Multi-robot cooperation chasing method based on density distribution in limited sensing range
By adopting a density-based multi-robot cooperative pursuit method, the problems of high computational complexity and insufficient adaptability of static decision models in existing technologies are solved, achieving efficient pursuit in dynamic environments and improving the robustness and success rate of the system.
Patent Information
- Application Number
- CN202511104718.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-07
- Publication Date
- 2025-11-21
AI Technical Summary
Existing pursuit game methods have high computational complexity within a limited perception range, making it difficult to meet real-time requirements. Furthermore, static decision-making models cannot effectively cope with changes in target distribution in dynamic environments, leading to resource allocation imbalances and a decrease in the overall success rate of the pursuit.
A density-based multi-robot cooperative pursuit method is adopted. Each pursuing robot acquires information within its perception range, calculates density and weighting values, and dynamically adjusts the pursuit strategy, including pursuit items, dynamic cooperation items, and collision avoidance items, to achieve cooperative pursuit among robots.
It improves the success rate of pursuit in dynamic environments, reduces communication dependence, and realizes the robustness and practicality of the system. The robot can autonomously adjust its cooperation strategy according to real-time environmental changes.
Smart Images
Figure CN120993903A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of unmanned vessel maritime pursuit technology, and relates to a multi-robot cooperative pursuit method based on density allocation within a limited perception range. Background Technology
[0002] Existing pursuit game methods suffer from several key drawbacks: traditional strategies such as the "nearest target priority" principle, while computationally simple, are prone to allowing distant targets to escape due to locally optimal decisions. While methods based on global path optimization are theoretically superior, their computational complexity increases exponentially with the number of targets, making them unsuitable for real-time requirements. More seriously, these methods generally rely on global information sharing, but in real-world scenarios, the robot's perception range is limited, and communication delays and errors significantly reduce collaborative efficiency. Furthermore, static decision-making models cannot effectively cope with changes in target distribution in dynamic environments, particularly in high-density target areas where resource allocation imbalances easily occur, ultimately leading to a significant decrease in the overall system's pursuit success rate and environmental adaptability. These limitations highlight the necessity of developing novel distributed collaborative algorithms.
[0003] Previous methods for robot multi-target pursuit mostly involved chasing the nearest target or enumerating various scenarios and selecting the one with the minimum sum of robot paths. Chasing the nearest target easily leads to missing targets that are relatively far away, while selecting the one with the minimum sum of paths is computationally complex, has poor real-time performance, and may result in failure to capture targets in practical applications. Furthermore, in real-world applications, it is difficult for the robot to obtain the exact positions and velocities of its companions and the target in real time, leading to poor cooperative performance. Summary of the Invention
[0004] To address the aforementioned problems, the technical solution adopted by this invention is: a multi-robot cooperative pursuit method based on density allocation within a limited perception range, comprising the following steps:
[0005] Each chasing robot acquires information on the number and location of N chasing robots and M escaping robots within its perception range, where N is greater than or equal to M;
[0006] The target escape robot is determined by the chasing robot. If there is no escape robot within the chasing robot's perception range, the chasing robot will not participate in the chase. If there is an escape robot, the target escape robot is directly determined. If there are multiple escape robots, the process of determining the target escape robot is as follows.
[0007] By integrating the positions of the pursuit robot and other pursuit robots within its field of vision, a distribution field of pursuit robot density in the plane is formed, and the density value of the positions of all escaping robots within its field of vision is calculated.
[0008] The density value of the evading robot and the distance between the pursuing robot and the evading robot are weighted and calculated. The evading robot with the smallest weighted value is selected as the target evading robot.
[0009] Calculate the chasing force required for the chasing robot to chase the target robot to escape, i.e., the chasing term. If it is found that it is necessary to avoid obstacles during the chasing process, calculate the detour point, which is the target point. If it is found that it is not necessary to avoid obstacles during the chasing process, then it is not necessary to calculate the detour point.
[0010] If there are other chasing robots within the chasing robot's perception range that are chasing the same escaping robot, then the dynamic long-distance repulsion force, i.e., the dynamic cooperation term, is calculated; if there are no other chasing robots within the chasing robot's perception range that are chasing the same escaping robot, then the dynamic cooperation term is 0.
[0011] Calculate the collision avoidance force required between chasing robots and between escaping robots to avoid collisions, i.e., the collision avoidance term;
[0012] If the chasing robot or the escaping robot is found to have exceeded the finite area during the chase, then the finite area constraint range of the chasing robot and the escaping robot during the chase is calculated, i.e., the finite area constraint term; if the chasing robot or the escaping robot is found not to have exceeded the finite area during the chase, then the finite area constraint term is zero.
[0013] The pursuit strategy for chasing robots is based on the pursuit terms, dynamic cooperation terms, collision avoidance terms, and finite area constraints, which enables N chasing robots to chase M escaping robots.
[0014] Furthermore, it also includes, when M>1, using a modified smoothing function to determine the target robot being chased by the chasing robot, which is an escaping robot; the expression of the modified smoothing function is as follows:
[0015]
[0016] Where: τ=r ij / r sen r ij =||r i -r j || is the distance from pursuer j to pursuer i, R sen It is the radius of perception of the pursuer; a d =R i / R sen A scaling factor, R, used to control the shape or truncation range of the kernel. i It is the individual radius of tracker i.
[0017] Furthermore, the formula for calculating the weighted value of the evading robot's density value and the distance between the pursuing robot and the evading robot is as follows:
[0018] press i (k)=Q i (r k )*(β)1+(β)2*r ik (k∈P i )
[0019] Among them, P i It is the set of evading robots perceived by the pursuing robot, where k is P i The dodge robot in the middle, r ik To escape the distance between robot k and pursuing robot i, Q i (r k ) is the density value of the evading robot k perceived by the pursuing robot in the density field, and β1 and β2 are weighting coefficients.
[0020] Furthermore, the formula used to calculate the chasing force required for the chasing robot to chase the target robot that is trying to escape, i.e., the chasing term, is as follows:
[0021]
[0022] r pred Predict the robot's next move; The maximum speed of the chasing robot; Chase the current location of robot i.
[0023] Furthermore, it also includes identifying obstacles within the perception range, and merging the two obstacles if the minimum distance between two obstacles is less than the pursuer's safe radius;
[0024] The robot first identifies obstacles within its perception range. If there are multiple obstacles, each obstacle calculates its nearest point to other obstacles. If the distance between the nearest points is less than the robot's own radius Ri, then the two obstacles need to be merged into one obstacle.
[0025] Detect whether an obstacle needs to be avoided; if the line between the tracker and the target point intersects with an obstacle, then the obstacle must be avoided.
[0026] To detect whether an obstacle needs to be avoided, connect the positions of the chasing robot and the target escape robot, and iterate through all obstacles within the chasing robot's perception range. If an obstacle intersects the line or the distance between the nearest point of the obstacle and the line is less than the chasing robot's own radius Ri, then the obstacle is considered an obstacle that needs to be avoided. If there are multiple obstacles that need to be avoided, then the one closest to the chasing robot's position is the target obstacle to avoid.
[0027] Furthermore, the process for determining the detour point is as follows:
[0028] First, the target obstacle to be avoided will expand outward by a distance Ri equal to the radius of the chasing robot itself.
[0029] Next, draw tangents from the position of the chasing robot to the left and right sides of the target obstacle to obtain two tangent points, which are considered as alternative detour points.
[0030] Finally, the angle between the left tangent and the connecting line. That is, the angle between the line connecting the positions of the chasing robot and the dodging robot, and the right tangent and the connecting line. like Less than If the left tangent point is chosen as the detour point, then the right tangent point is chosen as the detour point.
[0031] Furthermore, the formula for calculating the pursuit term is as follows:
[0032]
[0033] The maximum speed of the chasing robot; The location of the detour point for chasing robot i; Chase the location of robot i.
[0034] Furthermore: the process of calculating the dynamic long-distance repulsive force required for the robot to escape from the same chasing target, i.e., the dynamic cooperative term, is as follows:
[0035]
[0036] Where: d min (t): the shortest distance between the escaping robot and the chasing robot; α(d min (t)): Decay function, used to control the repulsive force to be effective only within a certain range and to decay; d ij : Used to represent the distance between chasing robot i and escaping robot j; The maximum speed of the chasing robot.
[0037] Furthermore: the formula for calculating the collision avoidance force required between chasing robots and between escaping robots to avoid collisions, i.e., the collision avoidance term, is as follows:
[0038]
[0039] in: Let θ be the displacement vector between the i-th and j-th chasing robots, and let Θ be the step function. safe =3r cd It is the set range of repulsive force, when d ij ≥d safe At that time, there exists a repulsive force that increases the distance between the chasing robots to prevent them from colliding with each other. ij <d safe At this point, the risk of collision can be considered low, and the repulsive force drops to 0.
[0040] This invention provides a multi-robot cooperative pursuit method based on density allocation within a limited perception range, applicable to underwater robot dynamic target capture, and unauthorized target intrusion detection and interception by UAVs. The method involves each robot selecting a suitable target to pursue based on density within its own perception range, and completing the pursuit of multiple targets through cooperation.
[0041] This invention overcomes the technical bottleneck of fixed robot collaborative structures in traditional research by introducing a density allocation method and a dynamic cooperation mechanism, effectively solving the core problem of insufficient adaptability of static models in complex environments. Compared with existing methods, this innovation enables the system to autonomously adjust its cooperation strategy according to real-time environmental changes, significantly improving the success rate of tracking dynamic targets. Furthermore, it reduces communication dependence through a distributed decision-making architecture, ultimately achieving a breakthrough in the robustness and practical application of the model in real-world scenarios.
[0042] This invention utilizes a dynamic collaboration mechanism to enable robot systems to autonomously adjust their collaborative strategies based on real-time environmental changes. In practical applications, when multiple robots collaboratively pursue a target, the system continuously assesses factors such as target distribution, robot positions, and environmental obstacles, dynamically allocating tracking tasks and optimizing encirclement paths. For example, in security scenarios, robots no longer fixated on tracking a single target but intelligently switch targets based on target movement trends and companion positions, sharing key information through local communication to ultimately achieve efficient collaborative interception. This adaptive collaboration significantly improves the success rate of pursuit and system robustness in complex environments. Attached Figure Description
[0043] 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0044] Figure 1 This is a flowchart of the method;
[0045] Figure 2 This is a schematic diagram of the density distribution at the initial moment of a scenario with 11 chasing robots and 2 robots.
[0046] Figure 3 This is a schematic diagram of the density distribution and target allocation after 10 seconds;
[0047] Figure 4 It is a diagram illustrating the chase;
[0048] Figure 5 This is a diagram illustrating obstacle avoidance in a pursuit scenario;
[0049] Figure 6 This is a diagram illustrating dynamic collaboration items;
[0050] Figure 7 This is a schematic diagram of a bounded region. Detailed Implementation
[0051] It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and embodiments.
[0052] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. 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.
[0053] Figure 1 This is a flowchart of the method;
[0054] A density-based multi-robot cooperative pursuit method within a limited sensing range includes the following steps:
[0055] S1: Each chasing robot obtains the number and location information of N chasing robots and M escaping robots within its perception range, where N is greater than or equal to M;
[0056] S2: Determine the target escape robot that the chasing robot is chasing. If there is no escape robot within the chasing robot's perception range, the chasing robot will not participate in the chase. If there is an escape robot, then directly determine the target escape robot. If there are multiple escape robots, the process of determining the target escape robot is as follows.
[0057] By integrating the positions of the pursuit robot and other pursuit robots within its field of vision, a distribution field of pursuit robot density in the plane is formed, and the density value of the positions of all escaping robots within its field of vision is calculated.
[0058] The density value of the evading robot and the distance between the pursuing robot and the evading robot are weighted and calculated. The evading robot with the smallest weighted value is selected as the target evading robot.
[0059] S3: Calculate the chasing force required for the chasing robot to chase the target robot to escape, i.e., the chasing term. If it is found that it is necessary to avoid obstacles during the chasing process, calculate the detour point. At this time, the detour point is the target point. If it is found that it is not necessary to avoid obstacles during the chasing process, then it is not necessary to calculate the detour point.
[0060] S4: If there are other chasing robots chasing the same escaping robot within the perception range of the chasing robot, then calculate the dynamic long-distance repulsion force, i.e., the dynamic cooperation term; if there are no other chasing robots chasing the same escaping robot within the perception range of the chasing robot, then the dynamic cooperation term is 0.
[0061] S5: Calculate the collision avoidance force required between chasing robots and between escaping robots to avoid collisions, i.e., the collision avoidance term;
[0062] S6: If the chasing robot or the escaping robot is found to be outside the finite area during the chase, the finite area constraint range of the chasing robot and the escaping robot during the chase is calculated, i.e., the finite area constraint term; if the chasing robot or the escaping robot is found not to be outside the finite area during the chase, the finite area constraint term is zero.
[0063] If all the dodging robots are captured, the algorithm terminates; otherwise, the above process continues.
[0064] S7: Based on the pursuit terms, dynamic cooperation terms, collision avoidance terms, and finite area constraints, a pursuit strategy is formed by N pursuing robots chasing M escaping robots, so as to realize the pursuit of M escaping robots by N pursuing robots.
[0065] The steps S1 / S2 / S3 / S4 / S5 / S6 / S7 are executed sequentially;
[0066] In the multi-objective assignment problem, we employ a density-based objective assignment method. Density is defined based on a smoothing function of the SPH method. The SPH method treats the entire matter as a single particle and connects the interactions between particles through a specific kernel function. The influence on the current particle is the sum of the forces exerted on it by all surrounding particles. The SPH method is used to form the density field, obscuring the influence of distance and enhancing its robustness. In the SPH method, the state of the system is represented by a set of particles with material properties that interact within a range controlled by weights or a smoothing function. The smoothing function is used for kernel and particle approximations. It determines the interpolation pattern and defines the cutoff distance of the particle influence region, which is crucial in the SPH method. A bell-shaped function is used in this method:
[0067]
[0068] Because the SPH smoothing function is better suited for microscale fluid particles, the number and density of particles in a fluid far exceed the number of agents in a chase-and-dodge game. If the SPH smoothing function is used to calculate the density, the calculated density value will be very small. To accommodate real-world robotic systems, the restriction that the integral is 1 within the smoothing function region is removed, amplifying density variations. The modified smoothing function is as follows:
[0069]
[0070] Where: τ=r ij / r sen r ij =||r i -r j || is the distance from pursuer j to pursuer i, R sen It is the radius of perception of the pursuer, a d =R i / R sen A scaling factor used to control the shape or truncation range of the kernel, where Ri is the individual radius of tracker i.
[0071] Integrating the density effects of the pursuing robot and all escaping robots within its field of vision, a distribution field is formed in the plane. The density at a point on the plane is calculated as follows:
[0072]
[0073] Where r j This is the location of the pursuit robot J, x iTo track points within the perception area of the tracking robots, the density field is determined by the planar distribution of the pursuit robot swarm and changes dynamically with the movement of the pursuit robots. To address the multi-target assignment problem, the density values of the escaping robots in the current pursuit robot density field are calculated. Subsequently, the density values of the escaping robots and the distance between the pursuing and escaping robots are weighted to calculate a weighted value.
[0074] press i (k)=Q i (r k )*(β)1+(β)2*r ik (k∈P i )
[0075] Among them, P i It is the set of evading robots perceived by the pursuing robot, where k is P i The dodge robot in the middle, r ik To escape the distance between robot k and pursuing robot i, Q i (r k β1 and β2 are weighting coefficients, where β1 represents the density value of the evading robot k perceived by the pursuing robot in the density field. A larger β1 indicates a higher density proportion in target selection. Similarly, a larger β2 indicates a higher proportion of distance in target selection. After calculation, the pursuing robot will select the evading robot with the lowest pressure from within its perception range. i The evasion robot is used as the target P choose (P choose ∈P i ).
[0076] Figure 2 This is a schematic diagram of the density distribution at the initial moment of a scenario with 11 chasing robots and 2 robots.
[0077] Figure 3 This is a schematic diagram of the density distribution and target allocation after 10 seconds;
[0078] Figure 4 It is a diagram illustrating the chase;
[0079] After determining the target of the chasing robot, the pursuit term needs to be calculated. In the pursuit term, the chasing robot selects the target escape robot within the arena and then moves towards the target robot. In the chase game, if the escape robot's speed is greater than or equal to that of the chasing robot, the chasing robot will directly chase the current position of the escape robot, thus always following behind the escape robot and never being able to catch it. Therefore, we will predict the escape robot's next position r. predAnd set as the target point. The position of the escaping robot in the next step is strongly correlated with the most recent historical trajectory point. Therefore, we can use a linear method to predict the position of the escaping robot in a short time. The pursuit term is calculated as follows:
[0080]
[0081] Where: r pred Predict the robot's next move;
[0082] The maximum speed of the chasing robot;
[0083] Chase the current location of robot i;
[0084] The method also includes identifying obstacles within the perception range, and merging two obstacles if the minimum distance between two obstacles is less than the pursuer's safe radius;
[0085] The robot first identifies obstacles within its perception range. If there are multiple obstacles, each obstacle calculates its nearest point to other obstacles. If the distance between the nearest points is less than the robot's own radius Ri, then the two obstacles need to be merged into one obstacle.
[0086] Detect whether an obstacle needs to be avoided; if the line between the tracker and the target point intersects with an obstacle, then the obstacle must be avoided.
[0087] To detect whether an obstacle needs to be avoided, connect the positions of the chasing robot and the target escape robot, and iterate through all obstacles within the chasing robot's perception range. If an obstacle intersects the line or the distance between the nearest point of the obstacle and the line is less than the chasing robot's own radius Ri, then the obstacle is considered an obstacle that needs to be avoided. If there are multiple obstacles that need to be avoided, then the one closest to the chasing robot's position is the target obstacle to avoid. Figure 5 This is a diagram illustrating obstacle avoidance in a pursuit scenario;
[0088] The process for determining the detour points is as follows:
[0089] First, the target obstacle to be avoided will expand outward by a distance Ri equal to the radius of the chasing robot itself.
[0090] Next, draw tangents from the position of the chasing robot to the left and right sides of the target obstacle to obtain two tangent points, which are considered as alternative detour points.
[0091] Finally, the angle between the left tangent and the connecting line. That is, the angle between the line connecting the positions of the chasing robot and the dodging robot, and the right tangent and the connecting line. like Less than If the left tangent point is chosen as the detour point, then the right tangent point is chosen as the detour point.
[0092] The formula for calculating the pursuit term is as follows:
[0093]
[0094] in: The maximum speed of the chasing robot; The location of the detour point for chasing robot i; Chase the location of robot i.
[0095] Figure 6 This is a diagram illustrating dynamic collaboration items;
[0096] When multiple chasing robots share the same escaping robot, if the chasing robots are far away from the escaping robot, they tend to separate to block the escape route; otherwise, they tend to move closer to surround the escaping robot. Based on this characteristic, we apply a dynamic force to chasing robots with the same target. This dynamic cooperative term is named the "dynamic long-range repulsive force." The calculation of the dynamic cooperative term is as follows:
[0097]
[0098] Collisions may occur between chasing robots and between escaping robots, so there is a repulsive force over a short distance to prevent them from colliding.
[0099]
[0100] Let d be the displacement vector between the i-th and j-th chasing robots, Θ be the step function, and d be the displacement vector between the i-th and j-th chasing robots. safe =3r cd It is the set range of repulsive force, when d ij ≥d safe At this time, a repulsive force exists that increases the distance between the chasing robots to prevent them from colliding. When d ij <d safe At this point, the risk of collision can be considered low, and the repulsive force drops to 0.
[0101] The bounded region is considered a bounded square region with side length L. The robot can only move within the arena's boundaries; if a robot goes beyond the arena's boundaries, it is considered to have collided with the boundaries. We divide the arena into two parts: the confrontation area D. confrontation and the buffer area D buffer The confrontation area is a region with side length L. c The square area is located in the center of the bounded area; the buffer zone refers to the portion of the arena excluding the central area, and its width is... If the chasing robot currently has no target, Evader, it will move towards the center of the arena. Therefore, we place a virtual robot at the centroid of the bounded area, with its position as follows:
[0102] Figure 7 This is a schematic diagram of a bounded region.
[0103] Since robot chase scenarios often occur within a bounded area, it's necessary to confine robots outside this area back to the designated zone. If a robot's calculated next position deviates from the zone's boundaries, its speed and position must be recalculated. The calculation of the zone-restricted chasing robot constraints is as follows:
[0104]
[0105] Where: x(r) p ) is defined as the shortest distance from the boundary.
[0106] To keep the robot within the arena, a boundary constraint is needed to prevent it from going beyond the boundary. The formula is as follows:
[0107]
[0108] r p =(x p ,y p ),r e =(x e ,y e () represents the position of the chasing or dodging robot in the coordinate system. and This represents the maximum speed for chasing and dodging robots. p and v e This represents the speed of the chasing robot and the speed of the dodging robot. Here, x(r) is a piecewise function, and the bounded region constraint term only applies within a certain range. The function X(r) is as follows:
[0109]
[0110] The final form of the pursuit strategy:
[0111]
[0112] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A multi-robot cooperative pursuit method based on density allocation within a limited sensing range, characterized in that: Includes the following steps: Each chasing robot acquires the position information of N chasing robots and M escaping robots within its perception range; The target escape robot is determined by the chasing robot. If there is no escape robot within the chasing robot's perception range, the chasing robot will not participate in the chase. If there is an escape robot, the target escape robot is directly determined. If there are multiple escape robots, the process of determining the target escape robot is as follows. By integrating the positions of the pursuit robot and other pursuit robots within its field of vision, a distribution field of pursuit robot density in the plane is formed, and the density value of the positions of all escaping robots within its field of vision is calculated. The density value of the evading robot and the distance between the pursuing robot and the evading robot are weighted and calculated. The evading robot with the smallest weighted value is selected as the target evading robot. Calculate the chasing force required for the chasing robot to chase the target robot to escape, i.e., the chasing term. If it is found that it is necessary to avoid obstacles during the chasing process, calculate the detour point, which is the target point. If it is found that it is not necessary to avoid obstacles during the chasing process, then it is not necessary to calculate the detour point. If there are other chasing robots within the chasing robot's perception range that are chasing the same escaping robot, then the dynamic long-distance repulsion force, i.e., the dynamic cooperation term, is calculated; if there are no other chasing robots within the chasing robot's perception range that are chasing the same escaping robot, then the dynamic cooperation term is 0. Calculate the collision avoidance force required between chasing robots and between escaping robots to avoid collisions, i.e., the collision avoidance term; If the chasing robot or the escaping robot is found to be outside the finite area during the chase, the finite area constraint force of the chasing robot and the escaping robot during the chase is calculated, i.e., the finite area constraint term. If, during the pursuit, it is found that the pursuing robot or the escaping robot has not exceeded the finite area, then the finite area constraint term is zero. The pursuit strategy for chasing robots is based on the pursuit terms, dynamic cooperation terms, collision avoidance terms, and finite area constraints, which enables N chasing robots to chase M escaping robots.
2. The multi-robot cooperative pursuit method based on density allocation within a limited sensing range according to claim 1, characterized in that: It also includes, when M>1; using a modified smoothing function to determine the target robot that the chasing robot is pursuing, which is an escaping robot; the expression of the modified smoothing function is as follows: Where: τ=r ij / r sen r ij =||r i -r j || is the distance R from the nearby chasing robot j to the chasing robot i. sen It is the sensing radius of the chasing robot; a d =R i / R sen A scaling factor, R, used to control the shape or truncation range of the kernel. i It is the individual radius of the chasing robot i.
3. The multi-robot cooperative pursuit method based on density allocation within a limited sensing range according to claim 1, characterized in that: The formula for calculating the weighted value of the evading robot density and the distance between the pursuing robot and the evading robot is as follows: press i (k)=Q i (r k )*(β)1+(β)2*r ik (k∈P i ) Among them, P i It is the set of evading robots perceived by the pursuing robot, where k is P i The dodge robot in the middle, r ik To escape the distance between robot k and pursuing robot i, Q i (r k ) is the density value of the evading robot k perceived by the pursuing robot in the density field, and β1 and β2 are weighting coefficients.
4. The multi-robot cooperative pursuit method based on density allocation within a limited sensing range according to claim 1, characterized in that: The formula used to calculate the chasing force required for the chasing robot to chase the target and escape the robot, i.e., the chasing term, is as follows: r pred Predict the robot's next move; The maximum speed of the chasing robot; Chase the current location of robot i.
5. A multi-robot cooperative pursuit method based on density allocation within a limited sensing range according to claim 1, characterized in that: It also includes identifying obstacles within the perception range, and merging two obstacles if the minimum distance between two obstacles is less than the pursuer's safe radius; The robot first identifies obstacles within its perception range. If there are multiple obstacles, each obstacle calculates its nearest point to other obstacles. If the distance between the nearest points is less than the robot's own radius Ri, then the two obstacles need to be merged into one obstacle. Detect whether an obstacle needs to be avoided; if the line between the tracker and the target point intersects with an obstacle, then the obstacle must be avoided. To detect whether an obstacle needs to be avoided, connect the positions of the chasing robot and the target escape robot, and iterate through all obstacles within the chasing robot's perception range. If an obstacle intersects the line or the distance between the nearest point of the obstacle and the line is less than the chasing robot's own radius Ri, then the obstacle is considered an obstacle that needs to be avoided. If there are multiple obstacles that need to be avoided, then the one closest to the chasing robot's position is the target obstacle to avoid.
6. A multi-robot cooperative pursuit method based on density allocation within a limited sensing range according to claim 1, characterized in that: The process for determining the detour points is as follows: First, the target obstacle to be avoided will expand outward by a distance Ri equal to the radius of the chasing robot itself. Next, draw tangents from the position of the chasing robot to the left and right sides of the target obstacle to obtain two tangent points, which are considered as alternative detour points. Finally, the angle between the left tangent and the connecting line. That is, the angle between the line connecting the positions of the chasing robot and the dodging robot, and the right tangent and the connecting line. like Less than If the left tangent point is chosen as the detour point, then the right tangent point is chosen as the detour point.
7. A multi-robot cooperative pursuit method based on density allocation within a limited sensing range according to claim 1, characterized in that: The formula for calculating the pursuit term is as follows: The maximum speed of the chasing robot; The location of the detour point for chasing robot i; Chase the location of robot i.
8. A multi-robot cooperative pursuit method based on density allocation within a limited sensing range according to claim 1, characterized in that: The process of calculating the dynamic long-distance repulsive force required for the robot to escape from the same chasing target, i.e., the dynamic cooperative term, is as follows: Where: d min (t): the shortest distance between the escaping robot and the chasing robot; α(d min (t)): Decay function, used to control the repulsive force to be effective only within a certain range and to decay; d ij : Used to represent the distance between chasing robot i and escaping robot j; The maximum speed of the chasing robot.
9. A multi-robot cooperative pursuit method based on density allocation within a limited sensing range according to claim 1, characterized in that: The formula for calculating the collision avoidance force required between chasing robots and between escaping robots to avoid collisions, i.e., the collision avoidance term, is as follows: in: Let θ be the displacement vector between the i-th and j-th chasing robots, and let Θ be the step function. safe =3r cd It is the set range of repulsive force, when d ij ≥d safe At that time, there exists a repulsive force that increases the distance between the chasing robots to prevent them from colliding with each other. ij <d safe At this point, the risk of collision can be considered low, and the repulsive force drops to 0.