Trajectory tracking control method of Mecanum wheel mobile robot based on fuzzy backstepping sliding mode

Abstract

A trajectory tracking control method for a Mecanum wheel mobile robot based on fuzzy inverse sliding mode includes the following steps: (A) establishing a multi-input multi-output model according to kinematic and dynamic mechanisms for an actual Mecanum wheel mobile robot; (B) designing an inverse sliding mode surface and an equivalent control law according to desired control performance; (C) designing a system state arrival control law based on the sliding mode surface and the equivalent control law set in step (B); (D) designing a fuzzy function to replace the sign function based on the inverse sliding mode control law designed in steps (B) and (C) to obtain a final control law so that chattering can be suppressed. The present invention provides a design method for a fuzzy inverse sliding mode control law that guarantees trajectory tracking performance for the control problem of a nonlinear multi-input multi-output Mecanum wheel omnidirectional mobile robot, which has high control accuracy and strong robustness and anti-interference.

Description

Technical Field

[0001] The present invention belongs to the technical field related to robot control, and more specifically, relates to a trajectory tracking control method of a Mecanum wheel mobile robot based on fuzzy inversion sliding mode. Background Art

[0002] Nowadays, wheeled mobile robots have become a powerful tool to assist people in completing specific tasks. In industry, wheeled mobile robots are used to complete material transportation and dynamic assembly in manufacturing workshops. In addition, they also play a pivotal role in many service fields. Among wheeled mobile robots, omnidirectional mobile robots have the advantage of moving in any direction without turning or turning back, and have broad application prospects.

[0003] In order to better exert the performance of the omnidirectional mobile robot, it is usually necessary to design a control method based on the establishment of kinematic and dynamic models, so as to control the movement of the robot by adjusting the motor input voltage. General methods include PID control, adaptive control, sliding mode control, fuzzy logic and neural network control, robust control, etc. Among the above control methods, sliding mode control has been widely used in the field of robot control due to its superior robustness and ease of implementation. However, sliding mode control also has disadvantages: 1. There is a jitter problem in the control process; 2. In the arrival stage of control, the robustness is weak. In the application of sliding mode control, the difficulty lies in how to overcome these disadvantages while retaining the advantages of sliding mode control. Summary of the invention

[0004] In order to overcome the problems of chattering and insufficient tracking accuracy in the prior art, the present invention provides a trajectory tracking control method for a Mecanum wheel mobile robot based on fuzzy inversion sliding mode.

[0005] The present invention provides a novel kinematic and dynamic modeling method for a Mecanum wheel mobile robot, and designs a fuzzy inversion sliding mode control method to improve the tracking performance of the mobile robot.

[0006] In order to achieve the above objectives, the technical solution of the present invention is: a trajectory tracking control method of a Mecanum wheel omnidirectional mobile robot based on fuzzy inversion sliding mode, comprising the following steps:

[0007] 1. According to the control input signal, the kinematic and dynamic models of the Mecanum wheel mobile robot are established and converted into unified differential equations;

[0008] 2. Design an inverse sliding surface based on the Mecanum wheel mobile robot model;

[0009] 3. Design equivalent control law based on Mecanum wheel mobile robot model and sliding surface;

[0010] 4. Construct the system state arrival control law based on the sliding surface;

[0011] 5. Use fuzzy functions instead of sign functions to suppress chattering in control.

[0012] The present invention provides a design method for a fuzzy inversion sliding mode control law that ensures trajectory tracking performance for the control problem of a nonlinear multi-input multi-output Mecanum wheel omnidirectional mobile robot, which has high control accuracy and strong robustness and anti-interference performance.

[0013] The beneficial effects of the present invention are mainly manifested in: 1. A new modeling method of a Mecanum wheel mobile robot is established, thereby improving the accuracy of the model; 2. Fuzzy rules are used to suppress the chattering phenomenon in control, thereby improving the control quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a structural diagram of the Mecanum wheel omnidirectional mobile robot of the present invention.

[0015] Figure 2 is the fuzzy function input s(t) and Δ s (t) The membership function setting diagram.

[0016] Figure 3 It is a setting diagram of the fuzzy function output membership function of the present invention.

[0017] Figure 4 The figure is a schematic diagram of the trajectory of the Mecanum wheel mobile robot of the present invention.

[0018] Figure 5 This is a graph of trajectory tracking results of the Mecanum wheel mobile robot of the present invention.

[0019] Figure 6 It is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0020] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0021] The trajectory tracking control method of a Mecanum wheel omnidirectional mobile robot based on fuzzy inversion sliding mode of the present invention comprises the following steps:

[0022] 1. According to the control input signal, the kinematic and dynamic models of the Mecanum wheel mobile robot are established and converted into unified differential equations; specifically including:

[0023] according to Figure 1 Establish the kinematic equations of the Mecanum wheel mobile robot:

[0024]

[0025] Among them, xl ,y l ,ψ l is the coordinate of the mobile robot in its own coordinate system, θ i is the rotation angle of the i-th wheel. The transformation matrix from the local coordinate system to the global coordinate system is:

[0026]

[0027] Right now,

[0028] The kinematic equation of the Mecanum wheel mobile robot is combined with the rotation matrix to obtain the kinematic equation of the Mecanum wheel mobile robot in the global coordinate system.

[0029]

[0030]

[0031] in, θ=[θ1θ2θ3θ4] T .

[0032] By deriving the kinematic equation of the Mecanum wheel mobile robot in the global coordinate system, we can obtain:

[0033]

[0034] The dynamic model of the Mecanum wheel motor is established and expressed as:

[0035]

[0036] Where J0 is the nominal moment of inertia of each wheel, b0 is the nominal viscous friction of each wheel, and d = [d1 d2 d3d4] T is the parameter perturbation of the four wheels, v = [v1 v2 v3 v4] T is the input voltage of the four motors. Combining the above two formulas, we get:

[0037]

[0038] Combining equation (6) with the dynamic equation (5), the Mecanum wheel mobile robot model is unified as:

[0039]

[0040] Then preliminarily design the control input signal The Mecanum wheel model can be simplified as:

[0041]

[0042] Among them, u is the control input signal that needs to be designed in the second step.

[0043] 2. Design an inverse sliding surface based on the Mecanum wheel mobile robot model; specifically include:

[0044] Define the error variable:

[0045]

[0046] Derivative of the error variable:

[0047]

[0048] set up Where c>0, ζ is the virtual control quantity, that is, Taking the derivative of ζ, we get:

[0049]

[0050] Define the sliding surface as: s = ζ, define the Lyapunov function Taking the first-order derivative of the function V yields:

[0051]

[0052] 3. Design equivalent control law based on Mecanum wheel mobile robot model and sliding surface; Specifically: First assume d = [d1 d2 d3 d4] T =

[0000] T , set the equivalent control law as:

[0053]

[0054] in,

[0055] 4. Construct the system state arrival control law based on the sliding surface; specifically including:

[0056] According to the sliding mode control principle and the above sliding surface design, the control law is:

[0057] u2=-h(ψ) -1 ·B·sign(s) (14)

[0058] in, is the upper bound of the parameter perturbation.

[0059] Combining the two control laws (13) and (14), we get the final control input signal:

[0060]

[0061] Substituting the designed control input signal into the first-order derivative of the Lyapunov function, we get:

[0062]

[0063] Thereby ensuring the stability of the control system.

[0064] 5. Design fuzzy functions to replace sign functions to suppress chattering in control; specifically include:

[0065] Since the switching term sign(s) in the control input signal will cause chattering in practical applications, a fuzzy rule function fuz(s) is established to replace sign(s). In the design, the input variables s(t) and Δ s The membership function of (t) is set to the states of N, Z, and P; the membership function of the output variable is set to the states of NB, NM, NS, ZE, PS, PM, and PB. By designing the following 9 fuzzy rules, while reducing the amount of calculation of the algorithm, a good vibration reduction effect is guaranteed. The specific membership is as follows Figure 2 , as shown in 3.

[0066] 1)If s(t)is N and Δ s (t)is N Then fuz(s)is NB

[0067] 2)If s(t)is N and Δ s (t)is Z Then fuz(s)is NB

[0068] 3)If s(t)is N andΔ s (t)is P Then fuz(s)is NM

[0069] 4)If s(t)is Z andΔ s (t)is N Then fuz(s)is NS

[0070] 5)If s(t)is Z andΔ s (t)is Z Then fuz(s)is ZE

[0071] 6)If s(t)is Z andΔ s (t)is P Then fuz(s)is PS

[0072] 7)If s(t)is P andΔ s (t)is N Then fuz(s)is PM

[0073] 8)If s(t)is P andΔ s (t)is Z Then fuz(s)is PB

[0074] 9)If s(t)is P andΔ s (t)is P Then fuz(s)is PB

[0075] Replace the sign(s) function in the control signal with fuz(s) to obtain the final control law:

[0076]

[0077] In order to more intuitively illustrate the solution and advantages of the present invention, the technical solution of the present invention is further described below in conjunction with embodiments. Figure 4 , 5.

[0078] Set the following parameters according to the actual mobile robot.

[0079] Variable Symbols describe value a Mobile robot half width 180mm b Front / rear axle half distance 200mm r Mecanum wheel radius 50mm <![CDATA[J0]]> Nominal moment of inertia of wheel <![CDATA[0.095kgm 2 ]]> <![CDATA[b0]]> Nominal viscous friction of the wheel 0.087Nms / rad d Maximum disturbance 16.5Nm

[0080] like Figure 4 As shown in the figure, the circular motion trajectory of the Mecanum wheel mobile robot is set with the heading angle unchanged, and the initial position of the mobile robot is set to (0,0) ， The speed is set to 0.5m / s.

[0081] The trajectory tracking effect is as follows Figure 5 As shown, the actual driving trajectory of the mobile robot tracks the given trajectory well and the jitter is very small, indicating that the method proposed in the present invention can achieve better control effect.

[0082] The contents described in the embodiments of this specification are merely enumerations of the implementation forms of the inventive concept and are for illustrative purposes only. The protection scope of the present invention should not be considered to be limited to the specific forms described in this embodiment, and the protection scope of the present invention also extends to equivalent technical means that can be thought of by ordinary technicians in this field based on the inventive concept.

Claims

1. A trajectory tracking control method for a Mecanum wheel omnidirectional mobile robot based on fuzzy inverse sliding mode comprises the following steps: Step 1: According to the control input signal, the kinematic and dynamic models of the Mecanum wheel mobile robot are established and converted into unified differential equations; Step 2: Design an inverse sliding surface based on the second-order Mecanum wheel mobile robot model; Step 3: Design the equivalent control law based on the second-order Mecanum wheel mobile robot model and sliding surface; Step 4: Design the system state arrival control law based on the sliding surface; Step 5: Design a fuzzy function to replace the sign function to suppress chattering in control; Step 1 specifically includes: Establish the kinematic equations of the Mecanum wheel mobile robot: Among them, x l ,y l ,ψ l is the coordinate of the mobile robot in its own coordinate system, θ i is the rotation angle of the i-th wheel; a is the half-width of the mobile robot, b is the half-distance of the front or rear wheel axle, and r is the radius of the Mecanum wheel; the transformation matrix from the local coordinate system to the global coordinate system is: Right now, Combining the above kinematic equation of the Mecanum wheel mobile robot with the rotation matrix, we can obtain the kinematic equation of the Mecanum wheel mobile robot in the global coordinate system: Among them, θ=[θ1θ2θ3θ4] T ; Derivative of the kinematic equation of the Mecanum wheel mobile robot in the global coordinate system: The dynamic model of the Mecanum wheel and the motor is established and expressed as: Where J0 is the nominal moment of inertia of each wheel, b0 is the nominal viscous friction of each wheel, and d = [d1 d2 d3 d4] T is the parameter perturbation of the four wheels, v = [v1 v2 v3 v4] T is the input voltage of the four motors; combining the above two formulas, we get: Combining equation (6) with the dynamic equation (5), the Mecanum wheel mobile robot model is unified as: Then preliminarily design the control input signal The Mecanum wheel mobile robot model can be simplified as: Among them, u is the control input signal required to be designed in the second step; Step 2 specifically includes: Define the error variable: Derivative of the error variable: set up Where c>0, ζ is the virtual control quantity, that is, Taking the derivative of ζ, we get: Define the sliding surface as: s = ζ, define the Lyapunov function Taking the first-order derivative of the function V yields: Step 3 specifically includes: Assume d = [d1 d2 d3 d4] T =[0000] T , set the equivalent control law as: in, Step 4 specifically includes: According to the sliding mode control principle and the above sliding surface design, the control law is: u2=-h(ψ) -1 ·B·sign(s) (14) in, is the upper bound of parameter perturbation; Combining the two control laws (13) and (14), we get the final control input signal: Substituting the control input signal into the first-order derivative of the Lyapunov function, we get: Thereby ensuring the stability of the control system; Step 5 specifically includes: Since the switching term sign(s) in the control input signal can cause chattering in practical applications, a fuzzy function fuz(s) is established to replace sign(s); in the design, the input variables s(t) and Δ s The membership function of (t) is set to the states of N, Z, and P; the membership function of the output variable is set to the states of NB, NM, NS, ZE, PS, PM, and PB; the fuzzy system establishes the following 9 fuzzy rules: 1)If s(t)is N andΔ s (t)is N Then fuz(s)is NB 2)If s(t)is N andΔ s (t)is Z Then fuz(s)is NB 3)If s(t)is N andΔ s (t)is P Then fuz(s)is NM 4)If s(t)is Z andΔ s (t)is N Then fuz(s)is NS 5)If s(t)is Z andΔ s (t)is Z Then fuz(s)is ZE 6)If s(t)is Z andΔ s (t)is P Then fuz(s)is PS 7)If s(t)is P andΔ s (t)is N Then fuz(s)is PM 8)If s(t)is P andΔ s (t)is Z Then fuz(s)is PB 9)If s(t)is P andΔ s (t)is P Then fuz(s)is PB Replace the sign(s) function in the control input signal with fuz(s) to obtain the final control law:

Images