Trajectory tracking control method for flexible arm under uncertain modeling error

Abstract

The invention provides a trajectory tracking control method for a flexible arm under an uncertain modeling error, adopts a fuzzy adaptive inversion control method based on a joint dynamics differential equation, and belongs to the field of flexible arm control. The method comprises the following steps: providing a fuzzy adaptive inversion control method for solving the problem of poor trajectory tracking precision of the flexible arm caused by an uncertain error in flexible arm modeling, and constructing a control method which enables the flexible arm joint trajectory quantity and the acceleration quantity to be finally consistent with a bounded tracking expected value by taking the flexible arm joint trajectory quantity and the acceleration quantity as control objects. Compared with other methods, according to the method, firstly, order reduction processing is conducted on a general dynamic differential equation based on the inversion control thought, then the robustness of the flexible arm due to modeling errors is enhanced in combination with the fuzzy self-adaptive control thought, then the trajectory tracking precision of the flexible arm is improved, and the practicability of the flexible arm is improved.

Description

Technical Field

[0001] The present invention relates to the field of flexible arm control, and in particular to a trajectory tracking control method of a flexible arm under uncertain modeling errors. Background Art

[0002] With the development of robot technology, the application fields of robots have also expanded, and there are many occasions that require flexible arms to work. Compared with traditional rigid robotic arms, flexible arms have advantages such as strong ability to imitate human arms, less prone to damage to the arms themselves and the objects they touch, and easier to adapt to the working environment. Therefore, flexible arms have been widely studied and applied in recent years.

[0003] However, most of the existing technologies only propose control schemes for a certain part of the flexible arm, or even do not propose any control schemes. For example, the Chinese patent publication number is CN 111055285 A, and its name is a vibration suppression method under variable load conditions of a humanoid flexible joint arm. It only studies the resonance problem caused by load changes; the Chinese patent publication number is CN213971281 U, and its name is a flexible arm structure with precise positioning of an industrial robot. It only proposes the hardware structure, and does not provide a control scheme for how to ensure the normal operation of the arm.

[0004] In fact, it is more difficult to control the motion trajectory of a flexible arm than a rigid robotic arm. First, the existence of flexible links will increase the modeling error during modeling, making it impossible for traditional control methods to work properly. Second, the flexible links will make the coupling between the parameters of the arm system more complicated, and the control of high-order systems is particularly difficult. Finally, the "compliance" of the flexible arm will require a longer "adaptation" time when the arm is moving or in contact with the object being contacted, and the control plan during this period is particularly important.

[0005] In view of this, the present invention proposes a trajectory tracking control method for a flexible arm under uncertain modeling errors. Summary of the invention

[0006] The purpose of the present invention is to provide a trajectory tracking control method for a flexible arm under uncertain modeling errors to solve the problems raised in the above background technology.

[0007] To achieve the above object, the present invention provides the following technical contents:

[0008] A trajectory tracking control method for a flexible arm under uncertain modeling errors is proposed. Considering the existence of uncertain errors in the modeling of the flexible arm, its dynamic differential equation is established and a fuzzy adaptive inversion control method is designed. The method is characterized by:

[0009] When there is an uncertain error in the modeling of the flexible arm, the dynamic differential equation of the flexible arm is expressed as:

[0010]

[0011] Among them, I 0 , J 0 , K 0 、M 0 and L 0 are the precise quantities of connecting rod inertia, motor rotor moment of inertia, spring coefficient, connecting rod mass and connecting rod length; θ m and are the trajectory and acceleration of the motor rotor respectively; θ l and are the arm joint trajectory and acceleration respectively; u is the controller to be designed; Ω 1 and Ω 2 represents the uncertain modeling error and has the following expression:

[0012]

[0013] Among them, I Δ , J Δ , K Δ 、M Δ and L Δ They are the modeling uncertainty errors of connecting rod inertia, motor rotor moment of inertia, spring coefficient, connecting rod mass and connecting rod length.

[0014] Preferably, the actual trajectory of the arm joint θ l and acceleration metrics As the control object, with a given desired trajectory θ ld and In order to track the target, a fuzzy adaptive inverse control method u is designed so that the controlled object eventually tracks the desired target in a bounded and consistent manner. The specific implementation of the control method includes the following steps:

[0015] Step 1: Select variable x 1 =θ l , x 3 =θ m , and x=[x 1 ,x 2 ,x 3 ,x 4 ] T , Equation (1) is reduced in order to adopt the inverse control idea. The equation after the reduction is expressed as:

[0016]

[0017] Among them, f 2(x) = -1 / I 0 (M 0 g 0 sin(x 1 )+K 0 (x 1 -x 3 ))-x 3 、f 4 (x) = -K 0 / J 0 (x 1 -x 3 ) and b = 1 / J 0 Determine the known, Δf 2 (x) = Ω 1 / I 0 , Δf 4 (x) = Ω 2 / J 0 represents the uncertain modeling error;

[0018] Step 2: Use fuzzy algorithm to model the uncertainty error term Δf 2 (x), Δf 4 (x) is approximated and has the following expression:

[0019]

[0020]

[0021]

[0022]

[0023] Step 3: Based on the actual trajectory of the joint and motor rotor θ l ,θ m and speed and the expected trajectory θ ld ,θ md and speed The deviation e i (i=1,2,3,4), introduce auxiliary variable z for equation (2) i (i=1,2,3,4)z i and virtual input α i (i=1,2,3):

[0024]

[0025]

[0026] Step 4: Design the following controller u:

[0027]

[0028] Complete trajectory tracking control of the flexible robotic arm.

[0029] The invention is beneficial in that a fuzzy adaptive inverse control method is used for a flexible manipulator with uncertain modeling errors. The control method relies on uncertain quantities such as trajectory tracking deviation and uncertain error approximation value, and constructs appropriate auxiliary variables, virtual variables and adaptive laws to complete the controller design and ensure that the trajectory tracking deviation is eliminated within a bounded range.

[0030] Compared with other methods, the method of the present invention first reduces the order of the general dynamic differential equation based on the inversion control idea, thereby improving the feasibility of the control algorithm, and then combines the fuzzy adaptive inversion control idea to enhance the robustness of the flexible arm due to modeling errors, thereby improving the trajectory tracking accuracy of the flexible arm and improving the practicability of the flexible arm. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a block diagram of the flexible arm trajectory tracking control system based on the fuzzy adaptive backstepping control method;

[0032] Figure 2 This is a schematic diagram of a typical flexible arm structure. DETAILED DESCRIPTION

[0033] The present invention will be further described below in conjunction with the accompanying drawings:

[0034] A trajectory tracking control method for a flexible arm under uncertain modeling errors uses a fuzzy adaptive inversion control method based on joint dynamics differential equations to track and control the arm motion trajectory. The block diagram of the flexible arm trajectory tracking control system using the fuzzy adaptive inversion control method is shown in the figure. Figure 1 The actual output θ of the flexible arm joint is shown in l and First, it is used as the input of the controller, and second, it is used as the feedback to compare with the given value to get the deviation. Inverse control reduces the order of the flexible arm model, and fuzzy adaptive control approximates the uncertain modeling error of the flexible arm. The two controls are combined to obtain the overall control method, which controls and eliminates the deviation based on the trajectory tracking deviation, thereby completing the control. The specific implementation steps are as follows:

[0035] Step 1: According to Figure 2 Schematic diagram of a typical flexible arm structure. When there is an uncertain modeling error, the dynamic equation of the system is established based on Lagrangian mechanics as follows:

[0036]

[0037] Among them, I0 , J 0 , K 0 、M 0 and L 0 are the precise quantities of connecting rod inertia, motor rotor moment of inertia, spring coefficient, connecting rod mass and connecting rod length; θ m and are the trajectory and acceleration of the motor rotor respectively; θ l and are the arm joint trajectory and acceleration respectively; u is the controller to be designed; Ω 1 and Ω 2 represents the uncertain modeling error and has the following expression:

[0038]

[0039] Among them, I Δ , J Δ , K Δ 、M Δ and L Δ They are the modeling uncertainty errors of connecting rod inertia, motor rotor moment of inertia, spring coefficient, connecting rod mass and connecting rod length;

[0040] Step 2: Select variable x 1 =θ l , x 3 =θ m , and x=[x 1 ,x 2 ,x 3 ,x 4 ] T , the above dynamic equations are reduced in order to adopt the inverse control idea. The equations after the reduction are expressed as:

[0041]

[0042] Among them, f 2 (x) = -1 / I 0 (M 0 g 0 sin(x 1 )+K 0 (x 1 -x 3 ))-x 3 、f 4 (x) = -K 0 / J 0 (x 1 -x 3 ) and b = 1 / J 0 Determine the known, Δf2 (x) = Ω 1 / I 0 , Δf 4 (x) = Ω 2 / J 0 represents the uncertain modeling error;

[0043] Step 3: Use fuzzy algorithm to model the uncertainty error term Δf 2 (x), Δf 4 (x) is approximated and has the following expression:

[0044]

[0045]

[0046]

[0047]

[0048] Step 4: Based on the actual trajectory of the joint and motor rotor θ l ,θ m and speed and the expected trajectory θ ld ,θ md and speed The deviation e i (i=1,2,3,4), introduce auxiliary variable z for equation (2) i (i=1,2,3,4)z i and virtual input α i (i=1,2,3):

[0049]

[0050]

[0051] Step 5: Design the following controller u:

[0052]

[0053] Step 6. Method proof: Select the Lyapunov function expression as follows:

[0054]

[0055] Then select the following adaptive law:

[0056]

[0057] Deriving the above Lyapunov function and considering the above equations and controllers, adaptive laws, we can get the following after simplification:

[0058]

[0059] in, It is proved that the tracking error is eventually uniformly bounded, that is, the actual trajectory of the flexible robotic arm shutdown can well track the expected trajectory.

[0060] For the flexible manipulator with uncertain modeling errors, a fuzzy adaptive inverse control method is used. This control method relies on uncertain quantities such as trajectory tracking deviation and uncertain error approximation value, and constructs appropriate auxiliary variables, virtual variables and adaptive laws to complete the controller design and ensure that the trajectory tracking deviation is eliminated within the final consistent bounded range.

[0061] The inversion control idea reduces the order of the general dynamic differential equation, improves the feasibility of the control algorithm, and then combines the fuzzy adaptive control idea to enhance the robustness of the flexible arm due to modeling errors, thereby improving the trajectory tracking accuracy of the flexible arm and thus improving the practicality of the flexible arm.

Claims

1. A trajectory tracking control method for a flexible arm under uncertain modeling errors, characterized by: Considering the uncertainty error of the flexible arm in modeling, its dynamic differential equation is established and a fuzzy adaptive inverse control method is designed.

2. The dynamic differential equation according to claim 1, characterized in that: When there is an uncertain modeling error in the flexible arm, the dynamic differential equation of the flexible arm is expressed as: Among them, I0, J0, K0, M0 and L0 are the precise quantities of connecting rod inertia, motor rotor moment of inertia, spring constant, connecting rod mass and connecting rod length respectively; θ m and are the trajectory and acceleration of the motor rotor respectively; θ l and are the arm joint trajectory and acceleration respectively; u is the controller to be designed; Ω1 and Ω2 represent the uncertain modeling errors, which have the following expressions: Among them, I Δ , J Δ , K Δ 、M Δ and L Δ They are the modeling uncertainty errors of connecting rod inertia, motor rotor moment of inertia, spring coefficient, connecting rod mass and connecting rod length.

3. The fuzzy adaptive inversion control method according to claim 1, characterized in that: The actual trajectory of the arm joint θ l and acceleration metrics As the control object, with a given desired trajectory θ ld and In order to track the target, a fuzzy adaptive inverse control method is designed so that the controlled object can eventually track the desired target in a bounded and consistent manner. The specific implementation of the control method includes the following steps: Step 1: Select variable x1 = θ l , x3=θ m , and x = [x1,x2,x3,x4] T , reduce the order of equation (1) to the following: Among them, f2(x)=-1 / I0(M0gL0sin(x1)+K0(x1-x3))-x3, f4(x)=-K0 / J0(x1-x3) and b=1 / J0 are known, Δf2(x)=Ω1 / I0, Δf4(x)=Ω2 / J0 represent uncertain modeling errors; Step 2: Use fuzzy algorithm to approximate the uncertain modeling error terms Δf2(x) and Δf4(x), and the following expressions are available: Step 3: Based on the actual trajectory of the joint and motor rotor θ l ,θ m and speed and the expected trajectory θ ld ,θ md and speed The deviation e i (i=1,2,3,4), introduce auxiliary variable z for equation (2) i (i=1,2,3,4)z i and virtual input α i (i=1,2,3): Step 4: Design the following controller u: Complete the trajectory tracking control of the flexible arm.

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