A method for adaptive fixed-time control of a robotic arm

Abstract

The invention provides a method for adaptive fixed-time control of a mechanical arm, which belongs to the field of mechanical arms. The method comprises: obtaining position information of each joint and speed information of each joint through a sensor at each joint of the mechanical arm; obtaining a position error based on an expected position of the mechanical arm and the position information of each joint, obtaining a virtual controller based on the position error and Lyapunov theory, and obtaining a speed error based on virtual control and speed information; obtaining an adaptive update law of a neural network basis function weight based on the speed error of each joint and a neural network basis function, and obtaining a neural network weight updated in real time according to the adaptive update law of the neural network basis function weight; obtaining a control torque of each joint of the mechanical arm based on the position error of each joint, the speed error of each joint, the neural network basis function and the neural network weight updated in real time. The method can achieve an accurate trajectory tracking effect.

Description

Technical Field

[0001] The present invention relates to the field of mechanical arms, and in particular to an adaptive fixed-time control method for mechanical arms. Background Art

[0002] Robotic manipulators are indispensable in modern industry and are widely used in aerospace, assembly lines, and healthcare. Advanced control algorithms are essential to achieve high-precision and high-efficiency motion control and effectively cope with complex environments and dynamic changes. However, robotic arms still face many challenges in control, including the model uncertainty problem of robotic arms, with nonlinear inputs and outputs. In the problem of robotic arm model uncertainty, most of the existing advanced control methods use radial basis neural networks or fuzzy algorithms to approximate the model of the robotic arm. However, these methods lack rationality in the selection of neural network nodes. Although any model can be approximated if there are enough nodes, a large number of redundant nodes may be generated, increasing the computational burden of the system.

[0003] In addition, the robot arm also faces the problem of input and output nonlinearity, including input saturation and output constraints. At present, many studies have studied one of them separately or only studied the symmetric input saturation and output constraints. There is a lack of research methods that solve asymmetric input saturation and output constraints at the same time. Summary of the invention

[0004] In order to solve the technical problems existing in the prior art, the embodiment of the present invention provides a method for adaptive fixed time control of a robot arm, which has the ability to handle asymmetric input saturation output constraints, can greatly improve the ability of the robot arm to work in a complex environment, and can avoid failure of the robot arm. The technical solution is as follows:

[0005] A method for adaptive fixed-time control of a robotic arm, comprising:

[0006] S1, obtain the position information and speed information of each joint through the sensor at each joint of the robotic arm;

[0007] S2. Obtaining a position error based on the expected position of the robot arm and the position information of each joint, obtaining a virtual controller based on the position error and Lyapunov theory, and obtaining a speed error based on the virtual controller and the speed information;

[0008] S3, based on the velocity error of each joint and the neural network basis function, an adaptive update law of the neural network basis function weight is obtained, and according to the adaptive update law of the neural network basis function weight, a real-time updated neural network weight is obtained;

[0009] S4. Based on the position error of each joint, the velocity error of each joint, the neural network basis function and the real-time updated neural network weights, the control torque of each joint of the robotic arm is obtained.

[0010] Optionally, the step of obtaining a position error based on the expected position of the robot arm and the position information of each joint, obtaining a virtual controller based on the position error and Lyapunov theory, and obtaining a speed error based on the virtual controller and the speed information in S2 includes:

[0011] S201, calculating the position error of each joint and constraining the position error, wherein the position error of each joint is defined as: , is the position error of the i-th joint of the robot, is the position of the i-th joint of the robotic arm, is the expected position of the i-th joint of the robotic arm;

[0012] S202, based on the position error of each joint, combined with Lyapunov theory, the position error satisfies the constraint condition, and a virtual controller of each joint is obtained, wherein the formula of the virtual controller of each joint is formula (1):

[0013] ; (1)

[0014] in, is the virtual controller of the ith joint, , , and is an adjustable constant;

[0015] ∈ , , is a positive gain moment;

[0016] ∈ , , is a positive gain moment;

[0017] As parameters, ;

[0018] S203, according to the virtual controller of each joint, based on the speed information of each joint, obtain the speed error of each joint, wherein the speed error of each joint is defined as: ;

[0019] is the velocity error for each joint, is the velocity vector for each joint.

[0020] Optionally, the S3 obtains an adaptive update law of a neural network basis function weight based on the velocity error of each joint and the neural network basis function, and obtains a real-time updated neural network weight according to the adaptive update law of the neural network basis function weight, including:

[0021] S301, converting an asymmetric saturation function in a mechanical model of the robot arm into a saturation function based on a hyperbolic tangent function;

[0022] S302, obtaining a parameter expression of a dynamic model of the robot arm based on an error of a hyperbolic tangent function approximating a saturation function using a neural network basis function;

[0023] S303, designing an adaptive update law for the weights of the neural network basis functions so that the neural network can approach the real robotic arm model;

[0024] Among them, the adaptive update law of the neural network basis function weight is formula (2):

[0025] ; (2)

[0026] in, , is the error between the actual value and the ideal value of the neural network basis function;

[0027] is the ideal weight of the neural network basis function, is the actual weight of the neural network basis function;

[0028] , , , , and is an adjustable parameter;

[0029] is the neural network basis function, and a is an adjustable controller parameter;

[0030] S303, the weights of the neural network basis functions are updated according to the adaptive update law to obtain real-time updated neural network weights.

[0031] Optionally, the control torque of each joint of the robotic arm is obtained based on the position error of each joint, the speed error of each joint, the neural network basis function and the real-time updated neural network weights in S4, including:

[0032] Define the controller as , , and As auxiliary variables, to facilitate the expression of the controller, is the auxiliary symmetric matrix;

[0033] Based on the position error of each joint, the velocity error of each joint, the neural network basis function, and the neural network weights updated in real time, the calculation and ;

[0034] in, The expression of is formula (3), The expression of is formula (4):

[0035] ; (3)

[0036] ; (4)

[0037] Where n is the number of joints, and For the new operations defined; for The Moore-Penrose generalized inverse matrix of , , , and is the positive gain matrix of the manipulator system;

[0038] , , ;

[0039] The control torque of the robotic arm is output according to the controller.

[0040] Optionally, the auxiliary symmetric matrix is defined as: ;

[0041] in, and is defined as:

[0042] ;

[0043] in, is the intermediate variable, is the intermediate variable, is the upper bound of the input saturation of the i-th joint of the robot, is the input saturation lower bound of the i-th joint, is the saturation upper bound of the controller torque received by the robot arm, It is the saturation lower bound of the controller torque received by the robot arm.

[0044] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0045] The example of the present invention fills the gap of the robot arm in handling asymmetric input saturation constraints and time-varying asymmetric output constraints under fixed time stability, and combines width learning with the model approximation of the robot arm. First, the present invention needs to obtain the position and speed information of the robot arm; secondly, by comparing with the expected trajectory, the position error of the robot arm is obtained, and a virtual controller is designed to implement the position constraint of the robot arm to obtain the speed error of the robot arm; after obtaining the error information, the neural network combines the error information, and adjusts the system parameters in real time through the designed adaptive update law, gradually approximating the specific model of the robot arm and compensating for the saturation error; finally, the error information and the actual weight data are used to generate the control torque of the robot arm through the provided controller, and the actual control torque can still enable the robot arm to complete the trajectory tracking task under the constraint of input saturation, and achieve accurate trajectory tracking effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are 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.

[0047] Figure 1 is a flow chart of a method provided by an embodiment of the present invention;

[0048] Figure 2 is a schematic diagram of input saturation nonlinearity provided by an embodiment of the present invention;

[0049] Figure 3 is a schematic diagram of the structure of a mechanical arm provided by an embodiment of the present invention;

[0050] Figure 4 is a schematic diagram of a width learning node structure provided by an embodiment of the present invention;

[0051] Figure 5 It is a schematic diagram of the tracking effect of the controller provided by the embodiment of the present invention acting on the joints of two mechanical arms;

[0052] Figure 6 is a schematic diagram of tracking error of a first joint provided by the implementation of the present invention;

[0053] Figure 7 Schematic diagram of tracking error of the second joint provided by the embodiment of the present invention. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solution and advantages of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0055] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, words such as "one", "one" or "the" do not indicate a quantitative limitation, but indicate the existence of at least one. Words such as "include" or "comprise" mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connect" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect.

[0056] It should be noted that the terms "up", "down", "left", "right", "front", "back", etc. used in the present invention are only used to indicate relative position relationships. When the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0057] At present, in the research on the robot controller, the method of neural network node selection used in the solution to its model uncertainty problem needs to be optimized, and there is a lack of research on the improved node selection method. In addition, there is no method that can simultaneously handle asymmetric input saturation and time-varying output constraints. The present invention provides a fixed-time adaptive controller based on width learning for a rigid robot with asymmetric input saturation and asymmetric time-varying output constraints, aiming to solve the model uncertainty problem in the trajectory tracking control of the robot and the input saturation and output constraint problems faced in complex environments. First, the position and speed information of the robot are obtained by the sensor, and the position error of the system is obtained by comparing with the equilibrium position, and the speed error is obtained by the difference between the speed information of the system and the designed virtual controller; secondly, according to the error information obtained, the radial basis neural network with a width learning architecture is used to adjust the system parameters in real time to approximate the unknown robot model and the error caused by saturation nonlinearity. Finally, the error information and the weight information of the neural network will be used as the input of the designed controller to generate the control torque of the robot to control the trajectory motion of the robot. This method realizes fixed time control, improves the node selection method of the neural network in the system, and solves the asymmetric input saturation output constraint problem of the robot arm at the same time, enabling the robot arm to achieve accurate trajectory tracking effect under various constraints, including:

[0058] like Figures 1 to 7 As shown, a method for adaptive fixed time control of a robot arm comprises:

[0059] S1, obtain the position information and speed information of each joint through the sensor at each joint of the robotic arm;

[0060] S2. Obtaining a position error based on the expected position of the robot arm and the position information of each joint, obtaining a virtual controller based on the position error and Lyapunov theory, and obtaining a speed error based on the virtual controller and the speed information;

[0061] S3, based on the velocity error of each joint and the neural network basis function, an adaptive update law of the neural network basis function weight is obtained, and according to the adaptive update law of the neural network basis function weight, a real-time updated neural network weight is obtained;

[0062] S4. Based on the position error of each joint, the velocity error of each joint, the neural network basis function and the real-time updated neural network weights, the control torque of each joint of the robotic arm is obtained.

[0063] The specific implementation of this method includes:

[0064] S1. Obtain the position information and speed information of each joint through the sensors at each joint of the robotic arm:

[0065] In this step, the position and speed information of the robot arm is obtained through the sensor; the information obtained is the position and speed information of all joints of the robot arm, and the dynamic model of the robot arm is expressed as:

[0066] ;

[0067] in, , is the velocity and position vector of the system; n is the number of joints of the robot arm,

[0068] is the inertia matrix, are the Coriolis matrix and the centrifugal matrix, is the gravity vector; is a saturation function, and its nonlinear effect is as follows Figure 2 As shown, u is the controller to be designed, is the torque output by the controller.

[0069] The specific formula for the output torque of each joint control is as follows:

[0070] ;

[0071] is the torque output by the controller of the i-th joint, , , , is a known saturation parameter, , is a smooth and continuous function of position.

[0072] like Figure 2 As shown, when the input torque of the controller is less than the minimum value of the saturation function When the input torque of the system is greater than the maximum value of the saturation function, it will be limited to the maximum value. Place.

[0073] The acquired position and velocity vectors are expressed as , .

[0074] In the provided implementation, a Kinova jaco2 robot is used as the control object of the controller. The Kinova jaco2 robot has advanced sensing technology, including torque, position, speed and temperature sensors. Figure 3The joint diagram of the Kinova jaco2 robot provided for this example. The designed controller will be applied to joints 2 and 3, and the remaining joints will be controlled by PID. The two external interfaces of KINOVASDK are Ethernet interface and USB interface. In the specific implementation, the interface used is the USB interface, through which the computer can read the position and speed information of each joint in real time. The acquired position and speed information is stored and used in Matlab 2023b.

[0075] In the provided implementation, the saturation parameters of joint 2 and joint 3 of the robot arm are respectively set to , , , , .

[0076] S2. Obtain a position error based on the expected position of the robot arm and the position information of each joint, obtain a virtual controller based on the position error and Lyapunov theory, and obtain a speed error based on the virtual control and speed information:

[0077] S201, calculating the position error of each joint and constraining the position error, wherein the position error of each joint is defined as: , is the position error of the i-th joint of the robot, is the position of the i-th joint of the robotic arm, is the expected position of the i-th joint of the robotic arm;

[0078] S202, based on the position error of each joint, combined with Lyapunov theory, the position error satisfies the constraint condition, and a virtual controller of each joint is obtained, wherein the formula of the virtual controller of each joint is formula (1):

[0079] ; (1)

[0080] in, is the virtual controller of the ith joint, , , and is an adjustable constant;

[0081] ∈ , , is a positive gain moment;

[0082] ∈ , , is a positive gain moment;

[0083] As parameters, ;

[0084] S203, according to the virtual controller of each joint, based on the speed information of each joint, obtain the speed error of each joint, wherein the speed error of each joint is defined as: ;

[0085] is the velocity error for each joint, is the velocity vector for each joint.

[0086] In step S2, the specific implementation is as follows:

[0087] Calculate the position error of the system and define it as ,in is the desired trajectory of each joint. Assume that the position error of the system is constrained to ,in are the lower and upper bounds of the constraints respectively. Auxiliary variables are defined to facilitate the design of subsequent controllers. .

[0088] definition: ;

[0089] ;

[0090] Design a virtual controller based on the obstacle Lyapunov theory so that the position error satisfies the given constraints. Designed to:

[0091] ;

[0092] in represents the virtual controller of the ith joint, is an adjustable constant, diag , diag is a positive gain moment. Parameters is defined as:

[0093] ;

[0094] According to the Lyapunov obstacle theory, it can be proved that the position error of the system will be constrained within a given range.

[0095] According to the designed virtual controller, the speed error of the system is defined as: .

[0096] In the specific implementation, data processing is performed in Matlab. The expected trajectories of joints 2 and 3 are both 2+0.2cos(t), so the expected trajectory vector can be expressed as [2+0.2cos(t),2+0.2cos(t)]. The output constraints of the two joints are set to 0.4+0.1cos(t). The value of is chosen to be 0.5, The value of is chosen to be 3. The gain matrix of the system is chosen to be: diag[38,38], The position information obtained from Kinova Jaco2 in step 1 is subtracted from the expected trajectory and the virtual controller in Matlab to obtain the position error and velocity error.

[0097] S3, based on the velocity error of each joint and the neural network basis function, an adaptive update law of the neural network basis function weight is obtained, and according to the adaptive update law of the neural network basis function weight, the real-time updated neural network weight is obtained, including:

[0098] S301, converting an asymmetric saturation function in a mechanical model of the robot arm into a saturation function based on a hyperbolic tangent function;

[0099] S302, obtaining a parameter expression of a dynamic model of the robot arm based on an error of a hyperbolic tangent function approximating a saturation function using a neural network basis function;

[0100] S303, designing an adaptive update law for the weights of the neural network basis functions so that the neural network can approach the real robotic arm model;

[0101] The adaptive update law of the neural network basis function weights is formula (2):

[0102] ; (2)

[0103] in, , is the error between the actual value and the ideal value of the neural network basis function;

[0104] is the ideal weight of the neural network basis function, is the actual weight of the neural network basis function;

[0105] , , , , and is an adjustable parameter;

[0106] is the neural network basis function, and a is an adjustable controller parameter;

[0107] S303, the weights of the neural network basis functions are updated according to the adaptive update law to obtain real-time updated neural network weights.

[0108] The specific implementation method in step S3 is:

[0109] Based on the error and weight information of the system, an adaptive update law is designed. A neural network with a width learning structure is used to approximate the unknown model and saturation error of the robot arm. The specific operations are as follows:

[0110] In order to solve the asymmetric saturation in the system, the hyperbolic tangent function will be used to approximate the saturation function and transform the asymmetric saturation function into a symmetric saturation function. In order to solve the saturation problem, the auxiliary symmetric matrix is ​​defined .in is defined as follows:

[0111] ;

[0112] Let the saturation function be equal to , is the saturation error caused by the conversion. is defined as:

[0113] ;

[0114] According to the mean value theorem, we can get the following equation:

[0115] ;

[0116] in, , u is the controller to be designed, , .

[0117] definition: ;

[0118] ;

[0119] Since the precise model of the robot arm is difficult, the model parameters of the robot arm will be approximated by the neural network. At the same time, the error of the hyperbolic tangent function approximating the saturation function is also approximated by the neural network. The specific form is:

[0120] ;

[0121] is the ideal weight of the neural network, is the number of nodes in the neural network, is the basis function. Represents the approximation error of the neural network and satisfies , .

[0122] ;

[0123] Z is the input vector of the neural network, defined as , is the center of the receptive field, is the width of the Gaussian function.

[0124] In this example, the node selection of the neural network is adjusted. Figure 4 Figure 1 is a schematic diagram of the width learning node structure. Traditional neural networks may generate a large number of redundant nodes, causing computational burden. Based on the structure of width learning, the node selection of the radial basis neural network is changed. The time when the starting node starts to update is defined as , the weight and receptive field center at this moment are defined as Among all the centers, select the m centers closest to the input vector and write them as , the updated receptive field center and weight can be expressed as follows:

[0125] ;

[0126] ;

[0127] ;

[0128] in The definition of is shown in the above formula, is an adjustable parameter vector. is the new weight vector, and will be updated later. After that, the receptive field center at all times is defined as follows:

[0129] ;

[0130] in is an adjustable threshold. When the value of is greater than the threshold, a new node will be generated. is the maximum number of nodes that can be set. New nodes are generated only when the number of nodes is less than the maximum number of nodes that can be set. By constraining the threshold and the maximum number of nodes, the generation of neural network nodes is more reasonable, the node structure of width learning performs better in approximating unknown functions, and can reduce the computational burden of the system. Design the adaptive update law of the neural network so that it can approximate the unknown robot model and make the weight error converge in a fixed time. Before designing the update law, define is the ideal weight, and the actual weight of the neural network is defined as Among them, the relationship between the actual weight and the true weight satisfies , is the error between the actual value and the ideal value.

[0131] The adaptive update law is designed as:

[0132] ;

[0133] in, and The definition is the same as for the virtual controller. is an adjustable system parameter. The update law has been proved to converge within a fixed time through the derivation of Lyapunov theory.

[0134] In the provided embodiment, , The initial weights of the neural network are all set to 0. The value of is set to 0.1, the initial number of nodes in the neural network is set to 50, and the maximum number of nodes is The neural network updates the weights through the adaptive update law each time it samples, and the number of nodes will continue to increase before reaching the maximum number of nodes, gradually approaching the unknown model of the Kinova robot and compensating for the saturation error of the system.

[0135] S4. Based on the position error of each joint, the velocity error of each joint, the neural network basis function and the real-time updated neural network weight, the control torque of each joint of the robotic arm is obtained, including:

[0136] Define the controller as , , and As auxiliary variables, to facilitate the expression of the controller, is the auxiliary symmetric matrix;

[0137] Based on the position error of each joint, the velocity error of each joint, the neural network basis function, and the neural network weights updated in real time, the calculation and ;

[0138] in, The expression of is formula (3), The expression of is formula (4):

[0139] ; (3)

[0140] ; (4)

[0141] Where n is the number of joints, and For the new operations defined; for Moore–Penrose generalized inverse matrix, , , and is the positive gain matrix of the manipulator system;

[0142] , , ;

[0143] The control torque of the robotic arm is output according to the controller.

[0144] Optionally, the auxiliary symmetric matrix is defined as: ;

[0145] in, and is defined as:

[0146] ;

[0147] in, is the intermediate variable, is the intermediate variable, is the upper bound of the input saturation of the i-th joint of the robot, is the input saturation lower bound of the i-th joint, is the saturation upper bound of the controller torque received by the robot arm, It is the saturation lower bound of the controller torque received by the robot arm.

[0148] In step S4, a fixed time controller is designed based on the error and the weight of the neural network to generate the control torque of the robot arm. In the designed controller, it is necessary to obtain information such as the position error, speed error, and weight of the neural network of the system. The specific operations include:

[0149] In order to facilitate the expression of the controller, a new operation is defined ,in For any vector, it can be expressed as ,but ;

[0150] The controller is defined as , in order to facilitate the expression of the controller, let it be . The inverse of the adjuvant matrix defined above. and is the controller to be given, where The definition of is as follows:

[0151] ;

[0152] is an adjustable system parameter, and is a positive system gain matrix, and The definition of is the same as before. for The definition of Moore-Penrose generalized inverse matrix can be expressed as:

[0153] ;

[0154] Designed as follows:

[0155] ;

[0156] By inputting the data in the previous step into the controller, the control torque of the robot arm can be obtained, which is used to control the robot arm to complete the trajectory tracking task.

[0157] In a specific implementation, diag [0.006,0.3], diag [0.006,0.3];

[0158] 10. The robot arm processes the acquired data through Matlab, and the designed controller inputs the torque to each joint of the robot arm, and transmits the torque to the Kinova robot through the USB data cable to achieve the control effect.

[0159] In the embodiment of the present invention, the designed controller is applied to the joints of the Kinova robot, and a good tracking effect is achieved under the constraint of input saturation, and the position error of the system can be constrained within a specified range. The ability of the robot to handle complex constraints is enhanced. In addition, in dealing with the problem of uncertainty in the robot model, the node structure of width learning is applied to the radial basis neural network, which reduces the computational burden of the system.

[0160] In addition, the designed controller makes it stable in fixed time. It has been proved that for a control system , if there exists a Lyapunov function satisfying ,in , , , , we can say that the system makes the actual fixed time stable. A system with fixed time stability can reach equilibrium at a fixed time under different initial conditions. When the robot arm is performing a task, it is inevitable that it will be in different initial positions. Fixed time stability allows the robot arm to be stable for a certain time under different initial conditions.

[0161] In this example, the constructed Lyapunov equation can be derived to satisfy:

[0162] .

[0163] Its parameters are shown in equations (5) to (8), and it can be seen that it satisfies the above conditions, that is, the control method provided by the present invention is stable within a fixed time.

[0164] ; (5)

[0165] ; (6)

[0166] ; (7)

[0167] ; (8)

[0168] in , , and Represent the minimum and maximum eigenvalues ​​of each matrix respectively. The remaining parameters are consistent with the previous definition.

[0169] The example of the present invention fills the gap of the robot arm in handling asymmetric input saturation constraints and time-varying asymmetric output constraints under fixed time stability, and combines width learning with the model approximation of the robot arm. First, the present invention needs to obtain the position and speed information of the robot arm; secondly, by comparing with the expected trajectory, the position error of the robot arm is obtained, and a virtual controller is designed to implement the position constraint of the robot arm to obtain the speed error of the robot arm; after obtaining the error information, the neural network combines the error information, and adjusts the system parameters in real time through the designed adaptive update law, gradually approximating the specific model of the robot arm and compensating for the saturation error; finally, the error information and the actual weight data are used to generate the control torque of the robot arm through the provided controller, and the actual control torque can still enable the robot arm to complete the trajectory tracking task under the constraint of input saturation, and achieve accurate trajectory tracking effect.

[0170] The following points need to be explained:

[0171] (1) The drawings of the embodiments of the present invention only involve structures related to the embodiments of the present invention. Other structures may refer to conventional designs.

[0172] (2) For the sake of clarity, in the drawings used to describe the embodiments of the present invention, the thickness of layers or regions is exaggerated or reduced, that is, these drawings are not drawn according to the actual scale. It is understood that when an element such as a layer, film, region or substrate is referred to as being "on" or "under" another element, the element may be "directly" "on" or "under" the other element or there may be intermediate elements.

[0173] (3) In the absence of conflict, the embodiments of the present invention and the features therein may be combined with each other to obtain new embodiments.

[0174] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. The protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for adaptive fixed-time control of a robotic arm, characterized in that: include: S1, obtain the position information and speed information of each joint through the sensor at each joint of the robotic arm; S2. Obtaining a position error based on the expected position of the robot arm and the position information of each joint, obtaining a virtual controller based on the position error and Lyapunov theory, and obtaining a speed error based on the virtual controller and the speed information; S3, based on the velocity error of each joint and the neural network basis function, an adaptive update law of the neural network basis function weight is obtained, and according to the adaptive update law of the neural network basis function weight, a real-time updated neural network weight is obtained; S4, based on the position error of each joint, the velocity error of each joint, the neural network basis function and the real-time updated neural network weight, obtain the control torque of each joint of the robotic arm; The S2 obtains the position error based on the expected position of the robot arm and the position information of each joint, obtains the virtual controller based on the position error and Lyapunov theory, and obtains the speed error based on the virtual control and speed information, including: S201, calculate the position error of each joint and constrain the position error, wherein the position error of each joint is defined as: 1i =x 1i -x di ,z 1i is the position error of the i-th joint of the robot arm, x 1i is the position of the i-th joint of the robot arm, x di is the expected position of the i-th joint of the robotic arm; S202, based on the position error of each joint, combined with Lyapunov theory, the position error satisfies the constraint condition, and a virtual controller of each joint is obtained, wherein the formula of the virtual controller of each joint is formula (1): Among them, v i is the virtual controller of the i-th joint, 0<α<1, β>1, α and β are adjustable constants; k 1i ∈K1,K1=diag[k 11 , k 12 , ..., k 1n ], K1 is the positive gain moment; k 2i ∈K2,K2=diag[k 21 , k 22 , ..., k 2n ], K2 is the positive gain moment; k i As parameters, S203, according to the virtual controller of each joint, based on the speed information of each joint, obtain the speed error of each joint, wherein the speed error of each joint is defined as: 2i =x 2i -υ i ; z 2i is the velocity error of each joint, x 2i is the velocity vector for each joint; The S3 obtains the adaptive update law of the neural network basis function weights based on the velocity error of each joint and the neural network basis function, and obtains the real-time updated neural network weights according to the adaptive update law of the neural network basis function weights, including: S301, converting an asymmetric saturation function in a mechanical model of the robot arm into a saturation function based on a hyperbolic tangent function; S302, obtaining a parameter expression of a dynamic model of the robot arm based on an error of a hyperbolic tangent function approximating a saturation function using a neural network basis function; S303, designing an adaptive update law for the weights of the neural network basis functions so that the neural network can approach the real robotic arm model; The adaptive update law of the neural network basis function weight is formula (2): in, is the error between the actual value and the ideal value of the neural network basis function; is the ideal weight of the neural network basis function, is the actual weight of the neural network basis function; b i >0,σ 1i >0,σ 2i >0,b i , σ 1i and σ 2i is an adjustable parameter; S(Z) is the neural network basis function, and a is an adjustable controller parameter; S303, the weights of the neural network basis functions are updated according to the adaptive update law to obtain real-time updated neural network weights.

2. The method for adaptive fixed-time control of a robotic arm according to claim 1, characterized in that: The control torque of each joint of the robot arm obtained by S4 based on the position error of each joint, the speed error of each joint, the neural network basis function and the real-time updated neural network weight includes: Define the controller as u, u=Λ -1 u a +u b ,u a and u b is an auxiliary variable, Λ is an auxiliary symmetric matrix; Based on the position error of each joint, the velocity error of each joint, the neural network basis function, and the neural network weights updated in real time, u is calculated. a and u b ; Among them, u a The expression is formula (3), u b The expression of is formula (4): Among them, n is the number of joints, Sig α (z2) and Sig β (z2) is the new operation defined; for The Moore-Penrose generalized inverse matrix of , K3 and K4 are positive gain matrices of the manipulator system; The control torque of the robotic arm is output according to the controller.

3. The method for adaptive fixed time control of a robot arm according to claim 2, characterized in that: The auxiliary symmetric matrix Λ is defined as: in, and is defined as: in, is the intermediate variable, is the intermediate variable, F i max is the upper bound of the input saturation of the i-th joint of the robot, F i min is the input saturation lower bound of the i-th joint, u i max is the saturation upper bound of the controller torque received by the robot arm, u i min It is the saturation lower bound of the controller torque received by the robot arm.

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