XXXX, VOL. XX, NO. XX, XXXX 2019 1

G-flocking: Flocking Model Optimization basedon Genetic Framework

Li Ma, Weidong Bao, Xiaomin Zhu, Member, IEEE , Meng Wu, Yuan Wang, Yunxiang Ling, and Wen Zhou

Abstract— Flocking model has been widely used to con-trol robotic swarm. However, with the increasing scala-bility, there exist complex conflicts for robotic swarm inautonomous navigation, brought by internal pattern main-tenance, external environment changes, and target areaorientation, which results in poor stability and adaptability.Hence, optimizing the flocking model for robotic swarmin autonomous navigation is an important and meaningfulresearch domain.

Index Terms— Robotic swarms, flocking model, multia-gent systems (MASs).

I. INTRODUCTION

ROBOTIC swarms pose an attractive and scalable solutionto accomplish complicated missions such as search-and-

rescue [1], mapping [2], target tracking [3], and full coverageattacking, which can prevent human beings from boring,harsh and dangerous environment. One main advantage of arobotic swarm solution is the simple local interactions betweenindividuals within a complex system that could generate somenew properties and phenomena observed at the system level,such as a set of collective behaviors [4]. Much like theirbiological counterparts such as fish schools [5], bird flocks[6], ant colonies [7], and cell populations [8], the resultingcollective patterns are robust and flexible to agents joining inand dropping out, especially when accidents like obstacles,dangers, and new missions emerge. While robotic swarm en-joys numerous advantages, the large-scale autonomous roboticswarm incurs a high robot-failure probability due to real-life conditions when delays, uncetainties, and kinematic con-straints are present. This phenomenon is even more noticeablein military projects like Gremlins [9] and LOCUST [10], sincethey are built on small, low-cost and semi-autonomous UAVswhose failure probability is expected to be much higher.

Among researches of flocking models with obstacle avoid-ance, Wang et al. [11] proposed an improved fast flockingalgorithm with obstacle avoidance for multi-agent dynamicsystems based on Olfati-Sabers algorithm. Li et al. [12]studied the flocking problem of multi-agent systems withobstacle avoidance, in the situation when only a fraction ofthe agents have information on the obstacles. Vrohidis et al.[13] considered a networked multi-robot system operating in

This work was supported in part by the National Natural ScienceFoundation of China under Grants 61872378, 91648204, 71702186, inpart by Postgraduate Research Innovation Project in Hunan Provinceunder grant CX2018B021, in part by the Scientific Research Project ofNational University of Defense Technology under Grants ZK17-03-48

an obstacle populated planar workspace under a single leader-multiple followers architecture.

Sensing

layer

Decision

layer

Action layer

Target orientationObstacle avoidance

Repulsion AlignmentAttraction

Generalized velocity update formula

Evaluation

layer

Evolution

layer

Average time

Death rate Anisotropy

Aggregation

Uniformity

Initial population

Fitness test

Select best

parents ChildrenBREED

MUTATE

Ultrasonic

Laser radar

Camera

Communication

One Generation

Rules Rules R

ob

ot(

Ag

en

t)E

nv

iro

nm

en

t

Fig. 1. Genetic flocking optimizing framework

To the best of our knowledge, few previous literaturesstudied the model that satisfies both stability and adaptivityof the autonomous robotic swarm. Thus, we design a novelgenetic flocking optimizing framework that can achieve bothstability and adaptivity of the robotic swarms. As shownin Fig. 1, a robot is seperated into three layers, includingsensing layer, decision layer, and action layer, which supportsthe basic navigation function. Besides, we generalize velocityupdating formula by rules described with weight parameters,which evolves through interaction with the environment. Theenvironment is divided into two layers: the evaluation layerand the evolutionary layer, where the former provides fitnessfunction for the latter.

II. GENERALIZED FLOCKING MODEL

As shown in Fig. 2, a robot agent i has four detection areas:repulsion area, alignment area, attraction area, and obstacleavoidance area. The velocity updating fomula is described asfollows:

In equation (1), we define the weight parametersa,b, c,d, e ∈ (0, 1), which is used to flexibly handle thegeneralization formula.

arX

iv:1

907.

1185

2v1

[cs

.MA

] 2

7 Ju

l 201

9

2 XXXX, VOL. XX, NO. XX, XXXX 2019

R0

zrep

R2

R3

zali

zatt

R1

zobs

Fig. 2. Pattern-formation areas (Zrep, Zali, Zatt) and obstacle-avoidance area (Zobs).

∆vi = a∑

j∈Zrep

(R0 − rij)pi − pjrij

+ b1

Nali

∑j∈Zali

vj|vj |

+ c∑j∈Zatt

(R2 − rij)pj − pirij

+ d∑

j∈Zobs

(R3 − rik)pi − pkrik

+ eptar − piritar

+ v(t).

(1)

Tunning the model above means that we propose four rulesreferring to classic reynolds’ boids model and we optimizethe parameters there. Note that the parameter space is 20-dimensional; therefore, manual tuning, global optimizationmethods, or parameter sweeping would be generally muchtime-consuming.

III. ORDER PARAMETERS AND FITNESS FUNCTION

In order to select the set of parameters that perform the bestin the simulation process, we propose a fitness function com-posed by several order parameters, which helps us to abstractthe mathematical model of single objective optimization. Thefitness function is described as flollows:

F =

∑j (T arrivej − T startj )

N× NdeathNtotal

×

∑t

∑j

√(pxj − rxt )

2+ (pyj − r

yt )

2

NT

×∑t (γt − γ̄)

T

×∑t

∑j (θtj − δt)

2

T× α,

(2)

where T startj is the time when the navigation is triggered,and T arrivej is the time when robotic agent j reaches the targetarea. Ndeath represents the number of the dead agent, andNtotal represents the number of the total agents in the roboticswarm. rxt and ryt are the abscissa and ordinate of the positionof the swarm’s centroid at time t. T is the total time of the

whole navigation process, while N is the agent number of theagents that arriving at target area.

We define the stability of the robotic swarm as the varianceof the γt sequence, which describes whether the flock structureof this swarm is stable.

s2γ =

∑Tt=0 (γt − γ̄)

2

T, (3)

γt =

∑j

√(pxj − rxt

)2+(pyj − r

yt

)2N

. (4)

We define anisotropic index to describe the variation ofpopulation velocity direction. Specifically, it needs to calculatethe average angle of each individual velocity direction andflock velocity direction at a certain time, and then calculatethe average value of the whole process, which is the indexof anisotropic index. The variance of the average angle of thewhole process represents the variation range of anisotropicindex, and the formula of anisotropy is as follows:

δt =

∑j

θj

N. (5)

With this method, we created a single-objective optimizationscenario, which can be solved using genetic algorithm.

IV. THE G-FLOCKING ALGORITHM

This research adopts Parameter Tuning of Flocking Modelbased on classical genetic algorithm (GA) framework. Themain algorithm is described as follows:

Algorithm 1 The G-flocking algorithmRequire: Rexp: a set of traditional expert’s rules; P (0):

randomly generate an initial population of rules; M : max-imum number of iterations; Np: number of the population;LR: length of the rules; Ns: number of seed used toproduce the next generation; r: member mutation rate;

Ensure: Ropt: an set of optimal rules;1: t = 02: while t <= T do3: for i = 1→M do4: Evaluate fitness of P (t)5: end for6: for i = 1→M do7: Select operation to P (t)8: end for9: for i = 1→M/2 do

10: Crossover operation to P (t) =Crossover(Ns, Np)

11: end for12: for i = 1→M do13: Mutation operation to P (t) = Mutation(P (t), r)14: end for15: for i = 1→M do16: P (t+ 1) = P (t)17: end for18: t = t+ 119: end while

LI MA et al.: PREPARATION OF PAPERS FOR XXXX (2019) 3

In the algorithm, the random rules Rexp are representedas:

{R1

0, R20, R

30, R

40

}, and Ri0 =

{ai0, b

i0, c

i0, d

i0, e

i0

}, i =

1, 2, 3, 4.The outputs of G-flocking are also a set of optimized

rules: Ropt ={R1opt, R

2opt, R

3opt, R

4opt

}, and Riopt ={

aiopt, biopt, c

iopt, d

iopt, e

iopt

}, i = 1, 2, 3, 4.

Once optimized, we can get the optimal rules for theflocking which composing the BRIAN model.

V. EXPERIMENT ANALYSIS

To reveal the performance improvements of BRIAN, wecompare it with basic rule-based model (BREAM). BREAMderives from the classical Reynolds’ flocking model that hasbeen widely used. To apply Reynolds’ flocking model to morecomplex environment, the comprehensive obstacle avoidancestrategies are integrated into BREAM.

0 5 10 15 20 25

0

5

10

15

20

25

(a) BREAM (20 robots)

0 5 10 15 20 25

0

5

10

15

20

25

(b) BRIAN (20 robots)

0 5 10 15 20 25

0

5

10

15

20

25

(c) BREAM (60 robots)

0 5 10 15 20 25

0

5

10

15

20

25

(d) BRIAN (60 robots)

0 5 10 15 20 25

0

5

10

15

20

25

(e) BREAM (100 robots)

0 5 10 15 20 25

0

5

10

15

20

25

(f) BRIAN (100 robots)

Fig. 3. BREAM and BRIAN traces of the robotic swarm in autonomousnavigation in test scenery ( We tested 3 groups of experiments using 20,60 and 100 robotic agents for simulation.)

In order to clearly observe the impacts of different parame-ters of the formula for velcocity updating, we compare theperformance of basic rule-based model (BREAM) and ouroptimized flocking model for robotic swarm in navigation(BRIAN) in scenary with three basic environmental elements

including tunnel obstacle, non-convex obstacle and convexobstacle.

Fig. 3 shows directly that BRIAN performs better thanBREAM in uniformity and stability. Fig. 3(a) and Fig. 3(b)represent the performance of these two models with 20 roboticagents, Fig. 3(c) and Fig. 3(d) with 60 robots, Fig. 3(e) andFig. 3(f) with 100 robots. Specific performance indicators areshown in Table I. We record the values of each evaluationindex of the two models in three situations of the numberand scale of robots. Generally, all the indicators of BRIANmodel perform better (the smaller, the better). Specifically,aggregation of BRIAN is 56% lower than that of BREAMwhile the reduction of other indicators (anisotropy, average-time, uniformity, deathrate, and fitness function) are 88.61%,32.55%, 89.69%, 100%, and 99.92%, respectively.

0 10 20 30 40 50 60 70 80 90 100 110

0

2

4

6

8

BREAM20

BRIAN20

BREAM60

BRIAN60

BREAM100

BRIAN100

Fig. 4. The uniformity of the robotic swarm with each experimentchanges through time.

Fig. 4 shows the change of uniformity in the whole timestep. The total time step of each group of experiments is notthe same, but it can be seen from the figure that the dataof each group of BRIAN are stable between 0 and 1, whichmeans that the stability and tightness of the cluster are verygood during the whole cruise. When BREAM passes throughobstacles, it can be seen that there will be large fluctuationsnear step 31 and step 71. Such fluctuations represent thesituation of low cluster tightness and stability when clusterpasses through narrow and non-convex obstacles, and theformation is not well maintained. At the same time, it canbe seen that BRIAN has completed the whole task in about84 seconds, while BREAM has completed the whole task.

VI. CONCLUSIONS AND FUTURE WORK

We presented in this paper an optimized flocking modelfor robotic swarm in autonomous navigation. This model isobtained through G-flocking algorithm proposed by us, whichis extended from the classical genetic algorithm and rule-basedflocking model in most relative researches. This is the firstof its kind reported in the literatures; it comprehensively ad-dresses the reliability, adaptivity and scalability of the roboticswarm during completing the navigation tasks.

The following issue will be addressed in our future work:First, we will extend our experiment to the real-world sys-tems such as unmanned aerial systems and unmanned groundsystems. Second, we will take more uncertainties of scenariesinto the model to verify the correctness of our model, such asadding the moving obstacle, the irregular barriers, and evenfluid barriers.

4 XXXX, VOL. XX, NO. XX, XXXX 2019

TABLE ICOMPARISONS BETWEEN BREAM & BRIAN WITH 20, 60 AND 100 ROBOTS

Evaluation Aggregation Anisotropy Averagetime Uniformity Deathrate Fitness FunctionAlgorithm BREAM BRIAN BREAM BRIAN BREAM BRIAN BREAM BRIAN BREAM BRIAN BREAM BRIANNum-20 0.8481 0.4666 38.6869 5.3094 130.0500 84.5000 0.2864 0.0076 0.3500 0.0000 6.1110 0.0079Num-60 0.8639 0.4326 42.8201 4.6934 128.7667 83.9167 0.3195 0.0435 0.3333 0.0000 7.6107 0.0371Num-100 1.1681 0.4557 50.1455 4.9927 115.8000 84.2500 0.2100 0.0330 2.7367 0.0000 92.8195 0.0317

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[13] Vrohidis, C. , Vlantis, P. , Bechlioulis, C. P. , & Kyriakopoulos, K. J.. (2018). Reconfigurable multi-robot coordination with guaranteed con-vergence in obstacle cluttered environments under local communication.Autonomous Robots, 42(4), 853-873.

Li Ma is currently working toward his Ph.D. de-gree in the College of Systems Engineering, Na-tional University of Defense Technology. Contacthim at mali10@nudt.edu.cn.

Weidong Bao is currently a professor in the Col-lege of Systems Engineering at National Univer-sity of Defense Technology, Changsha, China.Contact him at wdbao@nudt.edu.cn.

Xiaomin Zhu is currently an Associate Profes-sor in the College of Systems Engineering at Na-tional University of Defense Technology, Chang-sha, China. Contact him at xmzhu@nudt.edu.cn.

Meng Wu is currently pursuing the M.S. degreein the College of Systems Engineering, NationalUniversity of Defense Technology, China. Con-tact her at wumeng15@nudt.edu.cn.

Yuan Wang is currently a Ph.D Candidateof College of Systems Engineering,National University of Defense Technology,Changsha, China. Contact him atwy1020395067@hotmail.com.

Yunxiang Ling is currently a professor in Offi-cers college of PAP, Chengdu, China. Contacthim at 2923821396@qq.com.

Wen Zhou is currently an Assistant Professor inthe College of System Engineering at NationalUniversity of Defense Technology, Changsha,China. Contact him at zhouwen@nudt.edu.cn.