Fuzzy adaptive sliding mode control method for double-arm collaborative robot

Abstract

The invention relates to the technical field of robot control, in particular to a double-arm collaborative robot fuzzy adaptive sliding mode control method, which comprises the following steps: S1, establishing a dynamic model of a double-arm collaborative robot; s2, fusing a Taylor series expansion method on the basis of the dynamic model of the double-arm collaborative robot, and establishing an improved dynamic mathematical model suitable for a time delay condition; s3, using a fuzzy algorithm and an average residence time mechanism to develop a fuzzy adaptive sliding mode tracking controller; and S4, designing a neural network tracking control scheme based on fuzzy recursion to eliminate a time delay error existing in the model. According to the control method provided by the invention, the negative influence of the time delay on the system stability can be effectively overcome while the interference influence is eliminated, and the application range of the theoretical delay value is obtained on the basis of improving the control quality of the double-arm system.

Description

Technical Field

[0001] The invention relates to the technical field of robot control, in particular to a fuzzy adaptive sliding mode control method for a dual-arm collaborative robot. Background Art

[0002] In recent years, robotic manipulators have played an important role in industrial applications. Compared with single manipulators, multi-manipulators have a larger load-bearing capacity and can perform more versatile tasks. When multiple manipulators jointly manipulate an object, a set of kinematic and dynamic constraints are imposed on the manipulators' motion due to the formation of a closed kinematic chain. Therefore, the control of multiple robotic manipulators is much more complicated compared to the control of a single robotic manipulator. In most works, nonholonomic trajectories that can represent more complex motion requirements are not considered in the controller design.

[0003] Sliding mode control (SMC) is a robust control strategy widely used in dual-arm collaborative robot systems. Such systems are usually highly nonlinear, coupled, and dynamically uncertain, and face challenges from external disturbances. Dual-arm robots need to coordinate motion to complete complex tasks, such as grasping and handling, so they have high requirements for control accuracy and response speed. SMC introduces a sliding surface to guide the system state onto the surface, thereby effectively suppressing uncertainty and disturbances and ensuring the stability and tracking performance of the system. This feature makes SMC particularly suitable for real-time control requirements in dual-arm collaboration, and can cope with dynamic changes in task loads and environments. In addition, SMC has advantages in handling system switching and uncertainty, and can quickly adjust control strategies to ensure the efficiency and accuracy of collaboration. Therefore, SMC provides an effective control solution for dual-arm collaborative robots.

[0004] In many practical applications, the system state often depends on past input and state information. Traditional neural networks may face the problem of information loss when processing such time series data. At the same time, there is a time delay error in the traditional dual-arm robot dynamics mathematical model, and the interference caused by the time delay error cannot be eliminated, so that the time delay error has a negative impact on the stability of the system, and the system exhibits strong robustness to uncertainty and external disturbances, which further makes the mathematical model's response ability poor, reduces the efficiency and accuracy of the system, and cannot achieve accurate tracking of the preset trajectory in the joint space. Summary of the invention

[0005] In response to the above problems, this application provides a fuzzy adaptive sliding mode control method for a dual-arm collaborative robot. The time-delay neural network introduces a time-delay unit, which enables the network to store and use historical data, thereby improving the modeling accuracy. In addition, the time-delay neural network shows stronger robustness when modeling nonlinear dynamic systems, and can effectively deal with uncertainties and disturbances in the system. The time-delay neural network and sliding mode control can improve the accuracy of dual-arm collaboration.

[0006] The technical solution of the present invention is:

[0007] A fuzzy adaptive sliding mode control method for a dual-arm collaborative robot comprises the following steps:

[0008] S1. Establish the dynamic model of the dual-arm collaborative robot;

[0009] S2. Based on the dynamic model of the dual-arm collaborative robot, the Taylor series expansion method is integrated to establish a dynamic mathematical model suitable for time delay conditions;

[0010] S3. Design a fuzzy adaptive sliding mode tracking controller using fuzzy algorithm and average residence time mechanism;

[0011] S4. A fuzzy recursive neural network tracking control scheme is used to eliminate the time delay error in the model.

[0012] Preferably, in step S1, the specific steps are:

[0013] The dynamic equations of a collaborative robot system with two manipulators in the joint space are:

[0014] In the above formula: , ,and , respectively represent the position, velocity and acceleration of the joints in the first and second robotic arms, where t represents time t, , denote the positions of the joints in the first and second robotic arms, respectively. is the inertia matrix; It is the Coriolis force or centrifugal force; is the gravity term, , is the control torque term, , They represent the control torque terms of the first and second robotic arms respectively.

[0015] Preferably, in step S2, the specific steps are:

[0016] Since there is a time delay error in the system, the Taylor series expansion is used as a theoretical means of prediction approximation, and the delay term in the time delay system is expanded according to the Taylor series;

[0017] First, the joint positions of the robot arm containing the delay term , joint velocity and joint acceleration According to the first-order Taylor expansion and ignoring the remaining high-order terms, the expansion is:

[0018] in, They are the actual position, velocity and acceleration of the joint, t1 represents the time t1, and the delay ;

[0019] Substituting the joint parameters with time delay into the trigonometric function and simplifying it, we get:

[0020] Will , and Using Taylor series expansion we get:

[0021] Substituting the above formula into the dynamic equation of the dual-arm collaborative robot, we get:

[0022] Among them, ΔE is the residual term after expansion, that is, the delay error in the system.

[0023] Preferably, in step S3, it is specifically manifested as follows:

[0024] Through single-case fuzzification, product reasoning and central average defuzzification, the output of the dual-arm collaborative robot fuzzy logic system is:

[0025]

[0026] in is the relevant fuzzy set, represents the number of fuzzy rules, is a constant, is the input of the fuzzy logic system, is the output of the fuzzy logic system, is a general Gaussian function;

[0027]

[0028] In the formula, the center and width are respectively and represent, is the input of the target fuzzy logic system; therefore, It can also be expressed as:

[0029]

[0030] represents an adjustable weight vector, represents the fuzzy basis function;

[0031] Now set the reference signal to , the tracking error is defined as , the sliding mode variable is defined as

[0032] in is a diagonal positive definite matrix, in which case the control torque is defined as:

[0033]

[0034] are the estimated weights of the fuzzy logic system, is the symbolic function, is the basis function of the fuzzy logic system, is the adaptive law, K represents a positive definite diagonal matrix, is an adjustable factor, is a scalar, is a sliding mode variable.

[0035] Preferably, in step S4, it is specifically manifested as follows:

[0036] The time delay term ΔE is an unknown nonlinear function. Therefore, a fuzzy recursive neural network control algorithm is introduced to compensate for the time delay error. The neural network is combined with fuzzy control to form a fuzzy neural network with reasoning and induction capabilities, thereby improving the control performance. The characteristics of this comprehensive system make it more suitable for nonlinear control systems. The proposed fuzzy recursive neural network control algorithm adopts a three-input and three-output hierarchical network structure design.

[0037] The first layer accepts input variables and also serves as the input variables of the second layer. The expected and actual position errors and their velocity errors and acceleration errors can be written as:

[0038]

[0039] here , and They are the ideal position, velocity and acceleration of the joint respectively; under the premise that the posture joint is uncontrolled, the input variable is set to be the error function ,have

[0040] The second layer is the membership function value calculation stage, using Gaussian function as the membership function, each node has a membership function, namely:

[0041]

[0042] in For the The input Gaussian membership function output;

[0043] For the input variables; , , The first The input The center quantity, recursive weight quantity and basis function bandwidth,

[0044] The third layer is the fuzzy reasoning layer. The output of the second layer is multiplied by the rule to get the output of the third layer. The output of the third layer at the previous moment is go through The weighted value is fed back to the second layer to form a recursive structure, namely: .

[0045] The fourth layer is the output layer, and its output expression is:

[0046]

[0047] in: is the output of the fourth layer; is the connection weight between the fuzzy inference layer and the output layer, which is continuously adjusted through online training The third level The output of each node is integrated, and the final compensation control form is:

[0048]

[0049] In the above formula is the network weight matrix, is the final output variable;

[0050] In practical applications, it is difficult to achieve the ideal compensation control effect, so the estimated compensation control is :

[0051]

[0052] in To estimate the network weights, the final controller of the dual-arm collaborative robot is:

[0053]

[0054] in, It is the value set to keep the input control torque of the carrier attitude angle term on the right side of the equation constant at 0.

[0055] The beneficial effects of the present invention are as follows:

[0056] (1) The dual-arm sliding mode control of the present invention shows strong robustness to system uncertainty and external disturbances, and can effectively suppress the impact of dynamic loads and environmental changes, ensuring system stability. By designing the sliding surface, the sliding film control can quickly guide the system state to reach the target, significantly improve the tracking accuracy, meet the requirements of high-precision tasks, and have rapid response capabilities, and can adjust the control strategy in time to enhance the adaptability of the dual-arm robot in task switching. It can also handle complex nonlinear characteristics, provide stable control effects, and reduce tracking errors by dynamically adjusting the control input, thereby improving the efficiency and accuracy of the system.

[0057] (2) The present invention adopts a prediction method based on Taylor series expansion to extract the time delay term in the joint space coordinates, thereby deriving an improved dynamic equation of the dual-arm collaborative robot. Compared with the traditional dynamic equation, the proposed improved model better simulates the time delay error and reflects the objective situation in actual operation. The nonlinear function approximation capability of neural network control is utilized to overcome the limitations of the traditional calculation torque method in processing time delay errors. On the basis of the neural network controller, fuzzy control and recursive control methods are introduced to effectively reduce the jitter phenomenon of the system and improve the speed of online learning. In addition, through the online evaluation of the effective range of the delay value, it is ensured that the appropriate time delay range is determined on the basis of providing good quality control, so that the accurate tracking of the preset trajectory in the joint space can be achieved.

[0058] (3) The invention opens up new perspectives and solutions for the control technology of dual-arm collaborative robots, and at the same time provides strong technical support for their application in complex tasks such as field exploration and express delivery. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0060] Figure 1 A flow chart of a fuzzy adaptive sliding mode control method for a dual-arm collaborative robot provided by the present invention;

[0061] Figure 2Schematic diagram of a robotic arm for controlling two degrees of freedom of two arms of the same object according to the present invention. DETAILED DESCRIPTION

[0062] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the present invention will be briefly introduced below in combination with the drawings and the description of the embodiments or the prior art. Obviously, the following description of the structure of the drawings is only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. It should be noted that the description of these embodiments is used to help understand the present invention, but does not constitute a limitation of the present invention.

[0063] like Figure 1-Figure 2 As shown, an embodiment of the present invention provides a fuzzy adaptive sliding mode control method for a dual-arm collaborative robot. In the present invention, the control parameters of two planar two-degree-of-freedom (2-DOF) manipulators controlling an ordinary object along an expected trajectory are calculated to illustrate the performance of the proposed controller.

[0064] The base positions of the two robot manipulators are (0,0) and (1,0) respectively. Figure 2 middle , and Respectively represent Robot manipulator The length, mass and inertia of the connecting rod, such as the represents the mass of the first robot manipulator and the first link. In the figure, A, B, C and D represent the joint connection angles. Here, represents the inertia of the first robot manipulator and the second link, represents the length of the second robot manipulator and the second connecting rod. The length, mass and inertia of the remaining robot manipulators are similar to the above examples. It represents the angle of the first robot manipulator and the second connecting rod. The other angles are expressed similarly and will not be described in detail here.

[0065] definition For the Robot manipulator The joint positions of the links, the position and direction of the center of mass of the grasped object are , No. The position of the end effector of the robot manipulator is The kinematic relationship between the joint angle of each robot manipulator in the joint space and the position of the end effector in the Cartesian space is:

[0066]

[0067] In the formula, For the The base position of the robot manipulator, For the A robot manipulator Coordinate location, For the Robotic manipulator Coordinate location.

[0068] This embodiment provides a fuzzy adaptive sliding mode control method for a dual-arm collaborative robot, the method comprising the following steps:

[0069] Step S1, establish the dynamic equation of the dual-arm collaborative robot:

[0070]

[0071] here, , ,and , respectively represent the position, velocity and acceleration of the joints in the first and second robotic arms, is the inertia matrix, is the Coriolis force or centrifugal force, is the gravity term, , is the control torque term, , The dimensions are appropriate and all functions are continuous.

[0072] Step S2: Based on the dynamic model of the dual-arm collaborative robot, the Taylor series expansion method is integrated to establish an improved dynamic mathematical model suitable for the time delay condition:

[0073] Since there is a time delay error in the system, the Taylor series expansion is used as a theoretical means of prediction approximation. The delay term in the time delay system is expanded according to the Taylor series. First, the joint position of the manipulator containing the delay term is , joint velocity and joint acceleration According to the first-order Taylor expansion and ignoring the remaining high-order terms, the expansion can be obtained as

[0074]

[0075] in, They are the actual position, velocity, acceleration, and delay of the joint. .

[0076] Substituting the joint parameters with time delay into the trigonometric function and simplifying it, we can get

[0077] It can be seen that the calculation error mainly comes from the high-order terms of Taylor expansion.

[0078] Here will , and Using Taylor series expansion, we can get

[0079] Substituting the above formula into the dynamic equation of the dual-arm collaborative robot, we can get

[0080] Among them, ΔE is the residual term after expansion, that is, the delay error in the system.

[0081] Step S3: Using fuzzy algorithm and average residence time mechanism, a fuzzy adaptive sliding mode tracking controller is developed:

[0082] Through single-case fuzzification, product reasoning and central average defuzzification, the output of the dual-arm collaborative robot fuzzy logic system is:

[0083]

[0084] in is the relevant fuzzy set, represents the number of fuzzy rules, is a constant, is the input of the fuzzy logic system, is the output of the fuzzy logic system,

[0085] is a general Gaussian function.

[0086]

[0087] In the formula, the center and width are respectively and represent, is the input of the target fuzzy logic system. So It can also be expressed as

[0088]

[0089] here represents an adjustable weight vector, represents the fuzzy basis function.

[0090] Now set the reference signal to , the tracking error is defined as , so the sliding mode variable is defined as .

[0091] in is a diagonal positive definite matrix. In this case, the control torque is defined as:

[0092]

[0093] here are the estimated weights of the fuzzy logic system, is the symbolic function, is the basis function of the fuzzy logic system, is the adaptive law, K represents a positive definite diagonal matrix, is a scalar, is a sliding mode variable.

[0094] Step S4: design a fuzzy recursive neural network tracking control scheme, and use its overall approximation of any uncertain nonlinear terms to eliminate the time delay error in the model:

[0095] The delay term ΔE is an unknown nonlinear function. Therefore, a fuzzy recursive neural network control algorithm is introduced here to compensate for the delay error. Combining neural network with fuzzy control, a fuzzy neural network with reasoning and induction capabilities is formed to improve the control performance. The characteristics of this comprehensive system make it more suitable for nonlinear control systems. The proposed fuzzy recursive neural network control algorithm adopts a three-input and three-output hierarchical network structure design.

[0096] The first layer receives input variables and also serves as the input variables of the second layer. The expected and actual position errors and their velocity and acceleration errors can be written as

[0097]

[0098] here , and They are the ideal joint position, velocity, and acceleration. Under the premise that the posture joint is not controlled, let the input variable be the error function ,have

[0099]

[0100] The second layer is the membership function value calculation stage, using Gaussian function as the membership function, each node has a membership function, namely:

[0101]

[0102] in For the The input Gaussian membership function output;

[0103] For the input variables; , , The first The input The center quantity, recursive weight quantity and basis function bandwidth are included.

[0104] The third layer is the fuzzy reasoning layer. The output of the second layer is obtained by regular multiplication (fuzzy process) to obtain the output of the third layer, and the output of the third layer at the previous moment go through The weighted value is fed back to the second layer to form a recursive structure, that is,

[0105]

[0106] in: is the output of the fourth layer; is the connection weight between the fuzzy inference layer and the output layer, which is continuously adjusted through online training The third level The output of each node is integrated, and the final compensation control form is:

[0107]

[0108] here is the network weight matrix, is the final output variable.

[0109] In practical applications, it is difficult to achieve the ideal compensation control effect, so the estimated compensation control (actual input control) is assumed to be:

[0110]

[0111] in To estimate the network weights.

[0112] So the final controller of the dual-arm collaborative robot is

[0113]

[0114] in It is the value set to keep the input control torque of the carrier attitude angle term on the right side of the equation constant at 0.

[0115] The dual-arm sliding mode control of the present invention shows strong robustness to system uncertainty and external disturbances, can effectively suppress the impact of dynamic loads and environmental changes, and ensure system stability. By designing the sliding surface, the sliding film control can quickly guide the system state to reach the target, significantly improve the tracking accuracy, meet the requirements of high-precision tasks, and have a fast response capability, and can adjust the control strategy in time to enhance the adaptability of the dual-arm robot in task switching. It can also handle complex nonlinear characteristics, provide stable control effects, and reduce tracking errors by dynamically adjusting the control input, thereby improving the efficiency and accuracy of the system.

[0116] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A fuzzy adaptive sliding mode control method for a dual-arm collaborative robot, characterized in that: The following steps are involved: S1. Establish the dynamic equation of the dual-arm collaborative robot; S2. Based on the dynamic model of the dual-arm collaborative robot, the Taylor series expansion method is integrated to establish a dynamic mathematical model suitable for time delay conditions; S3. Design a fuzzy adaptive sliding mode tracking controller using fuzzy algorithm and average residence time mechanism; S4. A fuzzy recursive neural network tracking control scheme is used to eliminate the time delay error in the model.

2. A fuzzy adaptive sliding mode control method for a dual-arm collaborative robot according to claim 1, characterized in that: In step S1, the specific steps are: The dynamic equations of a collaborative robot system with two manipulators in the joint space are: In the above formula: , and Represent the position, velocity and acceleration of the joints in the first and second robotic arms respectively. The t in the above represents the time t. , denote the positions of the joints in the first and second robotic arms, respectively. is the inertia matrix; It is the Coriolis force or centrifugal force; is the gravity term, , is the control torque term, , They represent the control torque terms of the first and second robotic arms respectively.

3. The fuzzy adaptive sliding mode control method of a dual-arm collaborative robot according to claim 2 is characterized in that: In step S2, a dynamic mathematical model suitable for the time delay condition is established, and the specific steps are as follows: Since there is a time delay error in the system, the Taylor series expansion is used as a theoretical means of prediction approximation, and the delay term in the time delay system is expanded according to the Taylor series; First, the joint positions of the robot arm containing the delay term , joint velocity and joint acceleration According to the first-order Taylor expansion and ignoring the remaining high-order terms, the expansion is: ， in, They are the actual position, velocity and acceleration of the joint, where t1 represents the time t1, and the delay , Substituting the joint parameters with time delay into the trigonometric function and simplifying it, we get: ， Will , and Using Taylor series expansion we get: ， Substituting the above formula into the dynamic equation of the dual-arm collaborative robot, we get: ， Among them, ΔE is the residual term after expansion, and the delay term ΔE is an unknown nonlinear function, that is, the delay error existing in the system.

4. The fuzzy adaptive sliding mode control method of a dual-arm collaborative robot according to claim 3 is characterized in that: In step S3, a fuzzy adaptive sliding mode tracking controller is designed, which is specifically performed as follows: Through single-case fuzzification, product reasoning and central average defuzzification, the output of the dual-arm collaborative robot fuzzy logic system is: ， in is the relevant fuzzy set, represents the number of fuzzy rules, is a constant, is the input of the fuzzy logic system, is the output of the fuzzy logic system, is a general Gaussian function; ， In the above formula, Indicates the center, Indicates width, is the input of the target fuzzy logic system; therefore, It is expressed as: ， represents an adjustable weight vector, represents the fuzzy basis function; Now set the reference signal to , the tracking error is defined as , is the first-order derivative of the tracking error, and the sliding mode variable is defined as: ， in is a diagonal positive definite matrix, in which case the control torque is defined as: ， are the estimated weights of the fuzzy logic system, is the symbolic function, is the basis function of the fuzzy logic system, is the adaptive law, K represents a positive definite diagonal matrix, is an adjustable factor, is the sliding mode variable, thus forming a fuzzy adaptive sliding mode tracking controller.

5. A fuzzy adaptive sliding mode control method for a dual-arm collaborative robot according to claim 4, characterized in that: The step S4 of eliminating the delay error in the model is specifically as follows: The time delay term ΔE is an unknown nonlinear function. Therefore, a fuzzy recursive neural network control algorithm is introduced to compensate for the time delay error. The neural network is combined with fuzzy control to form a fuzzy neural network with reasoning and induction capabilities, thereby improving the control performance. The characteristics of this comprehensive system make it more suitable for nonlinear control systems. The proposed fuzzy recursive neural network control algorithm adopts a three-input and three-output hierarchical network structure design. The first layer accepts input variables and also serves as the input variables of the second layer. The expected and actual position errors and their velocity errors and acceleration errors are written as: ， here , and They are the ideal position, velocity and acceleration of the joint respectively; under the premise that the posture joint is uncontrolled, the input variable is set to be the error function , For the input variables, where: ， The second layer is the membership function value calculation stage, using Gaussian function as the membership function, each node has a membership function, that is, ， in For the The input Gaussian membership function output; , , The first The input The center quantity, recursive weight quantity and basis function bandwidth, The third layer is the fuzzy reasoning layer. The output of the second layer is multiplied by the rule to get the output of the third layer. The output of the third layer at the previous moment is go through The weighted value is fed back to the second layer to form a recursive structure, namely: ， The fourth layer is the output layer, and its output expression is: ， in: is the output of the fourth layer; is the connection weight between the fuzzy inference layer and the output layer, which is continuously adjusted through online training The third level The output of each node is integrated, and the final compensation control form is: ， In the above formula is the network weight matrix, is the final output variable; In practical applications, it is difficult to achieve the ideal compensation control effect, so the estimated compensation control is : ， in To estimate the network weights, the final controller of the dual-arm collaborative robot is: ， in It is the value set to keep the input control torque of the carrier attitude angle term on the right side of the equation constant at 0.

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