Global recursive reconstruction method for spatial robot recursive newton-euler dynamics algorithm

Abstract

The application provides a global recursive reconstruction method of a space robot recursive Newton-Euler dynamics algorithm, and relates to the technical field of space robot dynamics modeling. The method obtains the global closed matrix form of the mechanical arm movement screw and its differential by forward recursive reconstruction of the recursive Newton-Euler dynamics algorithm; the secondary diagonal matrix of the recursive operator is constructed to simplify the expression of the differential of the global closed matrix form of the mechanical arm movement screw; based on the global closed matrix form of the movement screw and its differential, the global closed matrix form of the required torque of each joint and the required force screw of the base is obtained by backward recursive reconstruction; based on the similarity of the backward recursive reconstruction results at the mathematical structure level, the global closed matrix form dynamics modeling of the space robot is completed. The method constructs an explicit matrix mapping form of the floating base space robot dynamics model, and realizes the direct mapping between the system state quantity and the input quantity.

Description

Technical Field

[0001] This invention relates to the field of space robot dynamics modeling technology, and in particular to a global recursive reconstruction method for a recursive Newton-Euler dynamics algorithm for space robots. Background Technology

[0002] With the rapid development of aerospace technology, space robots are increasingly widely used in space exploration, on-orbit servicing, spacecraft maintenance, and fault repair. As an important type of space robot, floating-based space robots have no fixed base and float freely in the microgravity environment of space. Their dynamic characteristics are more complex than those of ground-based fixed-base robots. The accuracy and efficiency of dynamic modeling directly determine the robot's control precision, motion stability, and mission execution reliability, making it one of the key research areas and core challenges in the field of space robot technology.

[0003] Dynamic modeling is the foundation for subsequent research on model-based control, trajectory planning, and fault diagnosis of floating space robots. Currently, various dynamic modeling methods have been developed in the industry. Among them, the Newton-Euler dynamics algorithm has become the mainstream technical path for dynamic modeling of floating space robots due to its advantages such as clear modeling logic, moderate computational efficiency, and adaptability to multi-joint robot structures.

[0004] Currently, most dynamic modeling methods for floating base space robots based on the Newton-Euler dynamics algorithm employ a recursive framework for numerical solutions. Specifically, these methods iteratively calculate the angular velocity, angular acceleration, inertial force, and inertial torque of each link of the robot joint by joint, gradually obtaining the dynamic equations of the entire robot system and ultimately describing the system's dynamic characteristics. Essentially, this modeling approach belongs to implicit dynamics modeling algorithms, where the expression of the dynamic equations is coupled with the solution process, making it impossible to directly obtain the mapping relationship between system state variables (such as joint angular displacement, angular velocity, base attitude and position) and input variables (such as joint driving torque).

[0005] The inherent characteristics of the aforementioned implicit dynamics modeling algorithms significantly limit their application scope and subsequent technological expansion. On the one hand, solving implicit dynamics models relies on iterative numerical calculations, which places high demands on computing hardware. In space-constrained and computationally limited on-orbit embedded control systems, it is difficult to achieve fast real-time solutions, thus affecting the real-time response speed of robot control commands and failing to meet the requirements of high-precision and high-dynamic on-orbit missions. On the other hand, since explicit dynamic mapping relationships cannot be directly obtained, it is difficult to perform analytical design and parameter optimization of controllers based on this model. This greatly hinders key research areas such as stable control and trajectory tracking accuracy improvement of floating-based space robots, restricting the application effectiveness of space robots in complex on-orbit missions.

[0006] Therefore, how to break through the limitations of traditional recursive implicit dynamic modeling, restructure the traditional recursive form of dynamic expression based on the Newton-Euler dynamics algorithm, and construct an explicit matrix mapping form of the dynamic model of a floating-based space robot to realize the direct mapping between system state variables and input variables, reduce the complexity of model solution, improve solution efficiency, and lay a solid foundation for subsequent research on model-based stable control and high-precision trajectory planning of floating-based space robots has become a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0007] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a global recursive reconstruction method for space robot recursive Newton-Euler dynamics algorithm, which constructs an explicit matrix mapping form of floating-based space robot dynamics model, and realizes the direct mapping between system state variables and input variables.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: On the one hand, the present invention provides a global recursive reconstruction method for the recursive Newton-Euler dynamics algorithm of space robots, comprising:

[0009] The spinor of the robotic arm motion and its differential global closed matrix form are obtained by forward recursion reconstruction using the recursive Newton-Euler dynamics algorithm;

[0010] Construct the second diagonal matrix of the recursive operator The spinor differential of the robotic arm motion in global closed matrix form is simplified by using this diagonal matrix.

[0011] Based on the global closed matrix form of the motion spinor and its derivative, the global closed matrix form of the torque required for each joint and the force spinor required for the base is obtained by backward recursion reconstruction through the recursive Newton-Euler dynamics algorithm.

[0012] Based on the similarity of the backward recursive reconstruction results of the recursive Newton-Euler dynamics algorithm at the mathematical structure level, a global closed matrix form dynamic model of the space robot is completed.

[0013] Furthermore, the specific method for obtaining the spinor of the robotic arm motion and its differential global closed matrix form through forward recursive reconstruction using the recursive Newton-Euler dynamics algorithm is as follows:

[0014] Based on the motion transfer relationship between rigid bodies, construct the recursive operator matrix. Obtaining the motion spinor of a space robot arm Space robot configuration and space velocity The mapping relationship between them is then used to obtain the spinor expression of the robotic arm's motion in the form of a globally closed matrix:

[0015] Specifically, there are:

[0016] ;

[0017] ;

[0018] In the formula, Let be the joint angular velocity of the robotic arm. The transformation matrix from satellite base to robotic arm; 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; Let be the spinor mapping matrix of the robotic arm, where The symbol represents a dimension reduction, indicating that the mapping matrix only provides the mapping relationship between the spatial velocity of the space robot configuration and the spinor of the robotic arm, without mapping the spinor of the satellite base. For the adjoint mapping matrix, , They are respectively The corresponding rotation and translation matrices, Let {i} be the configuration of the joint coordinate system {i} relative to the coordinate system {i-1}. For the satellite base motion spinor, For conjoined base angular velocity of the lower base For conjoined base Lower base linear velocity;

[0019] The differential of the spinor of the robotic arm's motion can be further obtained using a recursive reconstruction method, specifically:

[0020] ;

[0021] In the formula, For the spatial acceleration configuration of space robots, The global dual adjoint operator matrix, It is the second diagonal matrix of the recursive operator.

[0022] Furthermore, the recursive operator second diagonal matrix constructed based on the Neumann series expansion is described. The specific method for simplifying the expression of the spinor differential of the robotic arm motion in the form of a globally closed matrix by using this diagonal matrix is ​​as follows:

[0023] Constructing the second diagonal matrix of the recursive operator based on Neumann series expansion. As shown below:

[0024] ;

[0025] The recursive operator diagonal matrix It has the property of power-law oblique propagation, i.e., matrix The exponentiation operation has the following properties along the recursive operator matrix. Characteristics of oblique propagation along the second diagonal;

[0026] Based on matrix The zero-power property of the matrix is ​​determined by the matrix. Finite-dimensional power exponents are used to characterize recursive operator matrices, specifically:

[0027] ;

[0028] Equation Riding on both sides The simplified relation is obtained. This simplifies the spinor differential of robotic arm motion in the form of a globally closed matrix. Expressions, specifically:

[0029] ;

[0030] In the formula, Let be the differential operator matrix for the spinor mapping of the robotic arm's motion.

[0031] Furthermore, the specific method for obtaining the global closed matrix form of the required torque of each joint and the required force rotation of the base through backward recursive reconstruction using the recursive Newton-Euler dynamics algorithm is as follows:

[0032] Using kinetic spin and its differential The globally closed matrix form, combined with the recursive reconstruction method, is used to further refine the backward recursive content, namely the joint torques. Force rotation required for the base Express it in the form of a globally closed matrix:

[0033] ;

[0034] ;

[0035] In the formula, The generalized inertia matrix of the robotic arm; For robotic arm linkages Corresponding to the generalized inertia matrix, It is a robotic arm link The moment of inertia matrix, For robotic arm linkages quality, The force spinor recursive operator matrix, i.e., the recursive operator matrix. The transpose of the 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. This is the Coriolis force matrix.

[0036] Furthermore, based on the similarity in mathematical structure between the backward recursive reconstruction results of the recursive Newton-Euler dynamics algorithm, the specific method for completing the global closed matrix form dynamic modeling of the space robot is as follows:

[0037] The base force spinor expressed in global closed matrix form is used with the recursive operator matrix G. The velocity and acceleration related terms in the matrix are represented by a matrix mapping:

[0038] ;

[0039] ;

[0040] Joint torques expressed in global closed matrix form Reconstructing the matrix from the acceleration and velocity terms in the matrix yields:

[0041] ;

[0042] ;

[0043] Finally, the global closed matrix form dynamic equations of the floating space robot are obtained:

[0044] ;

[0045] ;

[0046] In the formula, The global inertia matrix. 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:

[0047] .

[0048] Secondly, this application proposes an electronic device, comprising: one or more processors, and a memory for storing instructions, which, when executed by the one or more processors, cause the one or more processors to execute the global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots.

[0049] Thirdly, this application proposes a computer-readable storage medium storing executable instructions that, when executed, cause a processor to perform the global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots.

[0050] Fourthly, this application proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots.

[0051] The beneficial effects of adopting the above technical solution are as follows: The global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots provided by this invention (1) Explicit expression of the control interface: The proposed global closed matrix form dynamic equation provides an explicit matrix mapping form for the dynamics of the floating-based space robot system, which will provide a direct design basis for algorithms such as impedance control and model predictive control. (2) System scalability: The proposed global closed matrix form dynamic equation realizes the modular expansion characteristics of the dynamic equation through its block matrix structure. To increase the number of... Taking a single joint as an example, the dynamic equations only need to be calculated in the second diagonal matrix of the recursive operator. Joint helical axis matrix and the generalized inertia matrix of the robotic arm Adding the corresponding diagonal blocks at the location can complete the update calculation. (3) Low computational efficiency: The recursive operator matrix is ​​simplified by using the result of the Neumann series expansion. By applying the result to the modeling of the dynamic equation, the multiplication operation of two high-dimensional matrices is transformed into a matrix subtraction operation. Experiments have shown that this method can be used in the degree of freedom of the robotic arm in a space robot system. Compared to traditional recursive methods, this method has higher computational efficiency. Attached Figure Description

[0052] Figure 1 This is a flowchart of the global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots provided in Embodiment 1 of the present invention;

[0053] Figure 2 The coordinate system of the floating-base space robot system provided in Embodiment 1 of the present invention;

[0054] Figure 3This is a pseudocode diagram of the recursive Newton-Euler dynamics algorithm for space robots provided in Embodiment 1 of the present invention;

[0055] Figure 4 The model verification test space robot configuration provided in Embodiment 1 of the present invention includes (a) a distribution diagram of the space robot's arms and (b) a schematic diagram of the relative positions of each link in the initial state of the space robot.

[0056] Figure 5 The output results of the traditional recursive Newton-Euler dynamics model and the globally closed matrix dynamics model provided in Embodiment 1 of the present invention are compared. Among them, (a) is the comparison of output results between models - base force part, (b) is the comparison of output results between models - base torque part, (c) is the comparison of output results between models - joint torque part, and (d) is the heat map of output error between models (maximum absolute error every 2 seconds).

[0057] Figure 6 The results show the performance comparison between the traditional recursive Newton-Euler dynamics model and the globally closed matrix dynamics model provided in Embodiment 1 of the present invention. Among them, (a) shows the relationship between the degrees of freedom of the robotic arm and the 9001-run time of the algorithm, and (b) shows the detailed data of the performance analyzer of the six-degree-of-freedom robotic arm space robot system. Detailed Implementation

[0058] 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.

[0059] Example 1:

[0060] In this embodiment, a global recursive reconstruction method for a recursive Newton-Euler dynamics algorithm for space robots is described, such as... Figure 1 As shown, it includes the following steps:

[0061] Step 1: Obtain the spinor of the robotic arm's motion and its differential global closed matrix form by forward recursion reconstruction using the recursive Newton-Euler dynamics algorithm;

[0062] In an example of the present invention, such as Figure 2 As shown, multiple coordinate systems are needed to describe the pose of a floating-based space robot and to establish its dynamic model. In the figure, the coordinate systems... A global coordinate system is defined. The coordinate system is located at the center of mass of the satellite platform. This is a combined base coordinate system. Since this coordinate system will also serve as the base coordinate system for the robotic arm, it can also be characterized as... Regarding robotic arms, the robotic arm joint coordinate system... Set on the robotic arm The joint corresponding to the proximal end of the root link. Space robot end effector coordinate system. This is then set at the far end of the corresponding actuator, where m is the number of degrees of freedom of the robotic arm. Further, the configuration space of the space robot is represented as... SE (3) denotes the Special Euclidean Group in 3D, and a point in configuration space can be represented by... Characterization is performed. Specifically, at this point... This can be represented as the satellite base attitude. This can be described as the joint angle of the robotic arm.

[0063] In an example of the present invention, such as Figure 3 As shown, the recursive Newton-Euler dynamics algorithm consists of three stages: initialization, forward recursion, and backward recursion. The main task of the forward recursion is to obtain the rotational motion of each rigid body of the space robot in a recursive form. and its differential The main task of backward recursion is to determine the rotational motion of each rigid body. and its differential Obtain the rotation of the forces acting on each link of the robotic arm. Furthermore, the output torque of each joint of the robotic arm can be analyzed. Rotation of forces on the base The parameters of the recursive Newton-Euler dynamics algorithm are shown in Table 1.

[0064] Table 1. Symbol Reference Table for Recursive Newton-Euler Dynamics Algorithms

[0065]

[0066]

[0067] The main work of the forward recursive reconstruction is to construct the recursive operator matrix based on the motion transfer relationship between rigid bodies. Obtaining the motion spinor of a space robot arm Space robot configuration and space velocity The mapping relationship between them is used to obtain the global closed matrix form of the manipulator's motion spinor expression, specifically:

[0068] ;

[0069] ;

[0070] ;

[0071] In the formula, Let be the joint angular velocity of the robotic arm. The transformation matrix from satellite base to robotic arm; 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; Let be the spinor mapping matrix of the robotic arm, where The symbol represents a dimension reduction, indicating that the mapping matrix only provides the mapping relationship between the spatial velocity of the space robot configuration and the spinor of the robotic arm, without mapping the spinor of the satellite base. For the adjoint mapping matrix, , They are respectively The corresponding rotation and translation matrices, Let {i} be the configuration of the joint coordinate system {i} relative to the coordinate system {i-1}. For the satellite base motion spinor, For conjoined base angular velocity of the lower base For conjoined base Lower base linear velocity;

[0072] For the differential of the spinor of the robotic arm motion, the form of this globally closed matrix can be further obtained based on a recursive reconstruction method, specifically:

[0073] ;

[0074] ;

[0075] In the formula, For the spatial acceleration configuration of space robots, is the global dual adjoint operator matrix.

[0076] Step 2: Construct the second diagonal matrix of the recursive operator based on the Neumann series expansion The spinor differential of the robotic arm motion in global closed matrix form is simplified by using this diagonal matrix.

[0077] The recursive operator second diagonal matrix constructed based on the von Neumann series expansion The specific form is as follows:

[0078] ;

[0079] Second diagonal matrix of recursive operators It has the property of power-law oblique propagation, i.e., matrix The exponentiation operation has the following properties along the recursive operator matrix. The characteristics of oblique propagation along the second diagonal. Combined with the Neumann expansion results, it can be seen that for [the condition] satisfying the spectral radius condition... square array Its series expansion result is: .

[0080] From the recursive operator second diagonal matrix The power-law propagation property shows that the matrix of The result of exponentiation is a zero matrix, i.e. Based on the above matrix The zero-power property of the recursive operator matrix can then be derived from the matrix Finite-dimensional power exponents are used for characterization, specifically including Multiply both sides of the above equation A simplified relation can be obtained. The above equivalence relation shows that the recursive operator matrix With recursive operator second diagonal matrix Matrix multiplication between them can be transformed into matrix subtraction between them and the identity matrix, which can further simplify the differential of the spinor of the robot arm in the form of a globally closed matrix. Expressions, specifically:

[0081] ;

[0082] In the formula, Let be the differential operator matrix for the spinor mapping of the robotic arm's motion.

[0083] Step 3: Based on the global closed matrix form of the motion spinor and its derivative, the global closed matrix form of the torque required for each joint and the force spinor required for the base is obtained by backward recursion reconstruction through the recursive Newton-Euler dynamics algorithm;

[0084] The backward recursive reconstruction uses motion spinors and its differential The globally closed matrix form, combined with the recursive reconstruction method, is used to further refine the backward recursive content, namely the joint torques. Force rotation required for the base The expression can be performed in the form of a globally closed matrix, specifically:

[0085] ;

[0086] ;

[0087] ;

[0088] In the formula, The rotation of force transmitted by each link. The generalized inertia matrix of the robotic arm; the link Corresponding generalized inertia matrix , It is a robotic arm link The moment of inertia matrix, For robotic arm linkages The recursive operator matrix for mass and spinor is the recursive operator matrix. The transpose matrix is ​​defined as . This is the transformation matrix from the actuator end effector to the robotic arm joint. The spinor of the force at the actuator end. This is the Coriolis force matrix.

[0089] Step 4: Based on the similarity of the backward recursive reconstruction results of the Newton-Euler dynamics algorithm at the mathematical structure level, complete the global closed matrix form dynamic modeling of the space robot;

[0090] Joint torques are expressed in the form of a globally closed matrix obtained by backward recursion reconstruction based on the Newton-Euler dynamics algorithm. Force rotation required for the base The significant similarity in mathematical structure can be obtained by reconstructing the acceleration and velocity matrices of the two results as follows.

[0091] The base force spinor expressed in global closed matrix form is used with the recursive operator matrix G. The velocity and acceleration terms in the analytical expression are represented by a matrix.

[0092] ;

[0093] ;

[0094] Joint torques expressed in global closed matrix form By reconstructing the matrix from the acceleration and velocity terms, we can obtain the following result:

[0095] ;

[0096] ;

[0097] The base force spinor expressed in the form of the above globally closed matrix and pitch torque By combining the results of the acceleration and velocity term matrix reconstructions, we finally obtain the global closed matrix form dynamic equations of the floating space robot:

[0098] ;

[0099] ;

[0100] In the formula, The global inertia matrix. 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 can be defined by the following equation:

[0101] .

[0102] The global mapping matrix introduced in step 4 Achieved spatial velocity configuration by space robots To global spinor differential The mapping of the global centrifugal force matrix. It is the global dual adjoint operator matrix. The extension. Global Coriolis force matrix. It is the Coriolis force matrix. Further extensions.

[0103] The parameters of the globally closed matrix form dynamic equations obtained in the examples of this invention are shown in Table 2.

[0104] Table 2. Symbol Reference Table for Globally Closed Matrix Form Dynamic Equations

[0105]

[0106]

[0107] In this invention example, to verify the consistency between the globally closed matrix form dynamic equation obtained by the method of this invention and the dynamic equation obtained by the traditional recursive Newton-Euler algorithm, and to compare computational efficiency, Figure 4 The space robot configuration shown is used as the test object. A traditional recursive Newton-Euler dynamics model and a globally closed matrix dynamics model are constructed, and relevant verification work is carried out.

[0108] In an example of the present invention, such as Figure 5As shown, by setting the satellite base trajectory, the robotic arm motion trajectory, and the force rotation at the robotic arm end effector, simulation outputs of two dynamic models were obtained, including 12 components: the force rotation required by the base and the control torque required by the robotic arm joints. In the figure, the solid line represents the output of the traditional recursive Newton-Euler dynamic model, and the dashed line represents the output of the globally closed matrix dynamic model. The results show that the outputs of the two dynamic models are basically consistent. To further quantify the consistency between the two dynamic models, the maximum absolute error of each output component was calculated at 2-second intervals within a 200-second simulation period, and heatmaps of the output errors of the traditional recursive Newton-Euler dynamic model and the globally closed matrix dynamic model were plotted, as shown below. Figure 5 As shown in (d). Error analysis shows that the errors of both models at each time point and at each output component are stable at approximately [value missing]. The magnitude, with a maximum error not exceeding .

[0109] In an example of the present invention, such as Figure 6 As shown, to systematically evaluate the performance differences between the two dynamic models, the traditional recursive Newton-Euler dynamics model and the globally closed matrix dynamics model were encapsulated into two independent function modules, InverseDynamicsFloat and InverseDynamicsClosedFormSp, respectively, on the MATLAB platform. A test program covering 1 to 11 degrees of freedom robotic arm configurations was designed, executing 9001 computational loops for each function, and the computation time and memory consumption data were collected using the performance analyzer in MATLAB. Figure 6 (a) shows the relationship between the robot arm's degrees of freedom and the algorithm's 9001 execution times. Figure 6 (b) presents detailed performance analyzer data for a six-DOF robotic arm space robot system.

[0110] Experimental results show that when the robotic arm has degrees of freedom At the same time, the globally closed matrix form dynamic modeling method proposed in this invention outperforms traditional recursive dynamic modeling methods in terms of execution efficiency. This advantage stems from the fact that the globally closed matrix method utilizes sparse matrix block operations, effectively optimizing the computational complexity of high-dimensional systems. Furthermore, it constructs a recursive operator subdiagonal matrix based on von Neumann series expansion. The optimization strategy also effectively suppressed the growth of memory usage.

[0111] Example 2:

[0112] 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 global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots.

[0113] 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 global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots as described in the embodiments. It is understood that the electronic device may also include input / output (I / O) interfaces and communication components.

[0114] The processor is used to execute all or part of the steps in the global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots 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.

[0115] 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 global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots described in the above embodiments.

[0116] Example 3:

[0117] 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.

[0118] 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 global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots described in the various embodiments of this application.

[0119] 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 aforementioned global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots.

[0120] Example 4:

[0121] This embodiment proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots.

[0122] 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.

[0123] 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.

[0124] 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. A global recursive reconstruction method for a recursive Newton-Euler dynamics algorithm for space robots, characterized in that, include: The spinor of the robotic arm motion and its differential global closed matrix form are obtained by forward recursion reconstruction using the recursive Newton-Euler dynamics algorithm; Construct the second diagonal matrix of the recursive operator The spinor differential of the robotic arm motion in global closed matrix form is simplified by using this diagonal matrix. Based on the global closed matrix form of the motion spinor and its derivative, the global closed matrix form of the torque required for each joint and the force spinor required for the base is obtained by backward recursion reconstruction through the recursive Newton-Euler dynamics algorithm. Based on the similarity of the backward recursive reconstruction results of the recursive Newton-Euler dynamics algorithm at the mathematical structure level, a global closed matrix form dynamic model of the space robot is completed.

2. The global recursive reconstruction method for the recursive Newton-Euler dynamics algorithm for space robots according to claim 1, characterized in that, The specific method for obtaining the spinor of the robotic arm motion and its differential global closed matrix form through forward recursive reconstruction using the recursive Newton-Euler dynamics algorithm is as follows: Based on the motion transfer relationship between rigid bodies, construct the recursive operator matrix. Obtaining the motion spinor of a space robot arm Space robot configuration and space velocity The mapping relationship between them is then used to obtain the spinor expression of the robotic arm's motion in the form of a globally closed matrix: Specifically, there are: ； ； In the formula, Let be the joint angular velocity of the robotic arm. The transformation matrix from satellite base to robotic arm; 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; Let be the spinor mapping matrix of the robotic arm, where The symbol represents a dimension reduction, indicating that the mapping matrix only provides the mapping relationship between the spatial velocity of the space robot configuration and the spinor of the robotic arm, without mapping the spinor of the satellite base. For the adjoint mapping matrix, , They are respectively The corresponding rotation and translation matrices, Let {i} be the configuration of the joint coordinate system {i} relative to the coordinate system {i-1}. For the satellite base motion spinor, For conjoined base angular velocity of the lower base For conjoined base Lower base linear velocity; The differential of the spinor of the robotic arm's motion is further obtained based on a recursive reconstruction method, specifically: ； In the formula, For the spatial acceleration configuration of space robots, The global dual adjoint operator matrix, It is the second diagonal matrix of the recursive operator.

3. The global recursive reconstruction method for the recursive Newton-Euler dynamics algorithm of space robots according to claim 2, characterized in that, The recursive operator second diagonal matrix constructed based on Neumann series expansion is described. The specific method for simplifying the expression of the spinor differential of the robotic arm motion in the form of a globally closed matrix by using this diagonal matrix is ​​as follows: Constructing the second diagonal matrix of the recursive operator based on Neumann series expansion. As shown below: ； The recursive operator diagonal matrix It has the property of power-law oblique propagation, i.e., matrix The exponentiation operation has the following properties along the recursive operator matrix. Characteristics of oblique propagation along the second diagonal; Based on matrix The zero-power property of the matrix is ​​determined by the matrix. Finite-dimensional power exponents are used to characterize recursive operator matrices, specifically: ； Equation Riding on both sides The simplified relation is obtained. This simplifies the spinor differential of robotic arm motion in the form of a globally closed matrix. Expressions, specifically: ； In the formula, Let be the differential operator matrix for the spinor mapping of the robotic arm's motion.

4. The global recursive reconstruction method for the recursive Newton-Euler dynamics algorithm of space robots according to claim 3, characterized in that, The specific method for obtaining the global closed matrix form of the required torque of each joint and the required force rotation of the base through backward recursive reconstruction using the recursive Newton-Euler dynamics algorithm is as follows: Using kinetic spin and its differential The globally closed matrix form, combined with the recursive reconstruction method, is used to further refine the backward recursive content, namely the joint torques. Force rotation required for the base Express it in the form of a globally closed matrix: ； ； In the formula, The generalized inertia matrix of the robotic arm; For robotic arm linkages Corresponding to the generalized inertia matrix, It is a robotic arm link The moment of inertia matrix, For robotic arm linkages quality, The force spinor recursive operator matrix, i.e., the recursive operator matrix. The transpose of the 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. This is the Coriolis force matrix.

5. The global recursive reconstruction method for the recursive Newton-Euler dynamics algorithm of space robots according to claim 4, characterized in that, Based on the similarity in mathematical structure between the backward recursive reconstruction results of the recursive Newton-Euler dynamics algorithm, the specific method for completing the global closed matrix form dynamic modeling of space robots is as follows: The base force spinor expressed in global closed matrix form is used with the recursive operator matrix G. The velocity and acceleration related terms in the matrix are represented by a matrix mapping: ； ； Joint torques expressed in global closed matrix form Reconstructing the matrix from the acceleration and velocity terms in the matrix yields: ； ； Finally, the global closed matrix form dynamic equations of the floating space robot are obtained: ； ； In the formula, The global inertia matrix. 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: 。 6. An electronic device for executing the global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots as described in any one of claims 1-5, 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 execute the global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots.

7. A computer-readable storage medium storing executable instructions for performing the global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots as described in any one of claims 1-5, characterized in that, When the instruction is executed, it causes the processor to perform the global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots.

8. A computer program product for executing the global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots as described in any one of claims 1-5, characterized in that, This includes a computer program or instructions that, when executed by a processor, implement the global recursive reconstruction method of the recursive Newton-Euler dynamics algorithm for space robots.

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