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Cooperative Planning Method for Swarm UAVs Based on Hierarchical Strategy

Dong ShiyouCollege of Astronautics

Northwestern Polytechnical University,Xian, China

e-mail: [email protected]

Zhu XiaopingResearch Institute 365



Long GuoqingCollege of Astronautics



AbstractIn this paper, the problem of controlling swarm

UAVs is studied by considering a hierarchical strategy based

on the local interactions. First swarm as a whole plans its own

initial path using Voronoi graph and Dijkstra algorithm.

Second swarm UAVs combine the low-level behaviors to yield

swarm behaviors. The results achieved for such a strategy are

verified by computer simulations.

Keywords- Swarm UAVs, Cooperative Planning,

Hierarchical Strategy;

I. INTRODUCTION

In recent years, the attention of researchers was attractedby the idea of creating groups of agents able to collaborateto accomplish predefined tasks at the same time. Manyapproaches were inspired by the observation of naturalsystems. In nature, it is possible to see social animalsworking together to perform complex social behaviors.Many examples can be found in the sea, on the ground andin the air. Ants can work together to build enormous nests;

birds can fly in formations during migrations in order tosave energy; fishes organize themselves in schools to

protect from enemies. A systems behavior emerges fromthe local interactions. This behavior is self-organizing,

being adaptive, completely decentralized.Researchers have begun to model swarms to better

understand how social animals interact and achieve goals.So there is a new research field that named swarm UAVs.Swarm UAVs have many applications such as exploration,surveillance, attack, mapping of unknown environments.Swarm UAVs can present many advantages such asimproving the mission efficiency and quality, achievingflexibility to the tasks execution. Decentralized approachesadapt to the cooperative control of a group of UAVs. It can

reduce the dimensionality of the problem. The number ofUAVs can be very large, ranging from hundreds tothousands. In [1], social potential approach was used tomodeling swarm aggregation and cohesion. In [2], Olfati-Saber used structure potential function to achieve collision-free, distributed formation stabilization of autonomousswarms. Similar results can be found in [3], where structure

potential are constructed by introduce virtual leader. In [4],behavior-based approach is another important method toform swarm behavior of creatures. In [5], Wang studied theleader/follower approach for formations keeping andattitude alignment based on nearest neighbor tracking.

The article use top-down control mechanism using

hierarchical strategy. By this architecture, self organizationis achieved using coordinated movements, while theindividual behavior is affected via top-down control, whichguides the system-wide behavior. The paper is organized asfollows: Section 2 presents the generation of initial path ofswarm using Voronoi graph and Dijkstra algorithm. Section3 describes basic behaviors of UAVs. In section 4, relevant

simulation results are presented. Finally the main conclusionand further research directions are outlined in section 5.

II. INITIAL SWARM PATH GENERATION

The dissertation incorporates top-down control to self-organizing UAVs, thereby guiding the self-organizing

process and making it possible to undertake problem solvingdirected by goal-oriented behavior. Initially swarm as awhole plans its own original optimal or sub-optimal pathsusing Voronoi graph and Dijkstra algorithm. Each Voronoicell contains one threat and every position within a givencell is closer to its associated threat than to any other threats.By using threat locations, the Voronoi polygon edges form a

initial path. The initial and target locations are containedwithin cells.

A. Voronoi Tessellations

A Voronoi tessellation refers to a region, containing pgenerating points, separated into cells where each cellcontains one generating point and every point in the cell isclosest to its generating point. Voronoi tessellations aremathematically defined as follows.

Given a region NR , and a set of generating

points k

iip 1 , let the Voronoi cell iV corresponding to

the generator ip be

,,...,1,,...,1|

kiijkjpqpqqV jii

(1)

where the set of Voronoi cells kii

V 1 creates a Voronoi

tessellation on .While the Euclidean norm is defined as22

222

11 )(...)()( iNNiii pqpqpqpq (2)

Equation (1) simply compares the distance betweenpoints on the region, q , and generators, p . If a point q is

closest to the generator ip ; then that point belongs to the

Voronoi cell iV . In this problem, the point ip is treated as

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threat locations. Then, the edges of the cells can be the bestpath to follow avoiding the site of two nearest threats

Figure 1. Voronoi diagram

Now we have to search the shortest and safest path to goto the nearest node to the target positions. Before this work,the costs of each Voronoi edge should be decided. The totalcost of each edge consists of both length and exposure cost.

B. Cost Function (Evaluation function of trajectory

planning )

Using the threat points as mother points, we can obtain aVoronoi graph. Furthermore, a directed graph can be easilygenerated by connecting each of the starting points andtarget points to their three closest nodes respectively in thediagram. To avoid the threat regions and save fuel and time,it is required to construct an optimal path to the target. Thetotal cost consists of two terms, first term is associated withlength cost and second one is the exposure cost. Thealgorithm will search for two costs: fuels cost and threatscost.

The threats cost means the degree that the threats pose toUAVs. Here we suppose that the degree is only related tothe distance between UAV and threat point, and is

proportional to the inverse of the quadratic distance whenflying along the edge of the diagram. In this paper wecalculate the threats cost at the segment points 1/6, 1/2, and5/6 on the edge of the graph and the overall threats costrelating to one edge is given by

dttdJt

ithreat )(/104

, (3)

N

j jijiji

iithreatddd

LJ1

4,,6/5

4,,2/1

4,,6/1

, )111

( (4)

Where ithreatJ , is the threat cost when UAV flying on the

ith edge, iL is the length of the ith edge, N is the total

number of the threat points.

j-1

j

j+1

1/6

1/2

5/6

1/6

1/2

5/6 1/6

1/2 5/6

d5/6,i-1,j-1d1/2,i,j

d1/6,i+1,j+1

i-1

i

i+1

Figure 2. Threats cost evaluation points of trajectory planning

Suppose that all the UAVs fly at a constant speed. Thefuel required for flying over an edge of the Voronoi diagramis therefore proportional to the length of the edge. We may

simply define the fuel cost for edge iL asiifuel LJ , (5)

and accordingly the total cost for flying along an edge is10)1( ,, kJkkJJ ifuelithreati (6)

Using Dijkstras algorithm, we can search for theVoronoi directed diagram, and determine a path for everyUAV, which has the minimal cost from its starting point tothe target point. The initial path is 1-2-3-4-5-6.

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-80

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target

swarm uavs

1

2 3

4 5

6

Figure 3. The initial positions of the swarm UAVs

III. ELEMENTARY BEHAVIORS OF SWARM UAVS

Behavior-based cooperative control techniques areethologically motivated and have solved foraging, task

allocation, and division of labor problems. Possiblebehaviors include neighbor tracking, collision and obstacleavoidance, and formation keeping. The whole behavior isdecomposed into elementary behaviors. In presence ofmultiple behaviors, each output is designed to achieve itsspecific goal but it is generally impossible that a singlecommand can accomplish all the assigned behaviors at thesame time.

The first and for some aspects the breakthrough work onthe flocking theory, is the paper presented in 1987 by C.Reynolds. In this section flocking theory is applied to SwarmUAVs. The elementary behaviors are collision avoidance,velocity matching, and flock centering. Collision avoidanceis to find the agents that are within the neighborhood and

sum up the vectors to push it away from them. Velocitymatching is to match the velocity of the agents in theneighborhood. This will lower the possibility of the agentscolliding with each other. Velocity matching is seen as adynamic version of collision avoidance. Flocking centeringis to find the graphical center of the agents in theneighborhood and to steer the agents to that point. Pathfollowing behavior enables a character to steer along a

predetermined path, such as a roadway, corridor or tunnel.This is distinct from constraining a vehicle rigidly to a pathlike a train rolling along a track. The goal of the pathfollowing steering behavior is to move a character along the

path while staying within the specified radius of the spine. If

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the character is initially far away from the path, it must firstapproach, then follow the path.

Collision Avoidance Velocity Matching Flock Centering

Path following

Figure 4. Elementary behaviors

The behaviors for flocking are modified to be used for

convenience. Each UAV describe the individual maneuversbased on its neighbors. Collision avoidance and flockcentering can be combined to a behavior named neighbor

behavior which can keep desired distance from neighborswhen there are no obstacles.

Here, we assume the sense range of UAV is larger thanthe desired distance d . For simplicity, we assume allobstacles are closed discs. The set of neighbors forUAV i can be described as:

},....3,2,1,,{ jirqqRNB jiji

where ji qq means the distance between iq and jq , ris

the sense radius.For UAV, the neighbor behavior can be computed as

follows:

1

)(

i

ij

NBj ij

ijineighbbor

N

dqq

qq

qqV

i

That is because the algorithm is distributed, and everyUAV moves to the target using the same algorithm. Whenthe number of a UAVs neighbors is larger than one, the sumof movement vectors between the UAV and its neighborswill be computed. When the distance between two UAVs islarger than the desired distance d , the UAVs will move

toward each other; otherwise, when the distance betweenthem is smaller than d , they will move away from eachother until they achieve the desired distance.

When there are threats in the environment, UAV willadjust the movement vector based on threats. We assumethreats have the safety margin l, if the distance betweenUAVs and threats is larger than l, then there is no force on aUAV; otherwise there will be a repulsive force on a UAV inorder to avoid threats.

}{ ikthreatNik ik

ikithreat qTlsat

qT

qTV

i

Where kT is threat centre. The closer a UAV is to an

threat ( ik qT is smaller), the larger the repulsive force will

become (ik

qTl becomes larger).

Swarm UAVs fly to the target to achieve mission, sothere is a migration vector to control all UAVs. The target ison the initial swarm path.

etti

ettiimigration

qq

qqvV

arg

arg

Where v denote the migration velocity.Once each of the rules has been calculated, they are

combined to produce a single steering force that defines theacceleration of the UAVs. In this most simple model, therules are scaled and added together.

Figure 5. The flow diagram of hierarchical strategy

IV. SIMULATION RESULTS

In this section, simulation results are shown to illustratethe effectiveness of the algorithms discussed in the

proceeding section. Consider ten UAVs, which are initiallylocated at U1 (-50,-80), U2(-93,-80),U3(-70,-75),U4(-95,-95)U5(-82,-90), U6(-84,-75), U7(-90,-65), U8(-78,-70), U9(-90,-90),U10(-77,-80). There are ten threat points located at T1(-50,-80), T2 (-75,-10), T3(-60,50), T4 (-25,-40), T5(-30,20), T6(-5,60),T7 (25,-70),T8 (25,0),T9(60,-40),T10(50,50) with radius15, 10, 15, 10, 10, 15, 10, 10, 15, 15. Targets value is set as

(90, 10). Here, figure 6 is a snapshot at a specific time. TheUAVs try to achieve the desired distance from theirneighbors and move forward. With time passing, the UAVsadjust their movement vectors to avoid collision withneighbors and threats. The swarm UAVs try to achieve the

path following.

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4 5

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(a) Position snapshot at 5.4 s.

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target

1

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(b) Position snapshot at 9.7 s

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target

1

2 3

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6

(c) Position snapshot at 14.6 s.

Figure 6. UAVs move together to avoid threats and others

V. CONCLUSIONS

The dissertation incorporates top-down control to self-organizing UAVs, guiding the self-organizing process to the

goal. First swarm as a whole plans its own initial, optimal orsub-optimal path using Voronoi graph and Dijkstra algorithm.Second swarm UAVs combine the low-level behaviors(basic, individual, and group) necessary to yield a swarm

behaviors. The primary strengths of this method are: 1) theability to that are easy to model or understand at a globallevel based only on an understanding of the individualelements; and 2) the decentralized approaches are flexible,scalable, robust and cost-effective.

REFERENCES

[1] V. Gazi and K. M. Passino, Stability analysis of swarms, IEEETrans. Trans. on Automatic Control, vol. 48, no. 4, pp. 692697, 2003.

[2] R. Olfati-Saber and R. M. Murray, Distributed cooperative controlof multiple vehicle formations using structural potential functions, inProceedings of the 15th IFAC World Congress, Barcelona, Spain,2002.

[3] N. E. Leonard and E. Fiorelli, Virtual leaders, artificial potentialsand coordinated control of groups, in Proceedings of the 40th IEEEConference on Decision and Control, Orlando, FL, 2001, pp. 29682973.

[4] C. W. Reynolds, Flocks, herds, and schools: A distributed behaviormodel, in Proceedings of SIGGRAPH 87, 1987.

[5] P. K. C. Wang and F. Y. Hadaegh, Coordination and control ofmultiple microspacecraft moving in formation, J. Astronautical Sci,vol. 44, no. 3, 1996.

[6] Timothy W.McLain, Trajectory Planning for CoordinatedRendezvous of Unmanned Air Vehicles, Proc. AIAA Guidance,

Navigation, and Control Conference, AIAA Press, 2000, pp. 1247-

1254,AIAA.2000-4369.[7] C. W. Reynolds. Steering behaviours for autonomous characters.

1999.

[8] M. Schwager. Unifying geometric, probabilistic, and potential fieldapproaches to multi-robot deployment. International Journal ofRobotics Research, 2010.

[9] Gianluca Antonelli. Decentralized deployment with obstacle voidancefor AUVs [C]//Proceedings 18th IFAC World Congress Italy August28 - September 2, 2011

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