Three-dimensional force reconstruction method for space manipulator based on load response base matrix superposition principle

Abstract

This invention provides a three-dimensional force reconstruction method for a space robotic arm based on the principle of superposition of load response basis matrices, relating to the field of space three-dimensional force reconstruction technology. The method includes the following steps: installing a three-dimensional force sensing module at the end effector of the space robotic arm, on which several fiber Bragg grating sensors are arranged; performing vector decomposition on the strain measured by the fiber Bragg grating sensors to obtain strain components along the orthogonal directions of the spatial coordinate system; constructing a dynamic load model of the sensing module, decomposing the orthogonal strain component matrix into a load-strain response basis matrix and a multidimensional load weight vector; calculating the displacement, velocity, and acceleration at the center position of the three-dimensional force sensing module based on the load-strain response basis matrix; solving the superimposed load components of the three-dimensional force sensing module in three-dimensional space using the dynamic response equation; and controlling the joints of the space robotic arm to achieve compliant operation based on the calculated superimposed load components.

Description

Technical Field

[0001] This invention relates to the field of spatial three-dimensional force reconstruction technology, and in particular to a spatial manipulator three-dimensional force reconstruction method based on the principle of load response basis matrix superposition. Background Technology

[0002] The three-dimensional force sensing module is a core component for achieving precise force control and interactive operation between the space robotic arm and the end effector. By calculating the three-dimensional load information in real time, the space robotic arm control system can establish a complete closed loop from sensing to execution: based on accurate force sensing data, the system maintains trajectory accuracy while achieving smooth interaction with the environment through a force / position hybrid control strategy; it effectively eliminates inertial force interference caused by the robotic arm's own motion by utilizing a dynamic feedforward compensation mechanism; and finally, through real-time force monitoring and intelligent decision-making, it achieves a technological leap from programmed operation to intelligent adaptation, providing reliable technical support for precision space operations.

[0003] Several limiting factors remain in the development of three-dimensional force sensing algorithms: First, traditional decoupling algorithms lack the ability to characterize nonlinear coupling effects, leading to a significant decrease in the accuracy of multidimensional force calculations as the load conditions change. Second, their real-time calculation capabilities under dynamic loads are limited, making it difficult to meet the stringent requirements of high-speed force control tasks for algorithm response speed while maintaining accuracy. Furthermore, traditional methods based on manual calibration suffer from limitations such as scarce samples and poor cost-effectiveness, making it difficult to establish a complete calibration database required for high-precision decoupling, severely restricting the improvement of decoupling accuracy in sensor algorithms. Summary of the Invention

[0004] Purpose of the invention: To address the shortcomings of existing technologies, this invention proposes a three-dimensional force reconstruction method for space robotic arms based on the principle of superposition of load response basis matrices. This method overcomes the deficiencies of traditional algorithms in representing nonlinear coupling, improves measurement accuracy under time-varying conditions, reduces computational complexity by relying on the linear superposition characteristics of basis matrices, and meets the real-time, accuracy, and reliability requirements of space robotic arms for force perception in dynamic operating environments.

[0005] This invention proposes a three-dimensional force reconstruction method for a space robotic arm based on the principle of superposition of load response basis matrices, the steps of which are as follows:

[0006] Step 1: Install a three-dimensional force sensing module at the end effector of the space robotic arm, on which several fiber optic grating sensors are arranged. Step 2: Perform vector decomposition on the strain measured by the fiber Bragg grating sensor to obtain the strain components along the orthogonal direction of the spatial coordinate system; Step 3: Construct a dynamic load model for the sensing module, decomposing the strain orthogonal component matrix into a load-strain response basis matrix and a multidimensional load weight vector; Step 4: Calculate the displacement, velocity, and acceleration at the center of the three-dimensional force sensing module based on the load-strain response basis matrix inversion. Step 5: Solve the dynamic response equation to obtain the superimposed load components of the three-dimensional force sensing module in three-dimensional space; Step 6: Based on the calculated superimposed load components, control the joints of the space robotic arm to achieve compliant operation.

[0007] As a preferred embodiment, the three-dimensional force sensing module includes a central frame consisting of three elastic beams arranged at 120-degree angles to each other, and three fiber optic grating sensors are respectively positioned at the centerline of the three elastic beams.

[0008] As a preferred embodiment, the strain measured by the fiber Bragg grating sensor is vector decomposed to obtain the strain components along the orthogonal directions of the spatial coordinate system. The mathematical relationship is expressed as follows:

[0009] In the formula, , , These are the strain values ​​measured by fiber Bragg grating sensors positioned at the centerline of the elastic beam. The three corresponding components are respectively , , ; The three corresponding components are respectively , , ; The three corresponding components are respectively , , ; , , , , , , , , These are the strain vector decomposition coefficients, calculated using the angles between the fiber Bragg grating sensor's orientation and the x, y, and z axes.

[0010] As a preferred embodiment, the mathematical expression of the dynamic load model of the sensing module in step 3 is as follows:

[0011] In the formula, M, C, and K represent the mass, damping, and stiffness of any point in the three-dimensional force sensing module, respectively. The load vector acting on the particle; , , The particles are respectively in The acceleration, velocity, and displacement vectors under action.

[0012] As a preferred approach, based on the principle of linear characterization of multidimensional load strain response, the strain orthogonal component matrix is... Decomposed into load-strain response basis matrix With multidimensional load weight vector :

[0013] strain orthogonal component matrix The mathematical expression is:

[0014] Load-strain response basis matrix The mathematical expression is:

[0015] Multidimensional load weight vector The mathematical expression is:

[0016] In the formula, , , These represent the strain response values ​​of the fiber Bragg grating sensors located at the centerline positions of the first, second, and third elastic beams under the individual action of the p-th load along the x-direction; , , These represent the strain response values ​​of the fiber Bragg grating sensors located at the centerline positions of the first, second, and third elastic beams under the individual action of the p-th load along the y-direction; , , These represent the strain response values ​​of the fiber Bragg grating sensors located at the centerline positions of the first, second, and third elastic beams under the individual action of the p-th load along the x-direction; , , These represent the weights of the p-th load along the x, y, and z directions in the combined load state, respectively.

[0017] As a preferred option, step 4 specifically includes: The displacement at the center of the three-dimensional force sensing module is decomposed into a load-displacement response basis matrix. Based on the inversion method of the principle of superposition of load response basis matrices, the displacement at the center of the three-dimensional force sensing module is calculated. The velocity at the center of the three-dimensional force sensing module is decomposed into a load-velocity response basis matrix. Based on the inversion method of the principle of superposition of load response basis matrices, the velocity at the center of the three-dimensional force sensing module is calculated. The acceleration at the center of the three-dimensional force sensing module is decomposed into a load-acceleration response basis matrix. Based on the inversion method of the principle of superposition of load response basis matrices, the acceleration at the center of the three-dimensional force sensing module is calculated.

[0018] As a preferred option, step 5 specifically includes: The load vector acting on the particle Vector decomposition yields the load components along the orthogonal directions of the spatial coordinate system, whose mathematical expressions are:

[0019] In the formula, , , These are the load components along the x-axis, y-axis, and z-axis, respectively. The superimposed load components of the three-dimensional force sensing module in three-dimensional space are obtained by solving the following formula:

[0020] In the formula, , , These represent accelerations along the x, y, and z directions, respectively. , , These represent the velocities along the x, y, and z directions, respectively. , , These represent displacements along the x, y, and z directions, respectively.

[0021] Beneficial Effects: The proposed three-dimensional force reconstruction method for space robotic arms based on the principle of load response basis matrix superposition utilizes a quasi-distributed fiber optic sensing network. By establishing a mapping relationship between multidimensional loads and fiber optic response signals, a basis matrix characterizing the sensor response features under loads of various dimensions is constructed. In actual measurements, changes in optical signals are acquired in real time, and superposition and inverse solving of the basis matrix are performed to achieve accurate decoupling and reconstruction of complex external loads. This method effectively overcomes the shortcomings of traditional algorithms in representing nonlinear coupling, significantly improves measurement accuracy under time-varying conditions, and greatly reduces computational complexity by relying on the linear superposition characteristics of the basis matrix, thus meeting the real-time, accuracy, and reliability requirements of space robotic arms for force sensing in dynamic operating environments. Attached Figure Description

[0022] Figure 1This is a flowchart of the method of the present invention.

[0023] Figure 2 This is a structural schematic diagram of the three-dimensional force sensing module of the present invention.

[0024] Figure 3 This is a schematic diagram of the layout of the fiber Bragg grating sensor of the present invention.

[0025] Figure 4 This is a schematic diagram of the load reconstruction effect along the X direction of the present invention.

[0026] Figure 5 This is a schematic diagram of the load reconstruction effect along the Y direction of the present invention.

[0027] Figure 6 This is a schematic diagram of the load reconstruction effect along the Z direction of the present invention.

[0028] The meanings of the labels in the attached figures are as follows: 1. Top cover; 2. Three-dimensional force sensor; 3. Base; 4. Fiber Bragg grating sensor (FBG). Detailed Implementation

[0029] In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention can be practiced without one or more of these details. In other instances, certain technical features well-known in the art have not been described in order to avoid obscuring the invention.

[0030] This invention discloses a three-dimensional force reconstruction method for a space robotic arm based on the principle of superposition of load response basis matrices. The flowchart is shown below. Figure 1 As shown, the specific steps are as follows: Step 1: Design a three-dimensional force sensing module for a space robotic arm and provide a fiber optic grating sensor layout scheme.

[0031] Based on the mechanical principles of double-ended fixed elastic beams, a three-dimensional force sensing module for the end effector of a space robotic arm is designed, such as... Figure 2 As shown, it includes a top cover 1, a three-dimensional force sensor 2, and a base 3. The three-dimensional force sensor 2 consists of three elastic beams arranged at 120-degree angles to each other and an outer ring frame. Fiber Bragg grating sensors FBG1, FBG2, and FBG3 are respectively arranged at the center lines of the three elastic beams to sense the strain response characteristics of the sensing module under multi-dimensional loads, such as... Figure 3 As shown.

[0032] Step 2: Perform vector decomposition on the measured strain of the fiber Bragg grating sensor to obtain the strain components along the orthogonal directions of the spatial coordinate system.

[0033] Vector decomposition of the measured strain from the fiber Bragg grating sensor yields strain components along orthogonal directions in the spatial coordinate system. The mathematical expression for these components can be:

[0034] In the formula, , , These are the strain values ​​measured by fiber Bragg grating sensors positioned at the centerline of the elastic beam. The three corresponding components are respectively , , ; The three corresponding components are respectively , , ; The three corresponding components are respectively , , ; , , , , , , , , These are the strain vector decomposition coefficients, calculated using the angles between the fiber Bragg grating sensor's orientation and the x, y, and z axes.

[0035] Step 3: Construct a dynamic load model for the sensing module. Based on the principle of linear characterization of multidimensional load strain response, decompose the orthogonal component matrix of strain into a load-strain response basis matrix and a multidimensional load weight vector.

[0036] (1) Construct a dynamic load model for the sensing module, the mathematical relationship of which can be expressed as:

[0037] In the formula, M, C, and K represent the mass, damping, and stiffness of any point in the three-dimensional force sensing module, respectively. The load vector acting on the particle; , , The particles are respectively in The acceleration, velocity, and displacement vectors under action.

[0038] (2) Based on the principle of linear characterization of multidimensional load strain response, the strain orthogonal component matrix is ​​decomposed into load-strain response basis matrix and multidimensional load weight vector;

[0039] strain orthogonal component matrix The mathematical expression is:

[0040] The load-strain response basis matrix can be obtained by using equations (3) and (4). The mathematical expression is:

[0041] Multidimensional load weight vector The mathematical expression is:

[0042] In the formula, , , These represent the strain response values ​​of the fiber Bragg grating sensors located at the centerline positions of the first, second, and third elastic beams under the individual action of the p-th load along the x-direction; , , These represent the strain response values ​​of the fiber Bragg grating sensors located at the centerline positions of the first, second, and third elastic beams under the individual action of the p-th load along the y-direction; , , These represent the strain response values ​​of the fiber Bragg grating sensors located at the centerline positions of the first, second, and third elastic beams under the individual action of the p-th load along the x-direction; , , These represent the weights of the p-th load along the x, y, and z directions in the combined load state, respectively.

[0043] Step 4: Based on the principle of superposition of load response basis matrices, calculate the physical quantities such as displacement, velocity, and acceleration at the center of the three-dimensional force sensing module.

[0044] (1) Based on the principle of linear characterization of multidimensional load displacement response, the displacement at the center of the three-dimensional force sensing module is decomposed into load-displacement response basis matrix and multidimensional load weight vector.

[0045] In the formula, The load-displacement response basis matrix; , , These represent the displacement response values ​​at the center of the three-dimensional force sensing module under the individual action of the p-th load along the x, y, and z directions.

[0046] The inversion method based on the principle of superposition of load response basis matrices calculates the displacement at the center of the three-dimensional force sensing module. The calculation process can be expressed as follows:

[0047] In the formula, adj represents the operation of finding the adjoint matrix of the load-strain response basis matrix, and det represents the operation of finding the determinant of the load-strain response basis matrix.

[0048] (2) Based on the principle of linear characterization of multidimensional load velocity response, the velocity at the center of the three-dimensional force sensing module is decomposed into load-velocity response basis matrix and multidimensional load weight vector.

[0049] In the formula, The load-velocity response basis matrix; , , This represents the velocity response value at the center of the three-dimensional force sensing module under the individual action of the p-th load along the x, y, and z directions.

[0050] The inversion method based on the principle of superposition of load response basis matrices calculates the velocity at the center of the three-dimensional force sensing module. The calculation process can be expressed as follows:

[0051] (3) Based on the principle of linear characterization of multidimensional load acceleration response, the acceleration at the center of the three-dimensional force sensing module is decomposed into load-acceleration response basis matrix and multidimensional load weight vector;

[0052] In the formula, The load-acceleration response basis matrix; , , These are the acceleration response values ​​at the center of the three-dimensional force sensing module under the individual action of the p-th load along the x, y, and z directions.

[0053] The inversion method based on the principle of superposition of load response basis matrices calculates the acceleration at the center of the three-dimensional force sensing module. The calculation process can be expressed as follows:

[0054] Step 5: Solve the dynamic response equation to obtain the superimposed load components of the three-dimensional force sensing module in three-dimensional space.

[0055] (1) By performing vector decomposition on the load vector {F} acting on the particle in equation (1), the load components along the orthogonal directions of the spatial coordinate system are obtained, and their mathematical expressions are as follows:

[0056] (2) The superimposed load components of the three-dimensional force sensing module in three-dimensional space are obtained by solving the dynamic response equations (1), (8), (10), and (12). The mathematical calculation formula is as follows:

[0057] Based on this formula, the vector three-dimensional force facing the end effector of the space robot arm can be reconstructed. The load reconstruction effects along the X, Y, and Z directions are shown below. Figure 4 , Figure 5 , Figure 6 As shown.

[0058] Step 6: Based on the calculated three-dimensional load information, the space robotic arm control system can achieve a closed loop from "perception" to "action".

[0059] (1) By using force / position hybrid control or impedance control strategies, the system can maintain trajectory accuracy while dynamically adjusting the end pose according to the contact force, thus achieving compliant interaction with the environment.

[0060] (2) Utilize force sensing data for dynamic feedforward compensation to effectively distinguish and counteract the inertial force generated by the movement of the robotic arm itself, ensuring accurate response to external contact forces.

[0061] (3) Through real-time force monitoring and autonomous decision-making mechanisms, the robotic arm can safely and skillfully complete complex tasks such as on-orbit insertion, capture, and assembly, enabling it to leap from programmed operation to intelligent adaptability.

[0062] The technical process of the three-dimensional force reconstruction method for a space robotic arm based on the principle of superposition of load response basis matrices disclosed in the above embodiments can be implemented entirely or partially through software, hardware, firmware, or other arbitrary combinations. When implemented using software, the above embodiments can be implemented entirely or partially in the form of a computer program product. A computer program product includes one or more computer instructions or computer programs.

[0063] When computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. Computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. Available media can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media. Semiconductor media can be solid-state drives (SSDs).

[0064] It should be understood that in the various embodiments of this application, the order of the above-mentioned processes does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0065] This invention provides a method for constructing a three-dimensional force fiber optic sensing module for a space robotic arm based on the principle of load response basis matrix superposition. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of this invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A three-dimensional force reconstruction method for a space robotic arm based on the principle of superposition of load response basis matrices, characterized in that, Includes the following steps: Step 1: Install a three-dimensional force sensing module at the end effector of the space robotic arm, on which several fiber optic grating sensors are arranged. Step 2: Perform vector decomposition on the strain measured by the fiber Bragg grating sensor to obtain the strain components along the orthogonal directions of the spatial coordinate system. The mathematical relationship is expressed as: In the formula, , , These are the strain values ​​measured by fiber Bragg grating sensors positioned at the centerline of the elastic beam. The three corresponding components are respectively , , ; The three corresponding components are respectively , , ; The three corresponding components are respectively , , ; , , , , , , , , These are the strain vector decomposition coefficients, calculated using the angles between the fiber Bragg grating sensor's orientation and the x, y, and z axes. Step 3: Construct a dynamic load model for the sensing module, decomposing the orthogonal strain component matrix into a load-strain response basis matrix and a multidimensional load weight vector; the mathematical expression of the dynamic load model for the sensing module is as follows: In the formula, M, C, and K represent the mass, damping, and stiffness of any point in the three-dimensional force sensing module, respectively. The load vector acting on the particle; , , The particles are respectively in Acceleration, velocity, and displacement vectors under action; Based on the principle of linear characterization of multidimensional load strain response, the strain orthogonal component matrix is... Decomposed into load-strain response basis matrix With multidimensional load weight vector : strain orthogonal component matrix The mathematical expression is: Load-strain response basis matrix The mathematical expression is: Multidimensional load weight vector The mathematical expression is: In the formula, , , These represent the strain response values ​​of the fiber Bragg grating sensors located at the centerline positions of the first, second, and third elastic beams under the individual action of the p-th load along the x-direction; , , These represent the strain response values ​​of the fiber Bragg grating sensors located at the centerline positions of the first, second, and third elastic beams under the individual action of the p-th load along the y-direction; , , These represent the strain response values ​​of the fiber optic grating sensors located at the centerline positions of the first, second, and third elastic beams under the individual action of the p-th load along the z-direction; , , These represent the weights of the p-th load along the x, y, and z directions in the combined load state, respectively. Step 4: Calculate the displacement, velocity, and acceleration at the center of the three-dimensional force sensing module based on the load-strain response basis matrix inversion. Step 5: Solve the dynamic response equation to obtain the superimposed load components of the three-dimensional force sensing module in three-dimensional space; Step 6: Based on the calculated superimposed load components, control the joints of the space robotic arm to achieve compliant operation.

2. The method for reconstructing the three-dimensional force of a space robotic arm based on the principle of superposition of load response basis matrices as described in claim 1, characterized in that, The three-dimensional force sensing module includes a central frame consisting of three elastic beams arranged at 120-degree angles to each other, and three fiber optic grating sensors are respectively positioned at the center line of the three elastic beams.

3. The three-dimensional force reconstruction method for a space robotic arm based on the principle of superposition of load response basis matrices as described in claim 1, characterized in that, Step 4 specifically includes: The displacement at the center of the three-dimensional force sensing module is decomposed into a load-displacement response basis matrix. Based on the inversion method of the principle of superposition of load response basis matrices, the displacement at the center of the three-dimensional force sensing module is calculated. The velocity at the center of the three-dimensional force sensing module is decomposed into a load-velocity response basis matrix. Based on the inversion method of the principle of superposition of load response basis matrices, the velocity at the center of the three-dimensional force sensing module is calculated. The acceleration at the center of the three-dimensional force sensing module is decomposed into a load-acceleration response basis matrix. Based on the inversion method of the principle of superposition of load response basis matrices, the acceleration at the center of the three-dimensional force sensing module is calculated.

4. The three-dimensional force reconstruction method for a space robotic arm based on the principle of superposition of load response basis matrices as described in claim 1, characterized in that, Step 5 specifically includes: The load vector acting on the particle Vector decomposition yields the load components along the orthogonal directions of the spatial coordinate system, whose mathematical expressions are: In the formula, , , These are the load components along the x-axis, y-axis, and z-axis, respectively. The superimposed load components of the three-dimensional force sensing module in three-dimensional space are obtained by solving the following formula: In the formula, , , These represent accelerations along the x, y, and z directions, respectively. , , These represent the velocities along the x, y, and z directions, respectively. , , These represent displacements along the x, y, and z directions, respectively.

5. An electronic device, characterized in that, It includes a processor and a memory storing computer program instructions; when the processor executes the computer program instructions, it implements the three-dimensional force reconstruction method for a space robotic arm based on the principle of superposition of load response basis matrices as described in any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that, The storage medium stores at least one executable instruction, which, when executed on the electronic device, causes the electronic device to perform the three-dimensional force reconstruction method for a space robotic arm based on the principle of superposition of load response basis matrices as described in any one of claims 1 to 4.

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