CN103336527A - Device node formation method, device and system - Google Patents

Abstract

The present invention provides a node formation method, device and system, the node formation method includes: step S102, detecting the first distance and the first azimuth between the first node and the second node, and detecting the first node and the second node The second distance and the second azimuth between the three nodes, and calculate the third distance between the second node and the third node; step S104, judge whether the first distance, the second distance and the third distance are all less than or Equal to the preset first threshold length, if yes, execute step S108, if not, execute step S106; step S106, calculate the average position point, and drive the first node to move to the average position point, and at a predetermined time interval Return to step S102; step S108, calculate the target location point, and drive the first node to move to the target location point, and execute step S110 at predetermined time intervals; step S110, judge whether the first node reaches the target location point, if not, Then return to step S102, if yes, the first node stops the formation process.

Description

Node formation method, device and system

technical field

The present invention relates to the field of automatic control, in particular to a node formation method, device and system. the

Background technique

At present, the distributed control methods for multi-agent formation behavior mainly include potential function method, artificial physics method, behavior-based method, network graph theory method, etc. These methods can achieve the aggregation behavior of three-nearest neighbor agents to some extent. the

However, the starting point of these current methods is not to form a multi-member regular formation structure. The potential function method and the artificial physics method have multiple control parameters, and the formation behavior is sensitive to parameters; while the behavior-based method has deviations in behavior control accuracy and relatively low Large behavior response delay; although the network graph theory method can form a specified formation, however, each individual action has a sequence and cannot be executed concurrently, which takes a lot of time. the

For the above-mentioned problems in the distributed control of multi-agent formation behavior in related technologies, no effective solution has been proposed yet. the

Contents of the invention

The present invention provides a node mobile formation method, device and system to at least solve the problems existing in the distributed control of multi-agent formation behavior in the prior art. the

According to one aspect of the present invention, a node formation method is provided, including: step S102, detecting the first distance and the first azimuth between the first node and the second node, and detecting the distance between the first node and the third node The second distance between and the second azimuth, and calculate the second node and the third azimuth according to the first distance, the first azimuth, the second distance and the second azimuth The third distance between nodes; step S104, judge whether the first distance, the second distance and the third distance are all less than or equal to the preset first threshold length, if yes, then execute step S108, if not, then execute step S106; step S106, according to the first distance, the first azimuth, the second distance and the second azimuth, calculate the average position point between the first node, the second node and the third node, and drive the first node to the average The position point moves, and returns to step S102 at a predetermined time interval; step S108, calculates the target position point according to the current first distance, the current first azimuth angle, the current second distance and the current second azimuth angle, wherein the target position point It is the position point whose distance to the second node and the third node are both half of the first threshold length and the distance to the first node is the smallest, and drives the first node to move to the target position point, and executes steps at predetermined time intervals S110; Step S110, judging whether the first node has reached the target point, if not, return to step S102, if yes, the first node stops the formation process. the

Preferably, after step S102, it also includes: when it is judged according to the current first azimuth angle and the second azimuth angle that the first node, the second node and the third node are on the same straight line, and the first node is located between the second node and the second node When the same side of the three nodes, stop driving the first node. the

Preferably, after step S102, it also includes: when it is judged according to the current first azimuth angle and the second azimuth angle that the first node, the second node and the third node are on the same straight line, and the first node is located between the second node and the second node In the middle of the three nodes, drive the first node to move along any side of the vertical line of the straight line. the

Preferably, the average position point is the center of gravity or incenter of the triangle formed by the first node, the second node and the third node. the

Preferably, during the above process, at the same time, the movement of the second node and the third node are independently driven in the same manner. the

Preferably, the first node, the second node and the third node are all intelligent robots. the

According to another aspect of the present invention, a node formation device is provided, located in a first node, the node formation device includes: a detection unit, configured to detect a first distance between a first node and a second node and a first Azimuth, and detecting the second distance and the second azimuth between the first node and the third node; the calculation unit is used to judge whether the first distance, the second distance and the third distance are all less than or equal to the preset first A threshold length, if not, then calculate the average position point between the first node, the second node and the third node according to the first distance, the first azimuth, the second distance and the second azimuth; if yes, then The target position point is calculated according to the first distance, the first azimuth, the second distance and the second azimuth, wherein the target position point is half of the first threshold length to the second node and to the third node, and The position point with the smallest distance to the first node; the driving unit, used to drive the first node to move to the average position point or the target position point according to the calculation result of the calculation unit. the

Preferably, the calculation unit is also used to judge whether the first node, the second node and the third node are on the same straight line and the adjacent relationship among them according to the current first azimuth angle and the second azimuth angle. the

Preferably, the drive unit is also used to control the first node, the second node and the third node to be on the same straight line and the first node to be on the same side of the second node and the third node when the calculation unit judges that The node stops moving. the

Preferably, the driving unit is also used to drive the first Nodes move along either side of a vertical line to that line. the

Preferably, the average position point is the center of gravity or incenter of the triangle formed by the first node, the second node and the third node. the

Preferably, the detection unit includes: an infrared sensor for detecting the first distance and the second distance; a digital compass for detecting the first azimuth and the second azimuth;

According to yet another aspect of the present invention, a node formation system is provided, including: the first node, the second node, and the third node mentioned above, wherein the second node and the third node respectively have the same detection unit, calculation unit and drive unit. the

Preferably, the first node, the second node and the third node are all intelligent robots. the

In the present invention, when the initial distance between the nodes is too large, the nodes are driven closer to the average position point, until the nodes meet the distance requirements, the position adjustment is directly transferred, and the multi-agent formation behavior in the related art is solved. The problems of low control precision and large response delay in the distributed control of the distributed control system have achieved the effect of improving the control precision of the multi-agent formation and speeding up the response. the

Description of drawings

The accompanying drawings described here are used to provide a further understanding of the present invention and constitute a part of the application. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations to the present invention. In the attached picture:

Fig. 1 is a node formation method flowchart according to an embodiment of the present invention;

Fig. 2 is a schematic diagram of a module structure of a node formation device according to an embodiment of the present invention;

Fig. 3 is a schematic diagram of the distribution of a node formation system according to an embodiment of the present invention;

Fig. 4 is an individual state transition model diagram according to Embodiment 1 of the present invention;

Fig. 5 is a schematic diagram of the process of obtaining local position information of adjacent individuals by individual A _i according to an embodiment of the present invention;

6a to 6d are schematic diagrams of calculating p _ig according to an embodiment of the present invention;

Fig. 7 is a schematic diagram of determining the relative distance and the ideal destination position of an individual A _i according to Embodiment 1 of the present invention;

Fig. 8 is a state flow diagram of individual A _i respectively executing simple CA and AA algorithms according to Embodiment 1 of the present invention;

Fig. 9 is a state flow chart when an individual A _i executes a TFS interactive control method according to Embodiment 1 of the present invention;

Fig. 10 is a schematic diagram of a collinear scene of three nearest neighbor individual positions according to Embodiment 1 of the present invention;

Fig. 11 is a flow chart of the correction sub-algorithm according to Embodiment 1 of the present invention;

Fig. 12 is a schematic diagram of a critical position when conversion will occur according to Embodiment 1 of the present invention;

Fig. 13 is a schematic diagram of the E formation process when three neighbor individuals CF-2 are distributed according to Embodiment 1 of the present invention; and

Fig. 14 is a schematic diagram of the relationship between the average side length error and time of three neighboring individuals under a typical initial distribution according to Embodiment 1 of the present invention. the

Detailed ways

Hereinafter, the present invention will be described in detail with reference to the drawings and examples. It should be noted that, in the case of no conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. the

Fig. 1 is a flowchart of a node formation method according to an embodiment of the present invention. As shown in Figure 1, the node formation method includes the following steps:

Step S102, detecting the first distance and the first azimuth between the first node and the second node, and detecting the second distance and the second azimuth between the first node and the third node, and according to the first The distance, the first azimuth, the second distance and the second azimuth calculate a third distance between the second node and the third node;

Step S104, judging whether the first distance, the second distance and the third distance are all less than or equal to the preset first threshold length, if yes, execute step S108, if not, execute S106;

Step S106, calculate the average position point between the first node, the second node and the third node according to the first distance, the first azimuth angle, the second distance and the second azimuth angle, and drive the first node to the average position point Move, and return to execute step S102 at predetermined time intervals;

Step S108, calculate the target position point according to the current first distance, the current first azimuth angle, the current second distance and the current second azimuth angle, wherein the target position point is the distance to the second node and the distance to the third node is Half of the first threshold length and the minimum distance to the first node, and drive the first node to move to the target position, and perform step S110 at predetermined time intervals;

Step S110, judging whether the first node has reached the target point, if not, return to step S102, if yes, the first node stops the formation process. the

In this embodiment, when the initial distance between the nodes is too large, the nodes are driven to move closer to the average position point, and the nodes are not driven to move to the target position point until the nodes meet the distance requirements, which solves the problem of multi-intelligence in related technologies. The distributed control of agent formation behavior has the problems of low control precision and large response delay, and then achieves the effect of improving the control accuracy and speeding up the response of multi-agent formation. the

In the above method, in addition to the first node, the second node and the third node also execute the same node formation strategy as the first node asynchronously at the same time, that is, the position adjustment of the first, second and third nodes is carried out dynamically . the

Wherein, after step S102, it also includes: when judging that the first node, the second node and the third node are on the same straight line according to the current first azimuth angle and the second azimuth angle, and the first node is located between the second node and the third node When the nodes are on the same side, the first node temporarily stays at the original position; if the first node, the second node and the third node are on the same straight line, and the first node is in the middle of the second node and the third node, the drive A node moves along either side of the vertical line of the line, so that each node can continue to implement the above moving strategy. the

Wherein, the average position point can be selected as the center of gravity or incenter of the triangle formed by the first node, the second node and the third node. the

Wherein, the first node, the second node and the third node are individuals that need to move in formation, for example, intelligent robots. the

Fig. 2 is a schematic structural diagram of a node formation device module according to an embodiment of the present invention. As shown in Figure 2, the node formation device includes the following functional modules:

A detection unit 120, configured to detect a first distance and a first azimuth between the first node 100 and the second node 200, and detect a second distance and a second azimuth between the first node 100 and the third node 300 ;

Calculation unit 140, for judging whether the first distance, the second distance and the third distance are all less than or equal to the preset first threshold length, if not, according to the first distance, the first azimuth, the second distance and the first distance The second azimuth calculates the average position point between the first node 100, the second node 200 and the third node 300; if yes, then calculates according to the first distance, the first azimuth, the second distance and the second azimuth Target position point, wherein, the target position point is the position point that the distance to the second node 200 and the distance to the third node 300 is half of the first threshold length and the distance to the first node 100 is the smallest;

The driving unit 160 is configured to drive the first node 100 to move to the average position point or the target position point according to the calculation result of the calculation unit 140 . the

Wherein, the detection unit 120 may include: an infrared sensor, for detecting the first distance and the second distance; a digital compass, for detecting the first azimuth and the second azimuth;

Wherein, the computing unit 140 is also used to judge whether the first node 100 , the second node 200 and the third node 300 are on the same straight line and the adjacent relationship among them according to the current first azimuth angle and the second azimuth angle. the

Wherein, the driving unit 160 is also used to judge in the calculation unit 140 that the first node 100, the second node 200 and the third node 300 are on the same straight line and the first node 100 is located on the same side of the second node 200 and the third node 300 In the case of controlling the first node 100 to stop moving, and the first node 100, the second node 200 and the third node 300 are on the same straight line and the first node 100 is located between the second node 200 and the third node 300 Next, drive the first node 100 to move along any side of the vertical line of the straight line. the

Fig. 3 is a schematic diagram of distribution of a node formation system according to an embodiment of the present invention. As shown in FIG. 3 , the node formation system includes the aforementioned first node 100, second node 200 and third node 300, wherein the second node 200 and the third node 300 have the same A detection unit 120 , a calculation unit 140 and a drive unit 160 . That is, in this system, the position adjustment of the first, second and third nodes is performed dynamically. In practical applications, the first, second and third nodes can be intelligent robots, of course, according to different practical applications, these nodes can also be other individuals with movement and control functions, such as drones, sensors and so on. The formation of three adjacent nodes can be realized through the node formation system provided by this implementation. the

Embodiment one

This embodiment describes in detail a practical application of realizing an E-structure formation of three adjacent individual robots according to the present invention. the

1. The individual state model of this instance:

In this embodiment, the structure of the actual individual robot is composed of four hardware modules: (1) infrared (proximity) sensor, used to observe the distance of adjacent individuals relative to itself; (2) digital compass, used to observe the relative distance of adjacent individuals own azimuth; (3) the calculation unit, using the local data obtained by the first two units, calculates the destination position at the next moment according to the pre-designed control algorithm; (4) the driver, the result obtained by the control algorithm Convert to the corresponding executable motion state, adjust the individual motion direction, and drive yourself to move to the destination. The first two modules are combined to complete the local position observation of neighboring individuals. the

In order to better focus the analysis on the control cooperation mechanism itself, the following individual state abstraction is given in combination with the individual hardware and the action characteristics of the actual task execution. the

Assumption: the individual robot only has the ability to obtain environmental information in a local range (observation radius r _s ), has three executable states of observation, calculation and movement, and cycles between these three states during operation (as shown in Figure 4) , state execution and transition between states without time delay and error interference.

In fact, each executable state of an individual robot takes time, and transitions between states also have time delays. For example, in the observation stage, the individual needs to do a rotation scan to obtain the distance of each neighbor relative to itself by using the proximity sensor, and at the same time, obtain the local azimuth of the corresponding neighbor through the digital compass; in the calculation stage, the individual uses the distance obtained in the observation stage It will take time to determine the neighbor’s local position based on the local azimuth information, and then execute the pre-designed interactive control method to obtain the destination position at the next moment. The process of any individual A _i using the directly observed radial distance and azimuth of its neighbors to determine its local position relative to itself is as follows. Fig. 5 shows the situation where the individual A _i uses the infrared sensor to scan counterclockwise from the positive semi-axis of the local coordinate system for one circle to obtain the local positions of two adjacent individuals A _i1 and A _i2 . The distance between individual A _i1 and individual Ai is d _i1 , and the local azimuth angle is θ _i1 . The distance between individual A _i2 and individual A _i is d _i2 , and the local _azimuth angle is θ _{i2 .} outside the observation range. The individual A _i will calculate the local position p _i1 of the neighbor individual A _i1 relative to itself according to formula (1) =(p _i1 (x), p _i1 (y)). Similarly, the local position of A _i2 can be calculated. As for A _i3 , since A _i1 cannot perceive its existence, its location information cannot be obtained.

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d\; i"\; filenames="HDA00003321227600051.png,HDA00003321227600091.png"\; state="\{\{state\}\}">d</figure-callout></span><figure-callout\; id="1"\; label="d\; i"\; filenames="HDA00003321227600051.png,HDA00003321227600091.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d\; i"\; filenames="HDA00003321227600051.png,HDA00003321227600091.png"\; state="\{\{state\}\}">d</figure-callout></span><figure-callout\; id="1"\; label="d\; i"\; filenames="HDA00003321227600051.png,HDA00003321227600091.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Obviously, due to the limited observation range of individuals, the prerequisite for the three entities to realize the formation E structure is that the three entities are mutually observable in the initial distribution. Therefore, the distribution of the three individuals should be sufficiently close to meet the condition of mutual observability. The analysis process here assumes that the initial distribution of the three adjacent individuals is mutually observable. the

The individual obtains the local position information of other individuals relative to itself through observation and simple calculation, and then executes the interactive control method designed in advance according to the task requirements, calculates the destination position at the next moment, and brings this destination position into the motion control The equation thus obtains the required motion state (ie speed, including size and direction) at the next moment. the

The following explains the meanings of the symbols used later, as well as related definitions and problem statements. the

For three adjacent individuals, any individual and its position are recorded as A _i and p _i respectively, and the other two individuals and their positions are respectively recorded as A _i1 , A _i2 and p i1 , _{p i2 ,} and NP _i ={p _i1 ,p _i2 } is the set of neighbor positions. The set of index numbers of three adjacent individuals is recorded as ID={i,i1,i2}.

Definition 1 (three-point structure, T): a geometric structure (usually triangular) determined by the distribution positions of three neighbors, recorded as T _i ={p _i ,p _i1 ,p _i2 }, where the three elements in T can be in the same line.

Definition 2 (equilateral triangle, E): When the distance between any two elements is D, the three-point structure is called an equilateral triangle, denoted as E (at this time D is called the side length of E). the

On the basis of the definition of T and E, define the formation behavior of the E structure of three adjacent individuals as follows. the

Three-nearest-neighbor individual E-structure formation: the process in which three-nearest-neighbor individuals self-organize into an E-structure formation from any initial distribution (satisfying mutual observability), that is, the T-structure with the three-nearest-neighbor individuals as vertices transforms into The process of E structure. the

2. The motion control equation of this embodiment

Based on the assumptions of the above state transition model, we propose a control equation for individual motion expressed in continuous discrete time. The individual calculates the destination position of the next time at each sampling time in the form of discrete time representation, and keeps the destination position unchanged during the interval between two sampling times. The motion control equation of the individual expressed in continuous time is given below:

${\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ig</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

f(p _i -p _ig )=-C·(p _i -p _ig ) (3)

Among them, p _i and p _ig respectively represent the current position of individual i and the destination position at the next moment; the negative sign indicates that individual i is moving towards the destination position; the constant C is determined by the maximum movement rate of the actual individual |v _max | and the observation radius r _s are jointly determined, which can be obtained by the following derivation process.

From formula (2) and formula (3), it can be seen that the individual moves at any time, and it satisfies the following relationship

$\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ig</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>$

显然，前者期望即时速率不能大于实际即时速率的最大值，记为

因此，合理的常数C值应该满足下式：  For a fixed constant C, the maximum value of C·|p _i -p _ig | on the left side of the above formula is C·r _s , which represents the expected maximum individual instant speed, while the right side of the above formula is the actual instant speed of the robot

Obviously, the former expected instant rate cannot be greater than the maximum value of the actual instant rate, denoted as

Therefore, a reasonable constant C value should satisfy the following formula:

$\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&le;</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

After the control constant C is determined, it can be seen from the motion control equation that the motion state at the next moment depends on the destination position. And this destination position is obtained by the individual at each moment by executing the interactive control method. Therefore, the interactive control method is the key to the individual's overall behavior decision-making, and it should be designed according to the specific global tasks of the three nearest neighbors. In the following, the E-structure formation is regarded as the global task of the three nearest neighbors, and the detailed implementation process of the corresponding interactive control method is given. the

3. The three-nearest neighbor individual E structure formation in this implementation

Although each individual executes the same interactive control method and their behavior is asynchronous, if the three neighbors want to form an E structure from any initial distribution through mutual motion coordination, each individual’s action at each moment Should tend to contribute to the achievement of global mission objectives (E-structure formations). This is consistent with the swarm robotics in which the actions of individuals in the swarm should be endowed with the tendency to achieve global task completion. Here, D is used to represent the desired side length of the E structure. Obviously, the value of D should be smaller than the observation radius r _s of the individual (ie D< _rs ), otherwise it will not be possible to form the desired E structure because they cannot observe each other. structure. According to the above ideas, a very natural behavior decision for any individual A _i is: at each moment, take the position p _ig which is equal in distance to individuals A _i1 and A _i2 and has a length of D as its destination position at the next moment . As far as the E-structure formation is concerned, the position p _ig is the most ideal place for the individual A _i to go at the next moment, because if the individual A _i is in the position p _ig , it can form a waist-length D formation with the individual A _i1 and the individual A _i2 Isosceles triangle structure. Obviously, if there are two p _igs that meet the requirements, here we uniformly take the p _ig that is closer to the individual A _i as the destination position of the individual A _i at the next moment. The condition to ensure that all individuals have a clear destination position p _ig at each moment is that the side length of the T structure composed of three adjacent individuals is not greater than 2D, that is, the following formula needs to be satisfied:

d _j,k ≤2D j≠k∈ID (5)

In this way, if the T structure at the subsequent time still satisfies the condition that the side length is not greater than 2D, the three experiences will cycle through the three execution states of observation, calculation, and movement, and finally complete the E structure through mutual motion coordination Formation, we refer to this process as the adjustment process (APr). During the adjustment process, the same simple adjustment algorithm (AA) is executed in each individual. the

3.1. Adjustment Process (APr)

Figure 6 shows all typical T structure types that satisfy formula (5) and the calculation method of p _ig corresponding to any individual A _i at this time (algorithm 1). The dotted arrow indicates the expected movement direction of the individual A _i at the next moment.

When the distances among the three nearest neighbors all satisfy the formula (5) at a certain sampling moment, all individuals can calculate a definite destination position p _ig for the next moment. The following two formulas describe the meaning of the destination position p _ig of individual A _i in mathematical language. In the formula, the symbol ||·|| is a 2-norm, which means the distance between any two positions in the plane. Table 1 gives the algorithm pseudo code corresponding to the adjustment process.

P={p|||pp _i1 ||=D and ||pp _i2 ||=D,p∈R ² } (6)

${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ig</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; arg</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Table 1

3.2 Cohesive process (CPr)

At a certain sampling moment, when the individual A _i knows that the distance between other two neighbor individuals satisfies the formula (5) through observation and calculation, the individual A _i can calculate a definite destination position p _ig for the next moment, where The location is the closest to individual A _i and the distance to the other two individuals is the same as D. Since this destination location and two other individuals can form an isosceles triangle structure with waist length D, it is obviously beneficial for individual A _i to move towards this destination location to form a structure E _i . However, the same sampling moment does not guarantee that the other two individuals will also be able to obtain their respective definite destination positions at the next moment. As shown in Figure 7, it describes the position distribution of three neighbor individuals A _i , A _i1 and A _i2 at a certain moment, d _i12 <2D, the destination position of individual A _i should be p _ig (note: not p′ _ig ) , because only p _ig satisfies p _ig,i1 =p _ig,i2 =D and is closest to individual A _i . Due to the large distance between individuals A _i and A _i1 , individual A _{i2 cannot} find a definite destination p ig satisfying the condition p _ig,i1 =p _ig,i2 =D. The individual A _i directly obtains d _i,i1 and d _i,i2 by using the proximity sensor, and obtains the azimuth angle θ _i,i1 and θ _i,i2 by using the digital compass, then the individual A _i1 and A _i2 can be calculated by formula (9) The distance between d _i1,i2

${\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\sqrt{{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

When the distances between the three neighbors do not all satisfy the formula (5), how to make all the individuals have the appropriate destination at the next moment, we propose the following cohesion strategy: at a certain sampling time, if the individual finds three individuals When the distances between them do not all satisfy the formula (5), the calculation of the definite destination position is stopped, and the average position of the three is calculated instead, and it is used as the approximate destination position at the next moment. Table 2 gives the pseudo code of this algorithm. The cohesion strategy itself has no special requirements on the position distribution of the three bodies, because the average position of the three bodies can always be obtained by calculating the positions of the three bodies. Here, the cohesion strategy is regarded as a part of the entire interaction control strategy, and a location distribution execution condition is added to the cohesion strategy. This is mainly to realize the closeness of the three neighbors when the distances between the three neighbors do not all satisfy the formula (5), so as to ensure that the distances between each other finally all satisfy the formula (5). Individuals will then enter the adjustment process, and the three-nearest neighbors will finally realize the E-structure formation through continuous behavioral coordination. the

Table 2

It can be seen from the above that the cohesion process, as part of the entire interactive control process, is mainly used to achieve the three neighbors sufficiently close to their average positions when the initial positions of the three neighbors are far apart from each other. When the distribution of the three bodies is close enough so that the distances between them all satisfy the formula (5), the individual will directly enter the adjustment process. The adjustment process is directly oriented to the target structure, so that the three-nearest neighbor robots form into the desired E-structure. Looking at the corresponding two algorithms independently, in fact, the cohesion algorithm (CA) does not have specific requirements for the robot position distribution, and the three nearest neighbors who execute the simple CA algorithm will gather at the same position. The adjustment algorithm (AA) has a specific requirement for the position distribution, that is, the distance between any two of the three bodies is the same, and it will be executed only when the formula (5) is satisfied, and it will drive the three nearest neighbors to form an E structure directly, otherwise it will happen A critical error that causes the destination location to fail to be calculated or cause the algorithm to abort execution. Fig. 8 shows a schematic diagram of the state flow when individual A _i respectively executes two simple algorithms.

3.3 Interactive control method (TFS)

Individuals choose whether to first enter the cohesion process or the adjustment process according to the current relative position structure between themselves and other neighbors. If the individual first enters the adjustment process facing the target structure, the individual will not enter the cohesion process again; on the contrary, if the individual enters the cohesion process first, it will still enter the adjustment process after the three neighbors have achieved sufficient cohesion. To finally complete the E structure formation. We refer to the behavior decisions adopted by individuals in the entire formation process as Triangle Formation Strategy, and the corresponding interactive control method is denoted as TFS. All individuals execute the same interactive control method, and their actions and the process of executing the TFS algorithm on them are asynchronous. In order to facilitate the further description of the TFS algorithm, the definitions of two relative position structures are given below to summarize all possible three-point structure types. the

Definition (cohesive structure, CF): There exists at least one T structure larger than the 2D side length. the

Definition (Adjustment Structure, AF): T structure whose side length is not greater than 2D. the

From the above definition, it can be known that the T structure formed by three neighbors at any time can only be one of the two types of structures defined above, that is, cohesive structure (CF) or adjusted structure (AF). The CA algorithm will be executed when the individual is in the CF structure, and the AA algorithm will be executed when it is in the AF structure, but the common purpose of the two algorithms is to realize the formation of the E structure of the three nearest neighbors. Individuals move to the average position of the three bodies by executing the CA algorithm to achieve sufficient cohesion among each other, so that the location distribution conditions for executing the AA algorithm are satisfied. In other words, the purpose of executing the cohesion algorithm is to ensure that the three bodies can be transferred to the execution of the AA algorithm. In order to achieve the successful formation of the target E structure, the AA algorithm is the program segment of the TFS algorithm that each individual must eventually execute. For the CA algorithm part of the TFS algorithm, individuals may not be able to execute it, which depends on whether the distribution structure of the three nearest neighbors is a CF structure. the

Therefore, the TFS interactive control method for the self-organized E-structure formation of three-neighboring individuals combines the simple CA algorithm and the simple AA algorithm. Which algorithm program the individual chooses to start execution depends on the position distribution structure of the three at that time. Table 3 and Table 4 respectively give the pseudo-code of the TFS interactive control method and the corresponding program segment (for the calculation of the destination position p _ig ). Figure 9 shows the state flow of an individual executing the TFS algorithm. The modified sub-algorithm part indicated by the dotted box in the flow chart needs to be considered when the TFS algorithm is used in the entity system.

table 3

Table 4

For a physical robot, when the positions of the three bodies are distributed collinearly, the individuals at both ends cannot observe each other due to the occlusion of the middle individual, and can only observe the middle individual. While the individual in the middle can observe the individuals at both ends at the same time, as shown in Figure 10. It is worth reminding that here we only discuss the situation that when the positions of the three bodies are collinear, they are still within the observation capability area of each other. The shaded strip area in the figure is the observation blind area of individual A _i1 caused by the occlusion of the middle individual. A _i2 is just in this blind area, and A _i1 cannot observe A _i2 . For similar reasons, A _i2 cannot observe A _i1 either.

Therefore, the modified sub-algorithm shown in Figure 11 can be introduced into the TFS interactive control method implemented in the physical robot. When an individual observes a single individual, it temporarily stays in place (note: the system is still running, performing observation and calculation processes). When two neighbors are observed and found to be collinear with their positions, you can judge that you are in the middle of the two neighbors, and move along any side of the vertical collinear. In this way, the individuals at both ends can perceive each other, thereby causing the individuals to continue to execute the TFS interactive control method (the CA algorithm or the AA algorithm part). the

4. E-structure formation stability analysis

The above describes in detail the design process of the TFS interactive control method to realize the E-structure formation of the three-nearest neighbor individual coordinated behavior, as well as the pseudo-code and program segments of the related algorithm. The following conclusions are given on the relevant properties of the E-structure formation of the three nearest neighbors using the TFS interactive control method:

不变，即有：  Lemma 4.1: The average position of three neighbors in the cohesion process

unchanged, that is:

$\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}$

prove:

并由运动控制方程(式(2)和式(3))可知  When the three bodies participate in the cohesion process, the CA algorithm is executed, as shown in Figure 8, defined by the algorithm

And from the motion control equation (type (2) and type (3)), it can be known that

${\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ig</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span>$

${\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span>$

${\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span>$

because After deriving both sides of this formula, we can substitute the above formula into

$\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="p\; i"\; filenames="HDA00003321227600051.png,HDA00003321227600091.png"\; state="\{\{state\}\}">p</figure-callout></span><figure-callout\; id="1"\; label="p\; i"\; filenames="HDA00003321227600051.png,HDA00003321227600091.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="p\; i"\; filenames="HDA00003321227600091.png"\; state="\{\{state\}\}">p</figure-callout></span><figure-callout\; id="2"\; label="p\; i"\; filenames="HDA00003321227600091.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}}{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}$

The proposition is proved. the

为中心的η邻域内：  Theorem 4.1: Through the simple CA algorithm, the three nearest neighbors will be stable and cohesive at the average position after time T

In the η neighborhood of the center:

${\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; \}</span>$

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; E.</span>}}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; )</span>$

Wherein n is any positive number, $\mathrm{E.}=\max \left(\right||p_i\left(0\right)-\stackrel{\&OverBar;}{p}||:i\&Element;\mathrm{ID}).$

prove:

From Lemma 4.1, we can see that the average position of the three bodies performing the CA algorithm satisfies

并对能量函数求导，可得：  For robot i, i∈ID, the error variable is e _i (t)=p _i -p _ig , and the energy function is

And deriving the energy function, we can get:

${\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; ig</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ig</span>}}<span\; class="notranslate">\; )</span>$

$={({\stackrel{\&Center\; Dot;}{p}}_i-\stackrel{\&Center\; Dot;}{\stackrel{\&OverBar;}{p}})}^T(p_i-\stackrel{\&OverBar;}{p})$ (by the cohesive process has $p_{\mathrm{ig}}=\stackrel{\&OverBar;}{p}$ )

$<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

$<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 0</span>}$

时，恒有

由Lyapunov稳定性理论可知，个体经过足够长的时间T必会稳定内聚到以

为中心的η邻域内。  Since for any positive number η, when

always have

From the Lyapunov stability theory, it can be known that after a long enough time T, the individual will be stable and cohesive to the following

In the η neighborhood of the center.

And by ${\stackrel{\&Center\; Dot;}{V}}_i\left(t\right)=-C{\left|\right|p_i-\stackrel{\&OverBar;}{p}\left|\right|}^2=-C{\left(e_i\left(t\right)\right)}^T{e}_i\left(t\right)=-2C{V}_i\left(t\right),$ Solving this differential equation gives V _i (t)=V _i (0)e ^-2Ct .

时，恒有当||e_i(t)||=η时，表示个体i已经进入了

的η邻域，用t_i表示个体i内聚到此η邻域内所需要的时间，则有V_i(t_i)=η²/2，所以

解得

因此，三近邻个体都内聚到以

为中心的η邻域内所需要的时间为：  For any positive number η, when

always have When ||e _i (t)||=η, it means that individual i has entered

η neighborhood, use t _i to represent the time required for individual i to cohere into this η neighborhood, then V _i (t _i )=η ² /2, so

Solutions have to

Therefore, the three nearest neighbors are all cohesive to the following

The time required in the η neighborhood of the center is:

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; :</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; ID</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span>}}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; :</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; ID</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; :</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; ID</span>}<span\; class="notranslate">\; )</span>$

$=\frac{1}{C}\ln \left(\frac{\sqrt{2}\mathrm{E.}}{\mathrm{\&eta;}}\right),$ in $\mathrm{E.}=\max \left(\right||p_i\left(0\right)-\stackrel{\&OverBar;}{p}||:i\&Element;\mathrm{ID})$

The proposition is proved. the

Lemma 4.2: The three nearest neighbors can transform from any CF structure to AF structure through the CA algorithm, and it is irreversible for the TFS interactive control method. the

prove:

According to Theorem 4.1, there is a positive number η to make the three bodies sufficiently cohesive so that the distance between them is small enough that max(||p _i -p _j ||:i,j∈ID and i≠j)≤ 2D holds, therefore, the first half of the proposition is proved.

For the TFS algorithm, AF structures are not converted to CF structures. When the three adjacent individuals are in the AF structure, they participate in the adjustment process and execute the AA algorithm. If the AF structure is to be transformed into a CF structure, it must go through a critical structure, as shown in Figure 12. At this time, max(||p _i -p _j ||:i,j∈ID and i≠j)=2D. Considering the symmetry, only analyze the case that the individual A _i is located in the area surrounded by two circles and the straight line connecting the individual A _i1 and A _i2 (Note: In the figure, A _i1 and A _i2 are the circle boundaries with a radius of 2D is used to aid in the analysis rather than represent the individual observation boundaries).

Apparently, if the AF structure wants to undergo this transition from the critical structure to the CF structure, the individual A _i1 and A _i2 must move away from each other. Considering the characteristic of symmetry, here only individual A _i1 is discussed, and the situation of individual A _i2 can be discussed similarly. If the departure movement occurs, the running direction of the individual A _i1 must be above the horizontal line _l1 (note: l1 is perpendicular to A _i1 and A _i2 ), that is to say, the destination position of A _i1 must be located above the _horizontal line. Here it is assumed that any position p _i1g in the area above the horizontal line _l1 is the destination position of individual A _i1 . It can be seen from the above figure that the distance between the destination position p _i1g and the individual A _i2 must be greater than 2D. Since the individual is still in the adjustment structure at this time, the individual is performing the adjustment process and the AA algorithm is executed. It is also known from the definition of the adjustment process that the distance from the destination position p _i1g to the individual A _i2 will not be greater than or equal to 2D, causing a contradiction. Therefore, it can be concluded that the assumption that the destination position p _i1g of individual A _i1 is located in the area above the horizontal line _l1 is not valid, that is, the destination position p _i1g of individual A _i1 must be in the area below the horizontal line _l1 . Similar analysis shows that the destination position p _i2g of individual A _i2 must be in the area above the horizontal line l ₂ . Therefore, individual A _i1 and A _i2 will not deviate, that is, under the TFS algorithm, the conversion from AF structure to CF structure will not occur, and the second half of the proposition is proved.

The proposition is proved. the

Theorem 4.2: The three nearest neighbors can realize E-structure formation from any AF structure through AA algorithm. the

prove:

取误差函数为e_i(t)=p_i-p_ig，取能量函数为并对此能量函数求导，可得：  For any individual i, i∈ID, since the destination position of the individual does not change within the sampling interval, that is,

Take the error function as e _i (t)=p _i -p _ig , and take the energy function as And taking the derivative of this energy function, we can get:

${\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; ig</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ig</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ig</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ig</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ig</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C</span>}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ig</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

$<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 0</span>}$

按照Lyapunov稳定性理论，p_i必渐进收敛到p_ig，即p_i=p_ig。  It can be seen that when ||p _i -p _ig || ² >0, there is always

According to the Lyapunov stability theory, p _i must asymptotically converge to p _ig , that is, p _i = p _ig .

From the definition of the adjustment process, it can be seen that

||p _ig -p _j ||=D,j∈ID\{i}

Further, substituting p _i =p _ig into the above formula, we can get

||p _i -p _j ||=D,j∈ID\{i}

That is, the distance from any individual i to its two neighbors is D. Therefore, the AF structure composed of three neighbors is finally transformed into the E structure. the

The proposition is proved. the

Theorem 4.3: The three-nearest neighbor individuals can realize the E-structure formation from any initial distribution through the TFS algorithm. the

prove:

If the initial position distribution of the three neighbors is a CF structure, according to the design of the TFS interactive control method, the individuals will execute the CA algorithm to enter the cohesion process. From Lemma 4.2, it can be seen that the three neighbors will convert from the CF structure to the AF structure through a cohesion process , and this conversion is irreversible. Once the AF structure is formed, the individuals will immediately enter the adjustment process. From Theorem 4.2, it can be seen that the three nearest neighbors will form an E structure. If the initial position distribution of the three nearest neighbors is an AF structure, it can be seen from the flow of the TFS interactive control method (see Figure 9) that the individual will directly execute the AA algorithm to enter the adjustment process. It can also be seen from Theorem 4.2 that the three nearest neighbors entering the adjustment process will directly form an E structure. the

The proposition is proved. the

5. Simulation

Next, the simulation analysis of the behavior of the three-nearest-neighboring individuals forming the E-structure through the TFS interactive control method is carried out to verify the effectiveness of the TFS algorithm for the formation of the E-structure of the three-nearest-neighboring individuals. Here, the compilation and operation of all experimental programs are carried out on the Breve simulation platform. Breve is a multi-agent simulation development platform for distributed systems and artificial life based on 3D environment. It uses the object-oriented language Steve as the simulation programming language of the platform. The Breve platform contains a class library of commonly used classes, which provides convenience for experimenters to realize fast model simulation and algorithm verification. the

Simulation parameter setting: E structure side length D=10; individual observation radius r _s =50; maximum motion velocity |v _max |=10, from formula (7) we take the constant C=v _max /r _s in the motion control equation =0.2; at the beginning of the simulation, the three bodies are randomly distributed in a circular area centered on the origin of the environment coordinates and the radius is r _d =r _s /2, and the individuals within this range can observe each other. In addition, the running time of the simulation is limited. When the velocity |v| of the robot satisfies |v|<0.01, the robot stops moving and the system ends the simulation. It can be seen from the motion control equation that this limitation on the speed actually specifies the closeness of the individual to its destination position, that is, the distance error of the destination position. Here, it is equivalent to using a specific destination distance error value as the stopping condition of individual movement and E-structure formation simulation.

For the two cases where the initial distribution of the three nearest neighbors is CF and AF, the E formation behavior simulation and the convergence test of the average side length error are carried out respectively. The average side length error is defined by the following formula, which is used to represent the relationship between the degree of three neighbors approaching the E structure and time. the

Among them, size(ID) indicates the number of elements in ID. the

The simulation experiment of E-structure formation behavior was carried out for the following typical initial distributions: (1) CF distribution, CF-1 means that only one side in the initial cohesive structure is larger than 2D, and the specific initial side length is (17.4716.0630.42); CF-2 means Two sides in the initial cohesive structure are larger than 2D, and the specific initial side length is (36.6615.7530.56); CF-3 indicates that the three side lengths in the initial cohesive structure are all larger than 2D, and the specific initial side length is (21.9424.4927.00). (2) AF distribution, which means the initial adjustment structure, that is, all three sides satisfy the formula (8), and the specific initial side length is (11.6015.6911.61). The simulation shows that the three nearest neighbors can be formed into an E structure with it as the vertex under any position distribution condition. Figure 13 shows the trajectories experienced by the three neighbors from the initial distribution of CF-2 to the target E structure, and the number in the upper left corner of the figure indicates the time taken in seconds. the

Figure 14 shows the variation of the average side length error over time in the process of the three-neighbor individuals dynamically approaching the E structure under the above typical initial distributions. From the average error convergence curve, it can be seen that no matter what kind of initial position distribution, all the side lengths of the T structure can converge to D in the end. The simulation experiment shows that the three nearest neighbors can realize E-structure formation from any initial distribution position by implementing the TFS interactive control method. the

In the above-mentioned embodiment, it is described in detail how to realize the control of the three-nearest neighbor intelligent robot formation. Through the technical means provided by the above-mentioned embodiment, the control precision existing in the distributed control of multi-agent formation behavior in the related art is solved. The problem of low and large response delay, and thus achieve the effect of improving the control accuracy of the multi-agent formation and speeding up the response. the

In another embodiment, interactive control software is also provided, and the software is used to execute the method for node E structure formation described in the above embodiment. the

In another embodiment, there is also provided a storage medium in which the above software is stored, and the storage medium includes but not limited to an optical disk, a floppy disk, a hard disk, a rewritable memory, and the like. the

Obviously, those skilled in the art should understand that each module or each step of the above-mentioned present invention can be realized by a general-purpose computing device, and they can be concentrated on a single computing device, or distributed in a network formed by multiple computing devices Alternatively, they may be implemented in program code executable by a computing device so that they may be stored in a storage device to be executed by a computing device, and in some cases in an order different from that shown here The steps shown or described are carried out, or they are separately fabricated into individual integrated circuit modules, or multiple modules or steps among them are fabricated into a single integrated circuit module for implementation. As such, the present invention is not limited to any specific combination of hardware and software. the

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention. the

Claims (14)

1. A node formation method, characterized in that, comprising: Step S102, detecting the first distance and the first azimuth between the first node and the second node, and detecting the second distance and the second azimuth between the first node and the third node, and according to the calculating a third distance between the second node and the third node by the first distance, the first azimuth, the second distance, and the second azimuth; Step S104, judging whether the first distance, the second distance and the third distance are all less than or equal to the preset first threshold length, if yes, execute step S108, if not, execute step S106; Step S106, calculating the distance between the first node, the second node and the third node according to the first distance, the first azimuth, the second distance and the second azimuth and drive the first node to move to the average position point, and return to execute the step S102 at predetermined time intervals; Step S108, calculating a target position point according to the current first distance, the current first azimuth angle, the current second distance and the current second azimuth angle, wherein the target position point is to the The distance between the second node and the third node is half of the first threshold length and the minimum distance to the first node, and drives the first node to move to the target position point ; Step S110, judging whether the first node has reached the target point at predetermined time intervals, if not, return to step S102, and if yes, the first node ends the formation process. 2. The node formation method according to claim 1, further comprising: after the step S102: When it is judged according to the current first azimuth angle and the second azimuth angle that the first node, the second node and the third node are on the same straight line, and the first node is located at the second node When it is on the same side as the third node, stop driving the first node. 3. The node formation method according to claim 1, further comprising: after the step S102: When it is determined according to the current first azimuth and the second azimuth that the first node, the second node and the third node are on the same straight line, and the first node is located at the first When the second node is in the middle of the third node, the first node is driven to move along any side of the vertical line of the straight line. 4. The node formation method according to claim 1, wherein the average position point is the center of gravity or the center of a triangle formed by the first node, the second node and the third node. 5. The node formation method according to claim 1, characterized in that, in the process of controlling the movement of the first node, the movement of the second node and the third node are independently controlled in the same manner, so as to A formation is formed for the first, second and third nodes. 6. The node formation method according to any one of claims 1-5, wherein the first node, the second node and the third node are all intelligent robots. 7. A node formation device located in the first node, characterized in that it comprises: a detection unit, configured to detect a first distance and a first azimuth between the first node and a second node, and detect a second distance and a second azimuth between the first node and a third node; a calculation unit, configured to calculate a third distance between the second node and the third node according to the first distance, the first azimuth, the second distance, and the second azimuth , and judge whether the first distance, the second distance and the third distance are all less than or equal to the preset first threshold length, if not, according to the first distance, the first azimuth angle , the second distance and the second azimuth to calculate the average position point between the first node, the second node and the third node; if so, according to the first distance, The first azimuth, the second distance, and the second azimuth calculate a target location point, wherein the target location point is a distance from the second node and a distance from the third node. a location point that is half the length of the first threshold and has the smallest distance to the first node; A driving unit, configured to drive the first node to move to the average position point or the target position point according to the calculation result of the calculation unit. 8. The node formation device according to claim 7, characterized in that, The calculation unit is also used to judge whether the first node, the second node, and the third node are on the same straight line and whether they are on the same straight line according to the current first azimuth angle and the current second azimuth angle. neighbor relationship. 9. The node formation device according to claim 8, characterized in that, The driving unit is further configured to determine that the first node, the second node and the third node are on the same straight line and the first node is located between the second node and the In the case of the same side of the third node, stop driving the first node. 10. The node formation device according to claim 8, characterized in that, The driving unit is further configured to determine that the first node, the second node, and the third node are on the same straight line when the computing unit determines that the first node is located between the second node and the third node. In the case of being between the third node, drive the first node to move along any side of the vertical line of the straight line. 11 . The node formation device according to claim 7 , wherein the average position point is the center of gravity or incenter of a triangle formed by the first node, the second node and the third node. 12. The node formation device according to any one of claims 7-11, wherein the detection unit comprises: an infrared sensor for detecting the first distance and the second distance; A digital compass, used to detect the first azimuth and the second azimuth. 13. A node formation system, characterized in that it comprises the first node, the second node and the third node according to any one of claims 7-12, wherein the second node and the third node respectively have The detecting unit, the calculating unit and the driving unit of the first node are the same. 14. The node formation system according to claim 13, wherein the first node, the second node and the third node are all intelligent robots.

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