Multi-UUV formation scaling control method based on dynamic scaling factor

Abstract

The invention provides a multi-UUV formation scaling control method based on a dynamic scaling factor, and the method comprises the steps: initializing the positions, speeds and course angles of UUV formation members, setting the relative relation and speed limitation between a virtual navigator and a follower, and achieving the formation control based on a dynamic model and a second-order consistency algorithm. When an obstacle is detected to exist in front, the system obtains obstacle information through a radar sensing module, calculates the width of a current feasible path, and dynamically generates a telescopic factor in combination with the safety buffer margin and the minimum physical width of the formation. The environment is divided into a loose mode, a limited mode and an extremely narrow mode according to the value of the scaling factor, and a formation scaling strategy or a linear formation switching strategy is adopted to keep the formation structure integrity and ensure safe passing. The system continuously optimizes the formation control and obstacle avoidance process through a closed-loop feedback mechanism. According to the invention, the passing efficiency, formation stability and obstacle avoidance capability of the multi-UUV formation in a complex environment can be effectively improved.

Description

Technical Field

[0001] This invention relates to the field of marine engineering equipment, and in particular to a multi-UUV formation scaling control method based on dynamic scaling factor. Background Technology

[0002] With the continuous development of underwater unmanned systems technology, the control of multiple unmanned underwater vehicles (UUVs) swarms has become an important research direction in the field of marine engineering equipment, and is widely used in complex tasks such as marine exploration, military reconnaissance, and underwater rescue. Among related technologies, an autonomous motion and formation maintenance system for multiple UUV swarms has been constructed through the collaborative operation of a leader-follower structure, dynamic model, and consensus algorithm. Specifically, this technology covers the entire process from environmental perception and path planning to formation adjustment and obstacle avoidance control, including key aspects such as radar perception, formation initialization, velocity constraints, and formation reconstruction, aiming to achieve efficient and stable operation of the swarm in dynamic obstacle environments.

[0003] However, existing multi-UUV formation scaling methods directly employ fixed scaling factors or preset formation switching strategies without dynamically adjusting the formation scale according to the actual obstacle environment. This can lead to problems such as formation disarray, large speed fluctuations, and insufficient safety distances in narrow passages or obstacle groups. Specifically, these technologies struggle to balance formation integrity and obstacle avoidance efficiency in confined environments, and lack effective formation reconstruction mechanisms in extremely narrow areas, easily causing formation jams or impassable passages, thus affecting the continuity and safety of mission execution. Furthermore, most methods do not fully consider the impact of UUV dynamics and communication latency on formation adjustments, resulting in insufficient stability and adaptability of the control strategies in practical applications. Summary of the Invention

[0004] The present invention aims to at least partially solve one of the technical problems in the related art.

[0005] This invention proposes a multi-UUV formation scaling control method based on dynamic scaling factors. In view of the problems of scattered formation, large speed changes and insufficient obstacle avoidance safety distance in the formation scaling process of existing methods, an adaptive reconstruction strategy that takes into account obstacle avoidance efficiency and formation changes is proposed, which can effectively solve the problem that the formation cannot adapt to formation changes in narrow passages.

[0006] Another objective of this invention is to propose a multi-UUV formation scaling control system based on a dynamic scaling factor.

[0007] To achieve the above objectives, this invention proposes a multi-UUV formation scaling control method based on a dynamic scaling factor, comprising: Initialize the positions, speeds, and heading angles of multiple UUV formation members, and set the relative positions and speed limits between a virtual navigator and multiple followers; In response to the motion state of the UUV formation, the following UUVs calculate their velocity and angular velocity according to the dynamic model and move towards the desired formation based on the second-order consensus algorithm; When there is an obstacle in front of the UUV formation's direction of movement, the obstacle information is obtained through the radar sensing module, and the width of the current feasible path is determined based on the sensing data; The dynamic scaling factor is calculated based on the ratio of the feasible path width to the current formation width, combined with the safety buffer margin and the minimum physical width of the formation. Based on the magnitude of the dynamic scaling factor, the environment is divided into three modes: relaxed environment, restricted environment, and extremely narrow environment. If the environment is relaxed or restricted, the formation width is scaled by the dynamic scaling factor to adjust the position information matrix of each follower UUV in the lateral direction in order to maintain the integrity of the formation structure. If in an extremely narrow environment, adjust the formation to a straight line to ensure that the formation can pass through narrow passages; The adjusted formation is fed back to the dynamics model module and the second-order consistency controller to continue the formation control and obstacle avoidance process, forming a closed-loop control.

[0008] The multi-UUV formation scaling control method based on dynamic scaling factor in this invention embodiment may also have the following additional technical features: In one embodiment of the present invention, the initialization further includes setting a speed limit for the follower UUV, the speed limit being set based on a scaling factor, the minimum and maximum speeds of the virtual navigator UUV, and the minimum and maximum speeds of the follower UUV.

[0009] In one embodiment of the present invention, the positions, speeds, and heading angles of multiple UUV convoy members are initialized, and the relative positional relationships and speed limits between a virtual navigator and multiple followers are set: (1) In the formula: The speed of the follower UUV at the current moment. This is the proportionality coefficient. Minimum speed for virtual navigator UUVs For the maximum speed of the virtual navigator UUV, The minimum speed of the follower, The maximum speed of the follower.

[0010] In one embodiment of the present invention, a dynamic scaling factor is calculated based on the ratio of the feasible path width to the current formation width, combined with the safety buffer margin and the minimum physical width of the formation, including: If the feasible path is located in the middle of the obstacle group, it is necessary to consider whether to change the UUV formation and calculate the dynamic scaling factor. Determine the formation width for traversing feasible paths ahead: (2) In the formula: It is the feasible path width, It is the current formation width, It is a safety buffer margin. It is the minimum physical width of the formation.

[0011] In one embodiment of the invention, in both relaxed and restricted environments, the formation does not need to break the structure, and the distance between members will be determined according to... Shorten: (3) In the formula: , The adjusted , The position information matrix of direction, , , respectively, before adjustment , A matrix of directional positional information.

[0012] To achieve the above objectives, another aspect of the present invention proposes a multi-UUV formation scaling control system based on a dynamic scaling factor, comprising: The initialization module is used to initialize the position, speed, and heading angle of multiple UUV formation members, and to set the relative positional relationship and speed limits between a virtual navigator and multiple followers; The dynamics model module is used to calculate the velocity and angular velocity of a UUV based on its dynamic characteristics. A second-order consistency controller is used to coordinate the movement of each follower UUV toward the desired formation; The radar perception module is used to perceive surrounding obstacle information in real time and determine the width of the feasible path ahead of the current formation's direction of movement. The dynamic scaling factor calculation module is used to calculate the dynamic scaling factor based on the feasible path width, the current formation width, the safety buffer margin, and the minimum physical width of the formation. The formation mode determination module is used to divide the environment into three modes based on the size of the dynamic scaling factor: a relaxed environment, a restricted environment, and an extremely narrow environment. The formation adjustment module is used to adjust the position information matrix of each follower UUV in the horizontal direction according to the dynamic scaling factor in a relaxed or restricted environment, so as to scale the formation width. The linear formation switching module is used to adjust the formation to a linear formation in extremely confined spaces. The feedback control module is used to feed back the adjusted formation information to the dynamics model module and the second-order consistency controller to achieve closed-loop control and continuous obstacle avoidance.

[0013] The multi-UUV formation scaling control method and system based on dynamic scaling factors in this invention classifies obstacles into three modes: relaxed environment, restricted environment, and extremely narrow environment. In relaxed and restricted environments, the formation is scaled using a scaling factor. In extremely narrow environments, a strategy of adjusting to a straight-line formation is employed to enable the formation to avoid obstacles. This invention allows for safe and rapid passage through narrow passages and obstacle clusters. It adaptively obtains the scaling factor based on the constraints of marine obstacles, uses this factor to scale the original formation, and selects a more efficient and safer formation to overcome obstacle constraints, ensuring stable and safe passage for formation members.

[0014] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0015] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart of a multi-UUV formation scaling control method based on a dynamic scaling factor according to an embodiment of the present invention; Figure 2 This is a flowchart of another multi-UUV formation scaling control method based on dynamic scaling factor according to an embodiment of the present invention; Figure 3 This is a diagram showing the formation changes of the formation in a group of obstacles according to an embodiment of the present invention; Figure 4 This is a formation error curve diagram according to an embodiment of the present invention; Figure 5 This is a speed curve diagram of formation members according to an embodiment of the present invention; Figure 6 This is a structural diagram of a multi-UUV formation scaling control system based on a dynamic scaling factor according to an embodiment of the present invention. Detailed Implementation

[0016] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0017] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0018] The following describes, with reference to the accompanying drawings, a multi-UUV formation scaling control method and system based on a dynamic scaling factor, according to embodiments of the present invention.

[0019] Figure 1 This is a flowchart of a multi-UUV formation scaling control method based on a dynamic scaling factor according to an embodiment of the present invention, such as... Figure 1 As shown, it includes: S1, initialize the position, speed and heading angle of multiple UUV formation members, and set the relative positional relationship and speed limit between a virtual navigator and multiple followers; S2, in response to the motion state of the UUV formation, the following UUVs calculate their velocity and angular velocity according to the dynamic model, and move towards the desired formation based on the second-order consensus algorithm; S3, when there is an obstacle in front of the UUV formation's direction of movement, the obstacle information is obtained through the radar sensing module, and the width of the current feasible path is determined based on the sensing data; S4. Calculate the dynamic scaling factor based on the ratio of the feasible path width to the current formation width, combined with the safety buffer margin and the minimum physical width of the formation. S5. Based on the size of the dynamic scaling factor, the environment is divided into three modes: relaxed environment, restricted environment, and extremely narrow environment. S6. If the environment is relaxed or restricted, the formation width is scaled by the dynamic scaling factor to adjust the position information matrix of each follower UUV in the horizontal direction in order to maintain the integrity of the formation structure. S7. In extremely narrow environments, adjust the formation to a straight line to ensure that the formation can pass through narrow passages. S8 feeds back the adjusted formation to the dynamics model module and the second-order consistency controller, continuing the formation control and obstacle avoidance process to form a closed-loop control.

[0020] Specifically, the multi-UUV formation scaling control method based on dynamic scaling factor of the present invention includes the following steps, such as... Figure 2 As shown: Step 1: Randomly initialize the position, speed, heading angle, and other information of the members in the UUV formation on the map. The formation includes one virtual navigator and four followers. Initialize the position information between the UUV followers and the virtual navigator, and initialize the speed limits of the followers in the UUV formation. (1) In the formula: The speed of the follower UUV at the current moment. This is the proportionality coefficient. Minimum speed for virtual navigator UUVs For the maximum speed of the virtual navigator UUV, The minimum speed of the follower, Set the maximum speed of the follower, and then proceed to step 2; Step 2: The follower UUVs obtain information such as velocity and angular velocity based on the dynamic model. Each follower UUV begins to move towards the desired formation. Second-order consistency controls the formation. Step 3 is then executed. Step 3: During the movement of the UUV convoy, the UUVs use their own radar to perceive surrounding obstacle information and obtain feasible paths ahead of the current convoy's direction of movement. If a feasible path is located in the middle of an obstacle group, it is necessary to consider whether to change the UUV convoy formation and calculate the dynamic scaling factor. Determine the formation width for traversing feasible paths ahead: (2) In the formula: It is the feasible path width, It is the current formation width, It is a safety buffer margin. It is the minimum physical width of the formation, determined by the scaling factor. For the size, the formation change is divided into three modes: loose environment, restricted environment, and extremely narrow environment. When the formation change is to a loose environment or a restricted environment, proceed to step 4; otherwise, proceed to step 5. Step 4: In both relaxed and restricted environments, the formation does not need to be broken; the distance between members will be determined according to... To shorten, specifically: (3) In the formula: , The adjusted , The position information matrix of direction, , , respectively, before adjustment , Obtain the position information matrix of the direction and proceed to step 2; Step 5: In extremely narrow environments, the formation cannot maintain its original shape, and scaling the formation will not allow it to pass through narrow passages. Therefore, the formation will be changed to a straight line, and then proceed to Step 2.

[0021] Furthermore, the method of the present invention was simulated using Matlab / Simulink software. Figure 3 The process of scaling up and down the formation of UUVs in a cross-shaped convoy through narrow ocean channels. At that moment, the UUVs maintained their initial cross-shaped formation as they moved towards the target point. The UUVs at that instant did not detect any width difference between the passageway ahead and the actual UUV formation, and thus maintained their original formation as they moved forward. At that time, the UUV formation reached a narrow passage area. Because the formation sensors detected that the actual width of the ocean passage was less than the actual width of the formation, the narrow passage... The formation width of UUV formations The scaling factor range is In this narrow passage area, the original formation cannot pass. The virtual navigation UUV, by combining a scaling factor to shrink the formation, achieves a more efficient way to pass through the narrow passage. However, the method described in patent CN202310946057X, "An Adaptive Method for Multi-UUV Formation Switching and Obstacle Avoidance," cannot adaptively obtain the scaling factor from environmental constraints in such environments. It can only mechanically set the scaling factor and scale the formation, lacking adaptive capability. The formation encountered an extremely narrow environment, and abandoned its original formation, changing to a single line to successfully pass through. Figure 4 As can be seen, the formation changed at 63s, 95s, and 145s, and the error curve showed significant oscillations. However, the UUV formation completed the transition from the original formation to the new formation within 20 seconds with zero error, achieving rapid formation scaling. Figure 5 It can be seen that the speed changes of each UUV after the formation change are all within a reasonable range, and there are no problems such as speed loss.

[0022] The present invention has the following beneficial effects: 1. This invention affects formation movement in narrow passages and confined environments, effectively improving problems such as member disarray during formation scaling and ensuring safe passage of the formation; 2. This invention categorizes obstacles into loose environments, restricted environments, and extremely narrow environments. When encountering loose or restricted environments, the formation is scaled using a scaling factor. When encountering extremely narrow environments, the formation is adjusted to a straight line, enabling the UUV formation to successfully avoid obstacles and enhancing the adaptability of the formation obstacle avoidance. 3. Compared with the existing patent CN202310946057X "An Adaptive Method for Multi-UUV Formation Switching and Obstacle Avoidance", this patent cannot adaptively obtain a scaling factor through environmental constraints when the original formation cannot pass through narrow passage areas. It can only mechanically set the scaling factor to scale the formation and does not have adaptive capability. In contrast, the virtual navigation UUV of this invention reduces the formation by combining the scaling factor, and achieves a more efficient way to pass through narrow passages.

[0023] According to an embodiment of the present invention, a multi-UUV formation scaling control method based on a dynamic scaling factor first initializes the position and velocity information of each UUV in a two-dimensional environment, imposes velocity constraints on the following UUVs, and then combines the UUV dynamics model with second-order consistency to control the formation during formation operation. Simultaneously, a formation scaling factor is introduced to scale the formation. This invention effectively solves the problem of formations being unable to adapt to changes in narrow passages.

[0024] To achieve the above embodiments, such as Figure 6 As shown, this embodiment also provides a multi-UUV formation scaling control system 10 based on a dynamic scaling factor, including: Initialization module 100 is used to initialize the position, speed and heading angle of multiple UUV formation members, and set the relative positional relationship and speed limit between a virtual navigator and multiple followers; The dynamic model module 200 is used to calculate the velocity and angular velocity of the UUV based on its dynamic characteristics. A second-order consistency controller 300 is used to coordinate the movement of each follower UUV toward the desired formation; The radar perception module 400 is used to perceive surrounding obstacle information in real time and determine the width of the feasible path ahead of the current formation movement direction; The dynamic scaling factor calculation module 500 is used to calculate the dynamic scaling factor based on the feasible path width, the current formation width, the safety buffer margin, and the minimum physical width of the formation. The formation mode determination module 600 is used to divide the environment into three modes—relaxed environment, restricted environment, and extremely narrow environment—based on the size of the dynamic scaling factor. The formation adjustment module 700 is used to adjust the position information matrix of each follower UUV in the horizontal direction according to the dynamic scaling factor in a relaxed or restricted environment, so as to scale the formation width. The linear formation switching module 800 is used to adjust the formation to a linear formation in extremely narrow environments; The feedback control module 900 is used to feed back the adjusted formation information to the dynamic model module and the second-order consistency controller to achieve closed-loop control and continuous obstacle avoidance.

[0025] Furthermore, the initialization module 100 is also used to set the speed limit of the follower UUV, which is set according to the scaling factor, the minimum and maximum speed of the virtual navigator UUV, and the minimum and maximum speed of the follower UUV.

[0026] Furthermore, the initialization module 100 is also used to randomly initialize the positions, speeds, and heading angles of the members in the UUV formation on the map. The formation includes one virtual navigator and four followers. It initializes the positional information between the UUV followers and the virtual navigator, and initializes the speed limits of the followers in the UUV formation. (1) In the formula: The speed of the follower UUV at the current moment. This is the proportionality coefficient. Minimum speed for virtual navigator UUVs For the maximum speed of the virtual navigator UUV, The minimum speed of the follower, The maximum speed of the follower.

[0027] Furthermore, the dynamic scaling factor calculation module 500 is also used for: If the feasible path is located in the middle of the obstacle group, it is necessary to consider whether to change the UUV formation and calculate the dynamic scaling factor. Determine the formation width for traversing feasible paths ahead: (2) In the formula: It is the feasible path width, It is the current formation width, It is a safety buffer margin. It is the minimum physical width of the formation.

[0028] Furthermore, in both relaxed and restricted environments, the formation does not need to break the structure; the distance between members will be determined according to... Shorten: (3) In the formula: , The adjusted , The position information matrix of direction, , , respectively, before adjustment , A matrix of directional positional information.

[0029] The multi-UUV formation scaling control system based on a dynamic scaling factor according to an embodiment of the present invention first initializes the position and velocity information of each UUV in a two-dimensional environment, and imposes velocity constraints on the following UUVs. Then, the UUV dynamic model is combined with second-order consistency to control the formation during formation operation. Simultaneously, a formation scaling factor is introduced to scale the formation. This invention effectively solves the problem that formations cannot adapt to changes in narrow passages.

[0030] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0031] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

Claims

1. A multi-UUV formation scaling control method based on dynamic scaling factor, characterized in that, Includes the following steps: Initialize the positions, speeds, and heading angles of multiple UUV formation members, and set the relative positions and speed limits between a virtual navigator and multiple followers; In response to the motion state of the UUV formation, the following UUVs calculate their velocity and angular velocity according to the dynamic model and move towards the desired formation based on the second-order consensus algorithm; When there is an obstacle in front of the UUV formation's direction of movement, the obstacle information is obtained through the radar sensing module, and the width of the current feasible path is determined based on the sensing data; The dynamic scaling factor is calculated based on the ratio of the feasible path width to the current formation width, combined with the safety buffer margin and the minimum physical width of the formation. Based on the magnitude of the dynamic scaling factor, the environment is divided into three modes: relaxed environment, restricted environment, and extremely narrow environment. If the environment is relaxed or restricted, the formation width is scaled by the dynamic scaling factor to adjust the position information matrix of each follower UUV in the lateral direction in order to maintain the integrity of the formation structure. If in an extremely narrow environment, adjust the formation to a straight line to ensure that the formation can pass through narrow passages; The adjusted formation is fed back to the dynamics model module and the second-order consistency controller to continue the formation control and obstacle avoidance process, forming a closed-loop control.

2. The method as described in claim 1, characterized in that, The initialization also includes setting the speed limit of the follower UUV, which is set according to the scaling factor, the minimum and maximum speed of the virtual navigator UUV, and the minimum and maximum speed of the follower UUV.

3. The method as described in claim 1, characterized in that, Initialize the positions, speeds, and heading angles of multiple UUV convoy members, and set the relative positions and speed limits between a virtual navigator and multiple followers: （1） In the formula: The speed of the follower UUV at the current moment. This is the proportionality coefficient. Minimum speed for virtual navigator UUVs For the maximum speed of the virtual navigator UUV, The minimum speed of the follower, The maximum speed of the follower.

4. The method as described in claim 1, characterized in that, Based on the ratio of the feasible path width to the current formation width, combined with the safety buffer margin and the minimum physical width of the formation, the dynamic scaling factor is calculated, including: If the feasible path is located in the middle of the obstacle group, it is necessary to consider whether to change the UUV formation and calculate the dynamic scaling factor. Determine the formation width for traversing feasible paths ahead: （2） In the formula: It is the feasible path width, It is the current formation width, It is a safety buffer margin. It is the minimum physical width of the formation.

5. The method as described in claim 1, characterized in that, In both relaxed and restricted environments, the formation does not need to be broken; the distance between members will be determined according to... Shorten: （3） In the formula: , The adjusted , The position information matrix of direction, , , respectively, before adjustment , A matrix of directional positional information.

6. A multi-UUV formation scaling control system based on a dynamic scaling factor, characterized in that, Includes the following steps: The initialization module is used to initialize the position, speed, and heading angle of multiple UUV formation members, and to set the relative positional relationship and speed limits between a virtual navigator and multiple followers; The dynamics model module is used to calculate the velocity and angular velocity of a UUV based on its dynamic characteristics. A second-order consistency controller is used to coordinate the movement of each follower UUV toward the desired formation; The radar perception module is used to perceive surrounding obstacle information in real time and determine the width of the feasible path ahead of the current formation's direction of movement. The dynamic scaling factor calculation module is used to calculate the dynamic scaling factor based on the feasible path width, the current formation width, the safety buffer margin, and the minimum physical width of the formation. The formation mode determination module is used to divide the environment into three modes based on the size of the dynamic scaling factor: a relaxed environment, a restricted environment, and an extremely narrow environment. The formation adjustment module is used to adjust the position information matrix of each follower UUV in the horizontal direction according to the dynamic scaling factor in a relaxed or restricted environment, so as to scale the formation width. The linear formation switching module is used to adjust the formation to a linear formation in extremely confined spaces. The feedback control module is used to feed back the adjusted formation information to the dynamics model module and the second-order consistency controller to achieve closed-loop control and continuous obstacle avoidance.

7. The system as described in claim 6, characterized in that, The initialization module is also used to set the speed limit of the follower UUV, which is set according to the scaling factor, the minimum and maximum speed of the virtual navigator UUV, and the minimum and maximum speed of the follower UUV.

8. The system as described in claim 6, characterized in that, The initialization module is also used to randomly initialize the positions, speeds, and heading angles of members in a UUV formation on a map. The formation contains one virtual navigator and four followers. It initializes the positional information between the UUV followers and the virtual navigator, and initializes the speed limits of the followers in the UUV formation. （1） In the formula: The speed of the follower UUV at the current moment. This is the proportionality coefficient. Minimum speed for virtual navigator UUVs For the maximum speed of the virtual navigator UUV, The minimum speed of the follower, The maximum speed of the follower.

9. The system as described in claim 6, characterized in that, The dynamic scaling factor calculation module is also used for: If the feasible path is located in the middle of the obstacle group, it is necessary to consider whether to change the UUV formation and calculate the dynamic scaling factor. Determine the formation width for traversing feasible paths ahead: （2） In the formula: It is the feasible path width, It is the current formation width, It is a safety buffer margin. It is the minimum physical width of the formation.

10. The system as described in claim 6, characterized in that, In both relaxed and restricted environments, the formation does not need to be broken; the distance between members will be determined according to... Shorten: （3） In the formula: , The adjusted , The position information matrix of direction, , , respectively, before adjustment , A matrix of directional positional information.

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