Locking velocity-based analytical solution of the reduced euler-lagrange equations of motion

Abstract

The application provides a kind of analytical method of reduced Euler-Lagrange dynamics equation based on locking speed, it is related to dynamics calculation technical field.The method is first based on the global closed matrix form dynamics equation of spatial robot to obtain the analytical form of reduced Lagrange function;Then based on Lagrange-D'Alembert equation, combined with the equivalence relationship of Lagrange function and reduced Lagrange function, the reduced Euler-Lagrange dynamics equation of spatial robot is obtained, and the base connected base velocity in the equation is decomposed into locking speed and the influence of arm movement on base;Then the reduced Lagrange function is reconstructed using locking speed, and the reduced Euler-Lagrange dynamics equation expressed by locking speed is obtained.Finally, based on the analytical expression of global inertia matrix in the global closed matrix form dynamics equation, the analytical results of related partial derivatives in the reduced Euler-Lagrange dynamics equation expressed by locking speed are derived.

Description

Technical Field

[0001] This invention relates to the field of dynamics calculation technology, and in particular to an analytical method for reducing Euler-Lagrange dynamic equations based on locked velocities. Background Technology

[0002] As core equipment in space exploration and on-orbit servicing missions, the dynamics modeling of floating-based space robots is fundamental for achieving precise control and path planning, directly impacting the reliability and accuracy of mission execution. The reduced Euler-Lagrange equations, as an effective dynamics modeling tool, have been widely used in floating-based space robot modeling. By simplifying and refining the system's dynamic characteristics, these equations can effectively describe the motion laws of the robot system, providing theoretical support for subsequent control strategy design.

[0003] Currently, when using the reduced Euler-Lagrange equations to model the dynamics of floating-based space robots, the velocity of the base-connected base is mainly selected as the independent variable of the model. This modeling method can meet the basic modeling requirements in conventional scenarios and has certain engineering applicability.

[0004] However, floating-based space robots possess the core characteristic of having an unconstrained base and the ability to float freely. This characteristic leads to significant dynamic coupling between the robotic arm and the base. The movement of the robotic arm significantly disturbs the attitude and position of the base, and conversely, the floating motion of the base affects the motion accuracy of the robotic arm. This strong coupling relationship imposes significant limitations on existing modeling methods that use the velocity of the base as the independent variable. Specifically, this form of independent variable cannot effectively separate the coupling between the robotic arm and the base, hindering research on decoupling modeling of space robots. This, in turn, restricts the design and optimization of subsequent decoupling control strategies, making it difficult to meet the high-precision on-orbit mission requirements for the refinement of robot dynamic models.

[0005] In the field of geometric mechanics, locking velocity, due to its direct correlation with the system's generalized momentum, has attracted widespread attention from researchers and has become a crucial breakthrough in solving the modeling problems of complex dynamic systems. Research has found that using locking velocity as the independent variable in the modeling of the reduced Euler-Lagrange equations can explicitly express the constraints of a floating-based space robot system, effectively weakening the dynamic coupling effect between the robotic arm and the base. This lays a solid theoretical foundation for decoupling modeling research of space robots and is expected to solve the decoupling difficulties existing in current modeling methods.

[0006] Furthermore, in the dynamics modeling of floating-based space robots, the global closed matrix form of the dynamic equations includes a global inertial quantum matrix. The analytical form of this sub-matrix can reflect the core information of the system's inertial characteristics. Currently, existing technologies do not fully utilize the global inertial quantum matrix, and its partial derivative form has not been explored in depth. This leads to an imperfect calculation process for reducing the Euler-Lagrange equations, resulting in insufficient computational accuracy and low efficiency, which further affects the practicality and reliability of the dynamics model.

[0007] In summary, the existing modeling method using the reduced Euler-Lagrange equations with the velocity of the base-connected base as the independent variable is not conducive to decoupling modeling due to the dynamic coupling characteristics of the floating base space robot. Furthermore, the insufficient utilization of the global inertial quantum matrix leads to imperfect equation calculation. Therefore, there is an urgent need for a modeling approach that can solve the above-mentioned technical defects in order to improve the dynamic modeling technology of floating base space robots. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide an analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity, thereby addressing the shortcomings of the prior art.

[0009] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: an analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity, which introduces the analytical form of locking velocity and global inertial quantum matrix, and provides a preliminary decoupled and computationally complete reduced Euler-Lagrange dynamic equation for floating-based space robot systems.

[0010] On the one hand, the present invention provides an analytical method for reducing the Euler-Lagrange dynamic equations based on locking velocity, including:

[0011] The reduced Lagrangian function analytical form is obtained from the global closed matrix form dynamic equation of a space robot; the global closed matrix form dynamic equation is obtained by the global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots.

[0012] Based on the Lagrange-d'Alembert equations, and combining the equivalence relations of the Lagrange function and the reduced Lagrange function, the reduced Euler-Lagrange dynamics equations of the space robot are obtained in the reduced space.

[0013] The base velocity of the base in the reduced Euler-Lagrange dynamics equations is decomposed into the locking velocity and the effect of the robotic arm motion on the base.

[0014] By reconstructing the reduced Lagrangian function using the locking velocity, we obtain the reduced Euler-Lagrangian dynamic equations expressed in terms of the locking velocity.

[0015] Furthermore, the analytical form of the reduced Lagrangian function obtained from the global closed matrix form dynamic equations based on the space robot is shown in the following formula:

[0016] ;

[0017] ;

[0018] In the formula, To reduce the Lagrange function, For the satellite base motion spinor, Shaped like a robotic arm For the space at the base of the ordinary master fiber bundle / the space shaped like a robotic arm, Let be the joint angular velocity of the robotic arm. The inertia matrix of the recursive operator, Here is the generalized inertia matrix of the robotic arm. This is a recursive operator matrix used to obtain the mapping relationship between the spinor motion of the space robot's robotic arm and the spatial velocity of the space robot's configuration. The global inertia matrix. For the base global inertial quantum matrix, The inertia matrix of the recursive operator, For the transformation matrix from satellite base to robotic arm, For the coupling term of the global inertia matrix, This is a joint helical axis matrix, which represents the helical axis of each joint of the robotic arm. Arranged sequentially along the diagonal of the matrix. For the global inertial quantum matrix of the robotic arm, denoted as the spatial velocity of the space robot configuration, and m as the degree of freedom of the robotic arm.

[0019] Furthermore, based on the Lagrange-d'Alembert equations, and combining the equivalence relations of the Lagrange function and the reduced Lagrange function, the specific method for obtaining the reduced Euler-Lagrange dynamics equations of the space robot in the reduced space is as follows:

[0020] By analyzing the trivial principal fiber bundle structure inherent in the space robot system, the Lagrange-d'Alembert equations are decomposed and expressed at the levels of the space robot base and the robotic arm, respectively.

[0021] Combining the equivalence relations between the Lagrange function and the reduced Lagrange function, the reduced Euler-Lagrange dynamic equations are further obtained by analysis on the reduced space, as shown in the following formula:

[0022] ;

[0023] in, For Lagrange multipliers, For constraint coefficients, Non-conservative forces in robotic arms Non-conservative forces on the satellite base for The adjoint operator matrix.

[0024] Furthermore, the base velocity of the base assembly in the reduced Euler-Lagrange dynamics equations is decomposed into the locking velocity and the influence of the robotic arm's motion on the base. The specific method is as follows:

[0025] Based on the analytical form of the reduced Lagrangian function, the generalized momentum of the space robot system is obtained. The parsing form:

[0026] ;

[0027] The joints of the robotic arm in the space robot system are fully locked. Under the premise that the base is connected to the base, the underlying inertial tensor is At this point, the speed is locked. With generalized momentum There is an obvious mapping relationship:

[0028] ;

[0029] In the formula, Defined as local mechanical connection, it characterizes the coupling effect of bottom space motion on the vertical component. The influence component of the shape-space velocity of the robotic arm on the base under the condition of momentum conservation.

[0030] Furthermore, the aforementioned reconstruction of the reduced Lagrangian function using locked velocity refers to locking the configuration space velocity. Space robot configuration and space velocity The mapping relationship between them yields the reduced Lagrangian function expressed in terms of locking velocity. Specifically, these include:

[0031] ;

[0032] ;

[0033] In the formula, This is the velocity mapping matrix. The block diagonal global inertia matrix. , These are the 6th and m-order identity matrices, respectively;

[0034] Further, the partial derivatives of the reduced Lagrange function expressed in terms of locking velocity are solved analytically, and the reduced Euler-Lagrange dynamic equations of the space robot are equivalently transformed based on the equivalence relationship between the Lagrange function and the reduced Lagrange function, thus obtaining the reduced Euler-Lagrange dynamic equations expressed in terms of locking velocity.

[0035] Furthermore, the method also derives the analytical results of the relevant partial derivatives in the reduced Euler-Lagrange dynamics equations in the form of a globally closed matrix dynamics equation based on the analytical expression of the global inertial quantum matrix, which facilitates the deployment of the reduced Euler-Lagrange dynamics equations.

[0036] Secondly, this application proposes an electronic device, comprising: one or more processors, and a memory for storing instructions that, when executed by the one or more processors, cause the one or more processors to execute the analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity.

[0037] Thirdly, this application proposes a computer-readable storage medium storing executable instructions that, when executed, cause a processor to perform the analytical method for the reduced Euler-Lagrange dynamic equations based on locking speed.

[0038] Fourthly, this application proposes a computer program product, including a computer program or instructions that, when executed by a processor, implement the analytical method for the reduced Euler-Lagrange dynamic equations based on locking velocity.

[0039] The beneficial effects of adopting the above technical solution are as follows: The analytical method of the reduced Euler-Lagrange dynamic equation based on locking velocity provided by the present invention (1) explicit characterization of system constraints: taking the locking velocity related to the system momentum as the independent variable of the equation, the constraint relationship of generalized momentum conservation of the space system under no external force is explicitly modeled and expressed, thereby enhancing the physical consistency and theoretical rigor of the model. (2) preliminary decoupling characteristics of the dynamic equation: the reduced Euler-Lagrange equation constructed based on locking velocity presents a diagonal structure of the inertia matrix block. This characteristic indicates that the dynamic equation has the potential to achieve dynamic decoupling between the base and the robotic arm in subsequent analysis. (3) completeness of computational expression: by adopting the analytical expression of the inertia quantum matrix in the dynamic equation in the form of a globally closed matrix, a clear analytical form is provided for the calculation of partial derivatives in the reduced Euler-Lagrange equation expressed by locking velocity, thereby improving the feasibility and completeness of the dynamic equation in practical applications and engineering deployment. Attached Figure Description

[0040] Figure 1A flowchart illustrating the analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity, provided in an embodiment of the present invention. Detailed Implementation

[0041] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0042] Example 1:

[0043] In this embodiment, the analytical method based on the reduced Euler-Lagrange dynamics equations using locking velocity is as follows: Figure 1 As shown, it includes the following steps:

[0044] Step 1: Obtain the analytical form of the reduced Lagrangian function based on the global closed-form matrix dynamics equations of the space robot;

[0045] In this embodiment, a global closed matrix form of the dynamic equations for the space robot is obtained using a global recursive reconstruction method based on the recursive Newton-Euler dynamics algorithm. This method obtains the global closed matrix form of the robotic arm's motion screws and their differentials through forward recursive reconstruction using the recursive Newton-Euler dynamics algorithm. Based on the global closed matrix form of the motion screws and their differentials, the global closed matrix form of the torques required for each joint and the force screws required for the base is obtained through backward recursive reconstruction using the recursive Newton-Euler dynamics algorithm. Based on the similarity in mathematical structure between the backward recursive reconstruction results of the recursive Newton-Euler dynamics algorithm, the global closed matrix form of the dynamic equations for the floating base space robot is finally obtained, as shown in the following formula:

[0046] ;

[0047] In the formula, The global inertia matrix. This is a recursive operator matrix used to obtain the mapping relationship between the spinor motion of the space robot's robotic arm and the spatial velocity of the space robot's configuration. The global Coriolis force-centrifugal force matrix. For the system force spinor, Global end-force spinor; This is the global centrifugal force matrix. The global Coriolis force matrix. For the generalized end force matrix, This is the transformation matrix from the actuator end effector to the robotic arm joint. The spinor of the force at the actuator end. , These are the generalized inertia matrices. Mapping matrix of robotic arm motion screws The corresponding global mapping matrix and global motion spinor mapping differential operator matrix are defined by the following equation:

[0048] .

[0049] Since the space robot system is not in a potential energy field, a reduced Lagrangian function can be defined. It is represented in the following explicit form:

[0050] ;

[0051] ;

[0052] In the formula, For the satellite base motion spinor, Shaped like a robotic arm For the space at the base of the ordinary master fiber bundle / the space shaped like a robotic arm, Let be the joint angular velocity of the robotic arm. The inertia matrix of the recursive operator, Here is the generalized inertia matrix of the robotic arm. This is a recursive operator matrix used to obtain the mapping relationship between the spinor motion of the space robot's robotic arm and the spatial velocity of the space robot's configuration. The global inertia matrix. For the base global inertial quantum matrix, The inertia matrix of the recursive operator, For the transformation matrix from satellite base to robotic arm, for The adjoint mapping matrix, The configuration of joint coordinate system {0} relative to coordinate system {1}. For the coupling term of the global inertia matrix, This is a joint helical axis matrix, which represents the helical axis of each joint of the robotic arm. Arranged sequentially along the diagonal of the matrix. For the global inertial quantum matrix of the robotic arm, denoted as the spatial velocity of the space robot configuration, and m as the degree of freedom of the robotic arm.

[0053] It should be noted that the above-mentioned reduced Lagrange function is achieved by reducing the Lie group elements in the independent variable to a Lie algebra. This is expressed at a certain level. For the satellite base in the global coordinate system The lower position, Let this be the space of the trivial principal fiber bundle / satellite base pose space. In other words, the Lagrangian function... It is a reduced Lagrange function The left-invariant extension of the equation, and the equivalence relationship between the two are shown in the following equation:

[0054] ;

[0055] Step 2: Based on the Lagrange-d'Alembert equations, and combining the equivalence relations of the Lagrange function and the reduced Lagrange function, derive the reduced Euler-Lagrange dynamics equations of the space robot in the reduced space;

[0056] The Lagrange-d'Alembert equations elaborate on the application of Lagrange functions in space robot systems. The dynamic equations under constraints and external forces are as follows:

[0057] ;

[0058] In the formula, For the configuration space of space robots, For Lagrange multipliers, For constraint coefficients, For non-conservative forces in space robot systems.

[0059] By analyzing the trivial principal fiber bundle structure inherent in the space robot system, the Lagrange-d'Alembert equations are decomposed and expressed at the levels of the space robot base and the robotic arm, respectively.

[0060] By further combining the equivalence relations between the Lagrange function and the reduced Lagrange function, the reduced Euler-Lagrange dynamic equations are obtained on the reduced space, as shown in the following formula:

[0061] ;

[0062] in, For constraint coefficients, Non-conservative forces in robotic arms Non-conservative forces on the satellite base for The adjoint operator matrix;

[0063] Step 3: Decompose the base velocity of the base in the reduced Euler-Lagrange dynamics equations into the locking velocity and the effect of the robotic arm motion on the base;

[0064] The locking velocity is proposed within the context of discussing the generalized momentum of space robot systems. For floating-based space robot systems, the generalized momentum is generally constant under the condition of no external force. By combining the previously discussed analytical form of the reduced Lagrangian function, the generalized momentum of the space robot system can be obtained. The parsing form:

[0065] ;

[0066] The joints of the robotic arm in the space robot system are fully locked. Under the premise that the base is connected to the base, the underlying inertial tensor is At this point, the speed is locked. With generalized momentum There is an obvious mapping relationship, specifically:

[0067] ;

[0068] In the formula, Defined as local mechanical connection, it characterizes the coupling effect of bottom space motion on the vertical component. This represents the influence component of the shape-space velocity of the robotic arm on the base under momentum conservation. For a space robot system, local mechanical connections quantitatively characterize the locking velocity of the robotic arm's motion on the system. The influence relationship.

[0069] Step 4: Reconstruct the reduced Lagrangian function using the locking velocity to obtain the reduced Euler-Lagrangian dynamic equations expressed in terms of the locking velocity;

[0070] The aforementioned method of reconstructing the reduced Lagrangian function using locked velocity refers to locking the configuration space velocity. Space robot configuration and space velocity The mapping relationship between them yields the reduced Lagrangian function expressed in terms of locking velocity. Specifically, these include:

[0071] ;

[0072] ;

[0073] In the formula, This is the velocity mapping matrix. The block diagonal global inertia matrix. , These are the 6th and m-order identity matrices, respectively.

[0074] Combined with local mechanical communication and matrix Symmetry It is easy to prove that the matrix It is a block diagonal matrix.

[0075] ;

[0076] in, The Schul complement matrix;

[0077] Furthermore, the partial derivatives of the reduced Lagrangian function expressed in terms of locking velocity are solved analytically, and the reduced Euler-Lagrangian dynamic equations of the space robot are equivalently transformed based on the equivalence relationship between the Lagrangian function and the reduced Lagrangian function.

[0078] The reduced Euler-Lagrange dynamic equations, expressed in terms of locking velocity, are then obtained as follows:

[0079] ;

[0080] ;

[0081] In the formula, To lock configuration space acceleration, For non-conservative forces of the robotic arm, For non-conservative forces on the satellite base, For the local curvature of the mechanical connection, For the remainder term of the dynamic equation, The generalized Coriolis matrix, whose elements are constructed from the partial derivatives of the Schur complement matrix, will be used to characterize the inertial coupling effect caused by joint velocity.

[0082] Step 5: Based on the analytical expression of the global inertial quantum matrix in the global closed matrix form of the dynamic equation, derive the analytical results of the relevant partial derivatives in the reduced Euler-Lagrange dynamic equation in the locked velocity representation, improve the calculation process, and facilitate the deployment of the reduced Euler-Lagrange dynamic equation.

[0083] The analytical results of the partial derivatives in the reduced Euler-Lagrange dynamics equations expressed in terms of locking velocity are mainly the Schur complement matrix and the partial derivatives of the mechanical connection related to the joint angles of the robotic arm. These results can be solved using the analytical form of the global inertial quantum matrix in the global recursive reconstruction method of the space robot recursive Newton-Euler dynamics algorithm. Specifically:

[0084] ;

[0085] ;

[0086] ;

[0087] In the formula, For the partial derivatives of mechanical connection, For the partial derivatives of the Schul complement matrix, For the partial derivatives of the global inertial quantum matrix of the base, For the partial derivatives of the coupling terms of the global inertia matrix, For the partial derivatives of the global inertial quantum matrix of the robotic arm, Defined as the global inertia derivative gradient operator, it is related to the partial derivatives of the global inertia matrix with respect to the joint angles of the robotic arm. For the adjoint gradient operator of the spiral axis, for The adjoint operator matrix, For robotic arm joints The angle.

[0088] In this embodiment, the parameters of the reduced Euler-Lagrange equations expressed in terms of locking velocity are shown in Table 1:

[0089] Table 1. Parameters of the reduced Euler-Lagrange equations expressed in terms of locking velocity.

[0090]

[0091]

[0092] Example 2:

[0093] This embodiment proposes an electronic device, including: one or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the analytical method for reducing Euler-Lagrange dynamic equations based on locked velocity.

[0094] The electronic device can be a mobile phone, computer, or tablet computer, etc., and includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, implements the floating-based space robot fusion decoupling dynamics modeling method as described in the embodiments. It is understood that the electronic device may also include input / output (I / O) interfaces and communication components.

[0095] The processor is used to execute all or part of the steps in the analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity as described in the above embodiments. The memory is used to store various types of data, which may include, for example, instructions for any application or method in the electronic device, as well as application-related data.

[0096] The processor can be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic components, and is used to execute the analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity described in the above embodiments.

[0097] Example 3:

[0098] This embodiment proposes a computer-readable storage medium that stores executable instructions. When these instructions are executed, if they are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0099] The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the analytical method for the reduced Euler-Lagrange dynamic equations based on locking velocity described in the various embodiments of this application.

[0100] The aforementioned storage media include: flash memory, hard disks, multimedia cards, card-type memory (e.g., SD (Secure Digital Memory Card) or DX (Memory Data Register, MDR) memory), random access memory (RAM), static random-access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic storage, disks, optical discs, servers, APP (Application) app stores, and other media capable of storing program verification codes. These media store computer programs, which, when executed by a processor, can implement the various steps of the analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity described above.

[0101] Example 4:

[0102] This embodiment proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the analytical method for the reduced Euler-Lagrange dynamic equations based on locking velocity.

[0103] Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a computer program product.

[0104] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0105] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the present invention.

Claims

1. An analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity, characterized in that, include: The analytical form of the reduced Lagrangian function is obtained from the global closed matrix form dynamic equation of a space robot. The globally closed matrix form dynamic equations are obtained using the global recursive reconstruction method of the space robot recursive Newton-Euler dynamics algorithm. Based on the Lagrange-d'Alembert equations, and combining the equivalence relations of the Lagrange function and the reduced Lagrange function, the reduced Euler-Lagrange dynamics equations of the space robot are obtained in the reduced space. The base velocity of the base in the reduced Euler-Lagrange dynamics equations is decomposed into the locking velocity and the effect of the robotic arm motion on the base. By reconstructing the reduced Lagrangian function using the locking velocity, we obtain the reduced Euler-Lagrangian dynamic equations expressed in terms of the locking velocity.

2. The analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity according to claim 1, characterized in that, The analytical form of the reduced Lagrangian function obtained from the global closed matrix form dynamic equations based on the space robot is shown in the following formula: ； ； In the formula, To reduce the Lagrange function, For the satellite base motion spinor, Shaped like a robotic arm For the space at the base of the ordinary master fiber bundle / the space shaped like a robotic arm, Let be the joint angular velocity of the robotic arm. The inertia matrix of the recursive operator, The generalized inertia matrix of the robotic arm. This is a recursive operator matrix used to obtain the mapping relationship between the spinor motion of the space robot's robotic arm and the spatial velocity of the space robot's configuration. The global inertia matrix, For the base global inertial quantum matrix, The inertia matrix of the recursive operator, For the transformation matrix from satellite base to robotic arm, For the coupling term of the global inertia matrix, This is a joint helical axis matrix, which represents the helical axis of each joint of the robotic arm. Arranged sequentially along the diagonal of the matrix. For the global inertial quantum matrix of the robotic arm, denoted as the spatial velocity of the space robot configuration, and m as the number of degrees of freedom of the robotic arm.

3. The analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity according to claim 2, characterized in that, The specific method for obtaining the reduced Euler-Lagrange dynamics equations of a space robot in the reduced space, based on the Lagrange-d'Alembert equations and combining the equivalence relations of the Lagrange function and the reduced Lagrange function, is as follows: By analyzing the trivial principal fiber bundle structure inherent in the space robot system, the Lagrange-d'Alembert equations are decomposed and expressed at the levels of the space robot base and the robotic arm, respectively. Combining the equivalence relations between the Lagrange function and the reduced Lagrange function, the reduced Euler-Lagrange dynamic equations are further obtained by analysis on the reduced space, as shown in the following formula: ； in, For Lagrange multipliers, For constraint coefficients, Non-conservative forces in robotic arms Non-conservative forces on the satellite base for The adjoint operator matrix.

4. The analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity according to claim 3, characterized in that, The specific method for decomposing the base velocity of the connected body in the reduced Euler-Lagrange dynamics equations into locking velocity and the influence of the robotic arm motion on the base is as follows: Based on the analytical form of the reduced Lagrangian function, the generalized momentum of the space robot system is obtained. The parsing form: ； The joints of the robotic arm in the space robot system are fully locked. Under the premise that the base is connected to the base, the underlying inertial tensor is At this point, the speed is locked. With generalized momentum There is an obvious mapping relationship: ； In the formula, Defined as local mechanical connection, it characterizes the coupling effect of bottom space motion on the vertical component. The influence component of the shape-space velocity of the robotic arm on the base under the condition of momentum conservation.

5. The analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity according to claim 4, characterized in that, The aforementioned method of reconstructing the reduced Lagrangian function using locked velocity refers to locking the configuration space velocity. Space robot configuration and space velocity The mapping relationship between them yields the reduced Lagrangian function expressed in terms of locking velocity. Specifically, these include: ； ； In the formula, This is the velocity mapping matrix. The block diagonal global inertia matrix. , These are the 6th and m-order identity matrices, respectively; Further, the partial derivatives of the reduced Lagrange function expressed in terms of locking velocity are solved analytically, and the reduced Euler-Lagrange dynamic equations of the space robot are equivalently transformed based on the equivalence relationship between the Lagrange function and the reduced Lagrange function, thus obtaining the reduced Euler-Lagrange dynamic equations expressed in terms of locking velocity.

6. The analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity according to claim 5, characterized in that, The method also derives analytical results of relevant partial derivatives in the reduced Euler-Lagrange dynamics equations in the form of global closed matrix dynamics equations based on the analytical expression of the global inertial quantum matrix, which facilitates the deployment of the reduced Euler-Lagrange dynamics equations.

7. An electronic device for executing the analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity as described in any one of claims 1-6, characterized in that, include: One or more processors, and a memory for storing instructions that, when executed by the one or more processors, cause the one or more processors to perform the analytical method for the reduced Euler-Lagrange dynamic equations based on locking velocity.

8. A computer-readable storage medium storing executable instructions for performing the analytical method for the reduced Euler-Lagrange dynamic equations based on locking velocity as described in any one of claims 1-6, characterized in that, When the instruction is executed, it causes the processor to perform the analytical method for the reduced Euler-Lagrange dynamic equations based on locking speed.

9. A computer program product for executing the analytical method for reducing Euler-Lagrange dynamic equations based on locking velocity as described in any one of claims 1-6, characterized in that, This includes a computer program or instructions that, when executed by a processor, implement the analytical method for the reduced Euler-Lagrange dynamic equations based on locked velocity.

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