Coverage and Goal Searching Behaviours of a Group of Agents

by a Special Single Query Roadmap

Its Benefits to Mutiple Query Roadmaps

Ali Nasri Nazif and Mohammad Torabi Rad

National Iranian Oil Company, Tehran, Iran

Keywords: Multi-agent, Single Query Roadmap, Coverage, Goal Searching.

Abstract: This paper tends to mainly target two different types of swarming behaviour in a 2D environment, namely

area coverage and goal searching within an environment occupied with obstacles. For such behaviours, we

introduce a roadmap (a tree) customized to behave well in multi-agent scenarios. We consider a variety of

situations and environments, and explain how the method we have proposed comes into operation under

such circumstances. A comparison is, also, made with respect to multiple query roadmaps.

1 INTRODUCTION

In our two former papers, Multi-Agent Area

Coverage Using a Single Query Roadmap (Nasri,

Davoodi and Pasquier, 2011) and Finding an

Unknown Goal in an Environment by a Group of

Agents (Nasri, Davoodi and Mohades, 2009), efforts

were made to introduce a new single-query roadmap

known as WMA-RRT which, is a form of graph,

spreads in free spaces of an environment, and is

applied to coordinate the movements of a group of

homogenous agents within the same environment.

What must be labelled as an important characteristic

of this roadmap is its construction on the basis of the

number of agents that do exist in the environment.

As a result, it is highly appropriate for multi-agent

scenarios. Further, as could be seen through the

following pages, such a roadmap plays the role of a

channel the agents employ to communicate.

The paper begins with an introduction on WMA-

RRT, and then it adheres to study coverage and goal

searching behaviours that benefit from the

constructed WMA-RRT in the environment. In brief,

the goal in coverage behaviour is to visually cover

an area by means of a group of agents, while the

primary aim in goal searchning behaviour is to find

an unknown goal by a group of agents in an

environment. Also in each part, experimental results

and comparision to multiple query roadmap methods

are presented.

2 WMA-RRT

Constructed in any given environment, a roadmap is

a graph able to capture the connectivity of free space

within the same environment. So far, two different

types of roadmaps have been introduced by

researchers, first of which is in demand of an

explicit representation of the workspace geometry.

Visibility Graphs as well as Generalized Voronoi

Diagrams could be named as cases belonging to this

group. However the roadmap introduced by the

paper falls in the second group which is constructed

based on sampling-based algorithms. They work by

generating sample points throughout the free space

of the environment and connecting them to build a

graph. There are two types of sampling planners:

multiple-query and single-query. In multiple-query

planners, in pre-processing phase, a roadmap is

constructed by simultaneously expanding some trees

from several randomly distributed starting points

and merging them to prepare the entire roadmap. It

is likely that the constructed roadmap is not

connected in a cluttered environment. Taking

multiple-query planners, PRM could be introduced

as the one most frequently used. (Kavaraki, Svestka,

Latombe and Overmars, 1996). The pre-processing

phase pertinent to multiple-query planners may be

occasionally very time consuming, but it is going to

answer many queries once the construction of the

roadmap has been completed.

Single-query planners, on the contrary, have

280

Nasri Nazif A. and Torabi Rad M..

Coverage and Goal Searching Behaviours of a Group of Agents by a Special Single Query Roadmap - Its Beneﬁts to Mutiple Query Roadmaps.

DOI: 10.5220/0004753802800287

In Proceedings of the 6th International Conference on Agents and Artiﬁcial Intelligence (ICAART-2014), pages 280-287

ISBN: 978-989-758-015-4

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

been introduced to handle situations in which it is

required to provide an answer to just a single query

as fast as possible. EST, Lazy RPM and RRT all

belong to this latter category of planners. Since the

planner introduced in this paper is a variation of

Rapidly-Exploring Random Tree (RRT) (Lavalle

and Kuffner, 2000), it is worth briefly explaining

how it operates.

The roadmap constructed by the RRT planner is

a tree which expands throughout the free space of a

given environment. This planner is probabilistically

complete, in other words, if the algorithm keeps

running for an adequate length of time, the

probability of covering every location of the

environment converges to one.

RRT construction algorithm is as follows: first a

uniform distribution is used to insert a sample point

qinit in the environment. When not colliding with any

obstacles, this sample point is added to the RRT tree

as its first node. In each iteration, another sample

point (

qrand) is randomly placed in the free space.

Then, among the previously added nodes, the nearest

neighbour node (

qnear) is selected for further

expansion. Next, a new node (qnew) is produced as a

result of moving the qnear by a predefined value

called step-size (ɛ) toward

qrand. Finally, if collision

free, the new node is added to the roadmap (Figure

1).

Figure 1: This figure illustrates how an RRT tree is

expanding given the current state of the tree.

Regardless of what swarming behaviour we are

going to contemplate, construction of WMA-RRT

begins by figuring out the location of the root of the

roadmap (Main Root) and continues by specifying

the adjacent nodes to the main root which we call

them Secondary Roots. The Secondary Roots are

exactly where the expansion of our tree starts.

We assume that at the beginning, all agents are

situated close to each other and can be surrounded

by a simple polygon. In order to build this polygon

in a way it could enclose all the agents, we apply

convex hull algorithm (Preparata and Hong, 1977).

The agents are considered as points in the

environment, thus the convex hull algorithm is able

to construct the minimal convex hull out of these

points, regardless of the obstacles in the

environment. We pick the point where the two

longest diameters of the polygon intersect as our

Main Root. In case that the intersection point is not

collision free, we will just replace the current longest

diameters by the next two ones.

Then it comes to assigning a particular node to

each agent. Here, the algorithm connects the agents’

initial locations to the Main Root and therefore some

edges are created. Our Secondary Roots are

produced by moving out a distance of at most ɛ in

the direction of these edges. Each of these

Secondary Roots is assigned to the corresponding

agents. From this point on, the algorithm works like

the RRT planner, but with two main differences.

First, in WMA-RRT all Secondary Roots are

considered as

qinit, in contrary to the RRT algorithm

in which we just have one

qinit that is inserted

randomly in the free space of the environment. The

second difference is that in WMA-RRT, our main

root is exempted from expansion. The tree expands

at a high pace, and it develops n sub-trees that we

assign as Branches, where n stands for the number

of agents in the environment.

3 SWARMING BEHAVIOURS

In this section, first we briefly discuss the works

formerly done on multi-agent systems, and then in

two different parts, we introduce our algorithms for

Coverage and Goal Searching behaviours using

WMA-RRT.

One of the earliest applications of multi-agent

systems is coordinating the movements of a group of

agents where each agent has its own starting point

and destination. There are two main approaches for

solving these kinds of problems: Centralized and

Decoupled.

In Centralized Planning, each agent is taken into

account as an end-effector of a multi-arm robot.

Paths for agents are planned simultaneously and

collisions between agents are self-collisions of the

robot’s arms. The main advantage of Centralized

Planning is completeness.

Decoupled Planning is less expensive than

Centralized Planning, but it is incomplete and it may

be unable to find a solution even if one does exist.

Swarm Intelligence, has recently been a source

of motivation for a lot of researches in multi-agent

systems. Swarm Intelligence is an AI technique

inspired by the collective behaviours observed in a

multitude of species which exhibit social life such as

ants and honey bees (Abraham and Guo, 2006).

௜௡௜௧

௡௘௔௥

௡௘௪

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CoverageandGoalSearchingBehavioursofaGroupofAgentsbyaSpecialSingleQueryRoadmap-ItsBenefitsto

MutipleQueryRoadmaps

281

Coordinating a group of agents by employing

honeybees’ foraging behaviour has been one of the

earliest attempts in SI (Gordon and Wagner, 2003).

Also Bayazit uses a multiple-query roadmap as a

means of indirect communication between agents

(Bayazit, 2004).

Moreover, the swarming behaviour probably

observed in flocks of birds, schools of fish and sheep

herds motivated Reynolds to introduce a bio-

inspired technique to steer a group of rule-based

autonomous agents, called Boids (Reynolds, 1999).

Researchers have also used grid-based

approaches to deal with the area coverage problem.

Hazon and Kaminka, for example, proposed a

mechanism by decomposing the environment into

same size cells. Considering the initial positions of

the robots, they found a spanning tree of the free

cells which could be decomposed to some balanced

sub-trees. Finally each sub-tree was assigned to a

robot (Hazon and Kaminka, 2008).

3.1 Area Coverage

The area coverage problem deals with the use of one

or more agents to sweep or visually sense the free

space of an area.

The agents rely on the WMA-RRT roadmap to

move through the free space of the environment, and

also use it as a means of indirect communication as

shown later. WMA-RRT is considered a weighted

tree and the weight of the edges of the roadmap is

initialized to 0 at the starting point of the algorithm.

As described before, the tree has branches equal to

the number of agents. During the covering operation,

at least one agent is assigned to each branch. The

weight of the edges is updated while traversing the

roadmap.

All the information that the agents need in order

to do their job well in the environment is available

through the roadmap’s nodes. Our agents here are

simple autonomous entities capable of following

some explicit condition-action rules. They are utility

based agents, that is, each of them will try to

maximize its own utility function, which is defined

as the average over the weight of all traversed edges.

At the beginning of the mission, each agent is

assigned to independently find a branch, and keep

operating until the branch is thoroughly traversed.

Our main data structure, used by the agents

during the covering process, is an array of n trees,

where n represents the number of branches (agents)

in the environment.

Graph Brach[i]; 0 ≤ i ≤ n-1

The Graph itself is a class using two other

classes: Node and Arc. The agents use these classes

to gather information such as the outgoing edges of a

node and their corresponding weight.

Two arrays, Sync and Weight are the other data

structures that are used in our algorithm. Sync is

used to keep the number of active agents in each

branch:

Sync[i]; 0 ≤ i ≤ n-1

In other words, Sync[k] shows the number of

agents that are currently using branch[k] as their

exploration roadmap. As we will see, there may be

situations that more than one agent use the same

branch. At the beginning, all members of Sync array

have value of zero. Entering a specific branch such

as Branch[j], each agent increases the related value

of sync which is sync[j] by one (and decreases the

same value by one when it exits that branch).

The last array is Weight which is used to hold the

weight of the first edge of each branch (the edge that

connects the Main Root to the Secondary Root). As

we will see, the agents use this as a way to rapidly

exchange some information.

Weight[i] ; 0 ≤ i ≤ n-1

Figure 2 depicts a scenario with four agents a

few seconds after their mission has just started. As

can be seen, the first-coming edges of each branch

(four edges here) connect the Main Root to the

Secondary Roots. As soon as choosing an edge to

traverse, each agent increases the weight of it. The

first edge each agent begins to traverse is the starting

(first-coming) edge of its corresponding branch. As

a result, by increasing the weight of that edge, the

value of the corresponding item in array Weight

will

increase too. Also as can be seen in this figure, the

value of all members of sync array is equal to one,

because each agent starts exploring its dedicated

branch and by increasing the default value of the

corresponding array member from 0 to 1, shows that

it is active on that branch. It also has been mentioned

that our agents are utility based and they will try to

minimize the average weight of visited edges.

Therefore, the outgoing edge with the minimum

weight is nominated at each node for exploration,

since the heavier edges have been already visited

more, the lighter ones are reasonably preferred to be

selected here.

One of our aims is to return our agents to the

location where they have started their mission by the

time they have finished traversing their

corresponding branches. By choosing the outgoing

edge with minimum weight at each step, the agents

actually use a Depth-first search (DFS) to traverse

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282

Figure 2: The values of items in arrays Sync and Weight a

few seconds after the start of the mission (all equal to 1).

the roadmap and this causes an automatic return of

the agents to their starting point. In fact in each

node, the edge with weight 1 shows the return path

to an agent as you can see in figure 3.

Because of the nature of the WMA-RRT

algorithm and the existence of various obstacles in

an environment, branches may differ in the number

of edges. It may cause the early return of some

agents to the origin while the other agents are still

working on their corresponding branches. In such

situations, an agent manages to maximize its

contribution by helping some other agents in their

exploration missions. In order to do that, it checks

the Weight array and chooses the member with the

minimum value such as Weight[k]. Then the

associated branch (here Branch[k]) is assigned to the

free agent in order to help the other agents working

on that branch to finish the exploration task.

Checking of the Weight array to choose its member

with minimum value is performed because of two

reasons: first, it shows the least traversed branch of

the roadmap by the other agents. Second, the agents

use this array to show the completion of traversing a

branch. When an agent returns to its origin, it has to

mark its traversed branch as completed to prevent

other agents from entering the same branch. This is

usually managed by assigning a special value (such

as a big number like 10000) to the corresponding

Weight member. Put it simply, checking the Weight

array enables an agent to avoid traversing a branch

which has been already explored by the other agents.

Even though a free agent can assist other

working agents, it may do more harm than good and

may trigger some problems. First, as provided

before, the agents use a DFS algorithm to traverse

their branch and the weight of the roadmap edges

causes an automatic return of the agents to the

origin. However, as the number of agents operating

in one branch exceeds one, the agents will be

paralyzed to find the return path inasmuch as the

other agents have already changed the weight

attributed to some edges of the roadmap.

Figure 3: Automatic return of an agent after traversing all

edges of its dedicated branch to its starting location.

In order to solve this problem, it is necessary for

each agent to have two copies of its branch,

dedicated and global. The global roadmap is shared

among all the active agents in a branch, but each

agent has its own dedicated roadmap, and agents do

not have access to each other’s dedicated roadmaps.

When an agent enters a branch, it makes a copy of

that branch’s global roadmap and, changes the

weight values belonging to its edges to zero. This

becomes that agent’s dedicated roadmap. The weight

of edges simultaneously alters in both roadmaps. By

default, agents use the global roadmap. Whenever

there are more than one agent in a branch, the agents

will reach a node for which all incoming and

outgoing edges have an equal weight. In that case,

the agents will use their dedicated roadmap to find

the return path.

Figure 4: The simultaneous arrival of two agents to a

node.

The second problem arises because the agents

have access to shared data. Consider the situation

shown in figure 4.

In figure 4, let’s imagine the situation in which

the right agent tends to choose the right edge (with

weight zero) for traversing, but prior to making any

change to its weight value, it come across with the

left agent that tries to choose the same edge. This

causes the exploration of a particular part of the

roadmap by more than one agent. To prevent such

an overlap, agents must have exclusive access to

shared data. Using the locking mechanism will

CoverageandGoalSearchingBehavioursofaGroupofAgentsbyaSpecialSingleQueryRoadmap-ItsBenefitsto

MutipleQueryRoadmaps

283

merely allow just one agent to access a specific

edge.

3.1.1 Experimental Results

We evaluated the introduced mechanism in a variety

of environments in order to examine the effects of

step size (distance between two nodes), number of

sample points and agents’ sensor range. All the

experiments were conducted in a Pentium 4 CPU

3.00GHz with 1 GB of RAM machine. In figure 5,

you can see a WMA-RRT roadmap constructed

based on 3 agents beside the covered areas by those

agents.

Figure 5: Left: WMA-RRT constructed based on three

agents. Right: The areas covered by those agents.

Table 1 summarizes the results of running our

proposed mechanism for covering the area

represented in figure 8.

Table 1: Percentage of the covered area for the

environment represented in figure 8.

Number

of Nodes

Step

Size

Number

Iterations

Agents’

Sensor

Range

Average

Coverage

Percentage

Coverage

Percentage

by Simple

PRM

Algorithm

400 20 10 r 74 71

400 20 10 2r 87 85

400 20 10 4r 90 90

400 20 10 Infinite 99 99

800 20 10 r 83 80

800 20 10 2r 88 84

800 20 10 4r 92 90

800 20 10 Infinite 99 99

200 40 10 r 88 86

200 40 10 2r 93 91

200 40 10 4r 95 94

200 40 10 Infinite 99 99

400 40 10 r 93 91

400 40 10 2r 95 94

400 40 10 4r 97 95

400 40 10 Infinite 99 99

800 40 10 r 97 93

800 40 10 2r 98 95

800 40 10 4r 99 98

800 40 10 Infinite 99 99

Table 1 bears testimony to the fact that our

proposed method is probabilistically complete. To

vividly clarify the point, it is possible to take a look

at the chart in figure 6; based on which increasing

the number of sample points improves the area

covered by the agents.

Figure 6: Area coverage percentage based on the number

of sample points (for step size=40 and sensor range=r).

3.1.2 Comparison with Multiple-Query

Roadmap based Methods

In addition to avoiding the extra time consumption

in the pre-processing phase of multiple-query

methods, there are also other benefits in using our

introduced method instead.

As mentioned before, one of the characteristics

of WMA-RRT roadmap is that it is a tree, and then

has no cycles. One of the problems with multiple-

query roadmaps is that the agents may get stuck in

roadmap loops. For example consider a simple

scenario with just one agent in figure 8.

As pictured in figure 7, after traversing two

triangular cycles, the agent returns to its staring

point, and it reaches a node with 4 outgoing edges

with the same weight. Because of the existence of

such cycles, it is quite common in multiple-query

roadmaps to observe a previously visited area being

re-traversed for multiple times. However, thanks to

the absence of any cycles in WMA-RRT, never does

such a phenomenon happen in our proposed method.

Figure 7: A multiple-query roadmap. An agent may get

stuck in a loop.

100

200 400 800

CoveragePercentage

II.

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284

The second advantage of using WMA-RRT over a

multiple-query roadmap is that by the time the

exploration task of a certain part of the environment

has been completed, it is going to be confidently

flagged as “finished”. The multiple-query roadmaps,

however, does not enjoy the same level of certainty.

For example, consider the environment depicted in

figure 8.

Figure 8: An agent enters a part of an environment.

As illustrated, an agent is entering this part, yet

after traversing some edges of the roadmap, it

reaches a node in which all outgoing edges have the

same weight (figure 9). As the agent chooses an

edge which leads it to the outside of that part,

traversing that part remains uncompleted. After that,

other agents may enter the same part, and after

traversing some edges they leave that part. Thus,

none can say for sure if the exploration task of that

part has been fully accomplished.

Figure 9: The agent after traversing some edges of the

roadmap is leaving this part of the environment.

3.2 Goal Searching

The second swarming behaviour we are going to

investigate is goal searching in which the agents’

target is to find an unknown goal in an environment

and inform other agents of the location of that. In

this behaviour, the first agent that finds the goal has

to notify the other agents and those agents have to

move to the location of that goal. This behaviour is

used in scenarios in which there is a task and the

agents have to do it collaboratively with each other.

Exploring the environment to find the goal is

done like the previous behaviour, area coverage. The

only difference here is that the agents have to look

for the goal while exploring the environment. As

mentioned in the previous behaviour, the edges with

weight one lead the agents to the main root (starting

point). When an agent finds the goal, it has to inform

the other agents about the location. To do so, this

agent has to change the weight of all edges in its

branch (in global roadmap so that the other agents

will be able to see it) with value 1 to a special value

such as ½. Suppose that the agent that is working in

branch k finds the goal (figure 10). Changing the

weight of edges with value 1 to ½ will also alter the

value of item k in array Weight (Weight[k]) to ½

(see previous behaviour, area coverage).

Figure 10: An agent in branch k finds the goal (the star)

and by changing the edges’ weights with value 1 to ½

informs the other agents.

In this behaviour, all agents in each node have to

check the array Weight items. If they find an item

with value ½, they know that another agent has

already found the goal. When both agents are within

the same branch (branch k in our example), the

second agent uses the global roadmap and follows

the edges with weight 1 until it reaches an edge with

weight ½. After that, the edges with weight ½ lead

the agent to the location of the goal (figure 10). But

in cases the so-called second agent falls into a

different branch, it has to return to the main root and

after that by following the edges with weight ½, it

reaches the goal.

3.2.1 Experimental Results

We tested our algorithm for finding an unknown

goal based on WMA-RRT roadmap in different

environments. The result for finding the goal (the

star) in the environment in figure 11 has been

depicted in table 2.

Here, like the coverage behaviour, you can see the

effect of changing step size, the agents’ sensor range

Weight[k] = 1

Weight[k] = ½

II.

CoverageandGoalSearchingBehavioursofaGroupofAgentsbyaSpecialSingleQueryRoadmap-ItsBenefitsto

MutipleQueryRoadmaps

285

Figure 11: The aim of the agents here is to find the goal

(the star).

and the number of sample points on the results.

Table 2: Percentage of finding the goal by one of the

agents for the environment shown in figure 11.

Number

of Nodes

Step

Size

Number

Iterations

Agents’

Sensor

Range

Proportion

successful

runs

Proportion

successful

runs by

Simple

PRM

Algorithm

200 20 30 r 76 72

200 20 30 2r 83 80

200 20 30 4r 93 91

200 20 30 Infinite 100 100

400 20 30 R 87 85

400 20 30 2r 97 94

400 20 30 4r 100 100

400 20 30 Infinite 100 100

200 40 30 R 80 76

200 40 30 2r 93 91

200 40 30 4r 97 96

200 40 30 Infinite 100 100

400 40 30 r 100 100

400 40 30 2r 100 100

400 40 30 4r 100 100

400 40 30 Infinite 100 100

3.2.2 Comparison with Multiple-Query

Roadmap based Methods

One of the problems with multiple-query roadmaps

is that the constructed graph may be consisted of

some isolated components (figure 12). This usually

happens in cluttered environments. In these

situations the goal may be inaccessible to agents.

Figure 12: A PRM roadmap constructed in an

environment. This roadmap has two isolated components.

But as we previously explained, WMA-RRT has

just one connected component and we will never

face such problems (figure 13).

Even in scenarios that the goal is completely

inaccessible to the agents, our method behaves in a

better way than methods based on multiple-query

roadmaps (figure 14). In this figure, the agents have

been completely surrounded by some walls, so they

will never reach the goal.

Figure 13: A WMA-RRT roadmap constructed in an

environment. This roadmap has just one connected

component.

Figure 14: A situation in which the goal is inaccessible by

the agents.

In situations like this, it does not matter whether

we use WMA-RRT or a multiple-query roadmap

like PRM. In both cases, the agents will not be able

to find the goal. But in methods based on multiple-

query roadmaps, as there are cycles in the

constructed graph, the agents may get stuck in

infinite loops and they will never be able to

understand that the goal is inaccessible by using the

constructed roadmap (figure 15).

Figure 15: A multiple-query roadmap constructed in an

environment. The agents will never be able to find the

goal and they will get stuck in infinite loops.

But by using WMA-RRT as depicted in figure

16, the agents after traversing their branch return to

the origin and tag their branch as completed. In that

case, we understand that the goal is unreachable by

the agents, so by changing the starting location of

the agents to the outside of the surrounded obstacles,

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286

Figure 16: A WMA-RRT roadmap constructed in the

environment. The agents will never be able to find the

goal, but they will find soon that the goal in unreachable.

one of the agents will finally be able to reach the

goal and inform the other agents (figure 17).

Figure 17: By changing the starting location of the agents,

one of them will find the goal.

4 CONCLUSIONS

In this paper, we discussed two of the most

important swarming behaviours, area coverage and

goal searching by using a special single-query

roadmap called WMA-RRT. WMA-RRT is used by

agents both as a roadmap and also as a

communication channel. The proposed method is

useful in situations in which there are some simple

agents, only capable of performing some simple

tasks and there are no communication devices

between them. The simplicity here means that the

agents do not have any special built-in memory to

memorize previously visited states and also they do

not need any communication devices to exchange

information. The only thing that they have is a

roadmap which is locally available to them. In future

works, we want to study another important

behaviour of agents “moving toward a goal”. In this

behaviour the agents move from a starting point to a

destination. We also would apply our algorithms to

3D environments. The effect of a calculated starting

configuration compared to a more improvised one

will also be discussed.

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The starting

location of

agents

CoverageandGoalSearchingBehavioursofaGroupofAgentsbyaSpecialSingleQueryRoadmap-ItsBenefitsto

MutipleQueryRoadmaps

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