Self-adaptive backstepping tracking control method for space manipulator and related equipment
By constructing an inverse step adaptive tracking controller in the space robot arm, the upper bound of approximation error is estimated and compensated by radial basis neural network functions, the accuracy problem of the space robot arm when tracking the expected trajectory is solved, and a higher trajectory tracking accuracy is achieved.
Patent Information
- Application Number
- CN202411859497.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-17
- Publication Date
- 2025-03-18
AI Technical Summary
The prior art is difficult to accurately track the desired trajectory in the space robotic arms, mainly due to factors such as highly nonlinear dynamics, uncertain parameters, limited input saturation, and external interference.
The radial basis neural network function is used to construct an inverse step adaptive tracking controller, and based on the tracking error model of the space robot arm, estimating and compensating the upper bound of the approximation error, thereby achieving the convergence of the state error of the closed-loop system.
Improves the accuracy of the space robotic arm tracking the desired trajectory, allowing it to complete tasks more accurately in the actual operating environment.
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Figure CN119644748A_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the technical field of robot arm control, and in particular to a space robot arm adaptive backstepping tracking control method and related equipment. Background Art
[0002] Space robotic arms are playing an increasingly important role in on-orbit services, and are often used to repair faulty satellites and remove space debris. In order to complete on-orbit tasks, space robotic arms need to accurately track the desired trajectory.
[0003] There are already many solutions to the problem of trajectory tracking control of space manipulators, but the existing solutions have not completely solved the problem. The main reasons are unfavorable factors such as highly nonlinear dynamics, parameter uncertainty, input saturation limitation, and external interference.
[0004] Since neural networks can arbitrarily approximate unknown quantities and have unique advantages, some existing technologies use neural networks to deal with the problem of system model uncertainty. However, in the process of use, most existing methods assume that there is an upper bound on the approximation error without further processing, resulting in poor processing results, making it difficult for the space robot to accurately track the desired trajectory.
[0005] Therefore, the prior art needs to be improved and enhanced. Summary of the invention
[0006] The purpose of the present application is to provide a space robot arm adaptive backstepping tracking control method and related equipment, which can improve the accuracy of the space robot arm in tracking the desired trajectory.
[0007] In a first aspect, the present application provides a space manipulator adaptive backstepping tracking control method for performing trajectory tracking control on a space manipulator, wherein the space manipulator comprises a spacecraft base and a manipulator connected to the spacecraft base; the method comprises the following steps: A1. Based on the system parameter uncertainty, external interference and input constraints, the tracking error model of the space manipulator is established according to the mechanical model of the space manipulator; A2. Based on the tracking error model, a backstepping adaptive tracking controller is constructed using a radial basis neural network function; the backstepping adaptive tracking controller can estimate and compensate for the upper bound of the approximation error; A3. Use the backstepping adaptive tracking controller to perform trajectory tracking control on the space robot arm.
[0008] This application takes into account the unfavorable factors of system parameter uncertainty, external interference and input limitation, and is more in line with the actual operating environment of the space manipulator. In addition, the radial basis neural network function is used to construct a backstepping adaptive tracking controller to estimate and compensate for the upper bound of the approximation error, so that the closed-loop system state error can converge to the ellipsoid area, thereby improving the accuracy of the space manipulator in tracking the desired trajectory.
[0009] Preferably, the mechanical model of the space manipulator is: ; ; ; ; ; in, is the angle vector of the space manipulator, , They are The first and second derivatives with respect to time, n is the dimension of the space manipulator, is the inertia matrix of the space manipulator, , They are The scalar part and the uncertain part of For the Coriolis and centrifugal matrices, , They are The scalar part and the uncertain part of is the control torque vector, for The 1st to nth components of For external interference, is the saturation function, is the symbolic function, for The i-th component of for The upper bound of , T is the transpose symbol.
[0010] Preferably, the tracking error model is: ; ; ; ; in, Based on and The conversion relationship of The equivalent matrix obtained by conversion is, Based on and The conversion relationship of The equivalent matrix obtained by conversion is, is the tracking error, , They are The first and second derivatives with respect to time, is the expected angle vector of the space manipulator corresponding to the expected trajectory, , They are The first and second derivatives with respect to time, is the total uncertainty, Based on and The conversion relationship of The equivalent matrix obtained by conversion is, Based on and The conversion relationship of The equivalent matrix obtained by conversion is, is the torque deviation.
[0011] This tracking error model introduces factors such as system parameter uncertainty, external interference and input restriction, which is more in line with the actual operating environment of the space manipulator, and is more conducive to ensuring the control accuracy of the subsequent backstepping adaptive tracking controller, so that the space manipulator can track the desired trajectory more accurately.
[0012] Preferably, step A2 comprises: Construct a radial basis neural network function for estimating total uncertainty; constructing an auxiliary state variable related to the tracking error; A backstepping adaptive tracking controller is constructed by utilizing the radial basis neural network function based on the tracking error model and the auxiliary state variables.
[0013] Preferably, the radial basis neural network function is constructed according to the following formula: ; ; ; ; in, for The i-th component of For the corresponding The optimal weight vector of For the corresponding The radial basis function vector, is the number of hidden layer nodes of the radial basis neural network function, for Corresponding to the 1st to the The components of hidden layer nodes, for The component corresponding to the jth hidden layer node in is the ith input, For the corresponding The central value of For the corresponding The width of For the corresponding The approximation error is For the corresponding The upper bound of the approximation error of ; The output of the radial basis neural network function is: ; in, for The estimated value of for The estimated value of .
[0014] Preferably, the auxiliary state variable is: ; ; in, is the first auxiliary state variable, is the second auxiliary state variable, is a dummy control variable, is a positive definite gain matrix.
[0015] Preferably, the backstepping adaptive tracking controller is: ; ; ; ; ; in, Based on and and The conversion relationship of The equivalent matrix obtained by conversion is, Based on and The conversion relationship of The equivalent matrix obtained by conversion is, for The first derivative with respect to time, is a positive definite matrix, For external signals, for The estimated value of is the output estimate of the radial basis neural network function, is the estimated value of the upper bound vector of the approximation error, for The estimated value of the upper bound of the approximation error corresponding to each component of is a constant greater than zero, is the diagonal matrix symbol, for The i-th component of ; Among them, the radial basis neural network function and The components of are determined by the following formula: ; ; ; in, for The first derivative with respect to time, For the corresponding The first control parameter, For the corresponding The second control parameter, for The i-th component of for The first derivative with respect to time, For the corresponding The third control parameter, For the corresponding The fourth control parameter.
[0016] The backstepping adaptive tracking controller can be used to accurately estimate and compensate the upper bound of the approximation error, thereby ensuring the accuracy of trajectory tracking.
[0017] In a second aspect, the present application provides a space manipulator adaptive backstepping tracking control device for performing trajectory tracking control on a space manipulator, wherein the space manipulator comprises a spacecraft base and a manipulator connected to the spacecraft base; comprising: A model building module is used to establish a tracking error model of the space manipulator according to the mechanical model of the space manipulator based on the system parameter uncertainty, external interference and input constraints; A controller construction module is used to construct a backstepping adaptive tracking controller based on the tracking error model and using a radial basis neural network function; the backstepping adaptive tracking controller can estimate and compensate for the upper bound of the approximation error; A control module is used to perform trajectory tracking control on the space robot arm using the backstepping adaptive tracking controller.
[0018] In a third aspect, the present application provides an electronic device comprising a processor and a memory, wherein the memory stores a computer program executable by the processor, and when the processor executes the computer program, it runs the steps in the adaptive backstepping tracking control method for a space robot arm as described above.
[0019] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, runs the steps of the adaptive backstepping tracking control method for a spatial manipulator as described above.
[0020] Beneficial effects: The adaptive backstepping tracking control method and related equipment for a space manipulator provided in the present application establish a tracking error model for the space manipulator according to the mechanical model of the space manipulator based on the conditions of system parameter uncertainty, external interference and input restriction; a backstepping adaptive tracking controller is constructed based on the tracking error model using a radial basis neural network function; the backstepping adaptive tracking controller can estimate and compensate for the upper bound of the approximation error; the backstepping adaptive tracking controller is used to perform trajectory tracking control on the space manipulator; thereby improving the accuracy of the space manipulator in tracking the desired trajectory. BRIEF DESCRIPTION OF THE DRAWINGS
[0021] Figure 1 A flow chart of an adaptive backstepping tracking control method for a space manipulator provided in an embodiment of the present application.
[0022] Figure 2 A schematic diagram of the structure of an adaptive backstepping tracking control device for a space manipulator provided in an embodiment of the present application.
[0023] Figure 3 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application.
[0024] Figure 4 This is a schematic diagram of the structure of the space robotic arm.
[0025] Figure 5 Trace the curve for the angle.
[0026] Figure 6 is the angular velocity time response curve.
[0027] Figure 7 It is the control input variation curve.
[0028] Explanation of reference numerals: 1. Model building module; 2. Controller building module; 3. Control module; 301. Processor; 302. Memory; 303. Communication bus. DETAILED DESCRIPTION
[0029] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. The components of the embodiments of the present application described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application claimed for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present application.
[0030] It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. At the same time, in the description of this application, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance.
[0031] Please refer to Figure 1 In some embodiments of the present application, a space manipulator adaptive backstepping tracking control method is used to perform trajectory tracking control on a space manipulator, wherein the space manipulator includes a spacecraft base and a manipulator connected to the spacecraft base (i.e., the space manipulator is a general term for the spacecraft base and the manipulator connected to the spacecraft base, such as Figure 4 As shown, B is the spacecraft base, C is the robotic arm, and A is the arm of the robotic arm); comprising the steps of: A1. Based on the system parameter uncertainty, external interference and input constraints, the tracking error model of the space manipulator is established according to the mechanical model of the space manipulator; A2. Based on the tracking error model, a backstepping adaptive tracking controller is constructed using the radial basis neural network function; the backstepping adaptive tracking controller can estimate and compensate for the upper bound of the approximation error; A3. Use the backstepping adaptive tracking controller to perform trajectory tracking control on the space robot.
[0032] This application takes into account the unfavorable factors of system parameter uncertainty, external interference and input limitation, and is more in line with the actual operating environment of the space manipulator. In addition, the radial basis neural network function is used to construct a backstepping adaptive tracking controller to estimate and compensate for the upper bound of the approximation error, so that the closed-loop system state error can converge to the ellipsoid area, thereby improving the accuracy of the space manipulator in tracking the desired trajectory.
[0033] Specifically, the mechanical model of the space manipulator is: ; ; ; ; ; in, is the angle vector of the space manipulator (it contains n components, at least one of which represents the attitude angle of the spacecraft base, and the other components represent the rotation angles of each arm of the manipulator), , They are The first and second derivatives of time, n is the dimension of the space manipulator (equal to the sum of the attitude dimension of the spacecraft base and the number of arms of the manipulator, that is, n=N1+N2, N1 is the number of arms of the manipulator, N2 is the attitude dimension of the spacecraft base, N2 is at least 1, that is, the spacecraft base can rotate around at least one axis, for example Figure 4 The unconstrained spacecraft base shown, N2 = 3), is the inertia matrix of the space manipulator, , They are The scalar part and the uncertain part of For the Coriolis and centrifugal matrices, , They are The scalar part and the uncertain part ( and Characterizes the uncertainty of system parameters), is the control torque vector, for The 1st to nth components of For external interference, is the saturation function, is the symbolic function, for The i-th component of for The upper bound of represents the case of input constraint), T is the transposition symbol.
[0034] According to the above-mentioned space manipulator mechanical model, the following tracking error model can be established: ; (1); ; ; in, Based on and The conversion relationship (refer to formula (1)) is The equivalent matrix obtained by conversion is, Based on and The conversion relationship of The equivalent matrix obtained by conversion is, is the tracking error, , They are The first and second derivatives with respect to time, is the expected angle vector of the space manipulator corresponding to the expected trajectory, , They are The first and second derivatives with respect to time, is the total uncertainty, Based on and The conversion relationship of The equivalent matrix obtained by conversion is, Based on and The conversion relationship of The equivalent matrix obtained by conversion is, is the torque deviation.
[0035] This tracking error model introduces factors such as system parameter uncertainty, external interference and input restriction, which is more in line with the actual operating environment of the space manipulator, and is more conducive to ensuring the control accuracy of the subsequent backstepping adaptive tracking controller, so that the space manipulator can track the desired trajectory more accurately.
[0036] Specifically, step A2 includes: A201. Construct a radial basis neural network function for estimating total uncertainty; A202. Construct auxiliary state variables related to tracking error; A203. Using radial basis function of neural network, a backstepping adaptive tracking controller is constructed based on tracking error model and auxiliary state variables.
[0037] In step A201, a radial basis neural network function is constructed according to the following formula: ; ; ; ; in, for The i-th component of For the corresponding The optimal weight vector of For the corresponding The radial basis function vector, is the number of hidden layer nodes of the radial basis neural network function, for Corresponding to the 1st to the The components of hidden layer nodes, for The component corresponding to the jth hidden layer node in is the i-th input (the i-th component of the input vector, the input vector is given by and The fitted vector), For the corresponding The center value of (set according to actual needs), For the corresponding The width (set according to actual needs), For the corresponding The approximation error is For the corresponding The upper bound of the approximation error of ; The output of the radial basis neural network function is: ; in, for The estimated value of for The estimated value of .
[0038] Specifically, in step A202, the following auxiliary state variables are constructed: (2); (3); in, is the first auxiliary state variable, is the second auxiliary state variable, is a dummy control variable, is a positive definite gain matrix (which can be set according to actual needs).
[0039] Furthermore, in step A203, the following backstepping adaptive tracking controller is constructed: ; ; ; ; ; in, Based on and and The conversion relationship (refer to formula (2) and (3)) is The equivalent matrix obtained by conversion is, Based on and The conversion relationship of The equivalent matrix obtained by conversion is, for The first derivative with respect to time, is a positive definite matrix (can be set according to actual needs), For external signals, for The estimated value of is the output estimate of the radial basis neural network function, is the estimated value of the upper bound vector of the approximation error, for The estimated value of the upper bound of the approximation error corresponding to each component of is a constant greater than zero (can be set according to actual needs), is the diagonal matrix symbol, for The i-th component of ; Among them, the radial basis neural network function and The components of are determined by the following formula: ; ; ; in, for The first derivative with respect to time, For the corresponding The first control parameter (can be set according to actual needs), For the corresponding The second control parameter (can be set according to actual needs), for The i-th component of for The first derivative with respect to time, For the corresponding The third control parameter (can be set according to actual needs), For the corresponding The fourth control parameter (can be set according to actual needs).
[0040] The backstepping adaptive tracking controller can be used to accurately estimate and compensate the upper bound of the approximation error, thereby ensuring the accuracy of trajectory tracking.
[0041] Specifically, through the backstepping adaptive tracking controller, it can be guaranteed that , , weight estimation error ( ) and the upper bound of the approximation error vector estimation error ( , is the upper bound vector of the approximation error) converges to the following ellipsoid region: ; ; in, for The i-th component in For and The ellipsoid area represented by the parameter and 0 as the origin, for , a column vector composed of; ; ; in, for The minimum eigenvalue of for The minimum eigenvalue of .
[0042] Specifically, step A3 includes: A301. Obtain the position data of the desired trajectory; A302. Using the position data of the expected trajectory as the target position data of the space manipulator, the expected angle vector of the space manipulator and the first-order derivative and second-order derivative of the expected angle vector with respect to time are calculated according to the target position data; for example, the inverse kinematics equation of the manipulator may be used to solve the expected angle vector according to the target position data, and the first-order derivative and second-order derivative of the expected angle vector are taken to obtain the first-order derivative and second-order derivative of the expected angle vector with respect to time; A303. Input the desired angle vector of the space manipulator and the first-order derivative and second-order derivative of the desired angle vector with respect to time into the backstepping adaptive tracking controller to obtain the control torque vector output by the backstepping adaptive tracking controller; A304. According to the control torque vector output by the backstepping adaptive tracking controller, the output torque of each actuator is controlled so that the output torque of each actuator is equal to the corresponding component in the control torque vector.
[0043] For a space manipulator with two arms and a spacecraft base with an attitude dimension (this space manipulator can be called a planar space manipulator, so n=3), the above space manipulator adaptive backstepping tracking control method is simulated and analyzed, where the system parameter uncertainty is set to , , the external interference is , t is the time, the upper bound of all control inputs are 10Nm, and the initial angle vector and initial angular velocity vector of the space manipulator are set to , , is the initial angle vector, is the initial angular velocity vector, the positive definite gain matrix , a positive definite matrix , represents the third-order identity matrix, for i=1,2,3, is 4000, 7.5×10 -3 , is 2, is 1, the number of hidden layer nodes of the radial basis neural network function is 7, the center value matrix , , (corresponding to the center value matrices of the three dimensions of the space manipulator) are all 3×7 matrices (i.e., matrices with three rows and seven columns), and each row is , for i=1,2,3, the width matrix ( Reason The matrix composed of j = 1, 2, ..., 7) is , the initial value of the optimal weight estimate of the radial basis neural network function is The initial estimate of the upper bound of each approximation error is , the expected angle vector is Based on the above conditions, the simulation results show that the angle tracking curve is Figure 5 As shown in the figure, the angular velocity time response curve is as follows: Figure 6As shown, the control input change curve is as follows Figure 7 As shown in the figure, it can be seen that the backstepping adaptive tracking controller can enable the space manipulator to accurately track the desired trajectory; in the figure, , , Track the curves at three angles. , , There are three angular velocity time response curves respectively. , , There are three control input change curves respectively.
[0044] From the above, it can be seen that the adaptive backstepping tracking control method of the space manipulator establishes a tracking error model of the space manipulator according to the mechanical model of the space manipulator based on the conditions of system parameter uncertainty, external interference and input limitation; based on the tracking error model, a backstepping adaptive tracking controller is constructed using the radial basis neural network function; the backstepping adaptive tracking controller can estimate and compensate for the upper bound of the approximation error; the backstepping adaptive tracking controller is used to perform trajectory tracking control on the space manipulator; thereby, the accuracy of the space manipulator in tracking the desired trajectory can be improved.
[0045] refer to Figure 2 The present application provides a space manipulator adaptive backstepping tracking control device, which is used to perform trajectory tracking control on a space manipulator connected to a spacecraft base; comprising: Model building module 1, used to establish a tracking error model of the space manipulator according to the mechanical model of the space manipulator based on the conditions of system parameter uncertainty, external interference and input limitation (refer to step A1 above for details); The controller building module 2 is used to build a backstepping adaptive tracking controller based on the tracking error model and using the radial basis neural network function; the backstepping adaptive tracking controller can estimate and compensate for the upper bound of the approximation error (refer to step A2 above for details); The control module 3 is used to perform trajectory tracking control on the space robot arm using a backstepping adaptive tracking controller (refer to step A3 above for details).
[0046] Please refer to Figure 3, is a structural schematic diagram of an electronic device provided in an embodiment of the present application. The present application provides an electronic device, including: a processor 301 and a memory 302. The processor 301 and the memory 302 are interconnected and communicate with each other through a communication bus 303 and / or other forms of connection mechanisms (not shown). The memory 302 stores a computer program executable by the processor 301. When the electronic device is running, the processor 301 executes the computer program to execute the adaptive backstepping tracking control method of the space manipulator in any optional implementation of the above embodiments to achieve the following functions: Under the conditions of system parameter uncertainty, external interference and input limitation, a tracking error model of the space manipulator is established according to the mechanical model of the space manipulator; based on the tracking error model, a backstepping adaptive tracking controller is constructed using a radial basis neural network function; the backstepping adaptive tracking controller can estimate and compensate for the upper bound of the approximation error; and the backstepping adaptive tracking controller is used to perform trajectory tracking control on the space manipulator.
[0047] An embodiment of the present application provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the adaptive backstepping tracking control method for a space robot in any optional implementation of the above-mentioned embodiment is executed to achieve the following functions: under the conditions of system parameter uncertainty, external interference and input limitation, a tracking error model of the space robot is established according to a mechanical model of the space robot; based on the tracking error model, a backstepping adaptive tracking controller is constructed using a radial basis neural network function; the backstepping adaptive tracking controller can estimate and compensate for the upper bound of the approximation error; and the backstepping adaptive tracking controller is used to perform trajectory tracking control on the space robot. Among them, the computer-readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable red-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk or optical disk.
[0048] In the embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some communication interfaces, and the indirect coupling or communication connection of the devices or units can be electrical, mechanical or other forms.
[0049] In addition, the units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, and may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
[0050] Furthermore, the functional modules in the various embodiments of the present application may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.
[0051] In this document, relational terms such as first and second, etc. are used merely to distinguish one entity or operation from another entity or operation, but do not necessarily require or imply any such actual relationship or order between these entities or operations.
[0052] The above description is only an embodiment of the present application and is not intended to limit the protection scope of the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims
1. A space manipulator adaptive backstepping tracking control method, used for performing trajectory tracking control on a space manipulator, wherein the space manipulator comprises a spacecraft base and a manipulator connected to the spacecraft base; characterized in that: Includes steps: A1. Based on the system parameter uncertainty, external interference and input constraints, the tracking error model of the space manipulator is established according to the mechanical model of the space manipulator; A2. Based on the tracking error model, a backstepping adaptive tracking controller is constructed using a radial basis neural network function; The backstepping adaptive tracking controller is capable of estimating and compensating the upper bound of the approximation error; A3. Use the backstepping adaptive tracking controller to perform trajectory tracking control on the space robot arm.
2. The adaptive backstepping tracking control method for a space manipulator according to claim 1, characterized in that: The mechanical model of the space manipulator is: ； ； ； ； ； in, is the angle vector of the space manipulator, , They are The first and second derivatives with respect to time, n is the dimension of the space manipulator, is the inertia matrix of the space manipulator, , They are The scalar part and the uncertain part of For the Coriolis and centrifugal matrices, , They are The scalar part and the uncertain part of is the control torque vector, for The 1st to nth components of For external interference, is the saturation function, is the symbolic function, for The i-th component of for The upper bound of , T is the transpose symbol.
3. The adaptive backstepping tracking control method for a space manipulator according to claim 2, characterized in that: The tracking error model is: ； ； ； ； in, Based on and The conversion relationship of The equivalent matrix obtained by conversion is, Based on and The conversion relationship of The equivalent matrix obtained by conversion is, is the tracking error, , They are The first and second derivatives with respect to time, is the expected angle vector of the space manipulator corresponding to the expected trajectory, , They are The first and second derivatives with respect to time, is the total uncertainty, Based on and The conversion relationship of The equivalent matrix obtained by conversion is, Based on and The conversion relationship of The equivalent matrix obtained by conversion is, is the torque deviation.
4. The adaptive backstepping tracking control method for a space manipulator according to claim 3, characterized in that: Step A2 includes: Construct a radial basis neural network function for estimating total uncertainty; constructing an auxiliary state variable related to the tracking error; A backstepping adaptive tracking controller is constructed by utilizing the radial basis neural network function based on the tracking error model and the auxiliary state variables.
5. The adaptive backstepping tracking control method for a space manipulator according to claim 4, characterized in that: The radial basis neural network function is constructed according to the following formula: ； ； ； ； in, for The i-th component of To correspond to The optimal weight vector of For the corresponding The radial basis function vector, is the number of hidden layer nodes of the radial basis neural network function, for Corresponding to the 1st to the The components of hidden layer nodes, for The component corresponding to the jth hidden layer node in is the ith input, To correspond to The central value of For the corresponding The width of For the corresponding The approximation error is For the corresponding The upper bound of the approximation error of ; The output of the radial basis neural network function is: ； in, for The estimated value of for The estimated value of .
6. The adaptive backstepping tracking control method for a space manipulator according to claim 5, characterized in that: The auxiliary state variables are: ； ； in, is the first auxiliary state variable, is the second auxiliary state variable, is a dummy control variable, is a positive definite gain matrix.
7. The adaptive backstepping tracking control method for a space manipulator according to claim 6, characterized in that: The backstepping adaptive tracking controller is: ； ； ； ； ； in, Based on and and The conversion relationship of The equivalent matrix obtained by conversion is, Based on and The conversion relationship of The equivalent matrix obtained by conversion is, for The first derivative with respect to time, is a positive definite matrix, For external signals, for The estimated value of is the output estimate of the radial basis neural network function, is the estimated value of the upper bound vector of the approximation error, for The estimated value of the upper bound of the approximation error corresponding to each component of is a constant greater than zero, is the diagonal matrix symbol, for The i-th component of ; Among them, the radial basis neural network function and The components of are determined by the following formula: ； ； ； in, for The first derivative with respect to time, For the corresponding The first control parameter, To correspond to The second control parameter, for The i-th component of for The first derivative with respect to time, To correspond to The third control parameter, To correspond to The fourth control parameter.
8. A space manipulator adaptive backstepping tracking control device, used for performing trajectory tracking control on a space manipulator, the space manipulator comprising a spacecraft base and a manipulator connected to the spacecraft base; characterized in that: include: A model building module is used to establish a tracking error model of the space manipulator according to the mechanical model of the space manipulator based on the system parameter uncertainty, external interference and input constraints; A controller building module, used to build a backstepping adaptive tracking controller based on the tracking error model using a radial basis neural network function; The backstepping adaptive tracking controller is capable of estimating and compensating the upper bound of the approximation error; A control module is used to perform trajectory tracking control on the space robot arm using the backstepping adaptive tracking controller.
9. An electronic device, characterized in that: It comprises a processor and a memory, wherein the memory stores a computer program executable by the processor, and when the processor executes the computer program, it runs the steps in the adaptive backstepping tracking control method for a space manipulator as described in any one of claims 1 to 7.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the adaptive backstepping tracking control method for a space manipulator as described in any one of claims 1 to 7 are executed.