An asynchronous interaction cluster regulation method based on spontaneous synchronization algorithm

Abstract

The present application relates to a kind of asynchronous interaction cluster regulation method based on spontaneous synchronization algorithm, using mathematical language to describe the problem of asynchronous interaction, the initial interaction time of cluster robot determines that the cluster is asynchronous interaction or synchronous interaction;Pulse coupling synchronization algorithm is used on cluster robot platform in combination with the characteristics of actual platform, the interaction pulse signal of individual in group is used as coordination mechanism, so that in the distributed cluster without synchronous clock, the whole cluster is spontaneously changed from asynchronous interaction to synchronous interaction;Self-organizing synchronization algorithm is applied to the cluster robot system of asynchronous interaction, realizes the gradually synchronization of distributed cluster robot interaction time, and finally spontaneously changes into synchronous interaction cluster.This method considers the characteristics of real cluster robot perception interaction, uses interaction pulse signal as coordination mechanism, which is convenient for use in physical platform;Asynchronous interaction cluster is spontaneously changed into synchronous cluster, which eliminates the negative effects of asynchronous interaction on cluster movement.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of self-organizing cluster control method, and relates to an asynchronous interactive cluster regulation method based on spontaneous synchronization algorithm. BACKGROUND

[0002] Swarming of organisms is a ubiquitous self-organizing behavior in nature. Flocks of European starlings arrange into unpredictable formations, herds of wildebeest migrate in groups, and schools of sardines scatter to escape predators. Simple local self-organizing interaction rules applied to individuals with limited capabilities can result in amazing swarm behavior in space.

[0003] With the progress of related technologies and the development of hardware and software, distributed swarm robot systems are widely used in various fields and have advantages over traditional single robot systems in many aspects. In engineering applications, most intelligent agents of distributed systems communicate with neighbors through wireless networks and use embedded processors for information processing. The individual capabilities are limited by network bandwidth and energy consumption. With the increasing complexity of tasks, continuous communication may not be possible, and periodic sampling is a common method in multi-agent control. One of the main features of distributed systems is the absence of a central node and a synchronous clock. The interaction period of individuals within the group is independent, and the interaction time is difficult to unify. Therefore, in the presence of a perception interaction period, asynchronous interaction swarm is likely to occur.

[0004] Asynchronous interaction will directly prevent swarm robots from obtaining information from all neighbors at the same time. In this case, it will hinder the further emergence of robot swarm movement, and the stability of the swarm will be poor, and the negative impact of environmental noise on swarm movement will be aggravated. Therefore, a new method needs to be considered to unify the interaction time of the swarm and convert the asynchronous interaction swarm into a synchronous interaction swarm to compensate for the shortcomings of the asynchronous interaction swarm.

[0005] In nature and engineering systems, there is another self-organizing behavior - synchronization. Fireflies flashing in synchronization, crickets chirping in unison, heart pacemaker cells beating in rhythm, and multiple pendulums in spontaneous synchronization; all exhibit the exquisite self-organizing emergence behavior of groups in the time domain. There are rich theoretical results on the theoretical study of synchronization, and there are a large number of synchronization algorithms applied to the swarm robot platform. When self-organizing swarms are plagued by the negative effects of asynchronous perception interaction, spontaneous synchronization algorithms can be used as an optimal solution to the swarm robot system. SUMMARY

[0006] Technical problems to be solved

[0007] In order to avoid the deficiencies of the prior art, the present application proposes an asynchronous interaction cluster regulation method based on a spontaneous synchronization algorithm, which aims to use the interaction signals of cluster robot individuals as a coordination mechanism, and then use a self-organizing synchronization algorithm to realize spontaneous synchronization of interaction time of a distributed cluster robot system without a synchronous clock, thereby changing asynchronous interaction into synchronous interaction, thereby effectively solving the problems mentioned in the background art.

[0008] Technical scheme

[0009] An asynchronous interaction cluster regulation method based on a spontaneous synchronization algorithm, characterized in that the steps are as follows:

[0010] Step 1: On a cluster robot platform, individual i represents each robot, which can only interact with other individuals, i.e., other robots, in the group at interaction time The calculation of the s-th interaction time of individual i is as follows:

[0011]

[0012] Wherein T is the period length, representing the time interval of each interaction of the individual;

[0013] When the interaction period T>1, T=1, 2, 3..., the initial interaction time of all individuals determines whether the cluster is asynchronous or synchronous, if the initial interaction time of the individual in the group is not equal, the cluster is asynchronous at this time:

[0014]

[0015] If the initial interaction time of the individual in the group is the same, the cluster is synchronous at this time:

[0016]

[0017] Step 2: The Mirollo-Strogatz model is used as a synchronization algorithm to change the cluster from asynchronous interaction to spontaneous synchronization, in which model, the individuals have an instantaneous influence on the neighbor phase through a fixed frequency pulse signal, thereby achieving synchronization of the group;

[0018] Specifically, in the Mirollo-Strogatz model, a single cluster robot individual can be regarded as a vibrator, each vibrator represents whether it is in the state variable x of interaction, and the state variable x monotonically increases along the threshold x=1; when x reaches the threshold, the individual emits a pulse signal, and the state variable x immediately falls to x=0, and then the cycle is repeated; the position of the vibrator in each period is represented by the phase variable , x only with correlation;

[0019] The function f satisfies f(0) = 0, f(1) = 1;

[0020] The phase variable And has the following properties:

[0021] (1) T is the period length,

[0022] (2) The oscillator is at the beginning of the cycle, and the oscillator state is the minimum value x = 0, indicating that the robot, i.e. the oscillator i, does not interact;

[0023] (3) The oscillator is at the end of the cycle, and the oscillator state reaches the threshold value x = 1, at which time the individual information is broadcast, indicating that the robot, i.e. the oscillator i, is interacting;

[0024] When the individual state reaches the threshold value, a pulse interaction signal will be sent out, and at the same time, an instantaneous influence τ on the state of the surrounding neighbors will be generated. The state transition equation of the individual is:

[0025]

[0026] Where: x i (t) represents the current state of individual i at time t, a i (t) represents the number of neighbors that affect the state of individual i at time t b is called the dissipation coefficient, and the function f is a concave curve;

[0027] Step 3: Apply the spontaneous synchronization algorithm based on the Mirollo-Strogatz model to the asynchronous interaction of the swarm robot system to adjust the interaction time of each robot individual i using the state transition equation of the oscillator, so as to gradually synchronize the interaction time of the asynchronous interaction swarm and spontaneously change into a synchronous interaction swarm.

[0028] The swarm robot platform has: this needs to ensure that the spatial distribution of the swarm robot is within a certain range, and the transmission rate of the interaction signal is fast.

[0029] The transmission delay of the interaction information can be ignored;

[0030] The interaction signal of the swarm robot individual can be regarded as a pulse signal, and the pulse frequency is equal and fixed; usually, the sensor of the swarm robot has a fixed refresh frequency, and common pulse signals include sound, light, radio, etc.

[0031] The internal communication topology of the platform should be fully connected. This means that the swarm robot can interact with any other individual in the group at the interaction time, without being constrained by space.

[0032] The influence tau is pulse intensity and tau>0.

[0033] The dissipation coefficient b>0.

[0034] Beneficial effects

[0035] The application provides an asynchronous interaction cluster regulation method based on a spontaneous synchronization algorithm, which is used in a self-organizing distributed cluster robot system and spontaneously changes the asynchronous interaction cluster robot system into a synchronous interaction cluster robot system. The method is mainly combined with the characteristics of the cluster robot interaction mode, the asynchronous interaction cluster robot is modeled, and then a synchronization algorithm is applied, so that the asynchronous interaction self-organizing cluster robot system is changed into synchronous interaction. The method is suitable for individual isomorphism, uses a fixed-frequency pulse signal to interact with neighbors, and the interaction between individuals is not restricted by space. Firstly, the problem of asynchronous interaction is described by using mathematical language, and the initial interaction time of the cluster robot determines whether the cluster is asynchronous or synchronous. Secondly, the pulse coupling synchronization algorithm is used on the cluster robot platform in combination with the characteristics of the actual platform, the interaction pulse signal of the individual in the group is used as a coordination mechanism, so that the whole cluster is spontaneously changed from asynchronous interaction to synchronous interaction in the distributed cluster without a synchronous clock. Then, the self-organizing synchronization algorithm is applied to the asynchronous interaction cluster robot system, so that the distributed cluster robot interaction time is gradually synchronized, and finally the asynchronous interaction cluster is spontaneously changed into a synchronous interaction cluster. The method fully considers the characteristics of the real cluster robot perception interaction, uses the interaction pulse signal as the coordination mechanism, facilitates the use of the method on the physical platform, spontaneously changes the asynchronous interaction cluster into a synchronous cluster, and eliminates the negative influence of asynchronous interaction on the cluster movement.

[0036] Some typical cluster robot platforms to which the application can be applied include a small-range distributed unmanned aerial vehicle cluster using radio communication and a communication network distributed land desktop cluster robot platform. The application is not applicable to a cluster robot platform with a wide spatial distribution and a long communication delay, such as a large-range unmanned vehicle cluster system using underwater acoustic communication.

[0037] Compared with the prior art, the application discloses an asynchronous interaction cluster regulation method based on a spontaneous synchronization algorithm, which has the advantages that

[0038] First, the self-organizing synchronization algorithm is applied to the distributed cluster robot platform, and the self-organizing coordination behavior in time is combined with the self-organizing coordination behavior in space.

[0039] Second, the characteristics of the perception interaction of the existing cluster robot platform are fully considered, the pulse coupling synchronization algorithm is selected as the coordination method, and the application difficulty of the algorithm on the physical platform is reduced.

[0040] Third, can be used in a distributed cluster robot platform without synchronous clock, the asynchronous interaction of the cluster is spontaneously transformed into synchronous interaction, eliminating the negative effects of asynchronous interaction on cluster motion mentioned in the background work. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 is the trajectory of the asynchronous interaction cluster.

[0042] Figure 2 is the change of the interaction time of the asynchronous interaction cluster under the action of the spontaneous synchronization method.

[0043] Figure 3 is the trajectory of the cluster under the action of the spontaneous synchronization method. DETAILED DESCRIPTION

[0044] The present application will be further described in conjunction with the embodiments, drawings:

[0045] To achieve the above object, the technical scheme adopted by the present application is as follows:

[0046] Step 1: modeling of asynchronous interaction of cluster robots.

[0047] The practical cluster robot platform to which the present application can be applied should have the following characteristics,

[0048] 1. The interaction information transmission delay can be ignored; this requires that the spatial distribution of the cluster robots be within a certain range, and the interaction signal transmission rate be fast.

[0049] 2. The interaction signal of the individual cluster robot can be regarded as a pulse signal, and the pulse frequency is equal and fixed; usually the sensor of the cluster robot has a fixed refresh frequency, and common pulse signals include sound, light, radio, etc.

[0050] 3. The internal communication topology of the platform should be fully connected; this means that the cluster robot can interact with any other individual in the group at the interaction time, without being constrained by space.

[0051] Some typical cluster robot platform examples to which the present application can be applied are small-range distributed unmanned aerial vehicle clusters using radio communication, and distributed land tabletop cluster robot platforms for communication networking; however, the present application is not applicable to cluster robot platforms with a wider spatial distribution and longer communication delay, such as large-range unmanned underwater vehicle cluster systems using underwater acoustic communication.

[0052] On a cluster robot platform consistent with the present application, for individual i, it can only interact with other individuals in the group at the interaction time The calculation method of the s-th interaction time of individual i is as follows:

[0053]

[0054] T is the length of the cycle, which represents the time interval of each individual interaction.

[0055] When the interaction cycle T>1, T=1, 2, 3..., the initial interaction time of all individuals determines whether the cluster is asynchronous interaction or synchronous interaction, if the initial interaction time of individuals in the group is not equal, at this time the cluster is asynchronous interaction:

[0056]

[0057] If the initial interaction time of individuals in the group is the same, at this time the cluster is synchronous interaction:

[0058]

[0059] Step 2: apply pulse coupling synchronization algorithm to the cluster robot system.

[0060] The spontaneous synchronization is a self-organizing coordination phenomenon in time, which widely exists in nature and engineering systems, and the classic example of spontaneous synchronization is the synchronous light emission of fireflies, which attracts many scholars to discuss the synchronization phenomenon, and the modeling of the synchronization problem can be divided into two categories, the continuous interaction synchronization model represented by the Kuramoto model and the pulse coupling synchronization model represented by the Mirollo-Strogatz model.

[0061] As a preferred technical scheme of the present application, the Mirollo-Strogatz model will be selected as the synchronization algorithm in this step, so that the cluster is spontaneously changed from asynchronous interaction to synchronous interaction, in which model, the individual has an instantaneous influence on the neighbor phase through the fixed frequency pulse signal, so as to achieve the synchronization of the group.

[0062] In the Mirollo-Strogatz model, a single cluster robot individual can be regarded as a vibrator, the state variable of each vibrator is x, and the state variable x is monotonically increasing along the threshold x=1. When x reaches the threshold, the individual emits a pulse signal, and the state variable x immediately falls to x=0, and then the cycle is repeated. The position of the vibrator in each cycle can be represented by the phase variable Here x is only related to .

[0063]

[0064] The phase variable has the following properties

[0065] (1) T is the length of the cycle,

[0066] (2) The oscillator is at the beginning of the cycle, and the oscillator state is at the lowest value x = 0.

[0067] (3) The oscillator is at the end of the cycle, and the oscillator state reaches the threshold value x = 1.

[0068] Therefore, the function f satisfies f(0) = 0 and f(1) = 1.

[0069] When the state of an individual reaches the threshold value, a pulse interaction signal will be emitted, and at the same time, an instantaneous influence τ on the states of the surrounding neighbors will be generated. τ is the pulse intensity, τ > 0, which reflects the strength of the influence of the pulse signal on the states of the neighbors. The state transition equation of the individual is as follows.

[0070]

[0071] x i (t) represents the current state of individual i at time t, a i (t) represents the number of neighbors that have an influence on the state of individual i at time t.

[0072] Mirollo and Strogatz proved that when the state variable and the phase variable of the oscillators in the group satisfy the following relationship, synchronization will occur:

[0073]

[0074] From g = f -1 , we have:

[0075]

[0076] b is called the dissipation coefficient, b > 0, and the function f is concave down, which is a crucial condition for spontaneous synchronization.

[0077] In summary, the state transition equation of the oscillator is obtained as follows:

[0078]

[0079] Step 3: Apply the self-organizing synchronization algorithm to the asynchronous interaction of the swarm robot platform, so that the asynchronous interaction of the swarm can gradually synchronize and spontaneously change into a synchronous interaction swarm. Specific embodiments:

[0081] The cluster robot platform applied in the present example is a desktop cluster robot system with a size of 60mm*60mm*60mm, and each individual is a wheeled robot moving in a differential mode of double wheels. Each robot has two 3.7V rechargeable batteries, and has the ability to continuously experiment for 60 minutes. The individual can obtain the current position information and heading information through an external positioning system, and can broadcast information to other individuals in the group at a fixed frequency at the interaction time through a 2.4G wireless radio frequency communication module. The experimental site of the system is a square site of 4m*4m. In the site, the group communication is fully connected, and the communication delay can be ignored.

[0082] Since the robots are put into the site and the switch is turned on at different times, the initial interaction time of the individual is not consistent. Moreover, the cluster robot is distributed and does not have a synchronous clock to unify the interaction time of the cluster individuals. Therefore, the cluster robot has problems such as unstable group heading and uneven distance between individuals after applying the cluster algorithm, and the simulation trajectory is as shown in Figure 1

[0083] The cluster model adopted by the cluster robot is a velocity average model. The velocity average model is a classical strategy based on SAC rules. SAC rules are a cluster rule proposed by Reynolds et al. in the 1980s, which can be summarized as "separate-alignment-cohesion". This rule has been widely used in cluster motion research and engineering. In the velocity average strategy, the individual adjusts its own speed by referring to the average speed of the perceived interaction neighbors, so as to realize the consistency of the group level speed. Many cluster models including the Vicsek model and the Couzin model choose the velocity average strategy to realize the consistent motion of the group.

[0084] The present example uses a social force framework to realize the velocity average model, which is composed of the following parts:

[0085] (1) Self-driving force

[0086]

[0087] v i is the velocity of individual i, is the maximum acceleration of individual i, and β is the damping coefficient representing the size of the environmental loss of acceleration.

[0088] (2) Velocity coordination force

[0089]

[0090]

[0091] k vel ​is the speed coordination coefficient, which is also the proportional coefficient in proportional control; v i , v j is the speed of individual i, individual j. d is the expected speed of individual i, N i is the set of individuals in the group that interact with individual i.

[0092] (3) Position coordination force

[0093] This example uses a common position coordination force design:

[0094]

[0095]

[0096]

[0097] k pos is the position coordination coefficient, used to adjust the size of the position coordination force, k pos The larger, the more obvious the position coordination force acting on the individual. is the unit vector of individual i pointing to individual j.

[0098] The function g ij (r ij ) is used to control the attraction or repulsion between individuals, r ij represents the distance between individual i and individual j, parameter l a is the balance point of attraction and repulsion, which represents the position where attraction and repulsion are balanced, i.e. g(r balance ) = 0, when r ij < r balance , individuals repel each other, when r ij > r balance , individuals attract each other. l c represents the correlation length, used to adjust the strength of the change of attraction with distance.

[0099] Finally, the self-driving force, speed coordination force and position coordination force are substituted into the standard social force differential equation to obtain the kinematic equation of the speed average model

[0100]

[0101]

[0102] The parameter values of this example are shown in Table 1:

[0103] Table 1: Parameter values of the example model

[0104]

[0105] Step one: Asynchronous interaction cluster modeling.

[0106] The interaction mode adopted by the cluster in this example is that individuals broadcast the current state information in the group, and the speed average model expression of the interaction period is:

[0107]

[0108]

[0109] N b For the individual who is broadcasting, if N b = 0, it means that there is no individual broadcasting information at the current time, so its social force continues the state of the last time, and is disturbed by noise

[0110]

[0111] The initial state of the cluster in this example is asynchronous interaction, that is,

[0112]

[0113] Due to asynchronous interaction, N b <N, which means that the cluster individuals cannot receive all the information of their neighbors at the same time, which will make the cluster heading unstable, and the position coordination effect between individuals in the group is poor. The simulation trajectory graph of the asynchronous interaction cluster robot is shown in Figure 1 .

[0114] Step two: use Mirollo-Strogatz synchronization algorithm

[0115] The interaction period length of the individual in the example is T = 5, which means that the individual robot broadcasts information inside the cluster every 5 control steps. The individual is regarded as a vibrator with state variable x and periodic variable , which means that x corresponds to whether the individual is interacting and the position of the individual in the interaction period, which satisfies

[0116]

[0117] And the vibrator phase variable has the following properties: represents

[0118] The individual state variable x represents whether it is interacting;

[0119] The periodic variable represents the position of the individual in the interaction period;

[0120] (1) T is the period length,

[0121] (2) Robot i is at the beginning of the interaction cycle, the state of the oscillator is the lowest value x = 0, indicating that the robot i does not interact.

[0122] (3) Robot i is at the end of the interaction cycle, the state of the oscillator reaches the threshold value x = 1, at this time the individual information is broadcast, indicating that the robot i is at the interaction time; Therefore, the function f satisfies f(0) = 0, f(1) = 1.

[0123] The broadcast signal can be regarded as a pulse signal in the original model, as a coordination mechanism for the group interaction time, when the individual reaches the perception interaction time, it will broadcast information within the group, at this time it will have a transient effect τ on the state of the neighbors within the group. The state transition equation of the individual, that is, whether the individual state variable x changes during interaction, can be represented by the following formula

[0124]

[0125] x i (t) represents the state of individual i at time t, a i (t) represents the number of neighbors that affect the state of individual i at time t.

[0126] The state variable of the individual within the group and the phase variable satisfy the following relationship

[0127]

[0128] From g = f -1 ,

[0129]

[0130] In summary, the state transition equation within the individual is finally obtained

[0131]

[0132] In order to ensure that synchronization can occur, the function f needs to be a concave curve, where the dissipation coefficient b = 3 and the pulse strength τ = 1 / 60. Figure 2 The spontaneous synchronization method regulates the interaction time of the cluster, and the initial interaction time of the individual within the group is not uniform. Under the action of the synchronization algorithm, the individual gradually changes from asynchronous interaction to synchronous interaction, and synchronization is completed in about 4 cycles. Step three: apply the synchronization algorithm shown in step two to the asynchronous interaction of the cluster robot system, and the cluster robot changes from asynchronous perception interaction to synchronous perception interaction. The interaction time of the cluster individual will be unified, and the individual state update rule will change from formula (17) and (18) to formula (19) and (20). All individuals within the group will broadcast individual information at the interaction time, that is, N = N b .

[0133] When the group is at the interaction moment, i.e. t = t s , the individual interaction rule is:

[0134]

[0135]

[0136] When the group is at other moments except the interaction moment, i.e. t ≠ t s , the individual will keep the speed at the last moment as:

[0137]

[0138] Synchronous interaction means that individuals can obtain information of all neighbors in the group at the interaction moment, form ordered movement, and the group course is more stable, and individuals can form more stable position coordination. The change of interaction moment and group formation state of the asynchronous interaction group is observed. Figure 3 It is shown that under the regulation of the spontaneous synchronization method, the group changes from asynchronous interaction to synchronous interaction, the group course is stable after group formation, and uniform position coordination can emerge.

Claims

1. A method for regulating an asynchronous interaction cluster based on a spontaneous synchronization algorithm, characterized in that The steps are as follows: Step 1: On the swarm robot platform, individual i represents each robot, which can only interact with other individuals, i.e. other robots, within the swarm at interaction time …s, individual i's s-th interaction time is calculated as follows: Wherein: T is the length of the cycle, indicating the time interval of each individual interaction; When the interaction cycle T>1, T=1, 2, 3... the initial interaction time of all individuals determines that the cluster is asynchronous interaction or synchronous interaction, if the initial interaction time of individuals in the group is not equal, at this time the cluster is asynchronous interaction: If the initial interaction time of individuals in the group is the same, at this time the cluster is synchronous interaction: Step 2: use Mirollo-Strogatz model as synchronization algorithm, the cluster is spontaneously changed from asynchronous interaction to synchronous interaction, in the model, the individual through the fixed frequency pulse signal to the neighbor phase instantaneous influence, so as to achieve the synchronization of the group; Specifically, in the Mirollo-Strogatz model, a single swarm robot individual can be regarded as a pendulum, each pendulum represents whether to carry out the interaction state variable x, and the state variable x monotonically increases along the threshold x = 1; When x reaches the threshold, the individual emits a pulse signal, and the state variable x immediately falls to x = 0, and then repeats the cycle; The position of the pendulum in each cycle is represented by the phase variable , x is only related to . The function f satisfies f(0) = 0, f(l) = 1; the phase variable and has the following properties: (1) T is the period length, (2) The oscillator is at the beginning of the cycle, the oscillator state is the lowest value x = 0, indicating that the robot, i.e. the oscillator i, does not interact; (3) The oscillator is at the end of the cycle, the oscillator state reaches the threshold x = 1, at this time the individual information is broadcast, indicating that the robot, i.e. the oscillator i, is in interaction; When the individual state reaches the threshold value, it will send out pulse interaction signal, at the same time, it will have instantaneous influence τ on the state of the surrounding neighbors, the state transition equation of individual is: where: x i (t) denotes the state of individual i at time t, a i (t) denotes the number of neighbors that have an influence on the state of individual i at time t, b is called dissipation coefficient, and the function f is a concave curve. Step 3: apply the spontaneous synchronization algorithm based on Mirollo-Strogatz model to the asynchronous interaction cluster robot system, adjust the interaction time of each robot individual i with the state transition equation of the oscillator, realize the gradual synchronization of the interaction time of asynchronous interaction cluster, and spontaneously change into synchronous interaction cluster.

2. The method of claim 1, wherein the method is characterized by: The cluster robot platform has: the interaction information transmission delay is negligible; the interaction signal of the cluster robot individual can be regarded as a pulse signal, and the pulse frequency is equal and fixed; the internal communication topology of the platform should be fully connected.

3. The method of claim 1, wherein the method further comprises: The influence τ is the pulse intensity and τ>0.

4. The method of claim 1, wherein the method further comprises: The dissipation coefficient b>0.

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