Robot adaptive path tracking control method based on improved model predictive control

Abstract

The application discloses a robot adaptive path tracking control method based on improved model prediction control, which comprises the following steps: 1, establishing a wheeled robot dynamics control system model; 2, designing a novel adaptive path tracking controller; 3, designing a lateral-longitudinal decoupled model prediction control algorithm, deducing a lateral error model prediction control law based on a relative error model; 4, designing an adaptive fuzzy control law to estimate a desired running speed value; and 5, designing a longitudinal speed sliding mode surface, deducing a speed sliding mode law, and proving the closed-loop stability of the speed control system by using a candidate Lyapunov function. The method can guarantee that the tracking controller has high stability and high real-time performance, solves the tracking error divergence problem in the steering process by using an adaptive law, solves the poor real-time performance problem of the model prediction control by using the controller decoupling, and improves the tracking control precision and system real-time performance of the wheeled robot under a large-curvature continuous steering path.

Description

Technical Field

[0001] This invention belongs to the field of path tracking control for wheeled robots, specifically an adaptive path tracking control method for robots based on improved model predictive control. Background Technology

[0002] Robots have wide applications in various modern work scenarios such as smart industry, smart agriculture, and smart transportation, requiring autonomous navigation under diverse and challenging working conditions. Autonomous robot navigation encompasses modules such as high-precision map construction, semantic environment perception, feasible path planning, and autonomous decision-making and control. Path tracking control is crucial for achieving autonomous robot navigation. Based on a safe path defined by a high-precision map, robot motion parameters are calculated to achieve high-precision, high-smoothness, and high-real-time path tracking.

[0003] Many scholars have applied model predictive control to the path tracking control problem of robots. However, the path tracking control problem of wheeled robots still faces the following challenges. First, it requires predicting the future path for optimization. During high curvature and long-distance turning, the predicted path differs significantly from the actual path, causing the predicted output to deviate from the expected output and resulting in large lateral tracking deviations. Second, the coupling of speed calculation and front wheel angle calculation leads to a high-dimensional prediction model matrix. During model prediction, the computational complexity of high-dimensional matrices increases exponentially, resulting in poor real-time control performance. Third, it is impossible to dynamically adjust parameters according to path conditions. The model predictive control algorithm only tracks based on a preset vehicle speed, resulting in poor environmental adaptability. If the robot operates on a turning path with continuous high curvature, the turning path tracking error will increase rapidly, which clearly contradicts the control requirements. These challenges make the turning path tracking control of wheeled robots a highly challenging research topic.

[0004] Research on steering path tracking control for wheeled robots will be conducted to improve the stability, real-time performance, control accuracy, and environmental adaptability of path tracking control, providing excellent control performance for the widespread application of wheeled robots in complex environments such as smart factories, smart agriculture, and smart transportation.

[0005] The existing technologies are as follows:

[0006] Application No.: CN201910266117.7, Patent Title: Design Method of Harvester Path Tracking Controller Based on Adaptive Model Predictive Control. This invention addresses the delay problem caused by the large hysteresis of the harvester by improving the prediction time domain of the model predictive control algorithm. First, based on the three-degree-of-freedom motion model of the harvester, a model predictive control algorithm is designed with the steering angle as the control variable. Second, the prediction time domain parameters are tuned for different path and speed conditions based on an improved particle swarm optimization algorithm. Finally, the corresponding prediction time domain is obtained by selecting the operating mode according to the path and travel speed. The particle swarm optimization algorithm is designed to calculate the optimal solution of the control parameters of the model predictive control algorithm, transforming the parameter selection problem into an algorithm optimization problem. Adaptive control is used to suppress the delay and improve the robustness of the harvester control. This invention proposes a prediction time domain estimation method based on an adaptive particle swarm optimization algorithm to ensure the path tracking accuracy of the control system.

[0007] This method utilizes an adaptive parameter control approach based on an improved particle swarm optimization algorithm for model predictive control, which effectively addresses the impact of speed, path, and operating mode on path tracking accuracy. This approach ensures system robustness and avoids the high latency issue inherent in model predictive control algorithms.

[0008] This patent addresses the tracking error divergence problem caused by large robot lag during robot turning path tracking by designing an adaptive law to estimate the running speed. A fuzzy controller speed estimation method is proposed, estimating the desired speed based on path curvature and current running speed, thus improving path tracking accuracy. Simultaneously, to address the high computational complexity of model prediction algorithms, longitudinal and lateral motion control is decoupled, and sliding mode control is introduced for speed tracking, reducing algorithm latency. It is worth noting that while the comparative patent uses an improved particle swarm optimization algorithm to estimate the prediction time domain for adaptive control, this patent uses a fuzzy control algorithm for adaptive speed adjustment and sliding mode control for speed tracking, while a model prediction algorithm is used for path tracking. The two path tracking control algorithms are completely different. Furthermore, the comparative patent can only achieve adaptive control in a fixed operating speed mode, while this patent adaptively adjusts the running speed, resulting in superior performance. Therefore, the design of the tracking control algorithms in these two patents is entirely different.

[0009] Application No.: CN202111469816.5, Patent Title: An Adaptive Speed ​​Intelligent Vehicle Path Tracking Method with Preview Characteristics Based on Model Predictive Control. This invention designs an intelligent vehicle path tracking method with preview characteristics based on model predictive control. First, the average curvature and average rate of change of curvature within a fixed distance in front of the vehicle are used as inputs to the fuzzy inference system, and the preview coefficients are used as the outputs of the fuzzy inference system. Then, the preview coefficients, the current vehicle speed, and the current vehicle lateral error are substituted into the proposed preview distance formula to obtain the preview distance value. Third, the preview distance is mapped onto the reference path to obtain the corresponding reference point, and the angle formed by the reference point, the vehicle's current position, and the X-axis in the world coordinate system is used as the reference heading angle of the model predictive controller at the current sampling time. Finally, a vehicle kinematic model is established, the prediction time-domain equation is obtained, and after optimization, the model prediction problem is obtained and solved to achieve path tracking of the autonomous vehicle. The method provided by this invention can improve the stability and tracking accuracy of the vehicle during turning during path tracking.

[0010] For unknown preview distances, it uses fuzzy inference to determine the road curvature and rate of change of road curvature within a fixed distance and calculates the preview coefficient. Based on the preview coefficient, vehicle speed, and current vehicle lateral error, it obtains the preview distance value through the preview distance formula, completing the calculation of control parameters for the model prediction algorithm and improving the algorithm's stability and tracking accuracy during vehicle steering.

[0011] This patent addresses the tracking error divergence problem caused by large robot lag during robot turning path tracking by designing an adaptive law to estimate the running speed. It proposes a fuzzy controller speed estimation method, estimating the desired speed based on path curvature and current running speed, thus improving path tracking accuracy. Simultaneously, to address the high computational complexity of the model prediction algorithm, it decouples the lateral and longitudinal motion control, introducing sliding mode control for speed tracking to reduce algorithm latency. Notably, the comparative patent calculates preview coefficients based on fuzzy inference and solves for the preview time of the model prediction algorithm using a preview distance formula to achieve adaptive control. This patent, however, uses a fuzzy control algorithm for adaptive speed adjustment and sliding mode control for speed tracking, while the model prediction algorithm is used for path tracking. The two path tracking control algorithms are completely different. Furthermore, the comparative patent only achieves adaptive control in a fixed operating speed mode, while this patent adaptively adjusts the running speed, resulting in superior performance. Therefore, these two patents are entirely different in their tracking control algorithm design. Summary of the Invention

[0012] To address the above issues, this invention proposes a robot adaptive path tracking control method based on improved model predictive control. This method can effectively estimate the upper bound of unknown disturbances, improve the convergence speed and control accuracy of attitude stabilization control, and enhance the stable attitude control performance of UAVs in complex environments.

[0013] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0014] The robot adaptive path tracking control method based on improved model predictive control includes the following steps:

[0015] (1) Establish a dynamic control system model for the Ackerman steering wheeled robot;

[0016] (2) Based on the model prediction algorithm motion tracking controller with lateral and longitudinal decoupling, design a lateral deviation controller;

[0017] (3) Design a longitudinal velocity control sliding surface and use candidate Lyapunov functions to prove the closed-loop stability of the velocity control system;

[0018] (4) Design an adaptive longitudinal velocity control law based on fuzzy algorithm.

[0019] As a further improvement to the present invention, in step (1), a dynamic control system model for the Ackerman steering wheeled robot is established:

[0020] (1.1) Establish a dynamic model of the wheeled robot;

[0021] Establish a global coordinate system and the carrier coordinate system The vehicle pose parameters in the global coordinate system are represented as follows: Based on dynamic analysis, computational robots in Force equations in the direction:

[0022]

[0023] Based on lateral dynamics analysis, lateral acceleration Depend on Components of acceleration in the direction and centripetal acceleration It consists of two parts:

[0024]

[0025]

[0026] Calculate the lateral forces acting on the front and rear wheels based on the small tire angle assumption. , Side slip angle and :

[0027]

[0028]

[0029]

[0030]

[0031] Based on the small angle assumption , The equations for the lateral acceleration and angular acceleration of the carrier are obtained as follows:

[0032]

[0033]

[0034] (1.2) Establish the dynamic state equations of the wheeled robot;

[0035] Lateral control of the wheeled robot is achieved through the front wheel rotation angle. A relative error dynamics model is established with relative road position error, position error rate, heading angle error, and heading angle error rate as state variables. The first-order differential of the state variables is calculated as follows:

[0036]

[0037] Using the front wheel deflection angle as the system input, the system dynamic state equation is obtained:

[0038]

[0039] in

[0040]

[0041] .

[0042] As a further improvement of the present invention, step (2) of designing the motion tracking controller for the model prediction algorithm with horizontal and vertical decoupling includes the following steps:

[0043] Based on the dynamic model, the system state variables Using the front wheel steering angle as the system's state input, the system's state-space equations are obtained:

[0044]

[0045] The system state variables are solved by transforming the robot's position information coordinates to the Frenet coordinate system:

[0046]

[0047] By desired vehicle speed and desired road curvature Calculate the vehicle's desired angular velocity

[0048]

[0049] The system dynamics equations are linearly approximated and discretized. Taylor expansion is performed at path points, and first-order terms are retained to obtain the discretized approximate linear time-varying equations:

[0050]

[0051] In the prediction time domain Internally, iterate over the future state of the system:

[0052]

[0053] future The system output in the time domain is represented as follows:

[0054]

[0055] in

[0056]

[0057] Based on the current desired trajectory, the error between the current pose and the desired trajectory is calculated and online rolling optimization is performed. The nonlinear objective function is transformed into a quadratic programming problem to achieve local optimal solutions at each time step.

[0058]

[0059] Maximum front wheel steering angle The constraints serve as the conditions for the quadratic programming problem. After solving the quadratic programming problem in each control cycle, the first element of the solution sequence is used as the control input for the system at the next moment. The model predictive control algorithm based on lateral error also needs to add the wheel angle before the feedback control quantity. Add feedforward angle later This makes the system tend to stabilize, and the lateral error converges to 0;

[0060]

[0061] .

[0062] As a further improvement of the present invention, in step (3), designing the longitudinal velocity control sliding surface and proving the closed-loop stability of the velocity control system using candidate Lyapunov functions includes the following steps:

[0063] Simplifying the speed control law using a vehicle kinematic model Achieve ideal speed The tracking equation for velocity error is:

[0064]

[0065] Pick Set the sliding mode function to ,but;

[0066]

[0067] The sliding mode control law is designed as follows:

[0068]

[0069] Pick ,but ,Right now It satisfies Lyapunov's stability theorem, and the velocity error... The exponent converges to zero, and the closed-loop system is stable.

[0070] As a further improvement of the present invention, in step (4), an adaptive longitudinal velocity control law is designed based on a fuzzy algorithm:

[0071] The system's lateral error diverges along the turning path, with the divergence rate proportional to the running speed; it converges along the straight path, with the convergence rate having little impact on the running speed. Therefore, the lateral deviation... and the average curvature of future roads in the predicted time domain The desired speed of the vehicle is used as the input to the fuzzy controller. As the output of the fuzzy controller, design the fuzzy controller:

[0072] (1) When the average curvature of the road remains unchanged during the preview time and the lateral deviation is large, the expected speed should be reduced to improve the stability of path tracking;

[0073] (2) When the lateral deviation changes little, and the average curvature of the road increases during the preview time, the expected speed should be reduced to ensure stable driving during the turning process;

[0074] (3) Adjustments based on the average curvature of the road have a higher priority than path tracking error, and priority should be given to ensuring the accuracy of steering path tracking;

[0075] lateral error The unit is m, the universe of discourse is [0, 0.4], the fuzzy subset is designed as {NS (minimum), MS (small), O (medium), ML (large), NL (maximum)}, and a triangular membership function is used to predict the average curvature of future roads in the time domain. The unit is 1 / m, the universe of discourse is [0, 0.17], the fuzzy subset is {NS (minimum), MS (small), O (medium), ML (large), NL (maximum)}, and a triangular membership function is used. The output variable is the expected velocity. The unit is m / s, the universe of discourse is [1,6], the fuzzy subset is {NS(minimum), MS(small), O(medium), ML(large), NL(maximum)}, and the triangular membership function is used.

[0076] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0077] 1. This method employs a fast non-singular fixed-time sliding mode control design. Compared to traditional sliding mode controllers, the controller designed in this method offers control continuity and further reduces chattering. Furthermore, the proposed algorithm achieves stable convergence within a fixed time, resulting in higher tracking accuracy.

[0078] 2. The fixed-time dynamic sliding surface designed by this method is itself non-singular, and there is no need to set up a critical layer to process the sliding surface in an indirect way to avoid the singularity problem, which further simplifies the design of the sliding surface and reduces the amount of computation.

[0079] 3. The adaptive control law designed in this method is used to effectively estimate the upper bound of the lumped disturbance, further improving the quality of the control input under unknown disturbance conditions. Attached Figure Description

[0080] Figure 1 This is a flowchart of the wheeled robot path tracking control method disclosed in this invention;

[0081] Figure 2 This is a comparison diagram of the effects of the method disclosed in this invention with other conventional methods in the embodiments;

[0082] Figure 3 The following is a simulation comparison diagram of the U-shaped turning method and the smooth turning method of the present invention in the embodiment. Detailed Implementation

[0083] The present invention will be further described below with reference to specific embodiments.

[0084] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0085] like Figure 1As shown, this invention discloses a robot adaptive path tracking control method based on improved model predictive control, comprising the following steps:

[0086] (1.1) Establish a dynamic model of the wheeled robot;

[0087] Establish a global coordinate system and the carrier coordinate system The vehicle pose parameters in the global coordinate system are represented as follows: Based on dynamic analysis, computational robots in Force equations in the direction:

[0088]

[0089] Based on lateral dynamics analysis, lateral acceleration Depend on Components of acceleration in the direction and centripetal acceleration It consists of two parts:

[0090]

[0091] Calculate the lateral forces acting on the front and rear wheels based on the small tire angle assumption. , Side slip angle and :

[0092]

[0093]

[0094]

[0095]

[0096] Based on the small angle assumption , From this, we can obtain the equations for the lateral acceleration and angular acceleration of the carrier:

[0097]

[0098] (1.2) Establish the dynamic state equations of the wheeled robot;

[0099] Lateral control of the wheeled robot is mainly achieved through the front wheel steering angle. By establishing a relative error dynamics model with relative road position error, position error rate, heading angle error, and heading angle error rate as state variables, the first-order differential of the state variables can be calculated as follows:

[0100]

[0101]

[0102] Using the front wheel deflection angle as the system input, the system dynamic state equation is obtained:

[0103]

[0104] in

[0105]

[0106]

[0107] (2.1) Establish a model predictive controller for lateral error

[0108] By decoupling the traditional model predictive control algorithm, the control method for lateral error is retained while the influence of longitudinal velocity is ignored. Based on the dynamic model, the system state variables are... Using the front wheel steering angle as the system's state input, the system's state-space equations are obtained:

[0109]

[0110] The system state variables can be solved by transforming the robot's position coordinates to the Frenet coordinate system.

[0111]

[0112] By desired vehicle speed and desired road curvature Calculate the vehicle's desired angular velocity

[0113]

[0114] The system dynamics equations are linearly approximated and discretized. Taylor expansion is performed at path points, and first-order terms are retained to obtain the discretized approximate linear time-varying equations:

[0115]

[0116] In the prediction time domain Internally, iterate over the future state of the system:

[0117] future The system output in the time domain can be represented as

[0118]

[0119] in

[0120]

[0121] Based on the current desired trajectory, the error between the current pose and the desired trajectory is calculated, and online rolling optimization is performed. The nonlinear objective function is transformed into a quadratic programming problem, achieving local optimal solutions at each time step.

[0122]

[0123] Maximum front wheel steering angle The constraints serve as the conditions for the quadratic programming problem. After solving the quadratic programming problem in each control cycle, the first element of the solution sequence is used as the control input for the system at the next time step. The model predictive control algorithm based on lateral error also requires the wheel angle to be considered in the feedback control input. Add feedforward angle later This makes the system tend to stabilize, and the lateral error converges to 0.

[0124]

[0125]

[0126] (3.1) Design a sliding mode controller for longitudinal velocity

[0127] Given the robot's relatively slow operating speed and small rate of change of speed, the longitudinal error caused by the system's dynamic characteristics is small. Therefore, the speed control law can be simplified using the vehicle's kinematic model. Achieve ideal speed The tracking equation for velocity error is:

[0128]

[0129] Pick Set the sliding mode function to ,but

[0130]

[0131] The sliding mode control law is designed as follows:

[0132]

[0133] Pick ,but ,Right now It satisfies Lyapunov's stability theorem, and the velocity error... The exponent converges to zero, the system closed-loop is stable, and speed tracking control with low computational load is achieved.

[0134] (4.1) Design an adaptive fuzzy control velocity estimator

[0135] Simulation results of steering path tracking at speeds from 2 m / s to 6 m / s based on traditional model predictive control algorithms show that the best path tracking performance is achieved at 3 m / s; at 5 m / s, path tracking accuracy is maintained while achieving fast path tracking. The system's lateral error diverges along the steering path, with the divergence rate proportional to the operating speed; however, it converges along the straight path, with the convergence rate having little impact on the operating speed. Therefore, the lateral deviation... and the average curvature of future roads in the predicted time domain The desired speed of the vehicle is used as the input to the fuzzy controller. As the output of the fuzzy controller, design the fuzzy controller:

[0136] 1) When the average curvature of the road remains constant during the preview time and the lateral deviation is large, the desired speed should be reduced to improve the stability of path tracking.

[0137] 2) When the lateral deviation changes little, and the average curvature of the road increases during the preview time, the expected speed should be reduced to ensure stable driving during the steering process.

[0138] 3) Adjustments based on the average curvature of the road have a higher priority than path tracking error, and priority is given to ensuring the accuracy of steering path tracking.

[0139] lateral error The unit is m, the universe of discourse is [0, 0.4], and the fuzzy subset is designed as {NS (minimum), MS (small), O (medium), ML (large), NL (maximum)}, using a triangular membership function. The average curvature of future roads in the time domain is predicted. The unit is 1 / m, the universe of discourse is [0, 0.17], the fuzzy subset is {NS (minimum), MS (small), O (medium), ML (large), NL (maximum)}, and a triangular membership function is used. The output variable is the expected velocity. The unit is m / s, the universe of discourse is [1,6], and the fuzzy subset is {NS(minimum), MS(small), O(medium), ML(large), NL(maximum)}, using a triangular membership function. The fuzzy rule table shown in Table 1 is constructed.

[0140] Table 1 Fuzzy Control Rule Table

[0141]

[0142] To verify the steering path tracking control performance of the wheeled robot disclosed in this invention, the parameters of the wheeled robot are shown in the table below.

[0143] Table 2 Parameter Table of Wheeled Robot Model

[0144]

[0145] Under U-turn conditions, initial position error and heading angle error are introduced as initial system errors to test the robustness of the designed controller. The designed controller is then compared with a traditional model predictive controller at speeds of 3 m / s, 4 m / s, and 5 m / s through simulation verification. The simulation starts at positions (-0.5 m, -0.5 m) and heading angles are... The initial velocity is 0 m / s; the starting position of the desired trajectory is (0 m, 0 m), and the heading angle is... The turning radius is 6 m. The simulation results are compared with those of traditional model predictive control algorithms as follows: Figure 2 As shown in the figure, (a) is the trajectory tracking effect, (b) is the lateral error of trajectory tracking, (c) is the heading angle error of trajectory tracking, (d) is the robot's speed, and (e) is the simulation time. The blue curve in the figure represents the traditional model predictive control speed of 3 m / s, the red curve represents the traditional model predictive control speed of 4 m / s, the yellow curve represents the traditional model predictive control speed of 5 m / s, and the purple curve represents the operating curve disclosed in this invention. The average lateral errors during U-shaped turning at speeds of 3 m / s, 4 m / s, and 5 m / s, and the method proposed in this invention, are 0.1352 m, 0.1868 m, 0.2275 m, and 0.1617 m, respectively; the average heading angle errors are 0.1175, 0.1527, 0.1679, and 0.0360, respectively; and the average simulation times are 0.0412 s, 0.0389 s, 0.0379 s, and 0.0151 s, respectively.

[0146] A comparison was made with the Pure Pursuit (PP) algorithm controller and the Linear Quadratic Regulator (LQR) controller, with simulation comparisons in U-turn and smooth steering modes. Figure 3As shown in the figure, (a) is the trajectory tracking diagram in the U-turn mode, (c) is the trajectory tracking error in the U-turn mode, (e) is the heading angle error in the U-turn mode, (b) is the trajectory tracking diagram in the smooth turn mode, (d) is the trajectory tracking error in the smooth turn mode, (f) is the heading angle error in the smooth turn mode, and (g) is the average simulation time of a single control cycle. The blue curve in the figure represents the PP algorithm, the red curve represents the LQR algorithm, and the yellow curve represents the method proposed in this invention. The average lateral deviations of the PP algorithm, LQR algorithm, and the method proposed in this invention during the U-turn process are 0.5796m, 0.1860m, ​​and 0.1244m, respectively, and the average heading angle errors are 0.1409, 0.0224, and 0.0340, respectively. In smooth steering mode, the average lateral deviations of the PP algorithm, LQR algorithm, and the method proposed in this invention are 0.5697m, 0.2205m, and 0.1292m, respectively, and the average heading angle deviations are 0.2758, 0.0295, and 0.4528, respectively. The average simulation time per control cycle for the PP algorithm, LQR algorithm, and the method proposed in this invention is 0.0274s, 0.0292s, and 0.0151s, respectively.

[0147] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A robot adaptive path tracking control method based on improved model predictive control, characterized in that, Includes the following steps: (1) Establish a dynamic control system model for the Ackerman steering wheeled robot; (2) Based on the model prediction algorithm motion tracking controller with lateral and longitudinal decoupling, design a lateral deviation controller; In step (2), designing the motion tracking controller for the model prediction algorithm with horizontal and vertical decoupling includes the following steps: Based on the dynamic model, the system state variables Using the front wheel steering angle as the system's state input, the system's state-space equations are obtained: ； The system state variables are solved by transforming the robot's position information coordinates to the Frenet coordinate system: ； By desired vehicle speed and desired road curvature Calculate the vehicle's desired angular velocity ; ； The system dynamics equations are linearly approximated and discretized. Taylor expansion is performed at path points, and first-order terms are retained to obtain the discretized approximate linear time-varying equations: ； In the prediction time domain Internally, iterate over the future state of the system: ； future The system output in the time domain is represented as follows: ； in; ； Based on the current desired trajectory, the error between the current pose and the desired trajectory is calculated and online rolling optimization is performed. The nonlinear objective function is transformed into a quadratic programming problem to achieve local optimal solutions at each time step. ； Maximum front wheel steering angle The constraints serve as the conditions for the quadratic programming problem. After solving the quadratic programming problem in each control cycle, the first element of the solution sequence is used as the control input for the system at the next moment. The model predictive control algorithm based on lateral error also needs to add the wheel angle before the feedback control quantity. Add feedforward angle later This makes the system tend to stabilize, and the lateral error converges to 0; ； ； (3) Design a longitudinal velocity control sliding surface and use candidate Lyapunov functions to prove the closed-loop stability of the velocity control system; (4) Design an adaptive longitudinal velocity control law based on fuzzy algorithm.

2. The robot adaptive path tracking control method based on improved model predictive control according to claim 1, characterized in that, In step (1), a dynamic control system model for the Ackerman steering wheeled robot is established: (1.1) Establish a dynamic model of the wheeled robot; Establish a global coordinate system and the carrier coordinate system The vehicle pose parameters in the global coordinate system are represented as follows: Based on dynamic analysis, computational robots in Force equations in the direction: ； Based on lateral dynamics analysis, lateral acceleration Depend on Components of acceleration in the direction and centripetal acceleration Two parts composition: ； ； Calculate the lateral forces acting on the front and rear wheels based on the small tire angle assumption. , Side slip angle and : ； ； ； ； Based on the small angle assumption , The equations for the lateral acceleration and angular acceleration of the carrier are obtained as follows: ； ； (1.2) Establish the dynamic state equations of the wheeled robot; Lateral control of the wheeled robot is achieved through the front wheel rotation angle. A relative error dynamics model is established with relative road position error, position error rate, heading angle error, and heading angle error rate as state variables. The first-order differential of the state variables is calculated as follows: ； ； Using the front wheel deflection angle as the system input, the system dynamic state equation is obtained: ； in; ； 。 3. The robot adaptive path tracking control method based on improved model predictive control according to claim 1, characterized in that, In step (3), the design of the longitudinal velocity control sliding surface and the proof of the closed-loop stability of the velocity control system using candidate Lyapunov functions include the following steps: Simplifying the speed control law using a vehicle kinematic model Achieve ideal speed The tracking equation for velocity error is: ； Pick Set the sliding mode function to ,but; ； The sliding mode control law is designed as follows: ； Pick ,but ,Right now It satisfies Lyapunov's stability theorem, and the velocity error... The exponent converges to zero, and the closed-loop system is stable.

4. The robot adaptive path tracking control method based on improved model predictive control according to claim 1, characterized in that, In step (4), an adaptive longitudinal velocity control law is designed based on a fuzzy algorithm: The system's lateral error diverges along the turning path, with the divergence rate proportional to the running speed; it converges along the straight path, with the convergence rate having little impact on the running speed. Therefore, the lateral deviation... and the average curvature of future roads in the predicted time domain The desired speed of the vehicle is used as the input to the fuzzy controller. As the output of the fuzzy controller.

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