A multi-mobile robot motion planning method for non-cooperative target encirclement

Abstract

The application relates to a multi-mobile robot motion planning method for non-cooperative target trapping, which proposes a multi-mobile robot cooperative motion framework in a complex environment. Firstly, the mobile robot approaches a randomly moving target in a pursuit process. Secondly, a surrounding strategy is applied in a surrounding process, so that the mobile robot team surrounds the non-cooperative target and follows the motion. Finally, a guidance strategy is adopted in a guidance process, so that the mobile robot team adaptively encircles the moving target, controls the motion direction, and guides the non-cooperative target to a destination. The application provides a cooperative motion planning framework combined with a path planning method, can be combined with any path planning algorithm, has advantages in the non-cooperative target trapping problem, and can improve the flexibility and motion efficiency of the cooperative formation operation of the robot in a complex limited environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of multi-mobile robot cooperative motion planning, and particularly relates to a multi-mobile robot motion planning method for non-cooperative target encirclement. BACKGROUND

[0002] In the past two decades, multi-mobile robot cooperation has been rapidly developed as an important research direction, and the driving force behind it lies in the fact that multi-mobile robot systems have shown significant advantages over single robots in various application scenarios, such as cooperative terrain mapping, cooperative material transportation, and joint detection tasks, etc.

[0003] Although there are many sophisticated theories and methods for motion planning and behavior strategy of single robot, these planning methods for single robot cannot be directly applied to multi-robot cooperation. Motion planning in multi-robot cooperation is particularly concerned, because it not only requires precise planning of the trajectory of each robot, but also fully considers the interaction and collision avoidance between robots, while ensuring that the whole robot cluster can maintain stable formation structure and efficient cooperation behavior in the process of cooperation to successfully complete the preset task. Therefore, constructing a comprehensive planning framework suitable for multi-robot cooperation environment has become an important task in the field of robotics. With the deepening of research, researchers have developed a variety of planning frameworks to meet the diversified needs of multi-robot motion planning. Specifically, Vukosavljev and his colleagues constructed a modular motion planning framework for multi-robot systems, which ingeniously integrated low-level motion basic elements and high-level control strategies, thus realizing flexible modular customization. At the same time, Motes and other scholars innovatively combined integrated task planning and motion planning, and introduced an interactive planning framework for heterogeneous robot team cooperation, which effectively promoted the task allocation and coordinated execution within the team. Li and other researchers started from the online optimization perspective, treated the formation control problem as an optimization problem, and successfully solved the optimal path layout in the process of formation and target tracking by using advanced neural dynamics optimization technology. In addition, Pierpaoli and others designed a distributed motion planning framework based on finite-time convergence control theory, which ensured that a group of robots could achieve the predetermined formation configuration within a limited time while meeting the specific requirements of various tasks. However, although the above-mentioned planning frameworks have shown significant results in solving cooperative tasks, the current research has not paid sufficient attention to the non-cooperative target situation. Non-cooperative target problems play a core role in many multi-robot cooperation applications, such as guiding the migration of wild animal groups, effectively driving away birds and drones in airport areas, orderly evacuation of chaotic crowds in emergency situations, and even using micro robots to regulate microbial behavior. Such tasks usually require multi-robot systems to work intelligently to effectively surround and manipulate non-cooperative targets.

[0004] In recent years, the planning strategies for multi-robot teams to hunt non-cooperative targets have attracted extensive attention from many researchers. For example, Pierson et al. constructed a global "area minimization" strategy based on Voronoi diagram, which achieved effective pursuit and siege of non-cooperative targets by a group of robots. Similarly, Wang et al. also adopted the area minimization strategy to cooperatively chase a single non-cooperative target with multiple mobile robots. Mahadevan et al. optimized the multi-robot coordination related scene modeling by means of sampling-based motion planning technology, thereby more effectively guiding the robots to pursue and capture non-cooperative targets. On the other hand, Li et al. proposed a path planning strategy based on an improved artificial potential field method to solve the local minimum problem, which helped quadcopters successfully gather a group of non-cooperative robots. Garcia et al. extended the classic differential game theory and successfully solved the problem of N robots pursuing multiple non-cooperative targets in various scenarios. Deng et al. conducted in-depth research on a variant of the hunting problem, namely the attack-defense confrontation game. They designed a distributed pursuit and defense strategy to ensure that the defensive robots can effectively block the aggressive non-cooperative targets outside the protection zone.

[0005] The existing planning strategies have made some achievements in dealing with the pursuit and siege of non-cooperative targets, but they lack attention to other complex challenges existing in the group of non-cooperative targets, such as how to effectively guide non-cooperative individuals to reach the preset destination, or how to flexibly adjust the team formation to adapt to and pass through the limited environment. Moreover, these strategies are often designed based on specific application scenarios, and lack a universal planning framework to implement diversified hunting tasks in different application scenarios. SUMMARY

[0006] The purpose of the present application is to provide a multi-mobile robot motion planning method for non-cooperative target hunting, which can be combined with any path planning algorithm as a general cooperative motion planning framework to achieve rapid completion of non-cooperative target hunting in complex environments.

[0007] To achieve the above purpose, the technical scheme adopted by the present application is as follows: a multi-mobile robot motion planning method for non-cooperative target hunting, comprising the following steps:

[0008] Step S1, pursuit reference path acquisition: using a global path planner, respectively acquiring the pursuit reference path of each hunter h i to the target e

[0009] Step S2, hunter approaches target: each hunter h i approaches the target e according to the pursuit reference path respectively;

[0010] Step S3, Surrounding Phase Transfer: Determine the status of each pursuer h. i Whether it enters the main orbit around target e or another secondary orbit of the pursuers in the circling phase, then h i Enter the encirclement phase and execute step S4; otherwise, return to step S1 and continue execution.

[0011] Step S4: Perform circling motion: The pursuer follows the target e while circling it according to the circling strategy;

[0012] Step S5, Guiding Phase Transfer: Determine all pursuers {h i} Whether all have entered the main orbit around target e or the secondary orbit of other pursuers in the circling phase, if yes, all pursuers enter the circling phase and execute step S6; otherwise, return to step S4 and continue execution.

[0013] Step S6, Obtaining Reference Path: Using the global path planner, obtain the path from target e to destination in real time. The guiding reference path σ g ;

[0014] Step S7: Determine whether the current direction of target e deviates from the expected direction. If yes, proceed to step S8; otherwise, proceed to step S9.

[0015] Step S8: The pursuers form an encirclement formation to block the current movement of target e, correct its direction of movement, and then execute step S10.

[0016] Step S9: The pursuers form a guiding formation, maintain the target e's current movement, and guide it towards the destination. Move, and then proceed to step S10;

[0017] Step S10: Determine whether the current formation interferes with the obstacle. If so, the hunters will change to a transitional formation and then proceed to step S11. Otherwise, proceed directly to step S11.

[0018] Step S11: Determine whether the planning termination condition is met. If yes, terminate the planning; otherwise, return to step S6 to continue execution.

[0019] Furthermore, the specific implementation method of step S3 is as follows: determine the pursuer h i Distance from target e ||eh i ||Is this the set main orbit radius r? surr Therefore, it is believed that h i Entering the main orbit; for those already in the main orbit... i To determine the other pursuers h k with h i The distance between them ||hk -h i || whether the set sub-orbit radius r inter is considered h k into the sub-orbit; when the distance between other hunters and any hunter that has entered the main orbit or the sub-orbit is r inter , it is also considered that the hunter enters the sub-orbit.

[0020] Further, the specific implementation method of the step S4 is: if the robot closest to the hunter h is the target e, the main orbit is executed, that is, the distance to e is kept as r surr and clockwise or counterclockwise rotation is performed around it to enter the target position h next , h next is determined by the following formula;

[0021]

[0022] wherein, and are the positions of the hunter h and the target e; denotes the selected direction of the hunting, clockwise or counterclockwise, and the function f rot (·) is defined as: f θ (·) function obtains the polar angle of the vector; if the robot closest to the hunter h is another hunter h', the target position in equation (1) is replaced by the position of the hunter h', and the main orbit radius r surr is replaced by the sub-orbit radius r inter , and the target position h next at the next moment is solved; when the closest distance between the target position h next and the closest environmental obstacle P ob is less than the safety distance r ob , the target position is updated to the safety distance.

[0023] Further, the specific implementation method of the step S7 is: the obtained guide reference path σ g is discretized, the discrete point closest to the target e is p exp , and the desired direction is set as If the included angle between the current direction of the target e and the desired direction is less than the set deviation threshold θ force , that is, , it is considered that the target e deviates from the desired direction.

[0024] Further, the specific implementation method of the step S8 is: according to the current direction of the target e The hunter queue is divided into left and right queues, denoted as Q L , Q R , respectively L The first hunter in Q R and Q esafe is closer to the target e from the left and right sides, respectively, and the distance between the first hunter and the target e is less than the minimum passing distance r of the target e, that is The target e is prevented from continuing to move in the deviated direction.

[0025] Further, the specific implementation method of the step S9 is as follows: according to the expected direction The hunter queue is divided into left and right queues, denoted as Q L , Q R , respectively L The first hunter in Q R and Q force is closer to the target e from the left and right sides, respectively, and the included angle between the first hunter and the expected direction is less than the deviation threshold θ , that is The deviation between the target e and the expected direction is continuously converged.

[0026] Further, the specific implementation method of the step S10 is as follows: when the hunter h in the team interferes with the obstacle in the environment, the hunter h is maintained on the main track and away from the obstacle, and the distance between the hunter h and the nearest obstacle is greater than r ob If the distance between the hunter h and other hunters is less than the minimum interference distance r inter , the hunter h deviates from the main track and enters the secondary track, and is marked as a wandering hunter; meanwhile, for the wandering hunter h that has moved in the secondary track, if the target position of the hunter h is located on the main track, the wandering hunter mark is removed.

[0027] Further, the specific implementation method of the step S11 is as follows: whether the target e enters the destination is determined, which is denoted as:

[0028]

[0029] Wherein, L l , L w are the center coordinates, length and width of the target area, respectively; when the target e enters the target area, the entering time t arr is recorded; if the target e is always located in the destination within the time period t∈[t arr , t arr +t stop ], the planning task is considered to be completed, wherein t stopis the time required to capture the target e; if the trapping task completion condition is not met, the algorithm continues to run until the maximum limit time T is exceeded max .

[0030] Compared with the prior art, the present application has the following beneficial effects:

[0031] (1) The present application proposes a multi-mobile robot motion planning method for non-cooperative target trapping, which is a cooperative motion planning framework that can be combined with any path planning algorithm to improve the performance of trapping non-cooperative targets in complex environments, has strong applicability and completeness.

[0032] (2) The present application proposes a surrounding strategy and a guiding strategy. The surrounding strategy enables the robot to flexibly adjust its position while maintaining effective tracking of the target to adapt to the target's movement. The guiding strategy improves the control of the robot team over the target by predicting and guiding the target's movement direction, thereby achieving rapid approach, surrounding follow-up and control guidance in the case of unpredictable target movement.

[0033] (3) For most multi-mobile robot cooperative motion planning algorithms, the formation is relatively fixed, lacking adaptability to changes in the scene, making it difficult to efficiently trap non-cooperative targets in narrow working environments. The present application combines trapping queues and free queues to achieve flexible environmental adaptive formation changes, ensuring the completeness of the algorithm while achieving efficient computation. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 is the method implementation flowchart of the present application embodiment;

[0035] Figure 2 is the surrounding strategy principle diagram in the present application embodiment;

[0036] Figure 3 is the guiding strategy principle diagram in the present application embodiment;

[0037] Figure 4 is the over-queue diagram in the present application embodiment;

[0038] Figure 5 is the simulation result diagram of simulation scene one in the present application embodiment;

[0039] Figure 6 is the simulation result diagram of simulation scene two in the present application embodiment;

[0040] Figure 7 is the simulation result diagram of simulation scene three in the present application embodiment;

[0041] Figure 8 is the experimental result diagram of experimental scene one in the present application embodiment;

[0042] Figure 9 is the experimental result figure of the second experimental scenario in the embodiment of the present application. DETAILED DESCRIPTION

[0043] The present application will be further described below in conjunction with the accompanying drawings and embodiments.

[0044] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the present application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0045] It should be noted that the terms used herein are only intended to describe specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and it should also be understood that when the terms "comprise" and / or "include" are used in the specification, they indicate the presence of the features, steps, operations, devices, components and / or combinations thereof.

[0046] As shown in Figure 1 , the present embodiment provides a multi-mobile robot motion planning method for non-cooperative target trapping, comprising the following steps:

[0047] Step S1, chase reference path acquisition: using a global path planner, respectively acquiring the chase reference path of each trapper h i to the target e

[0048] Step S2, trapper approaches target: each trapper h i approaches the target e according to the chase reference path respectively.

[0049] Step S3, transition to the surrounding stage: respectively judging whether each trapper h i enters the main track around the target e or the secondary track of other trappers in the surrounding stage, if yes, h i enters the surrounding stage and executes step S4, otherwise returns to step S1 for continuous execution.

[0050] Step S4, execute surrounding motion: the trapper follows the motion of the target e while surrounding it according to the surrounding strategy.

[0051] Step S5, transition to the guiding stage: judging whether all trappers h i} Whether all have entered the main orbit around target e or the secondary orbit of other pursuers in the circling phase (the judgment process for each pursuer is the same as the judgment process in step S3), if yes, all pursuers enter the circling phase and execute step S6, otherwise return to step S4 to continue execution.

[0052] Step S6, Obtaining Reference Path: Using the global path planner, obtain the path from target e to destination in real time. The guiding reference path σ g .

[0053] Step S7: Determine whether the current direction of target e deviates from the expected direction. If yes, proceed to step S8; otherwise, proceed to step S9.

[0054] Step S8: The pursuers form an encirclement formation to block the current movement of target e, correct its direction of movement, and then execute step S10.

[0055] Step S9: The pursuers form a guiding formation, maintain the target e's current movement, and guide it towards the destination. The movement is then performed, followed by step S10.

[0056] Step S10: Determine whether the current formation interferes with the obstacle. If so, the hunters will transform into a transitional formation and then proceed to step S11. Otherwise, proceed directly to step S11.

[0057] Step S11: Determine whether the planning termination condition is met. If yes, terminate the planning; otherwise, return to step S6 to continue execution.

[0058] The specific implementation method of step S3 is as follows: determine the hunter h i Distance from target e ||eh i ||Is this the set main orbit radius r? surr Therefore, it is believed that h i Entering the main track; for those already on the main track... i To determine the other pursuers h k with h i The distance between them ||h k -h i ||Is this setting the secondary orbit radius r? inter Therefore, it is believed that h k Enter the secondary orbit; when the distance between other pursuers and any pursuer already in the main or secondary orbit is r. inter If so, it is also considered that the pursuer has entered the secondary orbit.

[0059] The specific implementation method of step S4 is as follows: if the robot closest to the hunter h is the target e, then perform main orbit orbiting, that is, maintain a distance of r from e. surrAnd rotate around it clockwise or counterclockwise, such as Figure 2 As shown. Enter target position h. next h next It is determined by the following formula.

[0060]

[0061] in, and The positions of the pursuer h and the target e; The function f indicates the direction of the encirclement, which can be clockwise or counterclockwise. rot (·) is defined as: f θ The (·) function obtains the polar coordinate angle of the vector; if the robot closest to the hunter h is another hunter h′, then the target position in equation (1) is replaced with the position of the hunter h′, and the main orbit radius r is changed. surr Replace with suborbital radius r inter Solve for the target position h at the next moment. next ,like Figure 2 As shown. When the target position h is obtained. next Nearest environmental obstacle P ob The closest distance is less than the safe distance r ob If so, update its target location to a safe distance, such as Figure 2 As shown.

[0062] The specific implementation method of step S7 is as follows: select the obtained guide reference path σ g Discretize the data, and the discrete point closest to the target e is p. exp The desired direction is set to If the current direction of target e The angle between the desired direction and the set deviation threshold θ is less than the set deviation threshold θ. force ,Right now Then it is considered that target e deviates from the expected direction.

[0063] The specific implementation method of step S8 is as follows: based on the current direction of target e Divide the encirclement queue into left and right queues, denoted as Q respectively. L Q R Approaching the target e from the left and right sides respectively, let Q... L and Q R The distance between the first pursuers in the process is less than the minimum travel distance r of target e. esafe ,Right now To prevent target e from continuing to move in the deviated direction, such as... Figure 3 As shown.

[0064] The specific implementation method of step S9 is as follows: according to the desired direction Divide the encirclement queue into left and right queues, denoted as Q respectively. L Q R Approaching the target e from the left and right sides respectively, let Q... L and Q R The first pursuer and the expected direction The included angle between them is less than the deviation threshold θ force ,Right now Make target e align with desired direction The deviation between them continues to converge, such as Figure 3 As shown.

[0065] The specific implementation method of step S10 is as follows: when the hunter h in the team interferes with the obstacle in the environment, the hunter h maintains its main track and moves away from the obstacle, ensuring that the distance to the nearest obstacle is greater than r. ob If the distance between the pursuer h and other pursuers is less than the minimum interference distance r. inter If the pursuer h leaves the main track and enters the secondary track, it will be marked as a wandering pursuer. Figure 4 As shown. Simultaneously, for a wandering hunter h that has already moved onto the secondary orbit, if its target position is located on the main orbit, the wandering hunter marker is removed.

[0066] The specific implementation method of step S11 is as follows: determine whether target e has entered the destination. Represented as:

[0067]

[0068] in, L l L w These represent the center coordinates, length, and width of the target area, respectively; when target e enters the target area, the entry time t is recorded. arr If in the time interval t∈[t arr , t arr +t stop If target e remains at the destination throughout the entire process, the planning task is considered complete, where t... stop This is the time required to capture target e; if the conditions for completing the capture mission are not met, the algorithm continues to run until the maximum time limit T is exceeded. max .

[0069] The pseudocode for this method is as follows:

[0070]

[0071]

[0072]

[0073] The following detailed experiments further illustrate this method, primarily using simulation and real-world experiments to verify its effectiveness. The specific experimental setup is as follows:

[0074] Simulation experiment:

[0075] The simulation experiments were conducted in MATLAB R2020b software.

[0076] (1) Simulation Scenario 1

[0077] Simulation scenarios such as Figure 5 As shown in Figure (a), the map size is X = Y = 600m, all obstacles are static, the starting point is (150, 70), and the target point is (560, 420). The simulation results are as follows. Figure 5 As shown in (b), point S represents the starting point, G represents the target point, and the dark line represents the target's trajectory during the encirclement process.

[0078] (2) Simulation Scenario 2

[0079] Simulation scenarios such as Figure 6 As shown in Figure (a), the map size is X = Y = 500m. All obstacles in the map are dynamic obstacles that continuously reciprocate in the horizontal direction. The starting point is (220, 230), and the target point is (400, 460). The simulation results are as follows. Figure 6 As shown in (b), point S represents the starting point, G represents the target point, and the dark line represents the target's trajectory during the encirclement process.

[0080] (3) Simulation Scenario 3

[0081] Simulation scenarios such as Figure 7 As shown in Figure (a), the map size is X = 600m, Y = 700m, and all obstacles are static. The starting point is (150, 70), and the target point is (560, 420). The simulation results are as follows. Figure 7 As shown in (b), point S represents the starting point, G represents the target point, light color represents the explored path, and dark line represents the target's movement trajectory during the encirclement process.

[0082] Real experiment:

[0083] The application can be directly used in trajectory planning of path planning of multiple mobile robots, a new motion planning algorithm is written in MATLAB, and the proposed multiple robot cooperative motion planning framework is embedded to execute.

[0084] (1) Experiment scene one

[0085] The scene map size is X=Y=300cm, and all obstacles are known static obstacles, as shown in (a) of Figure 8 The robot starting position is (70, 118), and the target position is (245, 142). As shown in (b) and (c) of Figure 8 , it is a static real experiment process. Figure 8 (d) is the motion trajectory of the pursuer and the target.

[0086] (2) Experiment scene two

[0087] The scene map size is X=Y=300cm, and all obstacles in the map are known dynamic obstacles, as shown in (a) of Figure 9 The robot starting position is (70, 118), and the target position is (245, 142). As shown in (b) and (c) of Figure 9 , it is a dynamic real experiment process. Figure 9 (d) is the motion trajectory of the pursuer and the target.

[0088] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer usable program code.

[0089] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flowcharts and / or blocks Figure 1 means for functionally implementing the steps listed in the flowchart block or blocks.

[0090] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart block or blocks. Figure 1 one or more flowcharts and / or blocks Figure 1 means for functionally implementing the steps listed in the flowchart block or blocks.

[0091] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flowcharts and / or blocks Figure 1 means for functionally implementing the steps listed in the flowchart block or blocks.

[0092] The above description is only preferred embodiments of the present application, and is not intended to limit the present application to other forms described above. Any person skilled in the art can make modifications or improvements to the above-mentioned disclosed technical content without departing from the technical scope of the present application. However, any simple modification, equivalent change and modification of the above-mentioned embodiments according to the technical essence of the present application still belongs to the protection scope of the present application.

Claims

1. A multi-mobile robot motion planning method for the encirclement of non-cooperative targets, characterized in that, Includes the following steps: Step S1, Pursuit Reference Path Acquisition: Using the global path planner, acquire the reference path h of each pursuer in real time. i Pursuit reference path to target e Step S2, the pursuers approach the target: each pursuer h i Based on the chasing reference path Approaching target e; Step S3, Surrounding Phase Transfer: Determine the status of each pursuer h. i Whether it enters the main orbit around target e or another secondary orbit of the pursuers in the circling phase, then h i Enter the encirclement phase and execute step S4; otherwise, return to step S1 and continue execution. Step S4: Perform circling motion: The pursuer follows the target e while circling it according to the circling strategy; Step S5, Guiding Phase Transfer: Determine all pursuers {h i } Whether all have entered the main orbit around target e or the secondary orbit of other pursuers in the circling phase, if yes, all pursuers enter the circling phase and execute step S6; otherwise, return to step S4 and continue execution. Step S6, Obtaining Reference Path: Using the global path planner, obtain the path from target e to destination in real time. The guiding reference path σ g ; Step S7: Determine whether the current direction of target e deviates from the expected direction. If yes, proceed to step S8; otherwise, proceed to step S9. Step S8: The pursuers form an encirclement formation to block the current movement of target e, correct its direction of movement, and then execute step S10. Step S9: The pursuers form a guiding formation, maintain the target e's current movement, and guide it towards the destination. Move, and then proceed to step S10; Step S10: Determine whether the current formation interferes with the obstacle. If so, the hunters will change to a transitional formation and then proceed to step S11. Otherwise, proceed directly to step S11. Step S11: Determine whether the planning termination condition is met. If yes, terminate the planning; otherwise, return to step S6 to continue execution.

2. The multi-mobile robot motion planning method for encircling non-cooperative targets according to claim 1, characterized in that, The specific implementation method of step S3 is as follows: determine the hunter h i Distance from target e ||eh i ||Is this the set main orbit radius r? surr Therefore, it is believed that h i Entering the main orbit; for those already in the main orbit... i To determine the other pursuers h k with h i The distance between them ||h k -h i ||Is this setting the secondary orbit radius r? inter Therefore, it is believed that h k Enter the secondary orbit; when the distance between other pursuers and any pursuer already in the main or secondary orbit is r. inter If so, it is also considered that the pursuer has entered the secondary orbit.

3. The multi-mobile robot motion planning method for encircling non-cooperative targets according to claim 1, characterized in that, The specific implementation method of step S4 is as follows: if the robot closest to the hunter h is the target e, then perform main orbit orbiting, that is, maintain a distance of r from e. surr And rotate around it clockwise or counterclockwise to reach the target position h. next h next Determined by the following formula; in, and The positions of the pursuer h and the target e; The function f indicates the direction of the encirclement, which can be clockwise or counterclockwise. rot (·) is defined as: f θ The (·) function obtains the polar coordinate angle of the vector; if the robot closest to the hunter h is another hunter h', then the target position in equation (1) is replaced with the position of the hunter h', and the main orbit radius r is changed. surr Replace with suborbital radius r inter Solve for the target position h at the next moment. next When the target position h is obtained next Nearest environmental obstacle P ob The closest distance is less than the safe distance r ob If so, then update its target location to a safe distance.

4. The multi-mobile robot motion planning method for encircling non-cooperative targets according to claim 1, characterized in that, The specific implementation method of step S7 is as follows: select the obtained guide reference path σ g Discretize the data, and the discrete point closest to the target e is p. exp The desired direction is set to If the current direction of target e The angle between the desired direction and the set deviation threshold θ is less than the set deviation threshold θ. force ,Right now Then it is considered that target e deviates from the expected direction.

5. A multi-mobile robot motion planning method for encircling non-cooperative targets according to claim 1, characterized in that, The specific implementation method of step S8 is as follows: based on the current direction of target e Divide the encirclement queue into left and right queues, denoted as Q respectively. L Q R Approaching the target e from the left and right sides respectively, let Q... L and Q R The distance between the first pursuers in the process is less than the minimum travel distance r of target e. esafe ,Right now Prevent target e from continuing to move in the deviated direction.

6. The multi-mobile robot motion planning method for encircling non-cooperative targets according to claim 1, characterized in that, The specific implementation method of step S9 is as follows: according to the desired direction Divide the encirclement queue into left and right queues, denoted as Q respectively. L Q R Approaching the target e from the left and right sides respectively, let Q... L and Q R The first pursuer and the expected direction The included angle between them is less than the deviation threshold θ force ,Right now Make target e align with desired direction The deviation between them continues to converge.

7. A multi-mobile robot motion planning method for encircling non-cooperative targets according to claim 1, characterized in that, The specific implementation method of step S10 is as follows: when the hunter h in the team interferes with the obstacle in the environment, the hunter h maintains its main track and moves away from the obstacle, ensuring that the distance to the nearest obstacle is greater than r. ob If the distance between the pursuer h and other pursuers is less than the minimum interference distance r inter If the target h leaves the main track and enters the secondary track, it will be marked as a wandering target h. At the same time, for a wandering target h that has already moved to the secondary track, if its target position is on the main track, the wandering target h mark will be removed.

8. A multi-mobile robot motion planning method for encircling non-cooperative targets according to claim 1, characterized in that, The specific implementation method of step S11 is as follows: determine whether target e has entered the destination. Represented as: in, L l L w These represent the center coordinates, length, and width of the target area, respectively; when target e enters the target area, the entry time t is recorded. arr If in the time interval t∈[t arr ,t arr +t stop If target e remains at the destination throughout the entire process, the planning task is considered complete, where t... stop This is the time required to capture target e; if the conditions for completing the capture mission are not met, the algorithm continues to run until the maximum time limit T is exceeded. max .

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