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CN-121980734-A - Variable topology system dynamics recursion group set method based on graph theory description

CN121980734ACN 121980734 ACN121980734 ACN 121980734ACN-121980734-A

Abstract

A dynamic recursion set method of a variable topology system based on graph theory description belongs to the field of spacecraft dynamics. The implementation method of the invention comprises the steps of automatically calculating the circulating dimension based on a graph theory algorithm, matching non-tree edges, generating pseudo nodes, and converting the ring-containing structure into a tree structure without a communication ring. The dynamic model automatic group set does not need manual derivation, and the constraint equation is described in a body-pseudo body recurrence relation, and the automatic modeling updating can be realized by combining the unified recurrence relation of rigid body-rigid body, flexible body-flexible body and rigid body-flexible body connection, automatically calling modal parameters, generating a group set matrix and outputting a dynamic equation. The invention can realize the automatic dynamic assembly of the variable topology system, avoid dynamic reconstruction and is beneficial to the characteristic analysis and the gesture control of the on-orbit assembly system.

Inventors

  • YANG KEYING
  • Shi anrui
  • ZHANG JINGRUI
  • ZHANG ZELIN

Assignees

  • 北京理工大学

Dates

Publication Date
20260505
Application Date
20251204

Claims (10)

  1. 1. The dynamic recursion group set method of the variable topology system based on graph theory description is characterized by comprising the following steps: Aiming at the problem of ring contained in the topological structure, determining ring bases of the topological structure by using a spanning tree, converting each ring base into a chain/tree-shaped structure by using the operation of unbinding connection constraint, and converting the topological structure of the single module into a communicated and ring-free tree-shaped topological structure; Step 2, determining the recurrence relation among different connection types in the system; based on the tree topology structure obtained in the step 1, combining the dynamic relations among all the bodies according to the connection relation of the topology structure, constructing a system dynamic automatic group array, and realizing automatic group collection of models, wherein all the types comprise rigid body-rigid body, flexible body-flexible body, rigid body-flexible body and body-pseudo body; and 3, developing expansion application based on the automatic system dynamics array obtained in the step 2, for example, predicting the dynamics evolution of the system, summarizing the dynamics evolution law, further analyzing and judging the dynamics characteristics of the system, and designing and controlling the posture and vibration of the system based on the dynamics characteristics and analysis.
  2. 2. The method of claim 1, wherein in step 1, the topology structure of the single space truss assembly module is described by using a graph theory method, and the specific implementation method is as follows: After the vertex number, the rod number and the connection relation of the single truss module are input, the vertex and the rod of the single assembly module are divided, the vertex is regarded as a node, the rod is regarded as an edge, the nodes at two ends of the rod are used for determining the specific rod, so that the topological structure of the module is described through the nodes and the edge set formed by the nodes at two ends of the rod, and further, the topological structure description file of the single assembly module comprising the node set and the edge set is generated without manual drawing or marking.
  3. 3. The method of claim 2, wherein in step 1, aiming at the problem of ring-containing in the topology structure, ring bases of the topology structure are determined by using a spanning tree, each ring base is converted into a chain/tree structure by using an operation of releasing connection constraint, and the topology structure of a single module is converted into a connected and ring-free tree topology structure, and the specific implementation method is as follows: for the topology structure of a single assembly module, an initial diagram corresponding to a single module tree diagram Is the number of turns of (a) The method meets the following conditions: Wherein, the For the number of sides, the number of sides is the number of sides, For the number of nodes to be the number of nodes, The number of the connected domains; Determining a ring base of a topological structure by using a spanning tree, traversing the whole graph from any node by using a traversing method, recording edges passing when each node is accessed for the first time in the traversing process, wherein a subgraph formed by the edges is a spanning tree, after the spanning tree is obtained, the remaining edges in the graph are called non-tree edges, and each non-tree edge is added, a basic ring is formed with a path on the spanning tree only, and the edges are shared A set of basic rings forms a ring base; Defining the operation of releasing the connection constraint, namely, at any node i, releasing the connection constraint of two edges connected with the node i, adding a new pseudo node Therefore, each operation of unbinding the connection constraint adds a pseudo node, and the number of the edges is unchanged; for the determined ring base The base circles execute the operation of releasing the connection constraint, the larger node of the two end nodes in the edge which is released from the connection constraint is selected as the node which is executed with the operation of releasing the connection constraint, and the topology structure of the single module is converted into a connected and non-circle tree topology structure.
  4. 4. The method of claim 3, wherein in step 1, the node between the assembled modules is pruned and spliced to obtain a connected and endless tree topology structure of the system, and the specific implementation method comprises the following steps: The method for assembling and describing the two assembled parts, namely the A module and the B module, is described based on the method of claim 3, the repeated parts of the A module and the B module are deleted on the basis of the original structure of the A module, the topology of the B module and the rest of the A module are combined to obtain a new assembled topology, the method for assembling and describing the two modules has universal applicability, a truss system comprising a plurality of modules is gradually integrated according to the basis, and finally a complete and communicated and endless truss structure topology tree diagram is formed, so that the communicated and endless tree topology structure of the whole system is output.
  5. 5. The method of claim 4, wherein the rigid-rigid body connection method of step2 is as follows: For a certain body i in the tree structure, the internal connection body and the external connection body are respectively marked as And And both are rigid bodies, a matrix is defined: Wherein, the And Respectively the position vectors And a coordinate conversion matrix Corresponding position transformation matrix and extended coordinate transformation matrix: Wherein, the And Respectively is Identity matrix and zero matrix of (a) and in subsequent expressions And The matrix is a unit matrix and a zero matrix respectively, and the lower right corner is the dimension of the matrix; Is that Corresponding inverse matrix, and in subsequent expressions the upper right hand symbol The symbols as a reverse matrix; Is a dot Relative to the point Is a position vector of (2); Is a coordinate system To a coordinate system Coordinate transformation matrix of volume i Origin is located at Fixedly connected with the body i, and quasi-appendage coordinate system Origin is located at And body(s) Fixedly connecting; Rigid body i and rigid body The recursive relation between the two is represented as: Wherein, the And Respectively are bodies Upper point Angular acceleration of relative inertial system And acceleration Is a linear part of (2); Is that Corresponding transposed matrix, and upper right symbol in subsequent expressions A symbol as a transposed matrix; And Respectively joints Generalized rate of corresponding rotational angle and displacement allowed, volume i and volume Joint between them Connecting points respectively located on the two bodies Sum point ; And Respectively joints Corresponding point Moment and force applied to the body i and the body i Joint between them Connecting points respectively located on the two bodies Sum point ; And Respectively joints Corresponding point The moment and force to which it is subjected; And Respectively the relative points of the body i Inertia and static moment of (a); Is the mass of volume i; And Respectively are points on the body i Angular acceleration and acceleration relative to the inertial frame; And To describe the joint The projection matrix of the allowed and constrained motion directions are orthogonal complement matrices and satisfy the following relationship: Wherein, the And Respectively joints And Number of degrees of freedom; And Matrixing writing: Wherein, the And Respectively is Entries corresponding to the speed and angular speed; And Respectively is Entries corresponding to the speed and angular speed; And Decomposing into generalized constraint forces acting in joint constraint direction And Equivalent control force And 。
  6. 6. The method according to claim 5, wherein the soft-to-soft connection implementation method in step 2 is as follows: For adjacent volumes i and i In the case of soft bodies, the equations corresponding to the soft motion and modal force components need to be considered, namely: Wherein, the And Is a body And the modal coordinates of the volume i, And In the form of a modal force, 、 And A modal momentum coefficient matrix, a modal angular momentum coefficient matrix and a modal mass matrix of the body i respectively; And Respectively as dots A translational and rotational modal matrix; a projection matrix corresponding to the modal coordinates; Is flexible force Equivalent control force component of (a); flexible body i and flexible body The recursive relation between the two is represented as:
  7. 7. the method according to claim 6, wherein the rigid-flexible connection implementation method in step 2 is as follows: For the adjacent situation of rigid and flexible bodies, the combined type And (d) the When adjacent body i and The rigid body and the flexible body respectively satisfy the following conditions: When adjacent body i and The method comprises the following steps of:
  8. 8. the method of claim 7, wherein the method for implementing the body-pseudo-body connection in step2 comprises the steps of: Pseudo body And body The speed constraint should be satisfied in the original constraint direction: Wherein, the Is the projection matrix of the released constraint at the joint; And Respectively an expansion position vector matrix for connecting the two opposite bodies of the joint; And Are respectively a body And a dummy body The absolute velocity in the inertial frame corresponds to the velocity spin. Opposite type Deriving an acceleration constraint equation: If a pseudo body exists in the inter-body relation, because the pseudo body is an external body, the corresponding equation is written into a form similar to other connection modes so as to facilitate group collection: Wherein, the And Respectively are And the introduction of the dummy does not actually introduce an additional degree of freedom of movement, thus Due to the false body And body Is completely constrained, so the generalized constraint force meets Thus, the dynamics and constraint equations can be described consistently in recursive relationships.
  9. 9. The method of claim 8, wherein the step 2 of constructing the system dynamics automatic group array realizes automatic group collection of the model, and the specific implementation method is as follows: In the tree topology, each node represents a body, and the edges represent the connection relations between bodies, according to the structural characteristics, each node is combined with the dynamic relations between the nodes connected with each node in turn, as the combination is carried out, new dynamic relations are continuously combined with the dynamics formed before, and the like until the dynamic relations of all the nodes are incorporated, finally forming a complete system dynamic automatic group array, according to the above mode, the combination formula is formed 、 、 And Obtaining a system dynamics equation after the group set: Wherein, the 、 、 、 、 、 、 And Is a generalized mass array, and meets the following conditions: Wherein the subscript includes the term of i as the kinetic counterpart of the ith individual, formula In the process, the Is a generalized quality group array, and aims at a tree structure system, and a blocking matrix defined as follows is satisfied: Wherein the blocks are divided into Corresponding body i and external body thereof , ,···, The connection relation similar to the fork-shaped structure is written: And Middle partition block Corresponding to the connection relation similar to the chain structure, writing: And Middle partition block Corresponding to the coupling part between the fork-like structure and the chain-like structure, writing:
  10. 10. The method of claim 9, wherein the development application is developed based on a dynamic model of an automated group set, the development application is further developed based on a dynamic model of a topology-variable system constructed in the step 2, the dynamic automatic group set is not required to be reconstructed or manually adjusted in the assembly process, and the development application comprises the following steps of: ① The dynamic characteristic analysis is to analyze key dynamic behaviors of the system in the topology change process based on the model and provide data support for on-orbit assembly process optimization and structure parameter adjustment, wherein the key dynamic behaviors comprise structural vibration response rules, gesture evolution characteristics, stability and rigid-flexible coupling effects; ② The control strategy is designed and realized by taking the dynamic model as a core foundation of the control design and is used for constructing and verifying the control strategy, adapting to the scene requirement of the topological dynamic change in the in-orbit assembly process and guaranteeing the stability and reliability of the system operation, wherein the control strategy comprises attitude control, disturbance suppression and track planning.

Description

Variable topology system dynamics recursion group set method based on graph theory description Technical Field The invention belongs to the field of spacecraft dynamics, relates to a large space structure dynamics modeling method, and particularly relates to a variable topology system dynamics recursion set method based on graph theory description. Background With the continuous deep space activities of human beings, the space infrastructure rapidly develops to large-scale and modularized directions, and the research and development and deployment of systems such as large-scale space telescope, space solar power station, remote sensing satellite/antenna platform, space station and the like become important directions in the field of spaceflight. However, there are severe limitations on the envelope dimensions and launch carrying capacity of the launch vehicle fairings, and such large space structures cannot be staged in an overall configuration by a single launch, and in-orbit assembly technology becomes the core approach to achieving its construction. The large-scale truss structure in space is used as a key bearing component of the system, and has the characteristics of structural flexibility and topology change, wherein the system configuration is continuously changed along with module splicing in the assembly process, the topology relation is dynamically adjusted, and the flexibility of truss rod pieces can cause vibration response, so that the complexity of dynamic behaviors is further increased. These two major characteristics make system configuration descriptions and kinetic modeling necessary to break through automation constraints. The traditional on-orbit assembly topology description method has low automation degree, researchers need to manually identify ring-containing structures and divide topology units, a topological graph needs to be drawn again after each topology change, constraint relations are defined, and too many manual operations possibly introduce manual working errors, the traditional on-orbit assembly dynamics modeling method lacks an automatic linking mechanism, an integral dynamics model needs to be reconstructed after each new module is added, the model multiplexing rate is insufficient and cannot be separated from the work of the researchers, the traditional recursive assembly algorithm has poor automation suitability, and the method can realize the recursive modeling of fixed topology, is only suitable for tree structures, needs manual pretreatment when facing the ring-containing structures of large trusses, and is inconvenient for changing topology scenes and modeling of typical truss structures. Therefore, in the on-orbit assembly scene of the large-scale space truss, the traditional modeling method is highly dependent on manual operation, so that the dynamic change of the topological structure in the on-orbit assembly process is difficult to adapt, the modeling period is prolonged by repeated manual operation, the manual operation error is more likely to be introduced, and the frequency and the data volume of the world information interaction are greatly increased. While research is currently being directed to improving the properties of a varying topology, the automation problem of topology and model construction is not yet solved. Therefore, the development of the topology-changing recursive group set method from topology description to full-link automation of the dynamic group set thoroughly gets rid of the dependence of manual operation and has urgent demands and important significance for promoting engineering application of large-scale space structure on-orbit assembly technology. Disclosure of Invention Aiming at the problem of insufficient modeling automation caused by variable topology, flexible characteristics and the like in the in-orbit assembly process of a large space truss structure, the invention provides a dynamic recursion set method of a variable topology system based on graph theory description, which is used for realizing the automatic modeling of a variable topology rigid-flexible coupling system by fusing graph theory automatic processing, node number automatic continuation and unified recursion set algorithm. According to the invention, modeling and updating of the variable topology system can be completed without manual intervention, and the attitude control and the structural stability of the on-orbit assembly system are facilitated. The invention aims at realizing the following technical scheme: The invention discloses a dynamic recursion set method of a topology-variable system based on graph theory description, which is used for automatically calculating a circulating dimension, matching non-tree edges and generating pseudo nodes based on a graph theory algorithm, converting a ring-containing structure into a communicated ring-free tree-shaped structure, solving the construction problem of the tree-shaped topology structure and avoiding errors