low-Computational-Power Path Tracking Control Method for Ground Vehicles Considering Coupled Slope

Abstract

This invention belongs to the field of automotive technology, specifically a low-computational-power path tracking control method for ground vehicles considering coupled slope. First, a vehicle dynamics and kinematic model considering coupled slope is established through coordinate transformation and dynamic analysis to ensure the path tracking accuracy of unmanned ground vehicles on coupled slopes. Second, an unmanned ground vehicle path tracking system considering actuator time delay is constructed and its state-space equations are discretized, enabling its use in model predictive control. Finally, a path tracking control method is constructed, utilizing Laguerre function fitting to replace the quadratic programming solution for the optimal control sequence in traditional model predictive control, significantly reducing the computational power requirement of the control method. Simulation verification shows that the proposed control method can effectively reduce the computational power of the control method while ensuring the path tracking accuracy of unmanned ground vehicles.

Description

Technical Field

[0001] This invention belongs to the field of automotive technology, specifically a low-computing-power path tracking control method for ground vehicles that takes into account the coupling slope. Background Technology

[0002] Intelligent driving is a strategic high ground for future automotive technology, and its applications are becoming increasingly widespread. Beyond structured road scenarios in urban traffic, intelligent driving is also gradually being applied to unstructured road scenarios such as military missions, planetary exploration, and wilderness rescue. In these scenarios, unmanned ground vehicles serve as the application platform for intelligent driving technology, relying on chassis control to accurately track the vehicle's desired path. Unlike the relatively smooth road surfaces in urban environments, the complex ground conditions in unstructured roads significantly affect the accuracy of path tracking by unmanned ground vehicles. Therefore, ensuring that unmanned ground vehicles can quickly and accurately track the desired path under ground interference is a significant and challenging task.

[0003] Existing research typically focuses on improving the path tracking accuracy of unmanned ground vehicles under random environmental disturbances. Model predictive control (MDC) can predict future paths and adjust steering angle inputs in real time within a finite timeframe, thus it is widely used in unmanned ground vehicle path tracking control. However, current research still has limitations in several aspects. First, most current path tracking control methods neglect the nonlinearity caused by the time delay of the vehicle's steering actuators when building the vehicle model, resulting in the inability to guarantee the vehicle's tracking accuracy during actual control. Second, current control strategies ignore the impact of coupled slope on control performance. Unstructured roads contain numerous slope turning scenarios. When unmanned ground vehicles turn on slopes, they inevitably generate coupled slope effects encompassing both side and longitudinal slopes, generating additional longitudinal and lateral forces on the vehicle, thus affecting the accuracy of vehicle path tracking. Finally, although traditional MDC methods can significantly improve vehicle path tracking performance, the step of using quadratic programming to solve for the optimal control sequence greatly increases computational power, leading to prolonged computation time and making it difficult to apply in practical vehicles. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a low-computational-power path tracking control method for ground vehicles considering coupled slope. First, a vehicle dynamics and kinematic model considering coupled slope is established through coordinate transformation and dynamic analysis to ensure the path tracking accuracy of unmanned ground vehicles on coupled slopes. Second, an unmanned ground vehicle path tracking system considering actuator time delay is constructed, and its state-space equations are discretized to enable its use in model predictive control. Finally, a path tracking control method is developed, utilizing Laguerre function fitting to replace the quadratic programming step of solving for the optimal control sequence in traditional model predictive control, significantly reducing the computational power required for the control method. Simulation results demonstrate that the proposed control method effectively reduces the computational power of the control method while maintaining the accuracy of unmanned ground vehicle path tracking.

[0005] The technical solution of this invention is described below in conjunction with the accompanying drawings:

[0006] This invention provides a low-computing-power path tracking control method for ground vehicles that considers coupled slope, comprising the following steps:

[0007] Step 1: Establish vehicle dynamics and kinematics models that consider coupled slope through coordinate transformation and dynamic analysis to ensure the path tracking accuracy of unmanned ground vehicles on coupled slopes;

[0008] Step 2: Construct an unmanned ground vehicle path tracking system that considers actuator time delay and discretize the state-space equations for model predictive control;

[0009] Step 3: Design a path tracking control method. Use the Laguerre function to rewrite the state-space equation and cost function of the path tracking system. This transforms the quadratic programming step in traditional model predictive control into a differentiation step, reducing the computational requirements of the control method.

[0010] Furthermore, the specific method for step one is as follows:

[0011] S11: Define three coordinate systems, namely the global coordinate system. Vehicle coordinate system and vehicle projection coordinate system The global coordinate system is fixed on a flat ground, the vehicle coordinate system is located at the vehicle's center of gravity, and the origin of the vehicle projection coordinate system is the projection of the vehicle's center of gravity onto the XOY plane.

[0012] S12: The vehicle's gravity in the global coordinate system will be generated along the vehicle coordinate system. Additional force and As shown below:

[0013] (1)

[0014] (2)

[0015] (3)

[0016] In the formula, For longitudinal additional force; For lateral additional force; This is an additional vertical force; The coordinate transformation matrix from the vehicle projected coordinate system to the vehicle coordinate system; This is the coordinate transformation matrix from the global coordinate system to the vehicle projected coordinate system; The lateral slope of the road; The longitudinal slope of the road; Projected heading angle of the vehicle; For vehicle quality; ;

[0017] S13: Establish a vehicle dynamics model on a coupled slope that ignores the vehicle's roll, pitch, and vertical motion, as shown below:

[0018] (4)

[0019] (5)

[0020] In the formula, This refers to the vehicle's yaw torque. This refers to the vehicle's sideslip angle; The vehicle's yaw rate; The longitudinal speed of the vehicle; The vehicle's lateral speed; The longitudinal force of the four tires, The lateral forces of the four tires. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver; Ideal front wheel steering angle; This is the distance from the vehicle's center of gravity to the front axle. This is the distance from the vehicle's center of gravity to the rear axle. The wheelbase of the vehicle; For lateral additional force;

[0021] Assuming the vehicle's turning angle and longitudinal acceleration are zero, equations (4) and (5) can be rewritten as follows:

[0022] (6)

[0023] (7)

[0024] In the formula, This refers to the yaw moment of the vehicle caused by the coupling slope; This refers to the additional vehicle yaw moment caused by wheel torque distribution; The coefficient of friction of the ground; The vertical force acting on the right side of the vehicle; The vertical force acting on the left side of the vehicle;

[0025] Under the influence of coupling slope and lateral acceleration, the vertical force of the tires on both sides The calculation is as follows:

[0026] (8)

[0027] (9)

[0028] In the formula, Road slope; The height of the vehicle's center of gravity above the ground; This refers to the vehicle's wheelbase.

[0029] By linearizing the tire model, the lateral forces experienced by the tires on the front and rear axles are... It can be represented as follows:

[0030] (10)

[0031] (11)

[0032] (12)

[0033] (13)

[0034] In the formula, The lateral stiffness of the four tires. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver; This is the slip angle of the front wheel; This is the slip angle of the rear wheel;

[0035] Combining the above formulas (1)-(13), the following vehicle dynamics model considering the coupled slope is established:

[0036] (14)

[0037] (15)

[0038] In the formula, For the lateral stiffness of the vehicle's front axle; The rear axle lateral stiffness of the vehicle;

[0039] S14: Establish the Frenet coordinate system on the reference path ; lateral error The distance between the vehicle's center of gravity and the center of gravity of the reference path, and the heading error. The actual heading angle of the vehicle and Tangential angle of reference path difference;

[0040] The kinematic model of the vehicle for path tracking is represented as follows:

[0041] (16)

[0042] In the formula, The curvature of the road.

[0043] Furthermore, the specific method for step two is as follows:

[0044] S21: Combining the vehicle dynamics model considering the coupled slope and the vehicle kinematics model, we obtain the path tracking equation for the unmanned ground vehicle considering actuator time delay:

[0045] (17)

[0046] In the formula, This is the actual front wheel steering angle; The time constant characterizing the time delay properties of the actuator;

[0047] Selecting variables for the unmanned ground vehicle path tracking system: Selecting state variables Input variables Disturbance variables ;

[0048] S22: Based on the variables of the unmanned ground vehicle path tracking system, establish the state-space equation of the path tracking system considering actuator time delay:

[0049] (18)

[0050] In the formula, For state variables; For input variables; For disturbance variables;

[0051] ;

[0052] ;

[0053] ;

[0054] In the formula, This is the path tracking system matrix; Input matrix for path tracking; This is the path tracking state interference matrix;

[0055] S23: Discretize the state-space equation of the path tracking system; Model predictive control uses a discrete model to predict the future state of the controlled object and obtains the optimal control quantity through rolling optimization; Discretize the system state-space equation in continuous time; Discretize the continuous-time matrix in equation (18) using the zero-order hold discretization method to obtain the discretized state-space equation of the path tracking system:

[0056] (19)

[0057] (20)

[0058] In the formula, For the first State variables for each period; For the first Input variables for each cycle; For the first Disturbance variables for each period; For discrete path tracking system matrices; Input matrix for discrete path tracking; This is the discrete path tracking state disturbance matrix; For the first State variables for each period; It is discrete time.

[0059] Furthermore, the specific method for step three is as follows:

[0060] S31: Constructing a multi-objective optimization problem for unmanned ground vehicle path tracking:

[0061] (twenty one)

[0062] (twenty two)

[0063] In the formula, The cost function; For the first State variables for each period; For the first The input increment per cycle; This represents the maximum input increment. Maximum input amount; To predict the step size; To output the weight matrix; The input weight matrix; For input quantities; For the first The input increment per cycle; For the first Reference state quantity for each cycle;

[0064] S32: The Laguerre function is used to describe the vehicle's steering angle and additional yaw moment sequence; the discrete Laguerre function is shown in the following form:

[0065] (twenty three)

[0066] In the formula, For the first Discrete Laguerre function; These are the poles of the discrete Laguerre function; The number of terms in the discrete Laguerre function; For complex variables;

[0067] To simplify the analysis of discrete vehicle path tracking systems, conduct The transformation makes the discrete Laguerre function express in the following form:

[0068] (twenty four)

[0069] In the formula, yes of Transformation, for The number of transformation terms constitutes the polynomial of the discrete Laguerre function; For the first Item path tracing Laguerre polynomials;

[0070] To simplify the analysis of the path tracing system, the Laguerre polynomial recursive representation of path tracing is as follows:

[0071] (25)

[0072] (26)

[0073] (27)

[0074] In the formula, for The recurrence matrix; For the first Item path tracing Laguerre polynomials; The initial path is traced using the Laguerre polynomial;

[0075] The vehicle is Input at any given time The Laguerre polynomial description using path tracing is as follows:

[0076] (28)

[0077] (29)

[0078] In the formula, These are the Laguerre fitting coefficients; This is the steering angle increment; and These are the Laguerre fitting coefficients for the steering angle and the additional yaw moment, respectively. The Laguerre fitting coefficients for the steering angle increment; Laguerre fitting coefficients for the additional yaw moment; For the first Item path tracing in the Laguerre polynomial of the 1st term item Transform the discrete Laguerre function; For the first Item path tracing Laguerre polynomials;

[0079] Steering angle and additional yaw moment described by Laguerre polynomials via path tracking The discrete state-space equations and cost functions are rewritten; the input quantities are... Substituting into the discrete state-space equations and combining with equation (28), the following iterative derivation yields the system state variables and output variables expressed using the path-tracking Laguerre polynomials:

[0080] (30)

[0081] In the formula, For the first Path tracking of Laguerre polynomials over several cycles;

[0082] The cost function of the vehicle path tracking optimization problem can be rewritten using the path tracking Laguerre polynomial:

[0083] (31)

[0084] (32)

[0085] (33)

[0086] In the formula, The rewritten cost function; The state integration matrix; For Laguerre integration matrix; For the first Item path tracing Laguerre polynomials;

[0087] By analyzing the Laguerre fitting coefficients Differentiation yields the optimal input sequence for path tracking; the goal of path tracking control is to find a suitable input sequence that minimizes the established cost function; through transformation, the cost function... It has been described as having a relationship with the Laguerre fit coefficients. The function; therefore, by adjusting the cost function to Taking the derivative and setting it to zero yields the corresponding optimal Laguerre fit coefficients:

[0088] (34)

[0089] (35)

[0090] In the formula, The optimal Laguerre fit coefficients for path tracking; and They are respectively and The matrix:

[0091] (36)

[0092] (37)

[0093] By deriving and calculating, and combining with equation (28), the first result after fitting using the Laguerre function is obtained. Input variables for each period The first row in each control cycle is selected, which is the optimal steering angle increment for path tracking. and the additional vehicle yaw moment caused by wheel torque distribution .

[0094] The beneficial effects of this invention are as follows:

[0095] 1. This invention establishes a vehicle dynamics model and a vehicle kinematics model that consider coupled slope. It can dynamically adapt to the impact of road surfaces covering both cross and longitudinal slopes on vehicle path tracking performance, thus improving the accuracy of unmanned ground vehicle path tracking.

[0096] 2. This invention constructs a path tracking system for unmanned ground vehicles that incorporates actuator time delay. It can take into account the actuator time delay present in actual vehicles, thus improving the robustness of path tracking control for unmanned ground vehicles;

[0097] 3. This invention designs a path tracking model predictive control method based on the Laguerre function. By using Laguerre function fitting to replace the quadratic programming solution for the optimal control sequence in traditional model predictive control methods, the computational requirements of the control method can be significantly reduced. Attached Figure Description

[0098] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0099] Figure 1 Architecture diagram of a low-computing-power path tracking control method for unmanned ground vehicles that takes into account coupling slope and actuator time delay;

[0100] Figure 2 A schematic diagram illustrating the coupled slope driving of an unmanned ground vehicle.

[0101] Figure 3 This is a schematic diagram of the vehicle dynamics model;

[0102] Figure 4 This is a schematic diagram of the vehicle's kinematics model.

[0103] Figure 5 This is a schematic diagram of a double lane shifting operation on a ramp.

[0104] Figure 6 This is a diagram illustrating the comparison of path tracking performance;

[0105] Figure 7 This is a diagram showing the comparison of algorithm running times. Detailed Implementation

[0106] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0107] Example 1:

[0108] See Figure 1 This embodiment provides a low-computing-power path tracking control method for ground vehicles that considers coupled slope, including the following steps:

[0109] Step 1: Establish vehicle dynamics and kinematics models considering coupled slopes through coordinate transformation and dynamic analysis to ensure the path tracking accuracy of unmanned ground vehicles on coupled slopes, as detailed below:

[0110] S11: Define three coordinate systems, see [link / reference] Figure 2 The diagram contains three coordinate systems: the global coordinate system and the global coordinate system. Vehicle coordinate system and vehicle projection coordinate system The global coordinate system is fixed on a flat ground, the vehicle coordinate system is located at the vehicle's center of gravity, and the origin of the vehicle projection coordinate system is the projection of the vehicle's center of gravity onto the XOY plane.

[0111] S12: Due to the influence of the coupling slope, the vehicle's gravity in the global coordinate system will be generated along the vehicle coordinate system. Additional force and As shown below:

[0112] (1)

[0113] (2)

[0114] (3)

[0115] In the formula, For longitudinal additional force; For lateral additional force; This is an additional vertical force; The coordinate transformation matrix from the vehicle projected coordinate system to the vehicle coordinate system; This is the coordinate transformation matrix from the global coordinate system to the vehicle projected coordinate system; The lateral slope of the road; The longitudinal slope of the road; Projected heading angle of the vehicle; For vehicle quality; ;

[0116] S13: To focus on key characteristics of unmanned ground vehicle path tracking, establish as follows Figure 3 The vehicle dynamics model on the coupled slope, neglecting the vehicle's roll, pitch, and vertical motion, is shown below:

[0117] (4)

[0118] (5)

[0119] In the formula, This refers to the vehicle's yaw torque. This refers to the vehicle's sideslip angle; The vehicle's yaw rate; The longitudinal speed of the vehicle; The vehicle's lateral speed; The longitudinal force of the four tires, The lateral forces of the four tires. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver; Ideal front wheel steering angle; This is the distance from the vehicle's center of gravity to the front axle. This is the distance from the vehicle's center of gravity to the rear axle. The wheelbase of the vehicle; For lateral additional force;

[0120] Since vehicles generally travel slowly in off-road environments, it is assumed that the vehicle's turning angle and longitudinal acceleration are approximately zero. Therefore, equations (4) and (5) can be rewritten as follows:

[0121] (6)

[0122] (7)

[0123] In the formula, This refers to the yaw moment of the vehicle caused by the coupling slope; This refers to the additional vehicle yaw moment caused by wheel torque distribution; The coefficient of friction of the ground; The vertical force acting on the right side of the vehicle; The vertical force acting on the left side of the vehicle;

[0124] Under the influence of coupling slope and lateral acceleration, the vertical force of the tires on both sides The calculation is as follows:

[0125] (8)

[0126] (9)

[0127] In the formula, Road slope; The height of the vehicle's center of gravity above the ground; This refers to the vehicle's wheelbase.

[0128] By linearizing the tire model, the lateral forces experienced by the tires on the front and rear axles are... It can be represented as follows:

[0129] (10)

[0130] (11)

[0131] (12)

[0132] (13)

[0133] In the formula, The lateral stiffness of the four tires. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver; This is the slip angle of the front wheel; This is the slip angle of the rear wheel;

[0134] Combining the above formulas (1)-(13), the following vehicle dynamics model considering the coupled slope is established:

[0135] (14)

[0136] (15)

[0137] In the formula, For the lateral stiffness of the vehicle's front axle; The rear axle lateral stiffness of the vehicle;

[0138] S14: Establish the vehicle kinematics model. A schematic diagram of vehicle path tracking is shown below. Figure 4 As shown in the diagram. The two red dots represent the actual position of the vehicle's center of gravity and the reference path's center of gravity, respectively, while the blue dashed lines are tangents along the actual and reference paths. A Frenet coordinate system is established on the reference path. Lateral error The distance between the vehicle's center of gravity and the center of gravity of the reference path, and the heading error. The actual heading angle of the vehicle and Tangential angle of reference path difference.

[0139] Therefore, the kinematic model of the path-tracking vehicle is expressed as:

[0140] (16)

[0141] In the formula, The curvature of the road.

[0142] Step 2: Construct an unmanned ground vehicle path tracking system considering actuator time delay and discretize its state-space equations for model predictive control. The specific method is as follows:

[0143] S21: Construct a path tracking system considering actuator time delay. Due to the signal transmission delay between sensors, controllers, and actuators, the ideal steering angle output by the controller will become the actual steering angle output to the steering wheels after a certain time delay. Combining the vehicle dynamics model considering the coupled slope and the vehicle kinematics model, the path tracking equation for unmanned ground vehicles considering actuator time delay is obtained:

[0144] (17)

[0145] In the formula, This is the actual front wheel steering angle; The time constant characterizing the time delay properties of the actuator;

[0146] Selecting variables for the unmanned ground vehicle path tracking system: Selecting state variables Input variables Disturbance variables ;

[0147] S22: Based on the variables of the unmanned ground vehicle path tracking system, establish the state-space equation of the path tracking system considering actuator time delay:

[0148] (18)

[0149] In the formula, For state variables; For input variables; For disturbance variables;

[0150] ;

[0151] ;

[0152] ;

[0153] In the formula, This is the path tracking system matrix; Input matrix for path tracking; This is the path tracking state interference matrix;

[0154] S23: Discretize the state-space equations of the path tracking system. Model predictive control uses a discrete model to predict the future state of the controlled object and obtains the optimal control quantity through rolling optimization. Therefore, we need to further discretize the continuous-time system state-space equations. The continuous-time matrix in (18) is discretized using the zero-order hold discretization method, and the discretized state-space equations of the path tracking system are obtained as follows:

[0155] (19)

[0156] (20)

[0157] In the formula, For the first State variables for each period; For the first Input variables for each cycle; For the first Disturbance variables for each period; For discrete path tracking system matrices; Input matrix for discrete path tracking; This is the discrete path tracking state disturbance matrix; For the first State variables for each period; It is discrete time;

[0158] S3: Design a path tracking control method that rewrites the state-space equations and cost functions of the path tracking system using the Laguerre function. This transforms the quadratic programming step in traditional model predictive control into a differentiation step, reducing the computational requirements of the control method. The specific method is as follows:

[0159] S31: To ensure vehicle stability, ride comfort, and tracking accuracy, a multi-objective optimization problem for unmanned ground vehicle path tracking is constructed:

[0160] (twenty one)

[0161] (twenty two)

[0162] In the formula, The cost function; For the first State variables for each period; For the first The input increment per cycle; This represents the maximum input increment. Maximum input amount; To predict the step size; To output the weight matrix; The input weight matrix; For input quantities; For the first The input increment per cycle; For the first Reference state quantity for each cycle;

[0163] S32: Traditional MPC methods use quadratic programming to solve for the cost function and obtain the optimal input sequence. However, quadratic programming consumes significant computational resources and cannot meet the real-time requirements of vehicle operation. Therefore, this invention uses the Laguerre function to fit the optimal input, replacing the quadratic programming step in traditional MPC and reducing the computational resource consumption of the control method.

[0164] First, the Laguerre function is used to describe the vehicle's steering angle and additional yaw moment sequence; the discrete Laguerre function is shown in the following form:

[0165] (twenty three)

[0166] In the formula, For the first Discrete Laguerre function; These are the poles of the discrete Laguerre function; The number of terms in the discrete Laguerre function; For complex variables;

[0167] To simplify the analysis of discrete vehicle path tracking systems, conduct The transformation makes the discrete Laguerre function express in the following form:

[0168] (twenty four)

[0169] In the formula, yes of Transformation, for The number of transformation terms constitutes the polynomial of the discrete Laguerre function; For the first Item path tracing Laguerre polynomials;

[0170] To simplify the analysis of the path tracing system, the Laguerre polynomial recursive representation of path tracing is as follows:

[0171] (25)

[0172] (26)

[0173] (27)

[0174] In the formula, for The recurrence matrix; For the first Item path tracing Laguerre polynomials; The initial path is traced using the Laguerre polynomial;

[0175] The vehicle is Input at any given time The Laguerre polynomial description using path tracing is as follows:

[0176] (28)

[0177] (29)

[0178] In the formula, These are the Laguerre fitting coefficients; This is the steering angle increment; and These are the Laguerre fitting coefficients for the steering angle and the additional yaw moment, respectively. The Laguerre fitting coefficients for the steering angle increment; Laguerre fitting coefficients for the additional yaw moment; For the first Item path tracing in the Laguerre polynomial of the 1st term item Transform the discrete Laguerre function; For the first Item path tracing Laguerre polynomials;

[0179] Secondly, the steering angle and additional yaw moment are described by the Laguerre polynomial through path tracking. The discrete state-space equations and cost functions are rewritten; the input quantities are... Substituting into the discrete state-space equations and combining with equation (28), the following iterative derivation yields the system state variables and output variables expressed using the path-tracking Laguerre polynomials:

[0180] (30)

[0181] In the formula, For the first Path tracking of Laguerre polynomials over several cycles;

[0182] The cost function of the vehicle path tracking optimization problem can be rewritten using the path tracking Laguerre polynomial:

[0183] (31)

[0184] (32)

[0185] (33)

[0186] In the formula, The rewritten cost function; The state integration matrix; For Laguerre integration matrix; For the first Item path tracing Laguerre polynomials;

[0187] Finally, by analyzing the Laguerre fitting coefficients... Differentiation yields the optimal input sequence for path tracking; the objective of path tracking control is to find a suitable input sequence that minimizes the value of the established cost function; through the above transformation, the cost function... It has been described as having a relationship with the Laguerre fit coefficients. The function; therefore, by adjusting the cost function to Taking the derivative and setting it to zero yields the corresponding Laguerre fitting coefficients:

[0188] (34)

[0189] (35)

[0190] In the formula, The optimal Laguerre fit coefficients for path tracking; and They are respectively and The matrix:

[0191] (36)

[0192] (37)

[0193] By deriving and calculating, and combining with equation (28), the first result after fitting using the Laguerre function is obtained. Input variables for each period The first row in each control cycle is selected, which is the optimal steering angle increment for path tracking. and the additional vehicle yaw moment caused by wheel torque distribution .

[0194] Example 2:

[0195] To verify the effectiveness and superiority of the method proposed in this invention, the following were selected: Figure 5 The simulation verification was performed on the double lane-changing scenario on the ramp shown, with the road slope set at 20° and the vehicle speed at 10 m / s. The obtained path tracking performance and algorithm runtime are compared as follows: Figure 6 and Figure 7 As shown.

[0196] As can be seen, in terms of control performance, the unmanned ground vehicle path tracking control method proposed in this invention, which considers coupling slope and actuator time delay, can closely approximate the traditional model predictive control method and significantly reduce the vehicle's lateral tracking error. In terms of computing power, the proposed control method can significantly reduce the runtime of the traditional model predictive control method, meeting the computing power and real-time requirements of vehicle path tracking control.

[0197] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A low-computing-power path tracking control method for ground vehicles considering coupled slope, characterized in that, Includes the following steps: Step 1: Establish vehicle dynamics and kinematics models that consider coupled slope through coordinate transformation and dynamic analysis to ensure the path tracking accuracy of unmanned ground vehicles on coupled slopes; Step 2: Construct an unmanned ground vehicle path tracking system that considers actuator time delay and discretize the state-space equations for model predictive control; Step 3: Design a path tracking control method. Use the Laguerre function to rewrite the state-space equation and cost function of the path tracking system. This transforms the quadratic programming step in traditional model predictive control into a differentiation step, reducing the computational requirements of the control method.

2. The low-computing-power path tracking control method for ground vehicles considering coupled slope as described in claim 1, characterized in that, The specific method for step one is as follows: S11: Define three coordinate systems, namely the global coordinate system. Vehicle coordinate system and vehicle projection coordinate system The global coordinate system is fixed on a flat ground, the vehicle coordinate system is located at the vehicle's center of gravity, and the origin of the vehicle projection coordinate system is the projection of the vehicle's center of gravity onto the XOY plane. S12: The vehicle's gravity in the global coordinate system will be generated along the vehicle coordinate system. Additional force and As shown below: （1） （2） （3） In the formula, For longitudinal additional force; For lateral additional force; This is a vertical additional force; The coordinate transformation matrix from the vehicle projected coordinate system to the vehicle coordinate system; This is the coordinate transformation matrix from the global coordinate system to the vehicle projected coordinate system; The lateral slope of the road; The longitudinal slope of the road; Projected heading angle of the vehicle; For vehicle quality; ; S13: Establish a vehicle dynamics model on a coupled slope that ignores the vehicle's roll, pitch, and vertical motion, as shown below: （4） （5） In the formula, This refers to the vehicle's yaw torque. This refers to the vehicle's sideslip angle; The vehicle's yaw rate; The longitudinal speed of the vehicle; The vehicle's lateral speed; The longitudinal force of the four tires, The lateral forces of the four tires. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver; Ideal front wheel steering angle; This is the distance from the vehicle's center of gravity to the front axle. This is the distance from the vehicle's center of gravity to the rear axle. The wheelbase of the vehicle; For lateral additional force; Assuming the vehicle's turning angle and longitudinal acceleration are zero, equations (4) and (5) can be rewritten as follows: （6） （7） In the formula, This refers to the yaw moment of the vehicle caused by the coupling slope. This refers to the additional vehicle yaw moment caused by wheel torque distribution; The coefficient of friction of the ground; The vertical force acting on the right side of the vehicle; The vertical force acting on the left side of the vehicle; Under the influence of coupling slope and lateral acceleration, the vertical force of the tires on both sides The calculation is as follows: （8） （9） In the formula, Road slope; The height of the vehicle's center of gravity above the ground; This refers to the vehicle's wheelbase. By linearizing the tire model, the lateral forces experienced by the tires on the front and rear axles are... It can be represented as follows: （10） （11） （12） （13） In the formula, The lateral stiffness of the four tires. for The hour represents the front wheel. for The time represents the rear wheel. for The hour wheel represents the right wheel. for The hour wheel represents the revolver; This is the slip angle of the front wheel; This is the slip angle of the rear wheel; Combining the above formulas (1)-(13), the following vehicle dynamics model considering the coupled slope is established: （14） （15） In the formula, For the lateral stiffness of the vehicle's front axle; The rear axle lateral stiffness of the vehicle; S14: Establish the Frenet coordinate system on the reference path ; lateral error The distance between the vehicle's center of gravity and the center of gravity of the reference path, and the heading error. The actual heading angle of the vehicle and Tangential angle of reference path difference; The kinematic model of the vehicle for path tracking is represented as follows: （16） In the formula, The curvature of the road.

3. The low-computing-power path tracking control method for ground vehicles considering coupled slope according to claim 2, characterized in that, The specific method for step two is as follows: S21: Combining the vehicle dynamics model and vehicle kinematics model considering the coupled slope, the path tracking equation for unmanned ground vehicles considering actuator time delay is obtained: （17） In the formula, This is the actual front wheel steering angle; The time constant characterizing the time delay properties of the actuator; Selecting variables for the unmanned ground vehicle path tracking system: Selecting state variables Input variables Disturbance variables ; S22: Based on the variables of the unmanned ground vehicle path tracking system, establish the state-space equation of the path tracking system considering actuator time delay: （18） In the formula, For state variables; For input variables; For disturbance variables; ； ； ； In the formula, This is the path tracking system matrix; Input matrix for path tracking; This is the path tracking state interference matrix; S23: Discretize the state-space equation of the path tracking system; Model predictive control uses a discrete model to predict the future state of the controlled object and obtains the optimal control quantity through rolling optimization; Discretize the system state-space equation in continuous time; Discretize the continuous-time matrix in equation (18) using the zero-order hold discretization method to obtain the discretized state-space equation of the path tracking system: （19） （20） In the formula, For the first State variables for each period; For the first Input variables for each cycle; For the first Disturbance variables for each period; For discrete path tracking system matrices; Input matrix for discrete path tracking; This is the discrete path tracking state disturbance matrix; For the first State variables for each period; It is discrete time.

4. The low-computing-power path tracking control method for ground vehicles considering coupled slope according to claim 3, characterized in that, The specific method for step three is as follows: S31: Constructing a multi-objective optimization problem for unmanned ground vehicle path tracking: （21） （22） In the formula, The cost function; For the first State variables for each period; For the first The input increment per cycle; This represents the maximum input increment. Maximum input amount; To predict the step size; To output the weight matrix; The input weight matrix; For input quantities; For the first The input increment per cycle; For the first Reference state quantities for each cycle; S32: The Laguerre function is used to describe the vehicle's steering angle and additional yaw moment sequence; the discrete Laguerre function is shown in the following form: （23） In the formula, For the first Discrete Laguerre function; These are the poles of the discrete Laguerre function; The number of terms in the discrete Laguerre function; For complex variables; To simplify the analysis of discrete vehicle path tracking systems, conduct The transformation makes the discrete Laguerre function express in the following form: （24） In the formula, yes of Transformation, for The number of transformation terms constitutes the polynomial of the discrete Laguerre function; For the first Item path tracing Laguerre polynomials; To simplify the analysis of the path tracing system, the Laguerre polynomial recursive representation of path tracing is as follows: （25） （26） （27） In the formula, for The recurrence matrix; For the first Item path tracing Laguerre polynomials; The initial path is traced using the Laguerre polynomial; The vehicle is Input at any given time The Laguerre polynomial description using path tracing is as follows: （28） （29） In the formula, These are the Laguerre fitting coefficients; This is the steering angle increment; and These are the Laguerre fitting coefficients for the steering angle and the additional yaw moment, respectively. The Laguerre fitting coefficients for the steering angle increment; Laguerre fitting coefficients for the additional yaw moment; For the first Item path tracing in the Laguerre polynomial of the 1st term item Transform the discrete Laguerre function; For the first Item path tracing Laguerre polynomials; Steering angle and additional yaw moment described by Laguerre polynomials via path tracking The discrete state-space equations and cost functions are rewritten; the input quantities are... Substituting into the discrete state-space equations and combining with equation (28), the following iterative derivation yields the system state variables and output variables expressed using the path-tracking Laguerre polynomials: （30） In the formula, For the first Path tracking of Laguerre polynomials over several cycles; The cost function of the vehicle path tracking optimization problem can be rewritten using the path tracking Laguerre polynomial: （31） （32） （33） In the formula, The rewritten cost function; The state integration matrix; For Laguerre integration matrix; For the first Item path tracing Laguerre polynomials; By analyzing the Laguerre fitting coefficients Differentiation yields the optimal input sequence for path tracking; the goal of path tracking control is to find a suitable input sequence that minimizes the established cost function; through transformation, the cost function... It has been described as having a relationship with the Laguerre fit coefficients. The function; therefore, by adjusting the cost function to Taking the derivative and setting it to zero yields the corresponding optimal Laguerre fit coefficients: （34） （35） In the formula, The optimal Laguerre fit coefficients for path tracking; and They are respectively and The matrix: （36） （37） By deriving and calculating, and combining with equation (28), the first result after fitting using the Laguerre function is obtained. Input variables for each period The first row in each control cycle is selected, which is the optimal steering angle increment for path tracking. and the additional vehicle yaw moment caused by wheel torque distribution .

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