CN110737263B - Multi-robot formation control method based on artificial immunity - Google Patents

Multi-robot formation control method based on artificial immunity Download PDF

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CN110737263B
CN110737263B CN201911146197.9A CN201911146197A CN110737263B CN 110737263 B CN110737263 B CN 110737263B CN 201911146197 A CN201911146197 A CN 201911146197A CN 110737263 B CN110737263 B CN 110737263B
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robot
antibody
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interleukin
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黄艇
黄天骁
袁明新
王宇弛
王琪
王俊辉
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
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    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
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    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0276—Control of position or course in two dimensions specially adapted to land vehicles using signals provided by a source external to the vehicle
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Abstract

The invention discloses a multi-robot formation control method based on artificial immunity, which comprises the steps of firstly calculating the distance and the angle between each robot and the target position of the robot according to the position of each robot; then calculating the excitation value of the gravity center of each robot and the ideal formation, exciting and inhibiting the robots, and selecting proper speed for the robots to move according to the calculated excitation value; and finally, updating information such as position coordinates of the robots, judging whether the multi-robot system forms an expected formation, recalculating an excitation value between the robots and the centers of gravity of the formation and a stimulus value and a concentration value between the robots until the robots form the expected formation, and performing formation control on the multi-robot system by adopting the method.

Description

Multi-robot formation control method based on artificial immunity
Technical Field
The invention relates to the technical field of multi-robot formation control, in particular to a multi-robot formation control method based on artificial immunity.
Background
The robot is born in the 20 th century, represents a major breakthrough in the field of automation, with the birth of the first industrial robot in 1959, the research and application of robotics have been widely popularized, and in recent years, the development speed of robotics has been accelerated and the robot has rapidly integrated into the lives of people.
However, just as the human society has division of labor and cooperation, in real life, the single robot technology has its own limitations, and many problems in real life, such as robot cooperation and formation in intelligent warehousing, are difficult for a single robot to complete tasks. Therefore, researchers imitate division and cooperation of people in real life, and invent a multi-robot system. The method for controlling the formation of the multiple robots mainly comprises three methods: the leader following method, the behavior-based method and the virtual structure method, wherein the leader-based formation control method has the advantages that the behavior of the whole robot team can be controlled only through the behavior or track of a leader, the main disadvantage is that clear formation feedback is lacked in the system, and if a target leader is lost or the leader fails, the whole formation cannot be maintained; the behavior-based method is a distributed control method, has the characteristic of good flexibility, can dynamically add or reduce the number of robots in a formation, and simultaneously enables the robots to show certain intelligence, is similar to sensory reaction or decision thinking of people or other higher animals, and is easier to understand and recognize by people, and has the defects that proper motion behaviors are difficult to design, and data modeling and system stability analysis are difficult to perform on a system; the distributed formation control method based on the virtual structure reduces the communication quantity among the robots, can easily specify the behaviors of robot groups, has formation feedback, but the formation simulates the motion of a virtual structure, limits the application range of the formation and is not flexible enough.
In summary, the conventional formation control methods have many defects, and how to further improve the performance of the multi-robot system in the formation control aspect is still a subject worth of further research.
Disclosure of Invention
The invention aims to improve the formation control efficiency of multiple robots, and provides a method for controlling the formation of multiple robots based on artificial immunity.
In order to achieve the purpose, the invention adopts the technical scheme that: a multi-robot formation control method based on artificial immunity respectively takes the speed of each robot and the gravity center of the formation formed by each robot as an antibody and an antigen, and comprises the following steps:
s1) initializing the excitation level and the antibody concentration of each robot, and starting each robot;
s2) calculating the distance and angle between each robot and the target position of each robot according to the position of each robot;
s3) calculating the stimulation of the antigen to the antibody, the mutual stimulation and inhibition among the antibodies and the interleukin injection amount;
s4) each robot selects proper speed to move according to the calculated excitation value;
s5) updating information such as position coordinates of the robot, judging whether the multi-robot system forms an expected formation, recalculating stimulation of the antigen to the antibody, mutual stimulation and inhibition among the antibodies and interleukin injection amount, repeating the steps S2 to S4 until the robot forms the expected formation,
wherein, the antigen refers to the gravity center of the formation, the antibody refers to the speed of the robot, and the interleukin refers to the included angle between the connecting line of the real-time position of the robot and the target point and the x axis.
As a further optimization, the step S3 includes the following processes:
s3.1) affinity of antibody and antigen is defined as
Figure BDA0002282266910000031
In the formula, d i o Is the distance of robot i from center of gravity o;
s3.2) Interleukin regulatory factor is defined as d i ＝m·exp(A(i-1,k))，
Wherein A (i-1, k) refers to the line and the x-axis angle between the real-time position of the ith robot and the target point, and m is a weight coefficient, and as can be seen from the formula, when the line and the x-axis angle between the real-time position of the ith robot and the target point increase, the interleukin injection amount increases gradually, and the immune level of the system is enhanced, so as to maintain the stability of the system, wherein the weight coefficient m of the interleukin function mainly reflects the interleukin injection amount, the performance of the system when deviating from a preset track is directly influenced by the interleukin injection amount, and when the number of the robots is respectively 3, 4, 5 and 6, other algorithm parameters (namely, alpha =0.1, beta =1, k) are kept i =0.002,n = 0.9) and m is [0,1]]The range is changed from small to large, and the changes of the required steps, time, average displacement and average deviation angle when the formation of the formation are observed, when the value of m is 0.5,the performance is better;
s3.3) affinity coefficient between antibodies S = v j ·d j ，
Wherein s represents an affinity coefficient between antibodies, v j Representing the velocity, d, of the robot j j Represents the distance between the robot j and the gravity center of the formation;
s3.4) based on an immune system kinetic model proposed by Farmer et al, the following dynamic equation is defined by combining the function of interleukin:
Figure BDA0002282266910000041
Figure BDA0002282266910000042
in the formula: a. The i (t) the level of excitation of antibody i at time t, N the number of antibodies, where the first term in the right hand side extension is the interaction between antibody i and antibody j, s is the affinity coefficient of both, and the second term g i Stimulation of antibody i by antigen, item d i Is an interleukin regulatory factor, fourth term k i Natural depletion of the mock antibody, α and β are the coefficients of action of antibody i on the other antibody and antigen, respectively, a i (t)、a j (t) the concentrations of the antibodies i and j at the time t respectively, and as can be seen from the above formula, compared with the basic immune network, the immune network based on interleukin modulation increases interleukin modulation factors, when the robot deviates from a preset direction, the antibody concentration is increased, the track is retrieved again at a higher speed, and the excitation of the robot is calculated by using the formula.
As a further optimization, step S4 comprises the following process:
s4.1) calculating an excitation value of each robot;
s4.2) setting threshold values of excitation values received by the robot to N and N = N +1, when the robot receives the excitation between 0 and N, the robot moves at a low speed, when the robot receives the excitation between N and N, the robot moves at a medium speed, and when the robot receives the excitation between N and N, the robot moves at a medium speedWhen the stimulus is larger than N, the robot moves at a high speed, and the selection of the threshold determines the moving speed of the robot, so that the value of N in the algorithm influences the performance of the algorithm, and when the number of the robots is respectively 3, 4, 5 and 6, other algorithm parameters (namely alpha =0.1, beta =1, k) are kept i =0.002,m = 0.5), n is [0,1.5]]The range is changed from small to large, the changes of the steps, time, average displacement and average deviation angle required by formation of the formation are observed, and when the value of n is 0.9, the performance is better;
and S4.3) when the number of the robots is respectively 3, 4, 5 and 6, performing formation control by using the formation control method to form a desired formation.
Compared with the prior art, the invention has the following beneficial effects:
1. the multi-robot formation is controlled by using an immune network algorithm, so that the communication and cooperation among the robots are enhanced;
2. the speed of the multiple robots is divided into low, medium and high to control, so that the energy consumption is reduced and the control accuracy is improved;
3. the interleukin is introduced into the immune network algorithm for adjustment, and the robot can quickly return to the preset orbit when deviating from the preset orbit.
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FIG. 1 is a flow chart of the present invention;
FIG. 2-1 is a graph showing the results of an experiment regarding the number of steps for the weighting factor m according to the present invention;
FIG. 2-2 is a graph of the results of an experiment of the weight coefficient m with respect to time according to the present invention;
FIGS. 2-3 are graphs showing experimental results of the weight coefficient m with respect to the average displacement according to the present invention;
FIGS. 2-4 are graphs of experimental results of the weight coefficient m of the present invention with respect to the mean deviation angle;
FIG. 3-1 is a graph showing the results of an experiment of the threshold n with respect to the number of steps according to the present invention;
FIG. 3-2 is a graph of experimental results of threshold n with respect to time in accordance with the present invention;
FIGS. 3-3 are graphs of experimental results of threshold n versus average displacement for the present invention;
FIGS. 3-4 are graphs of experimental results of threshold n with respect to mean deviation angle for the present invention;
FIG. 4 is a diagram showing the results of formation control of the robot of the present invention 3;
FIG. 5 is a diagram showing the results of formation control of the robot of the present invention 4;
FIG. 6 is a diagram showing the results of formation control of the robot of the present invention 5;
fig. 7 is a diagram showing the results of formation control of the robot of the present invention 6.
Detailed Description
The following are specific embodiments of the present invention and are further described with reference to the drawings, but the present invention is not limited to these embodiments.
As shown in FIG. 1, the invention provides a method for controlling formation of multiple robots based on artificial immunity, in order to further improve the performance of a multi-robot system in the formation control aspect, the method of the invention firstly considers the speed of each robot and the gravity center of the formation formed by each robot as an antibody and an antigen respectively; then defining an interleukin regulatory factor according to the function of the interleukin; finally, the control of the formation of the multiple robots is finished by using the hypothesis of the unique immune network of Jerne for reference, and the specific control steps are as follows:
s1) initializing the excitation level and the antibody concentration of each robot, and starting each robot;
s2) calculating the distance and angle between each robot and the target position of each robot according to the position of each robot;
s3) calculating the stimulation of the antigen to the antibody, the mutual stimulation and inhibition among the antibodies and the interleukin injection amount;
s4) each robot selects a proper speed according to the calculated excitation value;
s5) updating information such as position coordinates of the robot, judging whether the multi-robot system forms an expected formation, recalculating stimulation of the antigen to the antibody, mutual stimulation and inhibition among the antibodies and interleukin injection amount, repeating the steps S2 to S4 until the robot forms the expected formation,
wherein, the antigen refers to the gravity center of the formation, the antibody refers to the speed of the robot, and the interleukin refers to the included angle between the line of the real-time position of the robot and the target point and the x axis.
As shown in fig. 2, in order to ensure that the robot can quickly return to the predetermined track when deviating from the predetermined track, it is necessary to select an appropriate interleukin function weight coefficient m, and improve the excitation of the robot by injecting interleukin, the specific process is as follows:
s3.1) affinity of antibody and antigen is defined as
Figure BDA0002282266910000071
In the formula (d) i o Is the distance of robot i from center of gravity o;
s3.2) Interleukin regulatory factor is defined as d i Where a (i-1, k) refers to the line and x-axis angle between the real-time position of the ith robot and the target point, and m is a weight coefficient, it can be seen from the equation that as the line and x-axis angle between the real-time position of the ith robot and the target point increase, the interleukin injection amount increases gradually to enhance the immunity level of the system, thereby maintaining the stability of the system, where the weight coefficient m of the interleukin function mainly reflects the interleukin injection amount, how much the interleukin injection amount directly affects the performance of the system when deviating from the predetermined track, and when the number of robots is 3, 4, 5 and 6, respectively, other algorithm parameters (i.e. α =0.1, β =1, k) are maintained (i.e. α =0.1, β =1, k) i =0.002,n = 0.9), m is [0,1 =]The range is changed from small to large, and the change of the required steps, time, average displacement and average deviation angle when the formation of the formation is observed, so that when the value of m is 0.5, the performance is better;
s3.3) affinity coefficient between antibodies S = v j ·d j Wherein s represents an affinity coefficient between antibodies, v j Representing the velocity, d, of the robot j j Representing the distance between the robot j and the gravity center of the formation;
s3.4) based on the immune system dynamics model proposed by Farmer et al, the following dynamic equations are defined in combination with the function of interleukins:
Figure BDA0002282266910000072
Figure BDA0002282266910000073
in the formula: a. The i (t) the level of excitation of antibody i at time t, N the number of antibodies, the first term in the right hand side extension the interaction between antibody i and antibody j, s the affinity coefficient of both, and the second term g i Stimulation of antibody i by antigen, item d i Is an interleukin regulatory factor, fourth term k i Simulating the natural extinction of the antibody, alpha and beta being the coefficient of action of the antibody i on other antibodies and antigens, respectively, a i (t)、a j (t) the concentrations of the antibodies i and j at the time t respectively, and as can be seen from the above formula, compared with the basic immune network, the immune network based on interleukin modulation increases interleukin modulation factors, when the robot deviates from a preset direction, the antibody concentration is increased, the track is retrieved again at a higher speed, and the excitation of the robot is calculated by using the formula.
As shown in fig. 3, the motion speed of the robot can be controlled by controlling the threshold of the excitation received by the robot, so as to control the performance of the robot to form the formation, as shown in fig. 4 to 7, the formation control results when the number of the robots is 3, 4, 5 and 6 respectively, the specific flow is as follows:
s4.1) calculating an excitation value of each robot;
s4.2) setting threshold values of an excitation value received by the robot as N and N = N +1, when the robot is excited between 0 and N, the robot moves at low speed, when the robot is excited between N and N, the robot moves at medium speed, when the robot is excited by more than N, the robot moves at high speed, and the selection of the threshold values determines the moving speed of the robot, so that the value of N in the algorithm influences the performance of the algorithm, and when the number of the robots is respectively 3, 4, 5 and 6, other algorithm parameters (namely alpha =0.1, beta =1, k) are kept i =0.002,m = 0.5), n is [0,1.5]]The range is changed from small to large, and the change of the required steps, time, average displacement and average deviation angle when the formation of the formation is observed;
and S4.3) when the number of the robots is respectively 3, 4, 5 and 6, performing formation control by using the formation control method to form a desired formation.
In order to specifically explain the technical effect of the technical scheme of the invention, performance tests of different formation control methods are carried out, and the number of the robots selected in the experiment is 3, 4, 5 and 6 respectively. The selected method is a navigator method, a navigator method based on genetic algorithm optimization, a navigator method based on immune genetic optimization, an immune network method and an interleukin immune network method, and the performance of the methods is tested, and the specific methods are shown in the following table:
Figure BDA0002282266910000091
it can be seen from the data in the table that, because the genetic algorithm and the immune genetic algorithm are intelligent optimization algorithms, and the optimization capability of the immune genetic algorithm is stronger than that of the genetic algorithm, compared with the basic navigator method, the navigator method optimized based on the genetic algorithm has better performance in the aspects of step number, time and average displacement than the basic navigator algorithm, but the average deviation angle is improved because a faster speed is selected when the target position is reached. The performance of the immune network method in terms of step number, time, average displacement and average deviation angle is superior to the former three methods, the average deviation angle is close to 0, the performance of the interleukin immune network method is further improved, and the average deviation angle is basically kept unchanged. The test results fully show that the method has higher execution efficiency.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (1)

1. A multi-robot formation control method based on artificial immunity is characterized in that the speed of each robot and the gravity center of the formation formed by each robot are respectively defined as an antibody and an antigen, and the method comprises the following steps:
s1) initializing the excitation level and the antibody concentration of each robot, and starting each robot;
s2) calculating the distance and angle between each robot and the target position of each robot according to the position of each robot;
s3) calculating the stimulation of the antigen to the antibody, the mutual stimulation and inhibition between the antibodies and the interleukin injection amount, and comprising the following steps:
s3.1) affinity of antibody and antigen is defined as
Figure FDA0003990898440000011
In the formula (d) i o Is the distance of robot i from center of gravity o;
s3.2) Interleukin regulatory factor is defined as d i ＝m·exp(A(i-1,k))，
In the formula, A (i-1, k) refers to a connecting line and an x-axis angle between the real-time position of the ith robot and a target point, m is a weight coefficient, and m belongs to [0,1];
s3.3) affinity coefficient between antibodies S = v j ·d j ，
Wherein s represents an affinity coefficient between antibodies, v j Representing the velocity of the robot j, d j Represents the distance between the robot j and the gravity center of the formation;
s3.4) defines the following dynamic equation:
Figure FDA0003990898440000012
Figure FDA0003990898440000013
in the formula: a. The i (t) is the excitation level of antibody i at time t, N is the number of antibodies, s is antibody i and anti-antibodyAffinity coefficient between bodies j, g i Stimulation of antibody i by antigen, d i Is an interleukin regulatory factor, k i Simulating the natural extinction of the antibody, alpha and beta being the coefficient of action of the antibody i on other antibodies and antigens, respectively, a i (t)、a j (t) the concentrations of antibody i and antibody j at time t, respectively;
s4) each robot selects proper speed to move according to the calculated excitation value, and the method comprises the following steps:
s4.1) calculating an excitation value of each robot;
s4.2) setting threshold values of excitation values received by the robot to N and N = N +1, when the excitation received by the robot is between 0 and N, the robot moves at a low speed, when the excitation received by the robot is between N and N, the robot moves at a medium speed, when the excitation received by the robot is greater than N, the robot moves at a high speed, N belongs to [0,1.5];
s4.3) when the number of the robots is respectively 3, 4, 5 and 6, performing formation control by using the formation control method to form an expected formation;
s5) updating the position coordinate information of the robot, judging whether the multi-robot system forms an expected formation, recalculating the stimulation of the antigen to the antibody, the mutual stimulation and inhibition among the antibodies and the interleukin injection amount, repeating the steps S2 to S4 until the robot forms the expected formation,
wherein, the antigen refers to the gravity center of the formation, the antibody refers to the speed of the robot, and the interleukin refers to the included angle between the line of the real-time position of the robot and the target point and the x axis.
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