A method for cooperative hunting control of a UAV cluster based on recursive mental theory

Abstract

The present application relates to the field of swarm intelligence and unmanned aerial vehicle cooperative control technology, in particular to a kind of unmanned aerial vehicle cluster cooperative hunting control method based on recursive mind theory, comprising: constructing recursive mind model;Updating the first-order belief of unmanned aerial vehicle corresponding, second-order belief obtains the first-order target belief of unmanned aerial vehicle, second-order target belief;Construct target function;Determine optimal acceleration and control unmanned aerial vehicle to approach task target;When the preset decoy trigger condition is satisfied, in turn, execute weakening maneuver and accelerate to block.This application enables unmanned aerial vehicle to realize formation self-repair, cooperative trapping and communication load reduction through second-order recursive belief reasoning.

Description

Technical Field

[0001] This invention relates to the field of swarm intelligence and UAV collaborative control technology, specifically to a UAV swarm collaborative encirclement and control method based on recursive mind theory. Background Technology

[0002] Multi-UAV cooperative encirclement is a typical task scenario in the field of swarm intelligence, requiring multiple UAVs to cooperate in an unknown dynamic environment to search, track, and intercept maneuvering targets. However, due to the dynamic nature of the environment, the high maneuverability of the targets, and the complexity of communication conditions, how to achieve efficient and robust cooperative encirclement remains a challenge for current research.

[0003] Existing technologies are mainly divided into two categories. The first category is based on reactive rules, with typical examples including artificial potential field methods and leader-follower methods. Artificial potential field methods guide drones towards a target while maintaining distance by constructing virtual gravitational and repulsive fields, as in the "swarm and prey" model, where drones adjust their direction of movement in real time based on their distance from the target and neighboring drones. Leader-follower methods designate one or more drones as "leaders," with the remaining drones maintaining relative geometric positions to follow, forming a formation. These methods rely only on local perception information, have low computational overhead, and strong real-time performance, making them suitable for scenarios with limited onboard resources. However, their inherent drawbacks lie in the lack of a global perspective and foresight: artificial potential field methods are prone to getting stuck in local potential minima, causing drones to stagnate in front of obstacles or fail to form an effective encirclement; leader-follower methods are overly dependent on the leader drone, and once the leader drone is interfered with or the target suddenly changes speed, the entire formation is easily disrupted, and there is a significant lag in response to the target's maneuvers, making it difficult to dynamically adjust the encirclement. The second category is based on communication negotiation methods, with typical technologies including distributed auction algorithms and consensus algorithms. Distributed auctions dynamically allocate encirclement roles (such as interception points and blocking positions) to each drone through multiple rounds of bidding, while consensus algorithms enable all drones to reach a consensus on the formation configuration by exchanging information such as position and speed among neighbors. These methods can achieve task self-organization and precise formation control, performing excellently in tasks such as multi-drone collaboration and area coverage. However, their performance is highly dependent on the quality and bandwidth of the communication link: in scenarios with limited communication, large latency, or electronic interference, information exchange delays will lead to role allocation mismatch, formation convergence oscillations, or even collaboration failure; if communication is completely interrupted, the drones will lose their negotiation capabilities.

[0004] In summary, the common shortcomings of existing technologies lie in the fact that drones can only perceive the environmental state and the surface behavior of others, and cannot recursively model and predict the "mental states" of others (such as intentions, beliefs, and cognitive levels). This makes it difficult for drones to understand the next action intention of their teammates, and also makes it impossible to predict the possible reaction of the target to the encirclement strategy. As a result, they perform poorly in complex scenarios that require tacit understanding and cooperation—for example, they cannot actively lure the target into the encirclement, and they cannot achieve rapid self-repair through intention sharing when the formation is damaged.

[0005] Therefore, a method for collaborative capture and control of drone swarms based on recursive mind theory is needed to solve the above problems. Summary of the Invention

[0006] To address the deficiency in existing collaborative capture methods that lack the ability to recursively reason about the cognitive states of others, this invention provides a collaborative capture control method for drone swarms based on recursive mind theory, thus solving the existing problems.

[0007] This invention provides a collaborative control method for drone swarms based on recursive mind theory, employing the following technical solution: A zero-order belief is constructed based on the drone's current role and the target point location corresponding to the current role; the probability that a drone considers a teammate drone to be of a certain role is taken as a first-order belief, and the first-order belief of a drone regarding a teammate drone regarding another teammate drone is taken as a second-order belief. A recursive mental model is constructed for each drone in the drone swarm based on the zero-order belief, first-order belief, and second-order belief. Obtain the observed state information of teammate drones for each drone, and update the first-order and second-order beliefs of the drones based on the state information of the teammate drones and the Bayesian filter update algorithm to obtain the first-order and second-order target beliefs of the drones. Construct an encirclement circle centered on the mission objective and based on a preset encirclement radius. Divide the encirclement circle into multiple sectors. Obtain the confidence level of each sector based on the second-order target belief of each UAV. Select the sector with the highest confidence level as the weak sector. The task term is constructed based on the drone's position and the target point position corresponding to the drone's role; the collision avoidance term is constructed based on the drone's position and the position of the teammate drone in the prediction time domain; the second-order cooperative term is constructed based on the drone's position and the center point position of the weak sector; the objective function is constructed based on the collision avoidance term, the second-order cooperative term, and the task term. Based on the current beliefs and objective function of the UAV, and using model predictive control to optimize the acceleration of the UAV in the prediction time domain, the acceleration that minimizes the objective function value is taken as the optimal acceleration, and the UAV is controlled to approach the mission objective based on the optimal acceleration; When the preset deception triggering conditions are met during the process of the UAV approaching the mission target based on the optimal acceleration control, the weakening acceleration and the containment acceleration are determined based on the maximum acceleration. The weakening maneuver is performed based on the weakening acceleration until the weakening maneuver ends. Then, the UAV that forms the potential gap is controlled based on the containment acceleration to accelerate and contain the mission target simultaneously.

[0008] A further technical solution of the present invention is that the recursive mental model is: The expression for zero-order belief is:

[0009] The expression for a first-order belief is:

[0010] The expression for a second-order belief is:

[0011] In the formula, Indicates drone Zero-order beliefs; Indicates drone First-order beliefs; Indicates drone Second-order beliefs; Indicates drone The current roles include: Interceptor, Drive-away, and Replacement; Indicates drone At the target point location corresponding to the current character; Indicates teammate's drone The current role; Indicates drone Deadline Constantly monitored drones belonging to teammates The status information includes velocity and position; Indicates drone Deadline Constantly monitored drones belonging to teammates Status information; Indicates drone exist Always think of your teammates' drones Current character is The posterior probability; Indicates drone exist Always think of your teammates' drones drones for teammates The current role is The posterior probability.

[0012] A further technical solution of the present invention is that the first-order target belief expression of the UAV is:

[0013] The second-order goal belief expression for the UAV is:

[0014]

[0015]

[0016] In the formula, This represents the first-order objective belief of the drone; This represents the second-order goal belief of the drone; Indicates drone exist Always think of your teammates' drones Current character is The posterior probability; This indicates that, assuming a teammate has a drone... The current role is Under these conditions, drones At the present moment Observed teammate drone Status information The observation likelihood function; This indicates that, assuming a teammate has a drone... The current role is Under these conditions, drones At the present moment Observed teammate drone Status information The observation likelihood function; Indicates drone exist Always think of your teammates' drones Current character is The posterior probability; Indicates drone Deadline Constantly monitored drones belonging to teammates Status information, including teammate drones Speed ​​and position; Indicates drone Deadline Constantly monitored drones belonging to teammates Status information; Represents the state transition kernel; Indicates teammate's drone Possible roles; Indicates time Teammate drone It is believed that the drone of the teammate It is a vector consisting of the probability distributions of the interceptor, the expeller, and the replacement; Indicates teammate's drone Based on its own time from time 1 to time 2 drones for teammates Observation status information It is estimated that the teammate's drone The posterior probability of the role being "interceptor"; Indicates teammate's drone Based on its own time from time 1 to time 2 drones for teammates Observation status information It is estimated that the teammate's drone The posterior probability of the role being "Expector"; Indicates teammate's drone Based on its own time from time 1 to time 2 drones for teammates Observation status information It is estimated that the teammate's drone The posterior probability of the role being "filler".

[0017] A further technical solution of the present invention is that the expression for the confidence level of each sector is:

[0018] In the formula, Indicates the first Confidence level of each sector; This represents the second-order goal belief of the drone; This indicates an indicator function, meaning the location of the unmanned aerial vehicle in space. Does the current position point to the first... Each sector.

[0019] A further technical solution of the present invention is that the expression of the objective function is:

[0020] In the formula, Represents the objective function value; Indicates drone Within the prediction time domain The position at that moment; Indicates drone Within the prediction time domain The position at that moment; Indicates drone exist The target point position corresponding to the role at any given moment; Indicates the time domain of prediction The location of the center point of the weak sector at any given moment; This is a task item, used to drive the drone. Approaching drone The current target location for the character; This is a collision avoidance measure used to penalize drones. With teammates drone Too close; This is a second-order cooperative term, used to guide the drone. Actively fill the gaps in weak areas; Indicates the weight of the task item; Indicates the weight of the collision avoidance term; Indicates the time domain of prediction The weights of the second-order cooperative terms at time step.

[0021] A further technical solution of the present invention is to predict within the time domain. The expression for the weight of the second-order cooperative term at time step is:

[0022] In the formula, For prediction in the time domain The weights of the second-order cooperative terms at time step; As the benchmark weight; This is the adjustment coefficient; The confidence level of the weak sector.

[0023] A further technical solution of the present invention is that the preset deception triggering conditions include: The angle between the velocity direction vector of the mission target and the center direction vector of the potential gap is less than the angle threshold, wherein the center direction vector of the potential gap is obtained based on the positions of the two adjacent UAVs constituting the potential gap; The distance between the two drones is less than the gap distance threshold; Within a preset time period, the proportion of time during which the velocity direction of the mission target points towards the gap is greater than a time proportion threshold. The drone believes that the mission objective's second-order objective belief that the drone's role is that of an interceptor is greater than a preset first-order belief threshold.

[0024] A further technical solution of the present invention is that the expression for the weakened acceleration is:

[0025] In the formula, To show weak acceleration; The amplitude of the weakened acceleration is less than the maximum acceleration. The duration of the show of weakness; The direction vector is the center of the gap; The triggering start time for a show of weakness maneuver.

[0026] A further technical solution of the present invention is that the expression for the containment acceleration is:

[0027] In the formula, For drones The acceleration of the encirclement; The magnitude of the containment acceleration is equal to the maximum acceleration. For drones Location; This is the position vector of the mission objective.

[0028] A further technical solution of the present invention is as follows: Based on the weakening acceleration, a weakening maneuver is performed until the weakening maneuver ends; then, based on the containment acceleration, all UAVs are controlled to synchronously accelerate towards the mission target to contain it. The drone moves towards the center of the gap with a weakening acceleration until the second-order target belief of the drone during the weakening maneuver is greater than the preset second belief threshold or the distance between the mission target and the center of the gap is less than the preset effective radius. The weakening maneuver ends when the drone's second-order target belief during the weakening maneuver is greater than the preset second belief threshold or the distance between the mission target and the center of the gap is less than the preset effective radius. Based on the containment acceleration, the two drones that constitute the potential gap are controlled to accelerate towards the mission target in a synchronized manner to contain it.

[0029] The beneficial effects of this invention are: This invention is the first to engineer recursive mind theory and apply it to UAV collaborative encirclement, enabling UAVs to simulate human second-order cognitive reasoning abilities and breaking through the bottleneck of traditional reactive collaboration in terms of intelligence level. Through second-order belief reasoning, UAVs can infer higher-order intentions by observing the behavior of teammates when communication is interrupted. This invention constructs an encirclement circle centered on the task objective with a preset radius, dividing the circle into multiple sectors. The confidence level of each sector is obtained based on the second-order target belief of each UAV, and the sector with the highest confidence level is designated as the weak sector. Task items are constructed based on the UAV's position and the target point position corresponding to its role; collision avoidance items are constructed based on the positions of the UAV and its teammates in the predicted time domain; and second-order collaborative items are constructed based on the UAV's position and the center point position of the weak sector. Based on collision avoidance, second-order cooperation, and task terms, an objective function is constructed. The optimal acceleration for controlling the UAV to approach the task target is obtained based on the objective function. Then, based on the optimal acceleration, when the preset deception trigger conditions are met during the approach process, the weakening acceleration and containment acceleration are determined based on the maximum acceleration. Weakening maneuvers are performed based on the weakening acceleration until the weakening maneuver ends. Finally, based on the containment acceleration, the UAVs forming the potential gap are controlled to synchronously accelerate towards the task target for containment. In other words, a recursive belief structure is used to enable the UAV to actively manipulate the target's beliefs, achieving an evolution from "passive containment" to "active trapping." This allows the UAV to proactively and without negotiation complete formation self-repair based on second-order reasoning of "I think you think I should fill in," thereby achieving containment control of the task target. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a schematic diagram of the overall structure of an embodiment of a drone swarm cooperative encirclement and capture control method based on recursive mind theory according to the present invention. Figure 2 This is a flight trajectory diagram of the target in the cluster encirclement mission in an embodiment of the present invention; Figure 3 This is an evolution diagram of individual role allocation in the cluster in an embodiment of the present invention; Figure 4 This is a trajectory diagram of the escape of the mission target in an embodiment of the present invention. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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 are within the scope of protection of the present invention.

[0033] An embodiment of the present invention provides a method for cooperative encirclement and control of drone swarms based on recursive mind theory, such as... Figure 1 As shown, it includes: S1. Construct a recursive mental model; Specifically, zero-order beliefs are constructed based on the current role of the drone and the target point location corresponding to the current role; the probability that a drone considers a teammate drone to be of a certain role is taken as a first-order belief, and the first-order beliefs of a drone regarding a teammate drone regarding another teammate drone are taken as second-order beliefs. Based on zero-order beliefs, first-order beliefs, and second-order beliefs, a recursive mental model is constructed for each drone in the drone swarm.

[0034] For example, in one specific embodiment, the steps for constructing a recursive mental model are as follows: Suppose that the drone swarm has N drones, numbered as follows: For each drone, a recursive mental model is constructed, which includes zero-order beliefs, first-order beliefs, and second-order beliefs.

[0035] In this embodiment, the drone The zeroth-order belief is defined as a pair of tuples, that is:

[0036] In the formula, Indicates drone Zero-order beliefs; Indicates drone The current roles include: interceptor, drive-away, and replacement; Indicates drone The target point is located at the current character's target location, which can be the interception point, the driving point, or the replacement point.

[0037] In this embodiment, the drone The first-order role belief is defined as: drone At any moment The teammate's drone Current character is The subjective probability is expressed as:

[0038] In the formula, Indicates drone First-order beliefs; Indicates drone Deadline Constantly monitored drones belonging to teammates The status information includes velocity and position; Indicates drone exist Always think of your teammates' drones Current character is The posterior probability.

[0039] In this embodiment, the drone The second-order role belief is defined as: drone drones for teammates Regarding teammate drones The first-order belief, namely, the drone. The teammate's drone drones for teammates The distribution of role beliefs is expressed as follows:

[0040] In the formula, Indicates drone Second-order beliefs; Indicates drone Deadline Constantly monitored drones belonging to teammates Status information; Indicates drone exist Always think of your teammates' drones drones for teammates The current role is The posterior probability.

[0041] At this point, the recursive mental model can be constructed.

[0042] S2. Update the first-order and second-order beliefs corresponding to the drone to obtain the drone's first-order and second-order target beliefs; Specifically, the system acquires the observed state information of teammate drones for each drone, and updates the first-order and second-order beliefs of the drones based on the state information of the teammate drones using a Bayesian filtering update algorithm to obtain the drones' first-order and second-order target beliefs.

[0043] For example, in one specific embodiment, each drone observes the status information of its teammate drones via onboard sensors or a communication link, wherein the drone... At any moment Observations were made regarding the teammate's drone. The status information is ,in, drones for teammates At any moment Location information, drones for teammates At any moment Speed ​​information.

[0044] For example, in one specific embodiment, the steps of obtaining the drone's first-order target belief and second-order target belief by updating the drone's first-order belief and second-order belief based on the drone's state information and using a Bayesian filtering update algorithm are as follows: The first-order objective belief of the drone is:

[0045] The second-order goal belief expression for the UAV is:

[0046]

[0047]

[0048] In the formula, This represents the first-order objective belief of the drone; This represents the second-order goal belief of the drone; Indicates drone exist Always think of your teammates' drones Current character is The posterior probability; This indicates that, assuming a teammate has a drone... The current role is Under these conditions, drones At the present moment Observed teammate drone Status information The observation likelihood function; This indicates that, assuming a teammate has a drone... The current role is Under these conditions, drones At the present moment Observed teammate drone Status information The observation likelihood function; Indicates drone exist Always think of your teammates' drones Current character is The posterior probability; Indicates drone Deadline Constantly monitored drones belonging to teammates Status information, including teammate drones Speed ​​and position; Indicates drone Deadline Constantly monitored drones belonging to teammates Status information; The state transition kernel is represented by a Dirichlet distribution in this embodiment; Indicates teammate's drone Possible roles; Indicates time Teammate drone It is believed that the drone of the teammate It is a vector consisting of the probability distributions of the interceptor, the expeller, and the replacement; Indicates teammate's drone Based on its own time from time 1 to time 2 drones for teammates Observation status information It is estimated that the teammate's drone The posterior probability of the role being "interceptor"; Indicates teammate's drone Based on its own time from time 1 to time 2 drones for teammates Observation status information It is estimated that the teammate's drone The posterior probability of the role being "Expector"; Indicates teammate's drone Based on its own time from time 1 to time 2 drones for teammates Observation status information It is estimated that the teammate's drone The role is the posterior probability of the "filler". It should be noted that the Bayesian filtering update algorithm is an existing technique and will not be described further in this embodiment.

[0049] At this point, the updated first-order and second-order objective beliefs of the UAV can be obtained. The objective function is then constructed. Specifically, an encirclement is constructed with the mission objective as the center and a preset encirclement radius. The encirclement is divided into multiple sectors. The confidence level of each sector is obtained based on the second-order target belief of each UAV, and the sector corresponding to the highest confidence level is designated as the weak sector. The predicted distance between the UAV and its teammates is obtained based on their predicted positions in the prediction time domain. A collision avoidance term is constructed based on the predicted distance between the UAV and its teammates and the minimum safe distance of the UAV. A task term is constructed based on the position of the UAV and the target point position corresponding to its role. A collision avoidance term is also constructed based on the positions of the UAV and its teammates in the prediction time domain. A second-order cooperation term is constructed based on the position of the UAV and the center point position of the weak sector. An objective function is constructed based on the collision avoidance term, the second-order cooperation term, and the task term.

[0050] For example, in one specific embodiment, the step of obtaining weak sectors is as follows: With the mission objective as the center, the preset encirclement radius is... The encircling circle is divided into M sectors. For each sector... The confidence score is calculated using the following expression:

[0051] In the formula, Indicates the first Confidence level of each sector; This represents the second-order goal belief of the drone; An indicator function whose value is 0 or 1 indicates the location of the unmanned aerial vehicle (UAV) in space. Does the current position point to the first... Each sector. In this embodiment, the sector corresponding to the highest confidence level is selected as the weak sector, and the center point of the weak sector is located at... .

[0052] For example, in one specific embodiment, the step of obtaining the objective function is as follows: Each UAV, taking its current belief state as input, uses a model predictive control method to continuously optimize its own acceleration control quantity within the prediction time domain T. In this embodiment, the prediction time domain... The step size; the UAV is treated as a point mass moving, and its state prediction model is:

[0053] In the formula, For drones exist Location information at any given time For drones exist Speed ​​information at any given moment; For drones exist Acceleration at any moment; This is the simulation step size; it should be noted that, , This indicates the maximum speed of the drone; This represents the maximum acceleration of the drone; in this embodiment, and .

[0054] The optimization variable is the acceleration sequence over the next T steps. The objective function is then:

[0055] In the formula, Represents the objective function value; Indicates drone Within the prediction time domain The position at that moment; Indicates drone Within the prediction time domain The position at that moment; Indicates drone exist The target point position corresponding to the role at any given moment; Indicates the time domain of prediction The location of the center point of the weak sector at any given moment; This is a task item, used to drive the drone. Approaching drone The current target location for the character; This is a collision avoidance measure used to penalize drones. With teammates drone Due to the excessively close distance, this embodiment Using potential function , , Minimum safe distance; This is a second-order cooperative term, used to guide the drone. Actively fill the gaps in weak areas; Indicates the weight of the task item; Indicates the weight of the collision avoidance term; Indicates the time domain of prediction The weights of the second-order cooperative terms at time step. It should be noted that in this embodiment, , Minimum safe distance The weak sector is divided using a spherical latitude and longitude grid, horizontally. Each sector, vertical direction Layers, total Each sector, with a bounding radius .

[0056] Among them, in the prediction time domain The expression for the weight of the second-order cooperative term at time step is:

[0057] In the formula, For prediction in the time domain The weights of the second-order cooperative terms at time step; As the benchmark weight; This is the adjustment coefficient; The confidence level of weak sectors; the weight of the second-order cooperation term is increased to guide the UAV to actively fill in gaps. In this embodiment, the baseline weight... adjustment coefficient .

[0058] S4. Determine the optimal acceleration and control the UAV to approach the mission target; Specifically, based on the UAV's current beliefs and objective function, and using model predictive control to optimize the UAV's acceleration in the prediction time domain, the acceleration that minimizes the objective function value is taken as the optimal acceleration, and the UAV is controlled to approach the mission objective based on the optimal acceleration.

[0059] It should be noted that the model predictive control method optimizes the acceleration of the UAV in the prediction time domain by solving for the optimal acceleration in each sampling period. The optimal acceleration is applied to the control of the corresponding UAV, so that all UAVs can approach the mission target.

[0060] S5. When the preset deception triggering conditions are met, execute the feigned weakness maneuver and accelerated encirclement in sequence; Specifically, when the preset deception triggering conditions are met during the process of the UAV approaching the mission target based on the optimal acceleration control, the weakening acceleration and the containment acceleration are determined based on the maximum acceleration. The weakening maneuver is performed based on the weakening acceleration until the weakening maneuver ends. Then, the UAV that forms the potential gap is controlled based on the containment acceleration to accelerate and contain the mission target simultaneously.

[0061] For example, in one specific embodiment, a drone is defined. With the latest teammate drone If a potential gap is formed, the center direction vector of the potential gap is obtained based on the positions of the two adjacent UAVs forming the potential gap. The velocity direction vector of the mission target , Given the target velocity, the angle between the target velocity direction vector and the center direction vector of the potential gap can be obtained. .

[0062] The conditions for triggering the deception are: (1) The angle between the velocity direction vector of the mission target and the center direction vector of the potential gap is less than the angle threshold. ; The included angle threshold; (2) The distance between the two drones is less than the gap distance threshold, i.e. ; The preset gap distance threshold; (3) At the preset time Within this timeframe, the proportion of time the mission target's velocity direction points towards the gap is greater than a time proportion threshold. ; (4) The UAV believes that the mission target's second-order objective belief that the UAV's role is that of an interceptor is greater than the preset first-belief threshold, that is, the UAV... The mission objective is considered to be the drone. The confidence level (second-order goal belief) of the interceptor tightening defense is greater than 0.5, that is... It should be noted that, in this embodiment, the included angle threshold... Preset gap distance threshold preset time Preset time ratio threshold .

[0063] If all four deception trigger conditions are met, then proceed with feigned weakness maneuvers and accelerated encirclement in sequence.

[0064] For example, in one specific embodiment, the steps of determining the weakening acceleration and the containment acceleration based on the maximum acceleration are as follows: The expression for the weakened acceleration is:

[0065] In the formula, To show weak acceleration; The amplitude of the weakened acceleration is less than the maximum acceleration. The direction vector is the center of the gap; The duration of the show of weakness (0.2 to 1.0 seconds); The trigger start time for the weakening maneuver; in this embodiment, the weakening acceleration amplitude Duration of showing weakness .

[0066] The expression for the containment acceleration is:

[0067] In the formula, For drones The acceleration of the encirclement; The magnitude of the containment acceleration is equal to the maximum acceleration. For drones Location; The position vector of the mission target; in this embodiment, the magnitude of the containment acceleration is taken as... .

[0068] For example, in one specific embodiment, the step of performing a show-of-defense maneuver based on the show-of-defense acceleration until the show-of-defense maneuver ends, and then controlling all UAVs to synchronously accelerate towards the mission target based on the containment acceleration, is as follows: moving towards the direction away from the center of the gap according to the show-of-defense acceleration, until the second-order target belief of the UAVs during the show-of-defense maneuver is greater than a preset second belief threshold or the distance between the mission target and the center of the gap is less than a preset effective radius. The weakened maneuver ends at the indicated time; in this embodiment, the effective radius... And based on the containment acceleration control, the drones that create the potential gap simultaneously accelerate towards the mission target to contain it. It should be noted that the drones... Based on second-order goal belief reasoning, the teammate's drone was identified. The decoy state (i.e., the drone) has been identified through symmetric recursion. Believe in drones Believe in drones The deception is in progress, and the second-order goal belief is greater than 0.7.

[0069] Therefore, drones in the encirclement and control The acceleration command that ultimately acts on the power system for:

[0070] In the formula, For drones The optimal acceleration, For drones The weakening acceleration; For drones The acceleration of the containment.

[0071] The invention will be further illustrated below with specific data and simulations: This embodiment builds a point motion model of five quadcopter UAVs and an escape dynamics model of the target in the MATLAB / Simulink environment. The mission target adopts an optimal escape strategy based on maximum and minimum distances, that is, at each time step, it selects the acceleration direction that maximizes the minimum distance between itself and all other UAVs. The simulation step size is set to... Total simulation time The maximum acceleration of the drone Maximum speed The maximum speed of the mission objective The maximum acceleration of the mission objective .

[0072] like Figure 2 As shown, the five UAVs (UAV1-UAV5) are initially positioned in a three-dimensional configuration, with UAV1-UAV3 evenly distributed on a horizontal plane with a radius of [missing information]. On the circle (azimuth angle) UAV4 (Unmanned Aerial Vehicle 4) is located directly above the mission target. UAV5 (UAV 5) is located directly below the UAV. The initial location of the mission objective is at the origin. . The trajectory of the mission objective. During the encirclement process, each drone approaches the target from different directions, and the trajectory forms a geometric shape similar to an "encirclement" in space. This indicates that the distributed cooperative strategy has successfully encircled the maneuvering target, demonstrating the cooperative encirclement effect driven by recursive belief.

[0073] like Figure 3 As shown, Figure 3 This demonstration showcased how five drones achieved dynamic and autonomous coordination during a capture operation, based on recursive mind theory. Initially, the drones were assigned roles as interceptors, chasers, and backups based on their three-dimensional configuration, forming an initial encirclement. As the target maneuvered and escaped, the system recalculated role assignments every 5 steps (0.5 seconds total) based on the real-time distance and orientation between the drones and the target. Figure 3 The frequent color changes visually reflect this dynamic adjustment. During the encirclement process, when the target attempts to break through between two drones, the closest drone quickly switches to intercepting it head-on, while the flanking drones become the chasers, driving the target back. The remaining drones actively fill the gaps. This tacit cooperation relies entirely on the recursive reasoning of first-order and second-order beliefs, without the need for explicit communication and negotiation.

[0074] like Figure 4 As shown, from Figure 4 The target trajectory exhibits clear maneuvering and turning characteristics, indicating that it adopted an optimal escape strategy in an attempt to break through the encirclement. However, under the collaborative recursive mental reasoning of the drone swarm, the escape path is continuously compressed. Initial roles are determined through distributed consensus negotiation, specifically as follows: Each drone calculates its role based on its initial position and the relationship with the mission target. Candidate role vectors (1 = Interceptor, 2 = Drive-away, 3 = Replacement), and then multiple values ​​are obtained through multiple rounds of adjacent communication until all convergence. In this embodiment, the negotiation result of the zero-order belief of each UAV is: UAV 1 and UAV 2 are: Interceptor (located on the horizontal plane) and ); Drone 3 is: the driver (located on the horizontal plane) ); Drone 4 and Drone 5 are: replacements.

[0075] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for collaborative encirclement and control of unmanned aerial vehicle (UAV) swarms based on recursive mind theory, characterized in that, include: A zero-order belief is constructed based on the drone's current role and the target point location corresponding to the current role; the probability that a drone considers a teammate drone to be of a certain role is taken as a first-order belief, and the first-order belief of a drone regarding a teammate drone regarding another teammate drone is taken as a second-order belief. A recursive mental model is constructed for each drone in the drone swarm based on the zero-order belief, first-order belief, and second-order belief. Obtain the observed state information of teammate drones for each drone, and update the first-order and second-order beliefs of the drones based on the state information of the teammate drones and the Bayesian filter update algorithm to obtain the first-order and second-order target beliefs of the drones. Construct an encirclement circle centered on the mission objective and based on a preset encirclement radius. Divide the encirclement circle into multiple sectors. Obtain the confidence level of each sector based on the second-order target belief of each UAV. Select the sector with the highest confidence level as the weak sector. Task items are constructed based on the drone's position and the target point position corresponding to the drone's role; collision avoidance items are constructed based on the drone's position and the position of teammate drones in the prediction time domain; and second-order cooperative items are constructed based on the drone's position and the center point position of the weak sector. Construct an objective function based on collision avoidance terms, second-order cooperative terms, and task terms; Based on the current beliefs and objective function of the UAV, and using model predictive control to optimize the acceleration of the UAV in the prediction time domain, the acceleration that minimizes the objective function value is taken as the optimal acceleration, and the UAV is controlled to approach the mission objective based on the optimal acceleration; When the preset deception triggering conditions are met during the process of the UAV approaching the mission target based on the optimal acceleration control, the weakening acceleration and the containment acceleration are determined based on the maximum acceleration. The weakening maneuver is performed based on the weakening acceleration until the weakening maneuver ends. Then, the UAV that forms the potential gap is controlled based on the containment acceleration to accelerate and contain the mission target simultaneously.

2. The method for collaborative encirclement and control of UAV swarms based on recursive mind theory according to claim 1, characterized in that, The recursive mental model is as follows: The expression for zero-order belief is: The expression for a first-order belief is: The expression for a second-order belief is: In the formula, Indicates drone Zero-order beliefs; Indicates drone First-order beliefs; Indicates drone Second-order beliefs; Indicates drone The current role includes: interceptor, drive-away, and replacement; Indicates drone At the target point location corresponding to the current character; Indicates teammate's drone The current role; Indicates drone Deadline Constantly monitored drones belonging to teammates The status information includes velocity and position; Indicates drone Deadline Constantly monitored drones belonging to teammates Status information; Indicates drone exist Always think of your teammates' drones Current character is The posterior probability; Indicates drone exist Always think of your teammates' drones drones for teammates The current role is The posterior probability.

3. The method for collaborative encirclement and control of UAV swarms based on recursive mind theory according to claim 1, characterized in that, The first-order target belief expression for the drone is: The second-order goal belief expression for the UAV is: In the formula, This represents the first-order target belief of the drone; This represents the second-order goal belief of the drone; Indicates drone exist Always think of your teammates' drones Current character is The posterior probability; This indicates that, assuming a teammate has a drone... The current role is Under these conditions, drones At the present moment Observed teammate drone Status information The observation likelihood function; This indicates that, assuming a teammate has a drone... The current role is Under these conditions, drones At the present moment Observed teammate drone Status information The observation likelihood function; Indicates drone exist Always think of your teammates' drones Current character is The posterior probability; Indicates drone Deadline Constantly monitored drones belonging to teammates Status information, including teammate drones Speed ​​and position; Indicates drone Deadline Constantly monitored drones belonging to teammates Status information; Represents the state transition kernel; Indicates teammate's drone Possible roles; Indicates time Teammate drone It is believed that the drone of the teammate It is a vector consisting of the probability distributions of the interceptor, the expeller, and the replacement; Indicates teammate's drone Based on its own time from time 1 to time 2 drones for teammates Observation status information It is estimated that the teammate's drone The posterior probability of the role being "interceptor"; Indicates teammate's drone Based on its own time from time 1 to time 2 drones for teammates Observation status information It is estimated that the teammate's drone The posterior probability of the role being "Expector"; Indicates teammate's drone Based on its own time from time 1 to time 2 drones for teammates Observation status information It is estimated that the teammate's drone The posterior probability of the role being "filler".

4. The method for collaborative encirclement and control of UAV swarms based on recursive mind theory according to claim 1, characterized in that, The expression for the confidence level of each sector is: In the formula, Indicates the first Confidence level of each sector; This represents the second-order goal belief of the drone; This indicates an indicator function, meaning the location of the unmanned aerial vehicle in space. Does the current position point to the first... Each sector.

5. The method for collaborative encirclement and control of UAV swarms based on recursive mind theory according to claim 1, characterized in that, The expression for the objective function is: In the formula, Represents the objective function value; Indicates drone Within the prediction time domain The position at that moment; Indicates drone Within the prediction time domain The position at that moment; Indicates drone exist The target point position corresponding to the role at any given moment; Indicates the time domain of prediction The location of the center point of the weak sector at any given moment; This is a task item, used to drive the drone. Approaching drone The current target location for the character; This is a collision avoidance measure used to penalize drones. With teammates drone Too close; This is a second-order cooperative term, used to guide the drone. Actively fill the gaps in weak areas; Indicates the weight of the task item; Indicates the weight of the collision avoidance term; Indicates the time domain of prediction The weights of the second-order cooperative terms at time step.

6. The method for collaborative encirclement and control of UAV swarms based on recursive mind theory according to claim 5, characterized in that, Within the prediction time domain The expression for the weight of the second-order cooperative term at time step is: In the formula, For prediction in the time domain The weights of the second-order cooperative terms at time step; As the benchmark weight; This is the adjustment coefficient; The confidence level of the weak sector.

7. The method for collaborative encirclement and control of UAV swarms based on recursive mind theory according to claim 1, characterized in that, The preset deception trigger conditions include: The angle between the velocity direction vector of the mission target and the center direction vector of the potential gap is less than the angle threshold, wherein the center direction vector of the potential gap is obtained based on the positions of the two adjacent UAVs constituting the potential gap; The distance between the two drones is less than the gap distance threshold; Within a preset time period, the proportion of time during which the velocity direction of the mission target points towards the gap is greater than a time proportion threshold. The drone believes that the mission objective's second-order objective belief that the drone's role is that of an interceptor is greater than a preset first-order belief threshold.

8. The method for collaborative encirclement and control of UAV swarms based on recursive mind theory according to claim 1, characterized in that, The expression for the weakened acceleration is: In the formula, To show weakness in acceleration; The amplitude of the weakened acceleration is less than the maximum acceleration. The duration of the show of weakness; The direction vector is the center of the gap; The triggering start time for a show of weakness maneuver.

9. A method for collaborative encirclement and control of UAV swarms based on recursive mind theory according to claim 1, characterized in that, The expression for the containment acceleration is: In the formula, For drones The acceleration of the encirclement; The magnitude of the containment acceleration is equal to the maximum acceleration. For drones Location; The position vector of the mission target.

10. A method for collaborative encirclement and control of UAV swarms based on recursive mind theory according to claim 1, characterized in that, The steps for performing a show-of-weak maneuver based on the show-of-weak acceleration, and then controlling all UAVs to synchronously accelerate and surround the mission target based on the containment acceleration, are as follows: The drone moves towards the center of the gap with a weakening acceleration until the second-order target belief of the drone during the weakening maneuver is greater than the preset second belief threshold or the distance between the mission target and the center of the gap is less than the preset effective radius. The weakening maneuver ends when the drone's second-order target belief during the weakening maneuver is greater than the preset second belief threshold or the distance between the mission target and the center of the gap is less than the preset effective radius. Based on the containment acceleration, the two drones that constitute the potential gap are controlled to accelerate towards the mission target in a synchronized manner to contain it.

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