Forklift path tracking control method based on MPC and ARC cooperation

Abstract

The invention discloses a forklift path tracking control method based on MPC and ARC cooperation, and belongs to the technical field of industrial vehicle automatic control. Comprising the steps that an upper-layer MPC is designed based on a forklift kinematics model, and an expected steering angle and an expected speed instruction are obtained through solving; a lower-layer ARC is designed based on the pump control steering system dynamics model to track an expected steering angle, and a PID controller is designed to track an expected speed; a time delay compensation mechanism is integrated in the upper-layer MPC, and a high-frequency execution strategy is adopted. According to the method, interference of the steering system is accurately observed and compensated, parameter uncertainty is adaptively processed through parameters, nonlinear uncertainty is processed through robust items, a time delay compensation mechanism is integrated in MPC, all control rates are display expressions, online solution is not needed, and the method is suitable for large-scale popularization and application. The influence of steering resistance dramatic change, external interference, unmodeled dynamics and system time delay on the control precision is effectively reduced, and high-precision and low-time-delay path tracking performance is achieved.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology for unmanned vehicles and industrial vehicles, and more specifically to a forklift path tracking control method based on MPC and ARC collaboration. Background Technology

[0002] Precise and stable path tracking is a core function for unmanned forklifts to achieve efficient and safe operation in complex environments such as warehousing and logistics. Traditional path tracking methods often employ a single LQR or pure-pursuit algorithm, which struggles to guarantee high-precision tracking performance when faced with the inherent strong nonlinearity of forklift systems, parameter uncertainties (such as changes in mass and moment of inertia due to load variations), and actuator delays. While Model Predictive Control (MPC) can handle multivariate constraints and optimization, its high computational complexity can easily introduce significant delays if directly applied to low-level execution, affecting system real-time performance and stability. Furthermore, forklift steering systems (especially pump-controlled systems) suffer from uncertainties such as hydraulic nonlinearity, friction, and leakage; relying solely on upper-level planning cannot guarantee the precise execution of steering angle commands.

[0003] In existing technologies, some solutions attempt to combine the MPC with the underlying controller, but most use simple PID controllers as the underlying actuators, which lack robustness and cannot effectively suppress strong interference and uncertainties in the steering system, resulting in limited actual tracking accuracy. Other solutions, while introducing robust control concepts, fail to achieve deep collaborative design with the upper-level MPC and do not systematically optimize latency for the characteristics of forklift operations (such as low speed, high inertia, and frequent starts and stops), making it difficult to simultaneously meet the dual requirements of high accuracy and low latency. Therefore, constructing a hierarchical collaborative control architecture that can leverage the global optimization capabilities of the MPC while utilizing a highly robust underlying controller to execute instructions accurately and quickly is key to improving the path tracking performance of unmanned forklifts. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a forklift path tracking control method based on MPC and ARC collaboration. This method employs a layered architecture design, with the upper-layer MPC responsible for global trajectory planning and reference command generation, and the lower-layer using adaptive robust control (ARC) to accurately track steering angle commands, supplemented by a PID controller to track speed commands. Simultaneously, it integrates a time delay compensation strategy, effectively addressing the impact of forklift system nonlinearity, uncertainty, and time delay on path tracking accuracy.

[0005] The present invention adopts the following technical solution: A forklift path tracking control method based on MPC and ARC collaboration, characterized by the following steps: Step 1: Establish the kinematic model of the forklift and the dynamic model of the pump-controlled steering system.

[0006] Step 2: Based on the forklift kinematic model, design the upper-level MPC and solve for the desired steering angle and desired speed commands.

[0007] Step 3: Based on the dynamic model of the pump-controlled steering system, design the lower-level ARC to track the desired steering angle. And design a PID controller to track the desired speed. .

[0008] Step 4: Integrate a latency compensation mechanism into the upper-layer MPC and adopt a high-frequency execution strategy to achieve the entire path tracking.

[0009] In step 1 above, the forklift kinematic model uses a single-rail model: ; in, For vehicle location, For heading angle, For longitudinal velocity, This refers to the front wheel steering angle. This refers to the wheelbase.

[0010] The dynamic model of the pump-controlled steering system in step 1 is based on the following assumptions: the hydraulic cylinder has only internal leakage and no external leakage; the load on the hydraulic cylinder is an inertial load and has no elastic load; the flow equation of the bidirectional fixed displacement pump is: ; In the formula: This refers to the displacement of a bidirectional fixed displacement pump. The rotational angular velocity of the bidirectional fixed displacement pump; The flow continuity equation for a hydraulic cylinder is: ; ; In the formula: and These represent the flow rates of the two chambers of the hydraulic cylinder, respectively. The effective area of ​​the hydraulic cylinder piston. For piston displacement, This is the internal leakage coefficient of the hydraulic cylinder. and These are the pressures in the two chambers of the hydraulic cylinder, respectively. and These are the volumes of the two chambers of the hydraulic cylinder. It is the bulk modulus of elasticity; Define load pressure as Load flow is defined as According to Newton's second law, the state variable is redefined. The state-space equations of the system are obtained as follows: ; In the formula: This refers to the total volume of the two chambers of the hydraulic cylinder. The total mass of the load, The viscous damping coefficient of the piston. For items that are difficult to model accurately, including external disturbance forces and unmodeled frictional forces.

[0011] The specific process of designing the upper-layer MPC in step 2 is as follows: 2.1 The continuous-time single-track model is discretized. The discretized model is as follows: ;

[0012] Where k represents the kth control cycle, The sampling period is represented by the discretized model, denoted by the state transition function: State vector , control input vector ; 2.2 Predicting the starting state after time delay compensation: Using the currently known control input, within the time delay window... Taking the open-loop integral of the state transition function, we get: ,in, These are the control commands sent to the actuator in the previous cycle; assuming a time delay... Cross If there are 1 complete sampling period, the predicted starting state is: ,in This indicates that the state transition function will be applied iteratively. Second-rate; 2.3 In each control cycle k, the upper-level MPC solves for a... This is a finite-time optimization problem with an initial state, and the prediction time domain length is N; specifically as follows: 2.3.1 Control input sequence for the next N steps: ; 2.3.2 Based on initial state and candidate control sequences Predicting future states using a recursive discretization model: ; 2.3.3 Construct the objective function, which is to minimize the weighted sum of path tracking error, control effort, and velocity tracking error: ; in: It is the predicted two-dimensional location. It is the position of the reference trajectory at the corresponding time point. It is the expected velocity corresponding to the reference trajectory. It is the position error weight matrix. It is the weight of the steering angle control quantity. It is the weight of the speed error. It is the terminal state weight; 2.3.4 To ensure that the generated instructions are physically feasible and safe, the following constraints are added: ① State constraints: derived from the state transition equations ensure; ② Control input constraints: , ; ③ Control the rate of change constraint: , ; in It is the maximum acceleration. It is the maximum steering angular velocity.

[0013] 2.4 In each control cycle, the upper-level MPC controller performs the following operations: Get Status: Read the current vehicle status ; Delay compensation: Predicted starting state after calculating delay. ; Construct and solve: with Using the initial values, construct and solve the above constrained nonlinear optimization problem online; Extraction instruction: from the optimal solution In the middle, only the first control variable is extracted: ; Send command: Send to the lower-level controller; Rolling time domain: in the next cycle Discard the old prediction sequence and repeat the above process to achieve rolling optimization.

[0014] The specific process of designing the lower-level ARC in step 3 is as follows: 3.1.1 Define the set of uncertain parameters as follows: ,in And define state variables. Combining the dynamic equations of the steering angle, the following state-space equations can be obtained: ; 3.1.2 The system disturbance is estimated and compensated using a nonlinear disturbance observer, which has the following form: ; In the formula: For the nonlinear function to be designed, The gain of the nonlinear observer satisfies ; The observation error of the nonlinear disturbance observer is defined as: For disturbances Without any prior data, it is assumed that its dynamic characteristics change slowly relative to the observer, i.e.: The dynamic equation of the observer error system is: ;choose As a constant, design ; 3.1.3 First Design Error ,in Design the second error , ;definition express The estimated value, This represents the estimation error. and Representing the maximum and minimum values ​​of an uncertain parameter, a projection of a discontinuous parameter is given in the following form: ; The adaptive law of parameters is expressed as: ,in It is a diagonal matrix representing the adaptive gain. Let represent an adaptive function; for any adaptive function By satisfying the adaptive law of the projection rule, the following will be true: ; Design a control law to make tending towards 0, The dynamic equation is expressed as: ; Design control law : ; Selecting Lyapunov functions: ; Differentiating it, we get: ; in For nonlinear error, in the formula: ; design The following conditions must be met for calming: ; From the parameter adaptive law and The dynamic equation can be obtained as follows: ; For any arbitrarily small positive number, this formula represents the system tracking error. It will eventually move into a domain that can be manually defined over time.

[0015] When the system only has parameter uncertainty, the Lyapunov function is defined as follows: ; Differentiating it, we get: ; Depend on and control law We can obtain: ; That is, when the only uncertainty in the system is the parameters, the lower-level ARC can achieve progressive tracking performance.

[0016] The standard PID control law of the PID controller in step 3: In the formula: For proportional gain, For integral gain, This is the differential gain.

[0017] Step 4 integrates a time delay compensation mechanism and adopts a high-frequency execution strategy, as follows: the operating frequency of the upper-layer MPC is set to 20-50Hz; the operating frequency of the lower-layer ARC and PID controllers is set to 200-500Hz; it is proven through Lyapunov stability theory that under the action of the designed upper-layer MPC, the steering angle tracking error is consistent and eventually bounded; under the time delay compensation mechanism, the closed-loop system can obtain asymptotically stable path tracking performance.

[0018] As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following advantages: (1) A hierarchical collaborative architecture is adopted, which realizes the organic combination of global optimization and local precise execution.

[0019] (2) The lower-level ARC controller can effectively handle the parameter uncertainty and external interference of the pump-controlled steering system, ensuring high-precision tracking of steering angle commands.

[0020] (3) By introducing delay compensation and high-frequency control strategies in MPC, the end-to-end delay of the system is significantly reduced and the dynamic response performance is improved.

[0021] (4) The overall solution takes into account control accuracy, robustness and real-time performance, and is particularly suitable for unmanned forklift application scenarios with strict requirements for operational efficiency and safety. Attached Figure Description

[0022] Figure 1 This is a flowchart of the forklift path tracking control method based on MPC and ARC collaboration according to the present invention.

[0023] Figure 2 This is a schematic diagram of the reference path used in this invention.

[0024] Figure 3 This is a diagram illustrating the effect of MPC+ARC control path tracking employed in this invention.

[0025] Figure 4 This is a comparison curve of the path lateral tracking error under the MPC+ARC control, LQR control and traditional Pure Pursuit control designed in this invention.

[0026] Figure 5 This is a comparison curve of the path tracking steering angle under the MPC+ARC control, LQR control and traditional Pure Pursuit control designed in this invention. Detailed Implementation

[0027] Specific embodiments of the present invention will now be described with reference to the accompanying drawings. Many details are described below to provide a comprehensive understanding of the invention; however, those skilled in the art will not need these details to implement the invention. Well-known components, methods, and processes will not be described in detail below.

[0028] Combination Figure 1 This invention discloses a forklift path tracking control method based on MPC and ARC collaboration, comprising the following steps: Step 1: Establish the kinematic model of the forklift and the dynamic model of the pump-controlled steering system, as follows: 1.1 The system model is established based on the following assumptions: the forklift is operating at low speed and the tire slip angle is ignored.

[0029] The kinematic model of the forklift uses a single-rail model: (1); in, For vehicle location, For heading angle, For longitudinal velocity, This refers to the front wheel steering angle. This refers to the wheelbase.

[0030] 1.2 The dynamic model of the pump-controlled steering system is established based on the following assumptions: the pump-controlled steering system is a second-order dynamic system; the hydraulic cylinder has only internal leakage and no external leakage; the load on the hydraulic cylinder is an inertial load and there is no elastic load. The flow equation of the bidirectional fixed displacement pump is: (2); In the formula: This refers to the displacement of a bidirectional fixed displacement pump. ; The rotational angular velocity of the bidirectional fixed displacement pump .

[0031] The flow continuity equation for a hydraulic cylinder is: (3); (4); In the formula: and These represent the flow rates of the two chambers of the hydraulic cylinder, respectively. ; The effective area of ​​the hydraulic cylinder piston. ; For piston displacement, ; This is the internal leakage coefficient of the hydraulic cylinder. ; and These are the pressures in the two chambers of the hydraulic cylinder, respectively. ; and These are the volumes of the two chambers of the hydraulic cylinder. ; For bulk modulus, .

[0032] Define load pressure as And the load flow is defined as Combining equations (3) and (4), we get: (5); In the formula: This refers to the total volume of the two chambers of the hydraulic cylinder. According to Newton's second law, the equilibrium equation between the output force and the load of a hydraulic cylinder is: (6); In the formula: The total mass of the load, ; The viscous damping coefficient of the piston. ; For items that are difficult to model accurately, including external disturbance forces and unmodeled frictional forces.

[0033] Define state variables Then, from equations (2) to (6), the system's state-space equations can be obtained as follows: (7); Step 2: Based on the forklift kinematics model, design the upper-level MPC, as follows: This step aims to design an upper-level MPC that can calculate the optimal steering angle and speed command sequence for a future period based on the global reference path and the current vehicle state, and use the first command in the sequence as the tracking target for the lower-level controller. This is to address the inherent communication and execution latency of the system. This design introduces a time delay compensation mechanism at the prediction starting point.

[0034] 2.1 Discretization of the forklift kinematic model The continuous-time forklift kinematic model (single-rail model) is discretized to facilitate its implementation in a digital controller. Specifically, the first-order Euler method (or the more accurate Runge-Kutta method) is used to discretize the above single-rail model, i.e., formula (1), with a sampling period of [missing information]. .

[0035] Discretized (first-order Euler): (8); Where k represents the kth control cycle, This represents the sampling period. The discretized model is denoted as the state transition function: (9); Wherein, the state vector , control input vector .

[0036] 2.2 Starting point for state prediction of time delay compensation Let the total latency from system perception to execution be... (For example, 50ms). If the current time is Then MPC at time The decisions made will actually be It begins to affect the system at any moment.

[0037] To make MPC's predictions more consistent with reality, its predictions should not be based on the current actual state. Instead of starting, we should begin with the predicted state after the time delay. start.

[0038] Open-loop prediction: using the currently known control input within the time delay window The system is then subjected to open-loop integration.

[0039] (10);

[0040] in It is the control command sent to the actuator in the previous cycle.

[0041] State Observer: Using a state estimator such as a Kalman filter (KF) or an extended Kalman filter (EKF), it directly outputs the best estimate of the future state. In this embodiment, an open-loop prediction method is used. Assume a time delay. Cross If there are 1 complete sampling period, the predicted starting state is: (11); in This indicates that the state transition function will be applied iteratively. Second-rate.

[0042] 2.3 Constructing a finite-time domain rolling optimization problem.

[0043] In each control cycle k, MPC solves a problem using... This is a finite-time optimization problem with an initial state and a prediction time domain length of N.

[0044] 2.3.1 Optimization Variable: The control input sequence for the next N steps: (12); 2.3.2 State Prediction: Based on Initial State and candidate control sequences Predicting future states using a recursive discretization model: (13); 2.3.3 Objective Function: The objective is to minimize the weighted sum of path tracking error, control effort, and velocity tracking error. (14); in: It is the predicted two-dimensional location.

[0045] It is the position of the reference trajectory at the corresponding time point.

[0046] It is the expected velocity corresponding to the reference trajectory.

[0047] It is the position error weight matrix.

[0048] It is the weight of the steering angle control quantity.

[0049] It is the weight of the speed error.

[0050] This is the terminal state weight, used to enhance stability (set to 0 in this embodiment).

[0051] 2.3.4 Constraints: To ensure that the generated instructions are physically feasible and safe, the following constraints are added.

[0052] State constraints (implicit): From the state transition equation (15) Guarantee.

[0053] Control input constraints: (16); (17); Control the rate of change constraint (to ensure the actuator is not overloaded): (18); (19); in It is the maximum acceleration. It is the maximum steering angular velocity.

[0054] 2.4 Online Solving and Command Output.

[0055] In each control cycle, the MPC controller performs the following operations: Get Status: Read the current vehicle status .

[0056] Delay compensation: Predicted starting state after calculating delay. .

[0057] Construct and solve: based on the above Using the initial values, construct and solve the above constrained nonlinear optimization problem online.

[0058] Extraction instruction: from the optimal solution In the middle, only the first control variable is extracted: (20); Send command: Send to the lower-level controllers (ARC and PID).

[0059] Rolling time domain: in the next cycle Discard the old prediction sequence and repeat the above process to achieve rolling optimization.

[0060] Step 3: Based on the dynamic model of the pump-controlled steering system, design the lower-level ARC to track the desired steering angle. And design a PID controller to track the desired speed. The details are as follows: 3.1 Design ARC for Tracking : Considering that J and B are parameters that cause uncertainty, the set of uncertain parameters is defined as follows: ,in .

[0061] Define state variables .

[0062] In summary, combining the dynamic equations of the rotation angle, the following state-space equations can be obtained: (twenty one); A nonlinear disturbance observer is used to estimate and compensate for disturbances in the pump-controlled steering system, which has the following form: (twenty two); In the formula: For the nonlinear function to be designed, For the gain of the nonlinear observer, it should satisfy... .

[0063] The observation error of the nonlinear disturbance observer is defined as: (twenty three); Due to the disturbance Since there is no prior data, it is assumed that its dynamic characteristics change slowly relative to the observer, that is: (twenty four); Considering the above equation, the dynamic equation of the observer error system is: (25); As can be seen from the above formula, by making appropriate selections... This can cause the observation error of the observer to converge exponentially.

[0064] choose As a constant, design: (26); Design the first error ,in .

[0065] Design the second error , .

[0066] definition express The estimated value, This represents the estimation error. and Representing the maximum and minimum values ​​of an uncertain parameter, a projection of a discontinuous parameter can be given as follows: (27); The adaptive law of parameters can be expressed as: (28); in It is a diagonal matrix representing the adaptive gain. Let represent an adaptive function. For any adaptive function... By satisfying the adaptive law of the projection rule, all of them will have the following properties: (29); From the system state-space equations, we know that the first equation has no uncertainties, and we can combine the first equation with the second equation in the design. From linear system theory, we know that when... When it approaches 0, It will also inevitably tend towards 0, therefore making The tendency toward 0 is equivalent to making Approaching 0, the design goal becomes designing a control law to make It tends towards 0. The dynamic equation can be expressed as: (30); Design control law : (31); Selecting Lyapunov functions: (32); Differentiating it, we get: (33); in For nonlinear error, in the formula: (34); design The following conditions must be met for calming: (35) From the formula, we can see that This is a robust controller used to manage various uncertainties in the system model. Therefore, from equations (28) and (30), we can derive: (36) For any arbitrarily small positive number, the above formula represents the system tracking error. It will eventually move into a domain that can be manually defined over time.

[0067] If, after a certain moment, the system only has parameter uncertainty, then the Lyapunov function is defined as follows: (37); Differentiating it, we get: (38); From conditions (24) and (31), we get: (39); From the above, it can be concluded that when the system only has parameter uncertainties, the controller can still achieve asymptotic tracking performance.

[0068] 3.2 Design a PID controller to track .

[0069] Design standard PID control law: (40); In the formula: For proportional gain, For integral gain, This is the differential gain.

[0070] Step 4: Integrate a latency compensation mechanism into the upper-layer MPC and adopt a high-frequency execution strategy to achieve the entire path tracing. Details are as follows: The MPC, ARC, and PID controllers are integrated. The MPC operates at 50Hz, while the ARC and PID controllers operate at 500Hz. Control commands are sent to the actuators via a high-speed communication bus (such as CAN FD). Lyapunov stability theory proves that under the designed ARC controller, the steering angle tracking error is consistently and eventually bounded. With the time delay compensation mechanism, the planning performance of the MPC can be effectively reproduced in the actual system, thus ensuring the high accuracy and low time delay characteristics of the entire path tracking system.

[0071] The following is a specific implementation example of the present invention.

[0072] To evaluate the performance of the designed controller, forklift parameters were set in the simulation environment: Wheelbase L=1.5m, maximum steering angle ±30°, maximum speed 5m / s.

[0073] Reference trajectory: such as Figure 2 .

[0074] Go straight to the right for 30m → to (30, 0); Turn left 180° semicircle (r=5m) upward → to (30, 10); Go straight to the left for 15m → to (15, 10); Turn right 180° semicircle (r=5m) upward → to (15, 20); Turn left 90° in a quarter circle (r=5m) and turn right and up → to (20, 25); Move straight up (at most y=30m, then the simulation will stop).

[0075] The following controller parameters are used in the simulation: MPC: Prediction time domain N=10, control time domain C=2, state weight matrix Q=diag(0.05, 0, 1), control weight R=2.

[0076] ARC: = 100, = 20, = 5, = 0.1.

[0077] PID: = 2.0, = 0.5, = 0.1.

[0078] Total system latency Set to 50ms.

[0079] Simulation results are as follows Figure 3 , Figure 4 and Figure 5 As shown. The path tracking error and steering angle response are as follows. Figure 4 and Figure 5 As shown, from Figure 4 It can be seen that the control strategy based on MPC+ARC has a maximum lateral tracking error of less than 0.4m, which is significantly better than PurePursuit and LQR control methods, resulting in higher path tracking accuracy and superior control performance. (System total delay) With a latency of 50ms, it demonstrates its low latency characteristics.

[0080] The above are merely specific embodiments of the present invention, but the design concept of the present invention is not limited thereto. Any non-substantial modifications made to the present invention using this concept shall be considered as infringing upon the protection scope of the present invention.

Claims

1. A forklift path tracking control method based on MPC and ARC collaboration, characterized in that, Includes the following steps: Step 1: Establish the kinematic model of the forklift and the dynamic model of the pump-controlled steering system; Step 2: Based on the forklift kinematic model, design the upper-level MPC and solve for the desired steering angle and desired speed command; Step 3: Based on the dynamic model of the pump-controlled steering system, design the lower-level ARC to track the desired steering angle. And design a PID controller to track the desired speed. ; Step 4: Integrate a latency compensation mechanism into the upper-layer MPC and adopt a high-frequency execution strategy to achieve the entire path tracking.

2. The forklift path tracking control method based on MPC and ARC collaboration as described in claim 1, characterized in that, In step 1, the kinematic model of the forklift adopts a single-rail model. ； in, For vehicle location, For heading angle, For longitudinal velocity, This refers to the front wheel steering angle. This refers to the wheelbase.

3. The forklift path tracking control method based on MPC and ARC collaboration as described in claim 2, characterized in that, The dynamic model of the pump-controlled steering system in step 1 is based on the following assumptions: the hydraulic cylinder has only internal leakage and no external leakage; the hydraulic cylinder load is an inertial load and has no elastic load; the flow equation of the bidirectional fixed displacement pump is: ； In the formula: This refers to the displacement of a bidirectional fixed displacement pump. The rotational angular velocity of the bidirectional fixed displacement pump; The flow continuity equation for a hydraulic cylinder is: ； ； In the formula: and These represent the flow rates of the two chambers of the hydraulic cylinder, respectively. The effective area of ​​the hydraulic cylinder piston. For piston displacement, This is the internal leakage coefficient of the hydraulic cylinder. and These are the pressures in the two chambers of the hydraulic cylinder, respectively. and These are the volumes of the two chambers of the hydraulic cylinder. It is the bulk modulus of elasticity; Define load pressure as Load flow is defined as According to Newton's second law, the state variable is redefined. The state-space equations of the system are obtained as follows: ； In the formula: This refers to the total volume of the two chambers of the hydraulic cylinder. The total mass of the load, The viscous damping coefficient of the piston. For items that are difficult to model accurately, including external disturbance forces and unmodeled frictional forces.

4. The forklift path tracking control method based on MPC and ARC collaboration as described in claim 3, characterized in that, The specific process of designing the upper-layer MPC in step 2 is as follows: 2.1 The continuous-time single-track model is discretized. The discretized model is as follows: ； Where k represents the kth control cycle, The sampling period is represented by the discretized model, denoted by the state transition function: State vector , control input vector ; 2.2 Predicting the starting state after time delay compensation: Using the currently known control input, within the time delay window... Taking the open-loop integral of the state transition function, we get: ,in, These are the control commands sent to the actuator in the previous cycle; assuming a time delay... Cross If there are 1 complete sampling period, the predicted starting state is: ,in This indicates that the state transition function will be applied iteratively. Second-rate; 2.3 In each control cycle k, the upper-level MPC solves for a... This is a finite-time optimization problem with an initial state and a prediction time domain length of N. 2.4 In each control cycle, the upper-layer MPC performs the following operations: Get Status: Read the current vehicle status ; Delay compensation: Predicted starting state after calculating delay. ; Construct and solve: with Using the initial values, construct and solve the above constrained nonlinear optimization problem online; Extraction instruction: from the optimal solution In the middle, only the first control variable is extracted: ; Send command: Send to the lower-level controller; Rolling time domain: in the next cycle Discard the old prediction sequence and repeat the above process to achieve rolling optimization.

5. The forklift path tracking control method based on MPC and ARC collaboration as described in claim 4, characterized in that, Step 2.3 specifically includes: 2.3.1 Control input sequence for the next N steps: ; 2.3.2 Based on initial state and candidate control sequences Predicting future states using a recursive discretization model: ； 2.3.3 Construct the objective function, which is to minimize the weighted sum of path tracking error, control effort, and velocity tracking error: ； in: It is the predicted two-dimensional location. It is the position of the reference trajectory at the corresponding time point. It is the expected velocity corresponding to the reference trajectory. It is the position error weight matrix. It is the weight of the steering angle control quantity. It is the weight of the speed error. It is the terminal state weight; 2.3.4 To ensure that the generated instructions are physically feasible and safe, the following constraints are added: ① State constraints: derived from the state transition equations ensure; ② Control input constraints: ， ； ③ Control the rate of change constraint: ， ； in It is the maximum acceleration. It is the maximum steering angular velocity.

6. The forklift path tracking control method based on MPC and ARC collaboration as described in claim 5, characterized in that: The specific process of designing the lower-level ARC in step 3 is as follows: 3.1.1 Define the set of uncertain parameters as follows: ,in, And define state variables. Combining the dynamic equations of the steering angle, the following state-space equations can be obtained: ； 3.1.2 The system disturbance is estimated and compensated using a nonlinear disturbance observer, which has the following form: ； In the formula: For the nonlinear function to be designed, The gain of the nonlinear observer satisfies ; The observation error of the nonlinear disturbance observer is defined as: For disturbances Without any prior data, it is assumed that its dynamic characteristics change slowly relative to the observer, i.e.: The dynamic equation of the observer error system is: ;choose As a constant, design ; 3.1.3 First Design Error ,in Design the second error , ;definition express The estimated value, This represents the estimation error. and Representing the maximum and minimum values ​​of an uncertain parameter, a projection of a discontinuous parameter is given in the following form: ； The adaptive law of parameters is expressed as: ,in It is a diagonal matrix representing the adaptive gain. Let represent an adaptive function; for any adaptive function By satisfying the adaptive law of the projection rule, the following will be true: ； Design a control law to make tending towards 0, The dynamic equation is expressed as: ; Design control law : ； Selecting Lyapunov functions: ; Differentiating it, we get: ; in For nonlinear error, in the formula: ; design The following conditions must be met for calming: ; From the parameter adaptive law and The dynamic equation can be obtained as follows: ; For any arbitrarily small positive number, this formula represents the system tracking error. It will eventually move into a domain that can be manually defined over time.

7. The forklift path tracking control method based on MPC and ARC collaboration as described in claim 5, characterized in that, When the system only has parameter uncertainty, the Lyapunov function is defined as follows: ； Differentiating it, we get: ; Depend on and control law u We can obtain: ; That is, when the system only has parameter uncertainty, the lower-level ARC obtains asymptotic tracking performance.

8. The forklift path tracking control method based on MPC and ARC collaboration as described in claim 5, characterized in that: The standard PID control rate of the PID controller in step 3 is: In the formula: For proportional gain, For integral gain, This is the differential gain.

9. The forklift path tracking control method based on MPC and ARC collaboration as described in claim 1, characterized in that: In step 4, a time delay compensation mechanism is integrated and a high-frequency execution strategy is adopted, as follows: the operating frequency of the upper-layer MPC is set to 20-50Hz; the operating frequency of the lower-layer ARC and PID controllers is 200-500Hz; it is proven through Lyapunov stability theory that under the action of the designed upper-layer MPC, the steering angle tracking error is consistent and eventually bounded; under the time delay compensation mechanism, the closed-loop system can obtain asymptotically stable path tracking performance.

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