CN110426721B - Modular reconfigurable satellite in-orbit self-reconfiguration method based on graph theory and A-x algorithm - Google Patents
Modular reconfigurable satellite in-orbit self-reconfiguration method based on graph theory and A-x algorithm Download PDFInfo
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Abstract
The invention relates to a modularized reconfigurable satellite in-orbit self-reconfiguration method based on graph theory and A-star algorithm. The invention aims to solve the problems of large fuel consumption, serious mechanical loss, long reconstruction process time and low reliability of the conventional modular satellite in the reconstruction process. Firstly, constructing a position and connection matrix; secondly, putting the initial configuration into an OPEN table; thirdly, sorting the nodes in the OPEN table; finding out a connecting module in the current configuration; fifthly, expanding the non-connection module in the current configuration; if the OPEN table has the configuration of a newly expanded node, updating three distances of the node; if the OPEN table does not exist, calculating three distances of the newly expanded nodes, and adding the three distances into the OPEN table; seventhly, judging whether the newly expanded node is a target point or not, and if so, finishing; if not, the current node is put into a CLOSED table. The invention is used in the field of satellite in-orbit self-reconstruction.
Description
Technical Field
The invention relates to an on-orbit self-reconstruction method for a satellite.
Background
With the continuous development of microsatellites, satellites with fixed structures are difficult to meet the requirements of multiple task execution capacity, strong environmental adaptability, risk resistance and the like proposed by various countries, so people look to the self-reconfigurable satellites with the on-orbit variable structures. The modularized reconfigurable satellite is a microsatellite which is composed of modules with similar structures and different functions and can change the shape and the structure in orbit, and is a new development trend of future satellites.
During the reconfiguration of the modular satellite, the sequence and manner of movement of the individual modules affects the number of steps that the configuration conversion generally needs to be performed, and obviously fewer steps means less fuel consumption and mechanical losses. The motion planning for the modular satellite is the key to the self-reconstruction of the modular satellite.
Disclosure of Invention
The invention aims to solve the problems of high fuel consumption, serious mechanical loss, long reconstruction process time and low reliability of the conventional modular satellite in the reconstruction process, and provides an on-orbit self-reconstruction method of the modular reconfigurable satellite based on graph theory and A-x algorithm.
The modular reconfigurable satellite in-orbit self-reconfiguration method based on the graph theory and the A-star algorithm comprises the following specific processes:
the method comprises the following steps that firstly, a modularized satellite is subjected to mathematical representation, a position matrix is constructed, and a connection matrix is constructed;
step two, placing the initial configuration into an OPEN table;
step three, sequencing the nodes in the OPEN table, and selecting the node with the minimum F (n) value as the current node for expansion;
step four, finding out a connection module in the current configuration;
step five, expanding the non-connection module in the current configuration;
step six, comparing the configuration of the newly expanded node with the node in the OPEN table, and updating three distances G (n), H (n) and F (n) of the node if the configuration exists in the OPEN table; if the OPEN table does not exist, calculating three distances G (n), H (n) and F (n) of the newly expanded node, and adding the distances G (n), H (n) and F (n) into the OPEN table;
step seven, carrying out configuration comparison on the newly expanded node and the target configuration, judging whether the newly expanded node is a target point or not, and if so, ending; if not, executing the third step, and putting the current node into the CLOSED table.
The invention has the beneficial effects that:
the patent provides a method based on graph theory and A-star algorithm to realize self-reconfigurable motion planning of a modular satellite; performing mathematical representation on the modular satellite, constructing a position matrix and constructing a connection matrix; place initial configuration (starting point) into OPEN table; sequencing the nodes in the OPEN table, and selecting the node with the minimum F (n) value as the current node for expansion; finding a connection module in the current configuration (current node); expanding the non-connection module in the current configuration (current node); comparing the configuration of the newly expanded node with the nodes in an OPEN table, if the configuration exists in the OPEN table, updating three distances G (n), H (n) and F (n) of the node, and if the configuration does not exist in the OPEN table, calculating the three distances G (n), H (n) and F (n) of the newly expanded node, and adding the three distances G (n), H (n) and F (n) into the OPEN table; comparing the configuration of the newly expanded node with the target configuration, judging whether the newly expanded node is a target point, and if so, ending; if not, executing the third step, and putting the current node into a CLOSED table; the method has the advantages of small fuel consumption, reduced mechanical loss, short reconstruction process time and high reliability in the reconstruction process of the modular satellite, and solves the problems of large fuel consumption, serious mechanical loss, long reconstruction process time and low reliability in the reconstruction process of the conventional modular satellite.
It can be seen from FIG. 7 that the final relationship between the number of steps and the number of modules can be fitted to a straight line with a slope of 1.7, and the O (n) algorithm given by the present invention is greater than O (n) given by Cynthia Sung et al2) The algorithm results are good. Meanwhile, the reconstruction into a linear intermediate configuration is avoided in the space, and the structural span of the intermediate configuration can be reduced, so that the large-amplitude vibration is avoided.
It can be seen from fig. 8 that the algorithm will not substantially fail to reconstruct with fewer than 30 modules. And analysis on a failed reconstruction process shows that most of modules complete reconstruction, only 1-2 modules have no path to enter a configuration blank position generating hollow, and in the face of the situation, adjustment can be carried out through manual control, and the algorithm is effective as a whole.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a reconfigurable modular satellite;
FIG. 3 is a view of a configuration topology connection architecture;
FIG. 4a is a schematic diagram of a module rotated 90 ° in a two-dimensional plane, where positions where the module cannot exist are marked white, motion modules are marked black, and positions where the module needs to exist are marked gray;
FIG. 4b is a schematic diagram of the module rotating 180 ° in a two-dimensional plane, where the positions where the module cannot exist are marked white, the motion module is marked black, and the positions where the module needs to exist are marked gray;
FIG. 4c is a diagram of the movement condition of the module rotating 90 degrees in a two-dimensional plane, wherein the positions where the module cannot exist are marked as white, the movement module is marked as black, and the positions where the module needs to exist are marked as gray;
FIG. 4d is a diagram of the movement condition of the module rotating 180 degrees in a two-dimensional plane, wherein the positions where the module cannot exist are marked as white, the movement module is marked as black, and the positions where the module needs to exist are marked as gray;
FIG. 5a is an initial configuration diagram consisting of 10 modules;
FIG. 5b is a diagram of a target configuration consisting of 10 modules;
FIG. 6a is a configuration diagram of configuration transition process 1 from an initial configuration to a target configuration;
FIG. 6b is a configuration diagram of configuration transition process 2 from an initial configuration to a target configuration;
FIG. 6c is a configuration diagram of configuration transition process 3 from an initial configuration to a target configuration;
FIG. 6d is a configuration diagram of the configuration transition process 4 from the initial configuration to the target configuration;
FIG. 6e is a configuration diagram of configuration transition process 5 from the initial configuration to the target configuration;
FIG. 6f is a configuration diagram of the configuration transition process 6 from the initial configuration to the target configuration;
FIG. 6g is a configuration diagram of configuration transition process 7 from an initial configuration to a target configuration;
FIG. 6h is a configuration diagram of the configuration transition process 8 from the initial configuration to the target configuration;
FIG. 6i is a configuration diagram of the configuration transformation process 9 from the initial configuration to the target configuration;
FIG. 6j is a configuration diagram of configuration transition process 10 from an initial configuration to a target configuration;
FIG. 6k is a configuration diagram of configuration transformation process 11 from the initial configuration to the target configuration;
FIG. 6l is a configuration diagram of configuration transition process 12 from an initial configuration to a target configuration;
FIG. 7 is a graph of the average number of motion steps to complete the reconstruction and a linear fit thereto;
fig. 8 is a graph of the number of failures in the reconstruction process.
Detailed Description
The first embodiment is as follows: the modular reconfigurable satellite in-orbit self-reconfiguration method based on the graph theory and the A-star algorithm comprises the following specific processes:
the method comprises the following steps that firstly, a modularized satellite is subjected to mathematical representation, a position matrix is constructed, and a connection matrix is constructed;
step two, putting the initial configuration (starting point) into an OPEN table;
step three, sequencing the nodes in the OPEN table, and selecting the node with the minimum F (n) value as the current node for expansion;
step four, finding out a connection module in the current configuration (current node);
step five, expanding the non-connection module in the current configuration (current node);
step six, comparing the configuration of the newly expanded node with the node in the OPEN table, and updating three distances G (n), H (n) and F (n) of the node if the configuration exists in the OPEN table; if the OPEN table does not exist, calculating three distances G (n), H (n) and F (n) of the newly expanded node, and adding the distances G (n), H (n) and F (n) into the OPEN table;
step seven, carrying out configuration comparison on the newly expanded node and the target configuration, judging whether the newly expanded node is a target point or not, and if so, ending; if not, executing the third step, and putting the current node into the CLOSED table.
The second embodiment is as follows: the first embodiment is different from the first embodiment in that the first step is to perform mathematical representation on the modular satellite, construct a position matrix, and construct a connection matrix; the specific process is as follows:
establishing a coordinate system, and simplifying the initial configuration and target configuration (for example, the initial configuration and the target configuration are both composed of 10 modules) into one point in the coordinate system on the premise of a given satellite module number, wherein the points composed of all modules in the configuration form a nonrepeating non-empty point set V, namely a position matrix;
the connection relation between the surfaces of the modules is regarded as the edge connecting the points in the graph, and all the surfaces in the configuration are connected to form an edge set E, namely a connection matrix;
the configuration topological connection structure diagram G ═ V, E of a complete satellite composed of several satellite modules is shown in fig. 2 and 3.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: this embodiment differs from either or both embodiments in that in step two, the initial configuration (starting point) is placed in the OPEN table; the specific process is as follows:
creating an OPEN table and a CLOSED table;
the OPEN table stores nodes to be expanded (the nodes represent an attribute value of the configuration), and the CLOSED table stores accessed nodes;
the initial configuration (starting point) is put into the OPEN table.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment and the first to third embodiments is that in the third step, the nodes in the OPEN table are sorted, and the node with the smallest f (n) value is selected as the current node to expand; the specific process is as follows:
the core of the a-algorithm is to directionally search for nodes that may reach the target first, which requires us to rank the expansion list.
The OPEN table is sorted from small to large according to F (n), which is a distance estimate from the initial configuration to the target configuration via the current configuration;
f (n) is equal, and the small nodes of H (n) are arranged in front; the expression is as follows:
F(n)＝G(n)+H(n)
wherein G (n) is the current configuration and the initialDistance of the initial configuration (number of allosteric steps for converting the initial configuration to the current configuration), H (n) estimation of distance between the current configuration and the target configuration (number of allosteric steps for converting the current configuration to the target configuration, heuristic function); k and p are constants which are the same,
for the best match metric of the current configuration and the target configuration,
number of modules not in the same position for current and target configurations, cnIn the current configuration, ctIs the target configuration.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is that in the fourth step, a connection module in the current configuration (current node) is found; the specific process is as follows:
and judging the connectivity of the current configuration, finding out a connection module, referring to the definition of a cut point in the graph theory, calculating the cut point of the configuration topology connection structure graph G (V, E) obtained in the step one by adopting a Tarjan algorithm, wherein the module represented by the cut point is the connection module of the configuration, so that all the connection modules of the current configuration are found, and the connection modules do not participate in configuration expansion in the reconstruction process.
Other steps and parameters are the same as in one of the first to fourth embodiments.
The sixth specific implementation mode: the difference between this embodiment and one of the first to fifth embodiments is that, in the fifth step, the non-connection module in the current configuration (current node) is expanded; the specific process is as follows:
the movement of a single module in three-dimensional space requires different conditions depending on the rotation axis, rotation direction and rotation angle. There should be some connection modules around the module and no modules can be present in the positions passed by during the movement.
The configuration is expanded according to 48 rotating motion conditions in the summarized three-dimensional space, and the motion of each module generates a new node. Fig. 4a, 4b, 4c, 4d are two-dimensional in-plane motion condition examples.
Other steps and parameters are the same as those in one of the first to fifth embodiments.
The seventh embodiment: the difference between this embodiment mode and one of the first to sixth embodiment modes is that, in the sixth step, the newly expanded node is compared with the configuration of the node in the OPEN table, and if the configuration already exists in the OPEN table, the three distances g (n), h (n), and f (n) of the node are updated; if the OPEN table does not exist, calculating three distances G (n), H (n) and F (n) of the newly expanded node, and adding the distances G (n), H (n) and F (n) into the OPEN table; the specific process is as follows:
calculating three distances G (n), H (n) and F (n) of the updated node and the newly expanded node, and the specific process is as follows:
g (n) of the updated node and G (n) of the newly expanded node are obtained by adding 1 to G (n) of the current node in the step four;
calculating H (n) of the updated node and H (n) of the newly expanded node by using the optimal matching metric of the configuration of the node and the target configuration; the process is as follows:
and calculating the one-to-one correspondence relationship between the node configuration and the modules of the target configuration by using a Kuhn-Munkres algorithm, so that the Manhattan distance sum of the satellite modules in the node configuration and the satellite modules in the target configuration is the shortest, and the Manhattan distance sum is called as an optimal matching measure and is used as a heuristic function of an A algorithm and is recorded as H (n).
Other steps and parameters are the same as those in one of the first to sixth embodiments.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
the subsection simulates the self-reconstruction path planning method of the isomorphic modular satellite based on the A-x algorithm. The modules are cubic modules with the side length of 1, the motion steps of each module are increased by 1 when the module rotates 90 degrees or 180 degrees, and a heuristic function
Where k is 10 and p is 100. First, a reconstruction process is given, and fig. 5a and 5b show an initial configuration and a target configuration which are randomly generated and contain 10 modules. The position matrix is
The simulation results are shown in fig. 6a-6l, which show the configuration transformation process from the initial configuration to the target configuration, and the total number of motion steps is 12 to complete the reconstruction.
And then simulating the number of the modules from 5 to 50, wherein each module randomly generates 10 groups of 460 initial configurations and target configurations, the average value of 10 groups of simulation results is taken for analysis, and reconstruction failure is defined when the expansion node exceeds 30000. The simulation results are shown in fig. 7 and 8:
it can be seen from FIG. 7 that the final relationship between the number of steps and the number of modules can be fitted to a straight line with a slope of 1.7, and the O (n) algorithm given by the present invention is greater than O (n) given by Cynthia Sung et al2) The algorithm results are good. Meanwhile, the reconstruction into a linear intermediate configuration is avoided in the space, and the structural span of the intermediate configuration can be reduced, so that the large-amplitude vibration is avoided.
It can be seen from fig. 8 that the algorithm will not substantially fail to reconstruct with fewer than 30 modules. And analysis on a failed reconstruction process shows that most of modules complete reconstruction, only 1-2 modules have no path to enter a configuration blank position generating hollow, and in the face of the situation, adjustment can be carried out through manual control, and the algorithm is effective as a whole.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.
Claims (4)
1. The modular reconfigurable satellite in-orbit self-reconfiguration method based on graph theory and A-star algorithm is characterized by comprising the following steps: the method comprises the following specific processes:
the method comprises the following steps that firstly, a modularized satellite is subjected to mathematical representation, a position matrix is constructed, and a connection matrix is constructed;
step two, placing the initial configuration into an OPEN table;
thirdly, sorting the nodes in the OPEN table, and selecting the node with the minimum F (n) value as the current node for expansion;
the node represents an attribute value of the configuration;
finding out a connection module in the current configuration corresponding to the current node;
step five, expanding the non-connection module in the current configuration;
step six, comparing the configuration of the newly expanded node with the node in the OPEN table, and updating three distances G (n), H (n) and F (n) of the node if the configuration exists in the OPEN table; if the OPEN table does not exist, calculating three distances G (n), H (n) and F (n) of the newly expanded node, and adding the distances G (n), H (n) and F (n) into the OPEN table;
step seven, carrying out configuration comparison on the newly expanded node and the target configuration, judging whether the newly expanded node is a target point or not, and if so, ending; if not, the current node is put into a CLOSED table, and the third step is executed;
in the first step, the modularized satellite is subjected to mathematical representation, a position matrix is constructed, and a connection matrix is constructed; the specific process is as follows:
establishing a coordinate system, and simplifying an initial configuration module and a target configuration module into one point in the coordinate system on the premise of giving the number of satellite modules, wherein the points formed by all the modules in the configuration form a nonrepeating non-empty point set V, namely a position matrix;
the connection relation between the surfaces of the modules is regarded as the edge connecting the points in the graph, and all the surfaces in the configuration are connected to form an edge set E, namely a connection matrix;
a configuration topological connection structure graph G (V, E) of a complete satellite consisting of a plurality of satellite modules is formed;
putting the initial configuration into an OPEN table in the second step; the specific process is as follows:
creating an OPEN table and a CLOSED table;
the OPEN table stores nodes needing to be expanded, and the CLOSED table stores accessed nodes;
placing the initial configuration into an OPEN table;
in the third step, the nodes in the OPEN table are sequenced, and the node with the minimum F (n) value is selected as the current node to be expanded; the specific process is as follows:
the OPEN table is sorted from small to large according to F (n), which is a distance estimate from the initial configuration to the target configuration via the current configuration;
f (n) is equal, and the small nodes of H (n) are arranged in front; the expression is as follows:
F(n)＝G(n)+H(n)
wherein G (n) is the distance between the current configuration and the initial configuration, and H (n) is the distance estimation between the current configuration and the target configuration; k and p are constants which are the same,
for the best match metric of the current configuration and the target configuration,
number of modules not in the same position for current and target configurations, cnIn the current configuration, ctIs the target configuration.
2. The on-orbit self-reconstruction method of the modular reconfigurable satellite based on graph theory and A-algorithm according to claim 1, characterized in that: finding out a connecting module in the current configuration in the fourth step; the specific process is as follows:
and (3) calculating the cutting points of the configuration topology connection structure diagram G (V, E) obtained in the step one by adopting a Tarjan algorithm, wherein the modules represented by the cutting points are the configured connection modules, so that all the connection modules of the current configuration are found, and the connection modules do not participate in configuration expansion in the reconstruction process.
3. The on-orbit self-reconstruction method of the modular reconfigurable satellite based on graph theory and A-algorithm according to claim 2, characterized in that: expanding the non-connection module in the current configuration in the fifth step; the specific process is as follows:
there should be a connection module around the module and no module can be present in the positions passed by during the movement.
4. The on-orbit self-reconstruction method of the modular reconfigurable satellite based on graph theory and A-algorithm according to claim 3, characterized in that: in the sixth step, the newly expanded node is compared with the node in the OPEN table in a configuration mode, and if the configuration exists in the OPEN table, the three distances G (n), H (n) and F (n) of the node are updated; if the OPEN table does not exist, calculating three distances G (n), H (n) and F (n) of the newly expanded node, and adding the distances G (n), H (n) and F (n) into the OPEN table; the specific process is as follows:
calculating three distances G (n), H (n) and F (n) of the updated node and the newly expanded node, and the specific process is as follows:
g (n) of the updated node and G (n) of the newly expanded node are obtained by adding 1 to G (n) of the current node in the step four;
calculating H (n) of the updated node and H (n) of the newly expanded node by using the optimal matching metric of the configuration of the node and the target configuration; the process is as follows:
and calculating the one-to-one correspondence relationship between the node configuration and the modules of the target configuration by using a Kuhn-Munkres algorithm, so that the Manhattan distance sum of the satellite modules in the node configuration and the satellite modules in the target configuration is the shortest, and the Manhattan distance sum is called as an optimal matching measure and is used as a heuristic function of an A algorithm and is recorded as H (n).
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