Distributed Artificial Potential Field-Based System for controlling swarm robots

Abstract

The present invention relates to a swarm robot control system, comprising a swarm robot in which individual robots of homogeneity form a swarm and operate in the same plane, and a controller that controls the operation of the swarm robot to form a pattern that surrounds a target having an arbitrary shape based on a Distributed Artificial Potential Field. According to the present invention, in controlling a swarm of robots to surround a target of an arbitrary shape at an equal distance, there is an effect of improving accuracy and operation speed, and improving overall control performance.

Description

Technology Field

[0001] The present invention relates to swarm robot control technology, and more specifically, to swarm robot control technology for encircling a target of any shape. Background Technology

[0003] In recent years, the topic of distributed or cooperative coordination and control of multiple autonomous agents has garnered significant attention in the field of engineering. This increased interest has been driven primarily by the emergence of engineering applications, such as the large-scale control of multi-robot teams and the deployment of autonomous vehicles. This trend is evident in the growing number of research articles covering applications in areas such as collective transport, search and rescue operations, collective security, and other related fields.

[0004] The key challenge in these applications is managing a multi-robot system that cooperates to surround a specific target in a desired shape using appropriate methodologies. Generally, the goal of the system is for the robots to converge on the target location and arrange themselves around it in a desired form. This often involves maintaining a uniform distance between the robots and the target or ensuring equal spacing between the robots. The most commonly observed form is a circular pattern, a behavior often referred to as encirclement. The concept of encirclement control originated from research on multi-agent circular tracking inspired by the existing "three bugs" problem, and this strategy requires a communication network described by a ring topology. However, this approach does not allow agents to form a flexible arrangement that adapts to the environment based on available environmental data.

[0005] Over the past decade, the artificial potential field (APF) method has become a widely used approach for target enclosure. Robots use attractive forces to form an enclosure by following the potential field gradient and repulsive forces to avoid collisions and obstacles. Existing techniques explore wolf-pack hunting using the APF method. While this approach eliminates the need for an explicit encirclement function, the wolf pack is limited to confining only a single target in a circular shape. Other conventional techniques disclose methods for encircling a target in a predefined shape by combining the virtual structure method and the APF approach; however, the virtual structure method treats the system as a rigid body, allowing each robot to adjust its behavior based on its position within the structure, whereas the APF helps the pack move toward and surround the target.

[0006] Another interesting strategy based on the fundamental principles of gene regulation and cell interactions during conventional multicellular development involves using gene regulatory networks (GRNs) as effective self-organizing systems for multirobot shape formation and targeted enclosure. Through this approach, multirobots can independently organize into complex forms following the dynamics of gene regulatory network models.

[0007] Conventional techniques are suitable for both single and multiple targets, whether static or dynamic, but these methods have the problem that significant adjustments are required when dealing with targets modeled with complex geometries rather than simple point masses. Prior art literature

[0008] Republic of Korea Published Patent 10-2013-0056586

[0009] Farivarnejad, Hamed, and Spring Berman. "Multirobot control strategies for collective transport." Annual Review of Control, Robotics, and Autonomous Systems 5.1 (2022): 205-219. Farivarnejad, Hamed, Sean Wilson, and Spring Berman. "Decentralized sliding mode control for autonomous collective transport by multi-robot systems." 2016 IEEE 55th conference on decision and control (CDC). IEEE, 2016. Saxena, Shubhankar, Rohan Jais, and Deepika Rani Sona. "Search and rescue operations using robots demonstrating swarm behaviour." 2020 5th International Conference on Communication and Electronics Systems (ICCES). IEEE, 2020. Powers, Stephen. Asset protection in escorting using multi-robot systems. Rochester Institute of Technology, 2016. Klamkin, M. S., and D. J. Newman. "Cyclic pursuit or “the three bugs problem”." The American Mathematical Monthly 78.6 (1971): 631-639. Kim, Tae-Hyoung, Shinji Hara, and Yutaka Hori. "Cooperative control of multi-agent dynamical systems in target-enclosing operations using cyclic pursuit strategy." International Journal of Control 83.10 (2010): 2040-2052. Wang, Chen, and Guangming Xie. "Limit-cycle-based decoupled design of circle formation control with collision avoidance for anonymous agents in a plane." IEEE Transactions on Automatic Control 62.12 (2017): 6560-6567. Escobedo, R., et al. "Group size, individual role differentiation and effectiveness of cooperation in a homogeneous group of hunters." Journal of the Royal Society Interface 11.95 (2014): 20140204. Rezaee, Hamed, and Farzaneh Abdollahi. "A decentralized cooperative control scheme with obstacle avoidance for a team of mobile robots." IEEE Transactions on Industrial Electronics 61.1 (2013): 347-354. Meng, Yan, Hongliang Guo, and Yaochu Jin. “A morphogenetic approach to flexible and robust shape formation for swarm robotic systems.” Robotics and Autonomous Systems 61.1 (2013): 25-38. Oh, Hyondong, and Yaochu Jin. “Evolving H-GRNs for Morphogenetic Adaptive Pattern Formation of Swarm Robots.” Evolutionary Computation in Gene Regulatory Network Research (2016): 327-361. Vecil, Francesco, Pauline Lafitte, and Jesus Rosado Linares. “A numerical study of attraction / repulsion collective behavior models: 3D particle analyzes and 1D kinetic simulations.” Physica D: Nonlinear Phenomena 260 (2013): 127-144. Gia Luan, Phan, and Nguyen Truong Thinh. “Collective Cognition on Global Density in Dynamic Swarm.” Sensors 23.10 (2023): 4648. The problem to be solved

[0010] The present invention was devised to solve the above-mentioned problems and aims to provide a distributed artificial potential field-based swarm robot control system.

[0011] The objectives of the present invention are not limited to those mentioned above, and other unmentioned objectives will be clearly understood by a person skilled in the art from the description below. means of solving the problem

[0013] The present invention, for achieving such an objective, relates to a swarm robot control system comprising a swarm robot in which individual robots of homogeneity form a swarm and operate in the same plane, and a controller that controls the operation of the swarm robot to form a pattern that surrounds a target having an arbitrary shape based on a Distributed Artificial Potential Field.

[0014] The above controller can control the swarm of robots such that the distance between each individual robot and the target is uniform, and the distance between adjacent individual robots is uniform.

[0015] The above controller can control the swarm of robots by calculating the interactions between individual robots and the target-robot interactions.

[0016] The above controller can model the interaction between individual robots and the target-robot interaction using a Morse potential field.

[0017] The above controller can control each individual robot to be positioned at the same distance from the target using a parameter adaptation algorithm. Effects of the invention

[0019] According to the present invention, in controlling a swarm of robots to surround a target of an arbitrary shape at an equal distance, there is an effect of improving accuracy and operation speed, and improving overall control performance. Brief explanation of the drawing

[0021] FIG. 1 conceptually illustrates a swarm robot control system according to one embodiment of the present invention. Figure 2 illustrates a swarm of robots surrounding a target in an equidistant formation. Here, the target is shown in blue. Figure 3 illustrates the stability phase diagram for a given dynamic system. Figure 4 illustrates the configuration of a swarm of robots according to three different controllers. Figure 5 is a table summarizing the controller parameter values ​​for the simulation in the experiment of the present invention. Figure 6 illustrates the target encirclement of a swarm of robots in the first simulation of the present invention. Figure 7 illustrates the appearance of a swarm of robots surrounding a target in the second simulation of the present invention. Figure 8 illustrates the appearance of a swarm of robots surrounding a square target in an experiment of the present invention. Specific details for implementing the invention

[0022] The present invention is capable of various modifications and may have various embodiments, and specific embodiments are illustrated in the drawings and described in detail. However, this is not intended to limit the present invention to specific embodiments, and it should be understood that it includes all modifications, equivalents, and substitutions that fall within the spirit and scope of the invention.

[0023] The terms used in this application are used merely to describe specific embodiments and are not intended to limit the invention. The singular expression includes the plural expression unless the context clearly indicates otherwise. In this application, terms such as "comprising" or "having" are intended to indicate the presence of the features, numbers, steps, actions, components, parts, or combinations thereof described in the specification, and should be understood as not precluding the existence or addition of one or more other features, numbers, steps, actions, components, parts, or combinations thereof.

[0024] Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as generally understood by those skilled in the art to which the present invention pertains. Terms such as those defined in commonly used dictionaries should be interpreted as having a meaning consistent with their meaning in the context of the relevant technology, and should not be interpreted in an ideal or overly formal sense unless explicitly defined in this application.

[0025] Furthermore, in the description referring to the attached drawings, identical components are assigned the same reference numeral regardless of drawing symbols, and redundant descriptions thereof are omitted. In describing the present invention, if it is determined that a detailed description of related prior art could unnecessarily obscure the essence of the present invention, such detailed description is omitted.

[0026] The present invention relates to a swarm robot control system.

[0027] This invention introduces an artificial potential field (APF)-based approach for swarm robots that surrounds a target object of arbitrary shape in an equidistant manner based on predefined parameters of distance between robots and robot-target distance. Here, it is assumed that the target is static, significantly larger than the robot, and of arbitrary shape, and that the robot can communicate only locally and recognize the relative positions of its neighbors. The target can be detected within a limited range, and the proposed method requires only information on the nearest point.

[0028] FIG. 1 conceptually illustrates a swarm robot control system according to one embodiment of the present invention.

[0029] Referring to FIG. 1, a swarm robot control system according to one embodiment of the present invention includes a swarm robot (100) and a controller (200).

[0030] A swarm robot (100) operates by having homogeneous individual robots (110) form a swarm in the same plane.

[0031] The controller (200) controls the operation of the swarm robot (100), and controls the operation of the swarm robot (100) so that it becomes a pattern of surrounding a target having an arbitrary shape based on a distributed artificial potential field.

[0032] The controller (200) can control the swarm robots (100) so that the distance between each individual robot (110) and the target is uniform, and the distance between adjacent individual robots is uniform.

[0033] The controller (200) can control the swarm of robots (100) by calculating the interactions between individual robots and the target-robot interactions.

[0034] The controller (200) can model the interaction between individual robots and the target-robot interaction using a Morse potential field.

[0035] The controller (200) can control each individual robot (110) to be positioned at the same distance from the target using a parameter adaptation algorithm.

[0037] Same planar surface A set representing n homogeneous robot groups operating in Considers. Such robots have a uniform radius for each robot It is modeled as a circular agent having. represents the position of robot i, and In this case, the scenario is simplified to the degenerate case of a point agent. The dynamics of each robot are controlled by a double integrator model, which can be expressed mathematically as follows.

[0038] (1)

[0039] Here, is the velocity of the i-th robot, represents the acceleration of the i-th robot.

[0040] The goal of each robot is to move from an initial position to a designated destination while collectively encircling a target object. At the same time, the robot must avoid collisions with other robots and targets. This collision avoidance is defined as ensuring that no overlap occurs between robots or between a robot and a target.

[0041] In the present invention, the target is a simple closed curve It is modeled as an object of arbitrary shape represented by. It is assumed that the target is static, larger than the robot, and initially visible to all robots in D.

[0042] Each robot is equipped with a radial sensor system that detects the relative distance and azimuth to surrounding robots and targets. This sensor has a limited range for obtaining information from surrounding robots, and this r s It is indicated as. The relative position of robot j with respect to robot i If indicated by , the measured distance between robots It can be expressed as. Projecting onto P If expressed as such, the resulting measured distance from the robot to the target is It can be defined as. D is denoted as the set of neighbors of the i-th robot, including all surrounding robots within the detection range, and it is assumed that as long as the robot is within D, the target is large enough to be continuously seen. Additionally, the robot possesses local communication capabilities within the same range as the detection system.

[0044] Figure 2 illustrates a swarm of robots surrounding a target in an equidistant formation. Here, the target is shown in blue.

[0045] Referring to FIG. 2, the objective of the multi-robot system in the present invention is to surround a target of any shape within a two-dimensional space by forming an equidistant configuration. To achieve this task, the multi-robot configuration must comply with the following conditions as much as possible.

[0046] * Condition 1: The distance between each robot and the target must be uniform.

[0047] * Condition 2: The distance between adjacent pairs of robots must also be uniform.

[0048] According to the aforementioned conditions, the uniform distance between adjacent robots is d 01 Represented as , and the uniform distance between each robot and the target is d 02 It is denoted as such. Therefore, the cooperative target encirclement problem by a multi-robot system can be defined as follows.

[0049] * Definition 1: The case where target P is equally surrounded by n≥3 robots in an equidistant manner can be expressed as follows.

[0050] (2)

[0051] (3)

[0052] Here, represents the two nearest neighbors of robot i.

[0053] However, the system is d 01 and d 02 Conditions cannot be satisfied simultaneously. In the present invention, d 02 While is fixed and predefined by the user, the robot adapts to the size of the target and the swarm size by d 01 I will change the conditions. For convenience robot i's d 01 It is to represent the value. Initially, this value is common to all robots, and d 01 It is displayed as.

[0054] If the swarm of robots satisfies the above conditions, it can be said to be a siege state surrounding the target.

[0056] In this invention, two types of interactions, namely robot-to-robot interaction and robot-to-target interaction, are described as follows. Both types of interactions use repulsive forces to ensure collision-free movement between the robot and the target. Furthermore, these interactions use attractive forces to maintain the robot in a desired shape. Each interaction can be modeled using a generalized second-order Morse potential field. and If so, the potential field y affecting robot i can be expressed as follows.

[0057] (4)

[0058] Here, C is the vertical scaling factor of U, and l represents the horizontal scaling factor of U. If C=l=1, it has a non-scale potential field. R c represents the ratio of the magnitudes between the attractive and repulsive components, and R l represents the ratio of the effective distance between the attraction and repulsion components, and these are important parameters that control the macroscopic behavior of swarm robots.

[0059] Figure 3 illustrates the stability phase diagram for a given dynamic system.

[0060] Referring to Fig. 3, given a dynamic system, R c and R l The resulting macroscopic behavior of the uniform particle system when varying according to [the equation] is consistent with the predictions shown in the stability phase diagram.

[0061] To form shapes without collisions, the potential field must be characterized by short-range repulsion and long-range attraction. This indicates that the typical length of repulsion is shorter than the length of attraction (R l (> 1), indicating that the force promoting cohesion between individuals at close range is greater than the force repelling them (R c > 1) Prevents dispersion. Consequently, in the present invention, R c and R l Restrict to regions VI and VII.

[0062] Also, since the Morse potential field is isotropic, the function U is the error vector d i It indicates that it depends only on the norm. Therefore, the following mathematical expression is valid.

[0063] (5)

[0064] (6)

[0065] (7)

[0066] For convenience It is written as .

[0067] * Lemma 1: If C,l>0 and R c , R l If >1, m(d)=0 has a unique non-trivial positive solution.

[0068] To find the non-trivial solution for m(d)=0, substituting mathematical formula (4) into m(d)=0 yields the following mathematical formula.

[0069] (8)

[0071] * Lemma 2: If C,l>0 and R c , R l If >1, m(d) is bounded.

[0072] * Remark 1: Unique d0 and Since this exists and am.

[0073] According to Lemma 2, d min wa d max Let and be the global minimum and global maximum of m(d), respectively. In Note 1 and You can know.

[0075] In the present invention, the enclosure control model for a robot is implemented primarily based on a Morse potential field. To maintain the integrity of the stability phase diagram, the control input a of robot i i It can be expressed by the following mathematical formula (9).

[0076] (9)

[0077] Here, control input a i self-propelled ship , robot interaction term , robot-target interaction term It consists of three components.

[0078] Initial self-propelled vessel It is defined in the following mathematical formula (10), which allows the robot to move at an appropriate speed.

[0079] (10)

[0080] To account for the mobility of the simulated agent and to mitigate unrealistic acceleration of individual robots and vibrations within the group, the coefficient of friction K in all simulations d I set =0.3. If If, Through this, it can be seen that robot i tends to approach equilibrium velocity 0.

[0081] Figure 4 illustrates the configuration of a swarm of robots according to three different controllers.

[0082] In Fig. 4, the left side is a grid configuration, the middle side is a configuration surrounding the target, and the right side is an equidistant formation configuration.

[0083] Referring to Fig. 4, and The approach to establishing a formula for includes the step-by-step configuration of the controller to satisfy the action procedure.

[0084] First, separate the target from the swarm robot, and ensure the swarm robot satisfies Condition 2. Defines.

[0085] Second, if there is a target, help the robots surround the target. Defines. However, d 01 , d 02 Conditions 1 and 2 may not both be perfectly satisfied due to the discrepancy between and n.

[0086] Third, to force the robot to form an equidistant line around the target, d 01 A parameter adaptation algorithm is proposed to modify it.

[0088] In order to preserve the original meaning of the stability phase diagram in the present invention, the interaction between robots is expressed mathematically as follows.

[0089] (11)

[0090] Here, U r is defined as in mathematical formula (4), where C, l, R c and R l C corresponding to each r , l r , R cr and R lr It has parameters.

[0091] In the absence of [something], mathematical formula (9) can apply the clustering behavior of regions VI and VII by adhering to the stability topology.

[0092] * Region VI: This region is expected to generate a grid state configuration with fixed mutual distances.

[0093] * Region VII: This parameter space is likely to generate a rotational state configuration in which the robot moves around the center of mass.

[0094] To satisfy condition 2, R cr and R lr is selected in region VI, and l r is a predefined mutual distance d 01 It becomes a function of. According to mathematical formula (8), l r It can be defined as follows.

[0095] (12)

[0096] In this invention, a parameter adaptation algorithm is proposed, and this algorithm d to force the robot to maintain an equidistant formation around a target. 01 Changes . However d 01 If you change l r It affects and eventually changes the boundary of m(d). This Due to the extreme value of , the robot's dynamic constraints may not be satisfied. Therefore, the boundary of m(d) must be kept constant. To achieve this, the size field is normalized for the non-scale field.

[0097] ul U r It is called the non-scale function of, and l defined by mathematical formula (12) r having second Let's assume that. According to Lemma 2 On the silver Each is a boundary. For each , It is done as. It can be obtained by applying mathematical formula (8), and field normalization is obtained by using the following mathematical formula to apply constraint C r It can be achieved by.

[0098] (13)

[0099] Here, K pr silver It is a new boundary of.

[0101] In this invention, it is assumed that there is only one target in the workspace and that each robot may have multiple neighbor robots. To prevent dominance resulting from interactions between robots, target-robot interaction is defined as follows.

[0102] (14)

[0103] Here, represents the size of the neighbor set. Ut is defined as in Equation (4), where parameter C t , l t , R ct and R lt C, l, R in the same formula c , R l Each corresponds to one.

[0104] Given that each robot participates in a single target-robot interaction, the results of the stability phase diagram can be neglected. However, since the target-robot interaction follows long-range attraction and short-range repulsion dynamics, the parameter R ct and R lt is limited within regions VI and VII. Parameter C t and l t It is derived from mathematical equation (8) and the field size normalization process, similar to the interaction between robots. For convenience cast Marked as a new boundary of. R regarding macroscopic behavior ct and R lt Numerous experiments were conducted to analyze the effects of.

[0105] R from the experimental results lt It was confirmed that influences the scope and size of workforce-related components. R lt If is reduced, the range of the force is compressed, causing robots near the target to converge faster than those far away, forming a separated network. Conversely, R lt As it increases, the range of the workforce expands and the size becomes flatter across the entire area, allowing the robot to converge more synchronized toward the target, but the speed slows down.

[0106] Also, R ct directly affects the size of the repulsion-related component. As can be seen from mathematical formula (4), R ct As increases, the magnitude of the repulsion also increases accordingly. Consequently, due to field size normalization, the size of the attraction component decreases.

[0107] In the experiment of the present invention, parameter R according to application, dynamic, and communication constraints ct and R lt is appropriately selected.

[0109] By applying the control input of mathematical formula (9), the robots can surround the target without collision. However, the number of robots is d01 and d 02 If it does not match the predefined value of, the robot may not satisfy both conditions described in Definition 1. represents the common distance required between injection robots to satisfy Definition 1. In this context, the following two unexpected forms may occur.

[0110] : In this scenario, the robot does not form a closed shape, but all satisfy condition 1.

[0111] : Robots form a closed shape, but not all of them satisfy condition 1.

[0112] In this invention, a parameter adaptation algorithm is proposed to solve this scenario. The core concept of the proposed parameter adaptation algorithm is that the robot globally detects these conditions and d 01 The purpose is to adjust the individual values ​​of to reach a global consensus on this parameter to satisfy Definition 1. The global detection of a closed formation is formulated in the following Definition 2.

[0114] * Definition 2: For every robot, at least two neighboring robots located in different half planes If separated by a line, the formation is considered globally closed. If the formation is globally closed, the indicator for 'is-globally-closed' is 1.

[0115] However, robots cannot directly access this type of global information. i Let's assume that represents the local perception of robot i indicating whether the formation is closed from the robot's perspective.

[0116] * Definition 3: ic i =1 and, When that happens, assume that there exists something satisfying the following mathematical equation.

[0117] (15)

[0118] (16)

[0119] then, The value of converges to 0 as time approaches infinity. Therefore Including helps to alleviate the slow convergence of this value.

[0120] * Note 2: For all robots If so, the indicator representing 'is-globally-closed' becomes 1.

[0121] In this invention, it is assumed that each robot participates in a collective decision-making process to verify global information regarding is-globally-closed and reach a consensus. For convenience, the consensus indicator for robot i is It is indicated as.

[0122] In the second case, In this case, the robot establishes a closed formation, but not all robots satisfy Condition 1. The indicator that robot i satisfies Condition 1 is If indicated, robot i satisfies the following case =1.

[0123] (17)

[0124] Here, silver class It represents a threshold value influenced by the ratio between the boundaries of. And from the perspective of robot i The consensus indicators of It is represented as such, and it is assumed that the robot can obtain this value through the same collective decision-making process.

[0125] * Note 3: 'is-globally-satisfy-condition1' Let's set it as the ground truth. For all robots If this happens, 'is-globally-satisfy-condition1' becomes 1.

[0126] By utilizing the introduced metric, the robots' d according to the rate of change defined below 01 You can adjust the value.

[0127] (18)

[0128] Here, the value of λ affects the robot's adaptability. As the value of λ increases, the formation speed of the swarm robot increases. However, the value of λ from vibration It must be small enough to prevent.

[0129] Applying mathematical equation (17) can help individual robots locally satisfy ‘Definition 1’. However, Without consensus on the value, swarm robots may experience unexpected behavior due to heterogeneous potential fields. In this invention, it is assumed that swarm robots continuously reach consensus using a conventional consensus method. As time approaches infinity, the conventional consensus method It guarantees access to a common value.

[0131] The approach proposed in the experiments of the present invention is rigorously verified and evaluated through numerical simulations considering various target shapes and parameters, thoroughly assessing its effectiveness and overall performance.

[0132] To evaluate the effectiveness of the algorithm proposed in this invention, two experiments involving multiple robot teams are conducted. First, a controller without parameter adaptation is examined. This part aims to establish criteria and fundamental grounds for utilizing parameter adaptation to solve the equidistant formation problem. Subsequently, a controller with parameter adaptation is examined to experiment with the influence of various key parameters on the formation.

[0133] In the experiments of the present invention, all simulations are performed in a consistent setting. The robot workspace D is a square with a corner length of 500 cm. To demonstrate the generalization of the proposed algorithm in the experiments of the present invention, two types of targets are used: 1) a square object with a corner length of 50 cm, and 2) a circular object with a radius of 46.15 cm.

[0134] In the experiment of the present invention, each robot has a uniform physical body radius and detection range It has. Initially, all robots are randomly distributed within a square area with a corner length of 100 cm, and the target is always located in the center of the workspace D. In the experiment of the present invention, the controller parameter values ​​for the simulation are shown in FIG. 5.

[0135] Figure 5 is a table summarizing the controller parameter values ​​for the simulation in the experiment of the present invention.

[0137] In the first simulation of the present invention, in the case where there is no parameter adaptation, i.e., d 01 When the number of robots is maintained constant throughout this simulation, the effect of the number of robots on the target encirclement task is as follows. When the number of robots is changed from 10 to 50, it can be observed that the formation pattern changes systematically. The equilibrium state of the swarm robots is recorded and displayed as shown in Figure 6.

[0138] Figure 6 illustrates the target encirclement of a swarm of robots in the first simulation of the present invention.

[0139] FIG. 6 illustrates a target encirclement without parameter adaptation in an experiment of the present invention, with cases where the number of robots (n) is 10 (a), 20 (b), and 50 (c), respectively, and the formation shape is represented by a green circle.

[0140] When using the circular target and basic parameters described in Fig. 5, at n=10, n=20, and n=50 The corresponding values ​​are 59.8, 30.3, and 12.16, respectively. The robot is n=10( It was observed that a closed formation cannot be formed when ). However, while the resulting pattern satisfies Condition 1, Condition 2 is not satisfied by all robots. As the number of robots increases, the formation begins to close, and the optimal scenario that nearly satisfies both conditions occurs at n=20, where As the size of the swarm continues to increase, there may not be enough space for all robots to join the reference pattern (indicated by the green circle). Consequently, these excess robots attempt to form a pattern similar to the reference pattern, resulting in the emergence of a multi-layered formation.

[0141] Because the outer layer robot is further away from the reference pattern (equilibrium state), it is pulled toward the target. To counteract this, the inner layer robot moves closer to the target and consequently experiences a repulsive force.

[0143] In the second simulation of the present invention, a parameter adaptation algorithm is applied to enable a swarm of 50 robots to surround a circular object (target) using the same settings as in the first simulation. The swarm pattern formation process from the initial position to the desired configuration is illustrated in FIG. 7.

[0144] Figure 7 illustrates the appearance of a swarm of robots surrounding a target in the second simulation of the present invention.

[0145] Figure 7 shows a snapshot of 50 swarm robots surrounding a circular target in a single simulation in which the parameter adaptation algorithm was implemented in the experiment of the present invention.

[0146] In Fig. 7, the white circle is It represents the robot when, and the gray circle is It represents the robot when, and the turquoise circle is Represents the robot when it is.

[0147] For all robots and It is assumed that the value of is the same as the ground truth value presented in Note 2 and Note 3.

[0148] Initially, the same basic local metric value for each robot and global indicator values This is assigned. However, not long after, due to interactions between robots, the robots are rapidly dispersed into a grid configuration, satisfying equations (15) and (16), so that almost all robots ...and thus it has. Furthermore, as can be seen in FIG. 7 (a), there are only 3 robots satisfying mathematical equation (17), so globally am.

[0149] As shown in FIG. 7 (b), when the group forms a closed formation, all robots satisfy conditions (15) and (16), and as a result ...becomes. However, most robots do not stay on the standard pattern, so As with This becomes. This forces all robots in other layers to return to the reference pattern. This process continues until all robots satisfy both conditions, and for all robots ...and, as seen in Fig. 7 (d), And, the process of encircling the target is completed.

[0150] To further confirm the effectiveness and generalizability of the method proposed in this invention, a second test is conducted using square targets. In this simulation, the cluster size is set to 50, and d 02 The range varies from 30 cm to 150 cm. All simulations of this experiment show that the robot consistently succeeds in surrounding the target. The results for extreme cases are shown in Fig. 8.

[0151] Figure 8 illustrates the appearance of a swarm of robots surrounding a square target in an experiment of the present invention.

[0152] In Fig. 8, the number of swarm robots is 50, and different d 02 It surrounds a square target with a value.

[0153] Based on these results, the following observations can be made.

[0154] In this case, the pattern formation speed is faster than in other scenarios. The main reason is that robots can utilize inter-robot interactions to disperse and rapidly encircle the target. Subsequently, so that all robots satisfy the encirclement state, d 01 This is adjusted.

[0155] In the case of, if the swarm robots have not yet surrounded the target, Even so, the pattern formation speed depends heavily on λ and the previously introduced consensus speed. However, as mentioned earlier, continuously when the swarm robots approach a state of encirclement To prevent fluctuations, λ must be kept small.

[0156] These experimental results demonstrate that the method proposed in this invention is scalable.

[0157] The present invention presents a novel controller based on artificial potential fields designed to autonomously solve the problem of a swarm of robots encircling a target of arbitrary shape. The controller design begins by forming a pattern in the absence of a target. Then, target-robot interactions are established to enable the robots to encircle the target. Notably, these proposed interactions also guarantee collision avoidance. Additionally, a parameter adaptation algorithm is proposed to guide the robots into the encircling state. Simulation and experimental results in the present invention demonstrate that the target enclosure controller proposed in this invention is effective, scalable, and generalizable for solving the problem of encircling a target of arbitrary shape.

[0158] Although the present invention has been described above using several preferred embodiments, these embodiments are illustrative and not limiting. Those skilled in the art will understand that various changes and modifications can be made without departing from the spirit of the invention and the scope of rights set forth in the appended claims. Explanation of the symbols

[0160] 100 swarm robots 200 controllers

Claims

Claim 1 A swarm robot control system comprising: a swarm robot in which individual robots of homogeneity form a swarm and operate in the same plane; and a controller that controls the operation of the swarm robot to form a pattern that encircles a target having an arbitrary shape based on a Distributed Artificial Potential Field. Claim 2 A swarm robot control system according to claim 1, wherein the controller controls the swarm robots such that the distance between each individual robot and the target is uniform and the distance between adjacent individual robots is uniform. Claim 3 A swarm robot control system according to claim 2, wherein the controller controls the swarm robots by calculating interactions between individual robots and target-robot interactions. Claim 4 A swarm robot control system according to claim 3, wherein the controller models interactions between individual robots and target-robot interactions using a Morse potential field. Claim 5 A swarm robot control system according to claim 2, wherein the controller controls each individual robot to be positioned at the same distance from the target using a parameter adaptation algorithm.

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