Agricultural unmanned vehicle narrow working condition control method based on nonlinear mapping

Abstract

The application discloses a kind of agricultural unmanned vehicle narrow working condition control method based on nonlinear mapping, belong to agricultural unmanned vehicle motion control technical field.The application first establishes kinematic model with Ackerman steering agricultural unmanned vehicle as object, decouples independent heading subsystem;Constitute adjustable speed exponential nonlinear mapping function, and the heading subsystem is nonlinearly mapped to obtain unconstrained system;Adopt backstepping control method to design heading constraint controller, and the system stability is proved by Lyapunov theory;Finally, the control effect is verified by simulation.The application can strictly guarantee that heading is in the constraint boundary all the time without crossing the boundary, can flexibly adjust control response speed, effectively solve the heading constraint control problem under the narrow working condition of agricultural unmanned vehicle, improve operation safety and tracking accuracy.

Description

Technical Field

[0001] This invention belongs to the field of motion control technology for agricultural unmanned vehicles, specifically relating to a control method for agricultural unmanned vehicles in narrow working conditions based on nonlinear mapping. Background Technology

[0002] With the rapid development of smart agriculture technology, agricultural unmanned vehicles have become core equipment in farmland preparation, sowing, plant protection, and harvesting. Their autonomous driving control capabilities directly determine operational efficiency and quality. In narrow working conditions such as greenhouses, densely planted orchards, and standardized ridge spacing, the driving space of agricultural unmanned vehicles is limited, placing extremely high demands on the boundary constraints of heading control, tracking accuracy, and anti-interference capabilities. Once the heading exceeds the constraint boundaries, accidents such as crop crushing and facility collisions are very likely to occur, causing economic losses.

[0003] Existing heading control methods for agricultural unmanned vehicles (UAVs) primarily rely on conventional PID control, backstepping control, and sliding mode control algorithms. These methods are mainly designed for open farmland operations and can only achieve heading tracking control. They cannot theoretically guarantee that the heading remains within preset constraint boundaries throughout the entire journey, making them unsuitable for the stringent constraint control requirements of confined working conditions. Some constraint control methods based on nonlinear mappings lack speed regulation capabilities in their mapping functions, making it impossible to adjust the control response speed according to the operational needs of different confined scenarios. This results in poor adaptability and unfavorable mathematical properties of the functions, increasing the complexity of controller design and the difficulty of engineering implementation. Summary of the Invention

[0004] To address the above problems, this invention provides a control method for agricultural unmanned vehicles in confined operating conditions based on nonlinear mapping, comprising the following steps: Step 1: Establish the kinematic model of the agricultural unmanned vehicle. Taking the agricultural unmanned vehicle with Ackerman steering geometry as the research object, the rear axle center of the vehicle is selected as the reference point. The vehicle kinematic state equation is established in the northeast coordinate system and the vehicle body coordinate system. The vehicle heading subsystem is decoupled from the complete vehicle kinematic model. Step 2: Construct an adjustable speed nonlinear mapping function. Based on nonlinear system theory, propose an adjustable speed exponential nonlinear mapping function and clarify the characteristic conditions satisfied by the nonlinear mapping function. Step 3: Construct an unconstrained system after mapping. Based on the vehicle heading subsystem established in Step 1, use the adjustable speed nonlinear mapping function constructed in Step 2 to perform nonlinear mapping on the vehicle heading subsystem to obtain an unconstrained vehicle heading subsystem. Step 4: Construct a heading constraint controller for agricultural unmanned vehicles under narrow operating conditions based on nonlinear mapping. Based on the unconstrained vehicle heading subsystem in Step 3, design the heading constraint controller for agricultural unmanned vehicles using the backstepping control method. Step 5: Simulation verification. The heading constraint controller for agricultural unmanned vehicles designed in Steps 1 to 4 based on adjustable speed nonlinear mapping is simulated on the Ackerman kinematic model to verify the heading constraint control effect.

[0005] Preferably, the kinematic model of the agricultural unmanned vehicle established in step 1 is based on the following assumptions: Low-speed driving assumption: Assume the vehicle speed is below 5m / s and ignore tire lateral deviation; No sideslip assumption: It is assumed that there is only pure rolling between the wheel and the ground, with no lateral or longitudinal slippage; In the northeast coordinate system Pointing due north, Pointing due east, Pointing towards the Earth's center of mass; The Ackermann vehicle kinematics model established in the northeast coordinate system is as follows: ; In the above formula, , These represent the vehicle's northward and eastward positions in the northeast coordinate system, respectively. , Representing northward and eastward speeds, For heading angle, Represents the angular velocity of the heading. For vehicle speed, Represents the vehicle's wheelbase. For heading control.

[0006] Preferably, the expression for the vehicle heading subsystem decoupled in step 1 is: ; The change depends only on , and Since the heading subsystem is not coupled with the vehicle's current position coordinates, it is decoupled from the complete vehicle kinematics model and a nonlinear mapping and constraint controller is designed separately for the heading subsystem.

[0007] Preferably, the expression for the adjustable speed exponential nonlinear mapping function constructed in step 2 is: ; In the above formula, As variables, For the mapped variables, This is the speed regulation coefficient. Representative variable Constraint boundaries, The base is the natural number; The nonlinear mapping function satisfies the following properties: The function itself is continuous and invertible; The function has a speed adjustment coefficient, which can be used to adjust the function's response speed; when hour, ,when hour, ; when hour, ; when hour, .

[0008] Preferably, in step 3, a mapping for the heading angle is defined. Its expression is: ; In the above formula, This is the mapped heading angle. represent Constraint boundaries, This is the corresponding nonlinear adjustment coefficient.

[0009] Preferably, in step 3, the mapping inverse mapping The expression is: .

[0010] Preferably, in step 3, the... Taking the derivative with respect to time, the mapped heading subsystem takes the following form: ; In the above formula, The angular velocity of the mapped heading angle. For heading control, the main auxiliary variable; The forms of expression are as follows: ; In the above formula, For heading control secondary auxiliary variables; The presentation format is as follows: .

[0011] Preferably, in step 4, the mapped heading error is defined. for: ; In the above formula, This represents the desired heading angle after mapping. The derivative with respect to time is as follows: ; The rate of change of the heading tracking error. The angular velocity of the desired heading after mapping; To prove the convergence of the heading angle error after mapping, a Lyapunov function is defined. as follows: ; The time derivative of the Lyapunov function is as follows: ; It is the first derivative of the Lyapunov function with respect to time.

[0012] Preferably, in step 4, the controlled variable output by the heading constraint controller for the agricultural unmanned vehicle in narrow operating conditions is defined as follows: ; In the above formula, Represents the positive definite heading control gain; Will Substituting, we get: ; According to Lyapunov's theorem and the above equation, we can obtain... It converges gradually.

[0013] Preferably, the simulation in step 5 uses a nonlinear mapping function to constrain the heading angle, and the simulation is performed using an Ackerman vehicle as the simulation object. The simulation results show that the control method can achieve constrained control of the heading angle of the Ackerman vehicle, and the variables are within the constraint range and do not exceed the limit throughout the entire control process, thus solving the heading constraint control problem of agricultural unmanned vehicles in narrow working conditions.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention transforms the constrained vehicle heading subsystem into an unconstrained system by constructing an adjustable speed nonlinear mapping function. It realizes full-process boundary constraints on heading angle from the system design level, ensuring that the heading angle of the agricultural unmanned vehicle is within the preset constraint range throughout the operation in narrow working conditions, and will not cause boundary overruns, thus avoiding crop crushing and facility collision accidents caused by heading overruns.

[0015] 2. This invention innovatively designs an adjustable speed exponential nonlinear mapping function. The function has a built-in independent speed adjustment coefficient, allowing for flexible adjustment of the control response speed based on the agricultural unmanned vehicle's operating scenario, driving speed, and constraint boundary width. It is adaptable to various narrow operating conditions, such as extremely narrow spaces in greenhouses, orchard rows, and field ridges, demonstrating strong generalization ability. Furthermore, this mapping function possesses excellent mathematical properties such as continuous invertibility, coincident zeros, and asymptotic boundaries, reducing the design difficulty of subsequent controllers and providing a mathematical foundation for engineering implementation.

[0016] 3. Based on the kinematic characteristics of low-speed Ackerman steering agricultural unmanned vehicles, this invention decouples the heading subsystem, which is not coupled with the position, from the complete kinematic model. Nonlinear mapping and controller design are performed only for the heading subsystem, which simplifies the complexity of the control algorithm, reduces the computing power requirements of the on-board controller, and eliminates the need for additional high-precision sensing equipment. It is compatible with the hardware configuration and kinematic model of existing mainstream agricultural unmanned vehicles. Attached Figure Description

[0017] Figure 1 This is a flowchart of the steps of the present invention; Figure 2 This is a characteristic diagram of the nonlinear mapping function of the present invention; Figure 3 This is a heading angle tracking curve diagram for the present invention; Figure 4 This is a diagram of the heading angle tracking curve after mapping according to the present invention; Figure 5 This is a schematic diagram of the northeast coordinate system. Detailed Implementation

[0018] The following combination Figures 1 to 5 The present invention will be further described in detail with reference to the embodiments. The present invention discloses a control method for agricultural unmanned vehicles in narrow working conditions based on nonlinear mapping, comprising the following steps: Step 1: Establish the kinematic model of the agricultural unmanned vehicle: The vehicle kinematic model established in this step is based on the following assumptions: 1. Low-speed driving assumption: Assume that the vehicle speed is low (<5m / s) and tire lateral deviation can be ignored.

[0019] 2. No sideslip assumption: It is assumed that there is only pure rolling between the wheel and the ground, with no lateral or longitudinal slippage.

[0020] A schematic diagram of the northeast coordinate system is shown below. Figure 5 As shown in the figure Pointing due north, Pointing due east, Pointing towards the Earth's center of mass.

[0021] Taking an agricultural unmanned vehicle with Ackerman steering geometry as the research object, the rear axle center of the vehicle is selected as the reference point, and the vehicle kinematic state equation is established in the northeast coordinate system and the vehicle body coordinate system. The Ackermann vehicle kinematics model in the northeast coordinate system is as follows: ; In the above formula, , These represent the vehicle's northward and eastward positions in the northeast coordinate system, respectively. , Representing northward and eastward speeds, For heading angle, Represents the angular velocity of the heading. For vehicle speed, Represents the vehicle's wheelbase. For heading control; This invention will map the vehicle heading subsystem and establish the heading subsystem as follows: ; From the above complete vehicle kinematics model and heading subsystem formula, we can obtain... The change depends only on , and Since the heading subsystem is not coupled with the vehicle's current position coordinates, it can be decoupled from the complete vehicle kinematics model, and nonlinear mapping and constraint controller design can be performed on the heading subsystem separately.

[0022] Step 2: Construct an adjustable speed nonlinear mapping function: Based on nonlinear system theory, a nonlinear mapping function is proposed and the conditions that the function satisfies are described. This invention proposes an innovative adjustable speed exponential nonlinear mapping function as follows: ; In the above formula, As variables, For the mapped variables, This is the speed regulation coefficient. Representative variable Constraint boundaries, The base is the natural number; The constructed mapping function has the following characteristics: The function itself is continuous and invertible; The function has a speed adjustment coefficient, which can be used to adjust the function's response speed; when hour, ,when hour, ; when hour, ; when hour, ; Step 3: Construct the unconstrained system after mapping: Based on the vehicle heading subsystem established in step 1, the adjustable speed nonlinear mapping function constructed in step 2 is used to perform nonlinear mapping on the vehicle heading subsystem to obtain an unconstrained vehicle heading subsystem. Define mapping as follows: ; In the above formula, This is the mapped heading angle. represent Constraint boundaries, This is the corresponding nonlinear adjustment coefficient; Through mapping It can be seen that the mapping function is a continuous elementary function, and the inverse mapping... The format is as follows: ; Taking the time derivative, the mapped heading subsystem takes the following form: ; In the above formula, The angular velocity of the mapped heading angle. For heading control, the main auxiliary variable; The forms of expression are as follows: ; In the above formula, For heading control secondary auxiliary variables; The presentation format is as follows: ; Step 4: Construct a heading constraint controller for agricultural unmanned vehicles under narrow operating conditions based on nonlinear mapping: Based on the unconstrained vehicle heading subsystem in step 3, an agricultural unmanned vehicle heading constraint controller based on adjustable speed nonlinear mapping is designed using the backstepping control method. Define the heading error after mapping for: ; In the above formula, This represents the desired heading angle after mapping. The derivative with respect to time is as follows: ; The rate of change of the heading tracking error. The angular velocity of the desired heading after mapping; To prove the convergence of the heading angle error after mapping, a Lyapunov function is defined. as follows: ; The time derivative of the Lyapunov function is as follows: ; It is the first derivative of the Lyapunov function with respect to time.

[0023] The controlled variable output of the heading constraint controller for the agricultural unmanned vehicle in confined working conditions is defined as follows: ; In the above formula, Represents the positive definite heading control gain; Will Substituting, we get: ; According to Lyapunov's theorem and the above equation, we can obtain... It converges gradually.

[0024] Step 5: Simulation Verification: The heading constraint controller for agricultural unmanned vehicles designed in steps 1 to 4 based on adjustable speed nonlinear mapping was simulated on the Ackermann kinematic model. Simulation condition settings: , , ; By using a nonlinear mapping function to constrain the heading angle, and taking an Ackerman vehicle as the simulation object, the present invention’s control method for agricultural unmanned vehicles in narrow working conditions based on nonlinear mapping is simulated and verified. Figure 2 The characteristics of the constructed nonlinear mapping function are shown, indicating that the constructed adjustable speed nonlinear mapping function satisfies the construction conditions. The lower the speed regulation coefficient, the faster the actual response speed. Figure 3 The heading tracking curve of the Ackerman vehicle under the present invention is shown. The curve shows that the heading angle under the present invention can track the desired angle, and the heading angle response curve remains within the constraint boundary throughout the simulation process. Figure 4 The heading tracking curve of the Ackerman vehicle after mapping under the present invention is shown. The curve shows that the heading angle after constraint processing can converge to the desired heading angle after mapping. Simulation results show that the nonlinear mapping-based control method for agricultural unmanned vehicles in narrow working conditions can achieve constrained control of the heading angle of the Ackerman vehicle, and the variables remain within the constraint range and do not exceed the limit throughout the entire control process, thus solving the heading constraint control problem of agricultural unmanned vehicles in narrow working conditions.

Claims

1. A control method for agricultural unmanned vehicles in narrow operating conditions based on nonlinear mapping, characterized in that, Includes the following steps: Step 1: Establish the kinematic model of the agricultural unmanned vehicle. Taking the agricultural unmanned vehicle with Ackerman steering geometry as the research object, the rear axle center of the vehicle is selected as the reference point. The vehicle kinematic state equation is established in the northeast coordinate system and the vehicle body coordinate system. The vehicle heading subsystem is decoupled from the complete vehicle kinematic model. Step 2: Construct an adjustable speed nonlinear mapping function. Based on nonlinear system theory, propose an adjustable speed exponential nonlinear mapping function and clarify the characteristic conditions satisfied by the nonlinear mapping function. Step 3: Construct an unconstrained system after mapping. Based on the vehicle heading subsystem established in Step 1, use the adjustable speed nonlinear mapping function constructed in Step 2 to perform nonlinear mapping on the vehicle heading subsystem to obtain an unconstrained vehicle heading subsystem. Step 4: Construct a heading constraint controller for agricultural unmanned vehicles under narrow operating conditions based on nonlinear mapping. Based on the unconstrained vehicle heading subsystem in Step 3, design the heading constraint controller for agricultural unmanned vehicles using the backstepping control method. Step 5: Simulation verification. The heading constraint controller for agricultural unmanned vehicles designed in Steps 1 to 4 based on adjustable speed nonlinear mapping is simulated on the Ackerman kinematic model to verify the heading constraint control effect. The expression for the adjustable speed exponential nonlinear mapping function constructed in step 2 is as follows: ； In the above formula, As variables, For the mapped variables, This is the speed regulation coefficient. Representative variable Constraint boundaries, The base is the natural number; The nonlinear mapping function satisfies the following properties: The function itself is continuous and invertible; The function has a speed adjustment coefficient, which can be used to adjust the function's response speed; when hour, ,when hour, ; when hour, ; when hour, .

2. The agricultural unmanned vehicle control method for narrow operating conditions based on nonlinear mapping according to claim 1, characterized in that, The kinematic model of the agricultural unmanned vehicle established in step 1 is based on the following assumptions: Low-speed driving assumption: Assume the vehicle speed is below 5m / s and ignore tire lateral deviation; No sideslip assumption: It is assumed that there is only pure rolling between the wheel and the ground, with no lateral or longitudinal slippage; In the northeast coordinate system Pointing due north, Pointing due east, Pointing towards the Earth's center of mass; The Ackermann vehicle kinematics model established in the northeast coordinate system is as follows: ； In the above formula, , These represent the vehicle's northward and eastward positions in the northeast coordinate system, respectively. , Representing northward and eastward speeds, For heading angle, Represents the angular velocity of the heading. For vehicle speed, Represents the vehicle's wheelbase. For heading control.

3. The agricultural unmanned vehicle control method for narrow operating conditions based on nonlinear mapping according to claim 2, characterized in that, The expression for the vehicle heading subsystem decoupled in step 1 is: ； The change depends only on , and Since the heading subsystem is not coupled with the vehicle's current position coordinates, it is decoupled from the complete vehicle kinematics model and a nonlinear mapping and constraint controller is designed separately for the heading subsystem.

4. The agricultural unmanned vehicle control method for narrow operating conditions based on nonlinear mapping according to claim 3, characterized in that, In step 3, a mapping for the heading angle is defined. Its expression is: ； In the above formula, This is the mapped heading angle. represent Constraint boundaries, This is the corresponding nonlinear adjustment coefficient.

5. The agricultural unmanned vehicle control method for narrow operating conditions based on nonlinear mapping according to claim 4, characterized in that, In step 3, the mapping inverse mapping The expression is: 。 6. The agricultural unmanned vehicle control method for narrow operating conditions based on nonlinear mapping according to claim 5, characterized in that, In step 3, Taking the derivative with respect to time, the mapped heading subsystem takes the following form: ； In the above formula, The angular velocity of the mapped heading angle. For heading control, the main auxiliary variable; The forms of expression are as follows: ； In the above formula, For heading control secondary auxiliary variables; The presentation format is as follows: 。 7. The agricultural unmanned vehicle control method for narrow operating conditions based on nonlinear mapping according to claim 6, characterized in that, In step 4, the mapping heading error is defined. for: ； In the above formula, This represents the desired heading angle after mapping. The derivative with respect to time is as follows: ； The rate of change of the heading tracking error. The angular velocity of the desired heading after mapping; To prove the convergence of the heading angle error after mapping, a Lyapunov function is defined. as follows: ； The time derivative of the Lyapunov function is as follows: ； It is the first derivative of the Lyapunov function with respect to time.

8. The agricultural unmanned vehicle control method for narrow operating conditions based on nonlinear mapping according to claim 7, characterized in that, In step 4, the controlled variable output by the heading constraint controller for the agricultural unmanned vehicle in narrow operating conditions is defined as follows: ； In the above formula, Represents the positive definite heading control gain; Will Substituting, we get: ； According to Lyapunov's theorem and the above equation, we can obtain... It converges gradually.

9. The agricultural unmanned vehicle control method for narrow operating conditions based on nonlinear mapping according to claim 8, characterized in that, The simulation in step 5 uses a nonlinear mapping function to constrain the heading angle. The simulation is performed using an Ackerman vehicle as the simulation object. The simulation results show that the control method can achieve constrained control of the heading angle of the Ackerman vehicle, and the variables are within the constraint range and do not exceed the limit throughout the entire control process, thus solving the heading constraint control problem of agricultural unmanned vehicles in narrow working conditions.

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