Adaptive sliding mode trajectory tracking control method based on fuzzy multi-objective function model

Abstract

The invention provides an adaptive sliding mode trajectory tracking control method based on a fuzzy multi-objective function model, and the method comprises the steps: firstly, building a kinematic model of an omnidirectional mobile robot, and generating a virtual path between the mass center of the mobile robot and a preset point in real time; a final sliding mode control law is obtained by defining a sliding mode surface and designing a sliding mode switching function and constructing a switching control law and an equivalent control law; for a plurality of sub-optimization targets, fuzzy logic is adopted to perform fuzzification processing, and a membership function is constructed by using a hexagonal fuzzy number, so that optimization of the controller is realized; besides, an adaptive controller is designed, and by combining an adaptive sliding mode control strategy of equivalent control and switching control and fusing a fuzzy multi-objective function model, the controller can adaptively adjust behaviors of the controller according to different external interferences and system states, and high-precision trajectory tracking is realized. According to the invention, the linear tracking trajectory and the circular tracking trajectory are simulated and controlled, and the trajectory tracking control performance of the mobile robot is improved.

Description

Technical Field

[0001] The present invention belongs to the field of industrial intelligent manufacturing, and in particular relates to an adaptive synovial trajectory tracking control method based on a fuzzy multi-objective function model. Background Art

[0002] With the continuous improvement of industrial manufacturing automation and intelligence, mobile robots have become an indispensable key equipment in smart factories. Intelligent wheeled robots are gradually replacing heavy physical work in traditional manufacturing. Path planning and path tracking of mobile robots are the basis for their autonomous navigation. Path tracking control guides the mobile robot to gradually approach and eventually reach the predetermined target position through specific control models and methods. As one of the core technologies in mobile robot research, path tracking control accurately controls the speed and direction of the robot while ensuring safety and stability, continuously reducing deviations during movement, thereby achieving efficient and accurate path tracking.

[0003] In existing research, although adaptive neuro-fuzzy controllers combined with sliding mode control (SMC) theoretical learning algorithms have appeared, and the stability of the learning process has been verified by Lyapunov functions, the actual learning performance and convergence speed may vary in adaptability to different operating conditions, depending on the specific implementation and adjustment of the algorithm. In addition, some studies have adopted mobile robot trajectory tracking based on PID fast terminal sliding mode inverse dynamic control. This method combines the proportional-integral-derivative PID control method with fast terminal sliding mode control and is applied to a specific mobile robot model (i.e., a two-wheel differential drive device). However, this often ignores factors such as the dynamic characteristics of the actuator, wheel slip, rolling torque, and mass distribution. These assumptions may oversimplify the actual dynamic behavior of the mobile robot and limit the scope of application of this method. Another method is to use TSK (Takagi-Sugeno-Kang) neural network to approximate the uncertainty of the system and design a robust compensation controller to compensate for the approximation error. Although sliding mode control has good transient performance and fast response, due to the discontinuous characteristics of the control law, it will cause chattering. This chattering can not only negatively impact the overall performance of the system, but is especially noticeable when dealing with unmodeled dynamics. Summary of the invention

[0004] Purpose of the invention: The present invention proposes an adaptive sliding mode trajectory tracking control method based on a fuzzy multi-objective function model. On the basis of considering the kinematic model of an omnidirectional mobile robot, an S-type sliding mode switching function with an integral term is designed, and an adaptive sliding mode controller with equivalent control and switching control is constructed, thereby improving the trajectory tracking control performance of the mobile robot.

[0005] Technical solution: The adaptive synovial trajectory tracking control method based on the fuzzy multi-objective function model of the present invention comprises the following steps:

[0006] (1) Construct a kinematic model of the omnidirectional mobile robot, covering both the global coordinate system and the local coordinate system;

[0007] (2) construct a virtual path between the center of mass of the mobile robot and the preview point in real time in the local coordinate system;

[0008] (3) Define the synovial surface and design the synovial switching function, construct the switching control rate and equivalent control rate, and thus obtain the final synovial control rate;

[0009] (4) Fuzzy logic is used to fuzzify multiple sub-optimization objectives, and hexagonal fuzzy numbers are used to construct membership functions to implement the optimization controller;

[0010] (5) Design an adaptive controller. By constructing an adaptive sliding mode controller with equivalent control and switching control and combining it with a fuzzy multi-objective function model, the adaptive controller can adaptively adjust its own behavior according to different external disturbances and system states to achieve high-precision trajectory tracking.

[0011] Furthermore, the omnidirectional mobile robot in step (1) is an omnidirectional mobile robot with four wheels distributed in a symmetrical structure; each wheel is driven by an independent DC servo motor, and the speed of the wheel is adjusted by adjusting the voltage of the motor, thereby controlling the speed of the motor.

[0012] Furthermore, the global coordinate system in step (1) is a fixed coordinate system used to describe the position and orientation of the robot in the entire environment; the local coordinate system is a coordinate system relative to the robot itself, which changes with the movement of the robot; the origin of the coordinate system is at the current position of the mobile robot, the x-axis points to the center direction of a mechanical wheel, that is, the current orientation of the robot, and the y-axis points to the direction of the wheel speed.

[0013] Furthermore, the implementation process of step (2) is as follows:

[0014] Establish a tracking coordinate system (x t ,y t ) According to the position and direction errors between the actual trajectory and the expected trajectory, the virtual trajectory equation is derived:

[0015]

[0016] in, k2=x e tanθ e , k3=k1x e2 ;y t =A1x 2 +A2x 3 +A3x 4 +A4x 5 , k1 is the proportional factor related to speed and angle, k2 is the relationship between path deviation and angle, and k3 is used to adjust the path curvature; x e ,y e It represents the error between the current position of the robot and the expected trajectory in the x-axis and y-axis. A1, A2, A3, A4 are the parameters of the virtual path equation.

[0017] Furthermore, the synovial switching function in step (3) is:

[0018]

[0019] Among them, l1 and l2 are constants, representing the control gain, which are used to adjust the response speed and stability of the sliding membrane controller; x e and e represents the difference between the robot’s current position and the desired trajectory, θ e represents the difference between the robot’s current direction and the desired direction, v g is the desired linear velocity, ω g is the desired angular velocity, ω t is the angular velocity of the robot, sigm is the sigmoid function, if S′=0, the equivalent control rate is obtained:

[0020]

[0021] Where B1=(w g +ι2sigm(R))(1+(v g y e )) 2 , B2=(v g ′y e )+ν g 2 sinθ e , B3=1+(v g y e ) 2 +v g x e ; B1, B2, B3 are used to simplify the expression of control rate;

[0022] In order to reduce the impact of chattering and external interference on control, a continuous function is used instead of a sign function for switching control:

[0023]

[0024] Among them, β1, β2 are switching gains used to reduce jitter and improve system robustness, Δ i is a positive decimal that tends to 0, which is used to avoid the denominator of the switching function being zero and increase the stability of the system; therefore, the sliding mode control law is:

[0025]

[0026] Among them, the equivalent control law U eq Used to approximate the ideal sliding mode control law, switching control law U sw Used to compensate for system uncertainty and external interference.

[0027] The coordinated action system XoY is based on the assumption that the wheels do not slip or rotate locked; the inverse kinematics model of the mobile robot is as follows:

[0028]

[0029] Where, N = 1 / R; M = (L + B) / R; R is the radius of the wheel, w i is the angular velocity of the wheel, L and B are the distances between the center of the wheel and the longitudinal and transverse axes, respectively.

[0030] Furthermore, the implementation process of step (4) is as follows:

[0031] Given that ξ1, ξ2, ξ3, ξ4, ξ5 and ξ6 are arbitrary real numbers and ξ1<ξ2<ξ3<ξ4<ξ5<ξ6, let γ be a given positive integer. If the membership function is defined as μ ξ :

[0032]

[0033] Then γ in (ξ1,ξ2,ξ3,ξ4,ξ5,ξ6) is called the nonlinear hexagonal fuzzy number NNHN, and this function is called the membership function of NNHN;

[0034] In the hexagonal fuzzy number diagram, the truncated basis is:

[0035]

[0036] in, represents the left side of the membership function, if The left side is redundant; represents the right side of the membership function, if The right side is redundant; if Then it represents the light end of the membership function; if It means that the two sides of the membership function are equally light; if This means that the two sides of the membership function are not equally light; thus we get:

[0037]

[0038] According to the fuzzy objective function, the decision maker's preference factor σ is set, the fuzzy optimization problem is solved, and the optimal control rate is obtained.

[0039] Furthermore, the implementation process of step (5) is as follows:

[0040] The adaptive rate is designed by applying the Lyapunov stability theory, and the parameters of the synovial control are adjusted online to compensate for the uncertainty of the system and external disturbances; specifically, the Lyapunov function is defined as:

[0041]

[0042] Combining equivalent control and switching control, an adaptive sliding film controller consisting of equivalent control and switching control is constructed; the equivalent control rate, switching control rate and adaptive rate are combined to form the final control rate:

[0043] U=U eq +U sw +U ad

[0044] Among them, U ad is the adaptive control rate.

[0045] Beneficial effects: Compared with the prior art, the present invention has the following beneficial effects: Without changing the simulation parameters, the present invention utilizes an S-type sliding mode switching function with an integral term to construct an adaptive sliding mode controller (AFSMC) combining equivalent control and switching control and an S-type sliding mode with an integral term to simulate and control the linear tracking trajectory and the circular tracking trajectory, respectively; the trajectory tracking control performance of the mobile robot is improved; from the comparison of the angular velocity, linear velocity and error of the adaptive sliding film controller AFSMC with the sliding film controller SMC, as well as the comparison of the angular velocity, linear velocity and error of the adaptive sliding film controller AFSMC with the sliding film controller SMC, it can be seen that the adaptive sliding mode control is more advantageous than the sliding mode control and has better control performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a flow chart of the present invention;

[0047] Figure 2 Schematic diagram of the adaptive synovial trajectory tracking control model proposed by the present invention;

[0048] Figure 3 It is a straight line trajectory tracking diagram;

[0049] Figure 4 is the straight line trajectory tracking error diagram;

[0050] Figure 5 This is the circular trajectory tracking result diagram for case 2;

[0051] Figure 6 This is the error diagram of trajectory tracking results in case 2;

[0052] Figure 7 This is the error comparison diagram of linear trajectory tracking AFSMC and SMC;

[0053] Figure 8 It is a comparison diagram of linear trajectory tracking between AFSM and SMC;

[0054] Fig. 9 Comparison diagram of circular trajectory tracking between AFSMC and SMC. DETAILED DESCRIPTION

[0055] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0056] like Figure 1 , Figure 2 As shown, the present invention proposes an adaptive sliding film trajectory tracking control method based on a fuzzy multi-objective function model, adopts an S-type sliding mode switching function with an integral term, and proposes a fuzzy multi-objective function sliding film control. On the basis of considering the kinematic model of an omnidirectional mobile robot, an adaptive sliding film controller with equivalent control and switching control is constructed. Compared with the sliding film control, this method has good trajectory tracking performance and can effectively improve the control accuracy. Specifically, it includes the following steps:

[0057] Step 1: Construct a kinematic model of the omnidirectional mobile robot.

[0058] The present invention takes an omnidirectional mobile robot with four wheels distributed in a symmetrical structure as a research object. Each wheel is driven by an independent DC servo motor. The rotation speed of the wheel is adjusted by adjusting the voltage of the motor, thereby controlling the rotation speed of the motor. Therefore, a kinematic model of an omnidirectional mobile robot with four independent wheels is defined. The global coordinate system (XGOGYG) is a fixed coordinate system used to describe the position and direction of the robot in the entire environment. In the global coordinate system, the position of the robot is represented by (x, y), which is used to describe the movement in the entire environment. The local coordinate system (OcXcYc) is a coordinate system relative to the robot itself, which changes with the movement of the robot. The origin of the coordinate system is at the current position of the mobile robot, the x-axis points to the center direction of a mechanical wheel, that is, the current orientation of the robot, and the y-axis points to the direction of the wheel speed.

[0059] Step 2: Design the virtual path.

[0060] In the local coordinate system (OcXcYc), a virtual path is constructed in real time between the center of mass of the mobile robot and the preview point. A tracking coordinate system (x t ,y t ). According to the position and direction errors between the actual trajectory and the expected trajectory, the virtual trajectory equation is derived. The virtual trajectory equation is:

[0061]

[0062] in, k3=k1x e 2 ;y t =A1x 2 +A2x 3 +A3x 4 +A4x 5 , k1 is a proportional factor related to speed and angle, k2 represents the relationship between path deviation and angle, and k3 is used to adjust the path curvature; A1 = k1; x e ,y e Represents the error between the robot's current position and the expected trajectory on the x-axis and y-axis; A1, A2, A3, and A4 are the parameters of the virtual path equation. These parameter factors are used to construct the virtual path, taking into account the speed, deviation, and angle changes, so that the mobile robot can accurately track the target position and direction. The map construction and positioning module constructs the global coordinate system of the mobile robot, completes real-time positioning, performs path planning based on the constructed map, obtains the expected motion path, integrates the real-time position information of the mobile robot with the expected motion path, and performs path tracking control and calculates the expected yaw angular velocity required to track the expected motion path at the current position, converts the expected yaw angular velocity into motor pulse output, and finally realizes the path tracking control of the mobile robot.

[0063] Step 3: Design the sliding membrane controller.

[0064] Define sliding surface: Select the sliding surface that contains the position error and velocity error to ensure that the system error can converge to zero.

[0065] Design of synovial switching function: Adopt sigmoid saturation function to reduce jitter and smooth switching control.

[0066] The switching function S is defined as follows:

[0067]

[0068] Among them, l1 and l2 are constants, representing the control gain, which are used to adjust the response speed and stability of the sliding membrane controller. e and erepresents the difference between the robot’s current position and the desired trajectory, θ e represents the difference between the robot’s current direction and the desired direction, v g is the desired linear velocity, ω g is the desired angular velocity, ω t is the angular velocity of the robot, sigm is the sigmoid function, if S′=0, the equivalent control rate is obtained:

[0069]

[0070] Where B1=(w g +ι2sigm(R))(1+(v g y e )) 2 , B2=(ν g ′y e )+v g 2 sinθ e , B3=1+(v g y e ) 2 +v g x e ; B1, B2, B3 are used to simplify the expression of control rate.

[0071] In order to reduce the impact of chattering and external interference on control, a continuous function is used instead of a sign function for switching control, as follows:

[0072]

[0073] Among them, β1, β2 are switching gains, which are used to reduce jitter and improve the robustness of the system; Δ i (i=1,2) is a positive decimal that tends to 0, which is used to avoid the denominator of the switching function being zero and increase system stability. Therefore, the sliding mode control law is:

[0074]

[0075] Among them, the equivalent control law U eq Used to approximate the ideal sliding mode control law, switching control law U sw Used to compensate for system uncertainty and external interference.

[0076] The coordinated action system XoY is based on the assumption that the wheels do not slip or rotate locked. The inverse kinematics model of the mobile robot is as follows:

[0077]

[0078] Where, N = 1 / R; M = (L + B) / R; R is the radius of the wheel, wi (i=1,2,3,4) is the angular velocity of the wheel, L and B are the distances between the center of the wheel and the longitudinal and transverse axes respectively.

[0079] Step 4: Design fuzzy multi-objective function.

[0080] In the mobile robot controller, the relationship between independent wheel angular velocity controllers is fuzzy. The membership function is used to optimize multiple sub-objectives of the kinematic model (motion parameters such as position, velocity, acceleration of the mobile robot) and the dynamic model of the robot (including factors such as motor drive and friction) to obtain the optimal solution of the model. Therefore, choosing a suitable membership function is the prerequisite for solving the fuzzy optimization problem, so the membership function is constructed using hexagonal fuzzy numbers. The fuzzy multi-objective function is introduced to optimize the control performance, and the hexagonal fuzzy function is used to represent the membership function of the constructed fuzzy target. The fuzzy multi-objective function model is used to represent the control objectives and control criteria of the trajectory tracking task.

[0081] Selecting membership functions: Constructing membership functions using hexagonal fuzzy numbers to handle uncertainties and nonlinearities in control systems.

[0082] First, given that ξ1, ξ2, ξ3, ξ4, ξ5 and ξ6 are arbitrary real numbers and ξ1<ξ2<ξ3<ξ4<ξ5<ξ6, let γ be a given positive integer. If the membership function is defined as μ ξ :

[0083]

[0084] Then, γ in (ξ1,ξ2,ξ3,ξ4,ξ5,ξ6) is called nonlinear hexagonal fuzzy number (NNHN), and this function is called the membership function of NNHN.

[0085] In the hexagonal fuzzy number diagram, the truncated basis is:

[0086]

[0087] in, represents the left side of the membership function, if The left side is redundant. represents the right side of the membership function, if The right side is redundant. It represents the light end of the membership function. If This means that both sides of the membership function are equally light. If This means that the two sides of the membership function are not equally important.

[0088] From these we can derive:

[0089]

[0090] Solve the fuzzy optimization problem: According to the fuzzy objective function, set the decision maker's preference factor σ, solve the fuzzy optimization problem, and obtain the optimal control rate.

[0091] The fuzzy multi-objective function design is combined with the sliding film controller design, and the uncertainty of the system is processed by fuzzy optimization to ensure the robustness and effectiveness of the control rate.

[0092] Step 5: Design an adaptive controller.

[0093] First, the adaptive rate is designed. The adaptive rate is used to adjust the synovial control parameters online to compensate for the uncertainty and external interference of the system. At the same time, the Lyapunov stability theory is used to design the adaptive rate to ensure the stability of the system. The stability of the control system is ensured by defining the Lyapunov function. The Lyapunov function can be defined as:

[0094]

[0095] Secondly, an adaptive sliding membrane controller consisting of equivalent control and switching control is constructed by combining equivalent control and switching control.

[0096] The equivalent control rate, switching control rate and adaptive rate are combined to form the final control rate:

[0097] U=U eq +U sw +U ad

[0098] Among them, U ad is the adaptive control rate.

[0099] The equivalent control component compensates for the uncertainty and disturbance of the system, while the switching control component ensures the robustness of the control system so that the deviation between the actual and desired postures of the mobile robot is zero as t tends to infinity. For the adaptive control rate, the control parameters are adjusted in real time to cope with the changing dynamics of the robot and external disturbances. The equivalent control method is used to ensure the expected tracking performance and is combined with the switching control and adaptive hole control to form the final control input. This adaptive mechanism also helps maintain the performance of the controller despite changes in the system or environment.

[0100] The simulation results of the tracking control of linear and circular trajectories show that the proposed method is superior to the traditional sliding mode control in trajectory tracking performance. The simulation results show that the proposed method has better control accuracy and stability, and can effectively reduce tracking errors and angle deviations.

[0101] In order to verify the effectiveness of the set control algorithm, the mobile robot was simulated and analyzed on MATLAB. Experimental parameters A self-controlled differential wheeled mobile robot was used, and its basic parameters are shown in Table 1.

[0102] Table 1 Basic parameters of differential wheeled mobile robot

[0103] Basic parameters unit gross weight 1.8kg Wheel spacing 287mm Wheel radius 66mm Moment of inertia J / (kg·m2) 1.35 Maximum no-load speed 2.5m / s Maximum acceleration 0.8m / s

[0104] The adaptive sliding film control method in this paper is tested in two cases, where case 1 is linear trajectory tracking and case 2 is circular trajectory tracking. In case 1, the ideal trajectory initial posture of the mobile robot is [1,0,π / 3]T, the actual tracking initial posture is [0.5,0,π / 3]T, the speed is set to 2.5m / s, and the simulation time is 20s. Figure 3 It can be seen that in case 1, the effect of the adaptive synovial control method starts from the set initial position, the actual trajectory coincides with the ideal trajectory quickly, and the operation is stable.

[0105] from Figure 4 It can be seen that although the error is large at the beginning and reaches a maximum value of 0.47m at 0.2s, it stabilizes at 2.2s when it runs to the (-26mm, 3mm) interval; xe, ye stabilizes at 2.7s and remains stable at (-25mm, -13mm); θ e Stable in the range (-0.0003rad, 0.0002rad).

[0106] Case 2: The mobile robot runs at a speed of 2.5 cm / s, the initial posture is set to [4, 2, 5π / 6]T, and the simulation time is 20 seconds. The simulation reference trajectory is designed as: x = 4costθ, y = 4sinθ. Figure 5 It can be seen that based on the adaptive sliding film control method of fuzzy multi-objective function, when the mobile robot moves in a straight line at a certain heading angle, the wheel angular velocity satisfies ω1=ω3, ψ2=ω4 and remains constant, showing that the mobile robot can track well2. Figure 6 It can be seen that the linear velocity of the mobile robot in circular trajectory tracking increases steadily after 0.7s and stabilizes after 2.9s. The angular velocity stabilizes after 3.7s; Xe stabilizes in the range of (0.0532m, 0.0550m) after 2.8s; ye stabilizes in the range of (0.0484m, 0.0557m) after 2.9s; and the heading angle deviation stabilizes in the range of (-0.0234rad, -0.0196rad) after 3.1s.

[0107] Without changing the simulation parameters, the adaptive sliding mode control (AFSMC) based on the fuzzy multi-objective function model constructed in this paper is compared with the traditional sliding mode control (SMC) in the simulation control of linear tracking trajectory and circular tracking trajectory. Figure 7 It can be seen that in linear trajectory tracking, the AFSMC method in this paper has smaller errors than the traditional SMC and is more likely to be stable.

[0108] exist Figure 8 and Fig. 9 It can be seen that in case 2, the comparison results of the adaptive synovial film control method AFSMC based on the fuzzy multi-objective function model in this paper and the traditional synovial film control method SMC in linear trajectory tracking and circular trajectory tracking show that the adaptive synovial film control AFSMC based on the fuzzy multi-objective function model has more advantages than the traditional synovial film control SMC and has good control performance.

[0109] Based on the kinematic model of the omnidirectional mobile robot, the present invention designs an adaptive sliding mode controller based on fuzzy multi-objective function and with equivalent control and switching control, and draws the following conclusions through MATLAB simulation: (1) When the initial posture is [1,0,π / 3]T, the mobile robot performs linear trajectory tracking at a speed of 2.5m / s, and the actual trajectory can quickly coincide with the ideal trajectory curve, xe stabilizes at (-0.0027m, 0.0003m), ye stabilizes at (-0.0026m, -0.0012m), and the heading angle deviation stabilizes at (-0.0003rad, 0.0002rad). (2) When the mobile robot runs at a speed of 2.5m / s with a circular trajectory of the actual initial posture [4,2,5π / 6]T, x=4cosθ, y=4sinθ, the circular trajectory can be well tracked. xe finally stabilized in the range of (0.0532m, 0.0550m), ye finally stabilized in the range of (0.0484m, 0.0557m), and the heading angle deviation stabilized in the range of (-0.0234rad, -0.0196rad).

[0110] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with the technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit of the present invention should be included in the protection scope of the present invention.

Claims

1. An adaptive synovial trajectory tracking control method based on a fuzzy multi-objective function model, characterized in that: The following steps are involved: (1) Construct a kinematic model of the omnidirectional mobile robot, covering both the global coordinate system and the local coordinate system; (2) In the local coordinate system, a virtual path is generated in real time between the center of mass of the mobile robot and the preview point; (3) Define the synovial surface and design the synovial switching function, construct the switching control rate and equivalent control rate, and thus obtain the final synovial control rate; (4) Fuzzy logic is used to fuzzify multiple sub-optimization objectives, and hexagonal fuzzy numbers are used to construct membership functions to achieve the design of the optimal controller; (5) Design an adaptive controller. By constructing an adaptive sliding mode controller with equivalent control and switching control and combining it with a fuzzy multi-objective function model, the adaptive controller can adaptively adjust its own behavior according to different external disturbances and system states to achieve high-precision trajectory tracking.

2. The adaptive synovial trajectory tracking control method based on fuzzy multi-objective function model according to claim 1 is characterized in that: The omnidirectional mobile robot described in step (1) is an omnidirectional mobile robot with four wheels distributed in a symmetrical structure; each wheel is driven by an independent DC servo motor, and the speed of the wheel is adjusted by adjusting the voltage of the motor, thereby controlling the speed of the motor.

3. The adaptive synovial trajectory tracking control method based on fuzzy multi-objective function model according to claim 1 is characterized in that: The global coordinate system in step (1) is a fixed coordinate system used to describe the position and orientation of the robot in the entire environment; the local coordinate system is a coordinate system relative to the robot itself, which changes with the movement of the robot; the origin of the coordinate system is at the current position of the mobile robot, the x-axis points to the center direction of a mechanical wheel, that is, the current orientation of the robot, and the y-axis points to the direction of the wheel speed.

4. The adaptive synovial trajectory tracking control method based on fuzzy multi-objective function model according to claim 1 is characterized in that: The implementation process of step (2) is as follows: Establish a tracking coordinate system (x t ,y t ) According to the position and direction errors between the actual trajectory and the expected trajectory, the virtual trajectory equation is derived: in, k2=x e tanθ e , k3=k1x e 2 ;y t =A1x 2 +A2x 3 +A3x 4 +A4x 5 , k1 is the proportional factor related to speed and angle, k2 is the relationship between path deviation and angle, and k3 is used to adjust the path curvature; x e ,y e It represents the error between the current position of the robot and the expected trajectory in the x-axis and y-axis. A1, A2, A3, A4 are the parameters of the virtual path equation.

5. The adaptive synovial trajectory tracking control method based on fuzzy multi-objective function model according to claim 1 is characterized in that: The synovial switching function in step (3) is: Among them, l1 and l2 are constants, representing the control gain, which are used to adjust the response speed and stability of the sliding membrane controller; x e and e represents the difference between the robot’s current position and the desired trajectory, θ e represents the difference between the robot’s current direction and the desired direction, v g is the desired linear velocity, ω g is the desired angular velocity, ω t is the angular velocity of the robot, sigm is the sigmoid function, if S′=0, the equivalent control rate is obtained: in, B2=(v g ′y e )+v g 2 sinθ e , B3=1+(v g y e ) 2 +v g x e ; B1, B2, B3 are used to simplify the expression of control rate; In order to reduce the impact of chattering and external interference on control, a continuous function is used instead of a sign function for switching control: Among them, β1, β2 are switching gains used to reduce jitter and improve system robustness, Δ i is a positive decimal that tends to 0, which is used to avoid the denominator of the switching function being zero and increase the stability of the system; therefore, the sliding mode control law is: Among them, the equivalent control law U eq Used to approximate the ideal sliding mode control law, switching control law U sw Used to compensate for system uncertainty and external interference; The coordinated action system XoY is based on the assumption that the wheels do not slip or rotate locked; the inverse kinematics model of the mobile robot is as follows: Where, N = 1 / R; M = (L + B) / R; R is the radius of the wheel, w i is the angular velocity of the wheel, L and B are the distances between the center of the wheel and the longitudinal and transverse axes, respectively.

6. The adaptive synovial trajectory tracking control method based on fuzzy multi-objective function model according to claim 1 is characterized in that: The implementation process of step (4) is as follows: Given that ξ1, ξ2, ξ3, ξ4, ξ5 and ξ6 are arbitrary real numbers and ξ1<ξ2<ξ3<ξ4<ξ5<ξ6, let γ be a given positive integer. If the membership function is defined as μ ξ : Then γ in (ξ1,ξ2,ξ3,ξ4,ξ5,ξ6) is called the nonlinear hexagonal fuzzy number NNHN, and this function is called the membership function of NNHN; In the hexagonal fuzzy number diagram, the truncated basis is: in represents the left side of the membership function, if The left side is redundant; represents the right side of the membership function, if The right side is redundant; if Then it represents the light end of the membership function; if It means that the two sides of the membership function are equally light; if This means that the two sides of the membership function are not equally light; get: According to the fuzzy objective function, the decision maker's preference factor σ is set, the fuzzy optimization problem is solved, and the optimal control rate is obtained.

7. The adaptive synovial trajectory tracking control method based on fuzzy multi-objective function model according to claim 1 is characterized in that: The implementation process of step (5) is as follows: The adaptive rate is designed by applying the Lyapunov stability theory, and the parameters of the synovial control are adjusted online to compensate for the uncertainty of the system and external disturbances; specifically, the Lyapunov function is defined as: Combining equivalent control and switching control, an adaptive sliding film controller consisting of equivalent control and switching control is constructed; the equivalent control rate, switching control rate and adaptive rate are combined to form the final control rate: U=U eq +U sw +U ad Among them, U ad is the adaptive control rate.

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