AN IDIOTYPIC NETWORK APPROACH TO TASK

ALLOCATION IN THE MULTI-ROBOT DOMAIN

Use of an Artificial Immune System to Moderate the Greedy Solution

Amanda Whitbrook

, Gabriel Gainham

and Wen-Hua Chen

BAE Systems, Systems Engineering Innovation Centre (SEIC), Loughborough University

Loughborough, Leicestershire, LE11 3TU, U.K.

Department of Aeronautical and Automative Engineering, Loughborough University

Loughborough, Leicestershire, LE11 3TU, U.K.

Keywords: Multi-Robot Task Allocation (MRTA), Artificial Immune System (AIS), Idiotypic Network, Autonomous

Mine Clearance.

Abstract: This paper presents and explains a set of equations for governing simultaneous task allocation in multi-robot

systems and describes how they are used to construct a novel algorithm - the Idiotypic Task Allocation

Algorithm (ITAA); the equations are based on Farmer's model of an idiotypic immune network but are

adapted to include 2-dimensional stimulation and suppression and the use of affinity rather than

concentration levels to select antibodies. This novel approach is taken to render the model suitable for

simultaneous task allocation where robots must act individually; other idiotypic algorithms have only been

applicable to problems where many robots are required to perform one task at a time using swarming

behaviours. The paper describes the analogy between idiotypic network theory and the problem of task

allocation and shows how the former can be used to increase the fitness of solutions to the latter, also

discussing the types of Multi-Robot Task Allocation (MRTA) problem that might benefit from this

approach. The results of applying ITTA to a number of simulated mine-clearance problems (with increasing

numbers of robots and mines) are presented, and clear advantage over the greedy solution in both simple

and more complex scenarios is demonstrated.

1 INTRODUCTION

There are many different types of Multi-Robot Task

Allocation (MRTA) problem including varying

combinations of single-task (ST) robots, multi-task

(MT) robots, single-robot (SR) tasks, multi-robot

(MR) tasks, instantaneous assignments (IA, with no

planning for future allocations), time-extended

assignments (TA, which allows for future allocation

planning) and online assignment variations of IA

(OA, where tasks are introduced one at a time). The

interested reader is directed to Gerkey and Mataric

(2004), which presents a comprehensive,

architecture-independent taxonomy. In addition,

robots may be heterogeneous in their capabilities

and performance, and tasks may differ in

complexity, difficulty and solution requirements.

Whilst all types of MRTA problem may be solved

by implementing a greedy algorithm, characterised

by repeatedly taking the 'best' valid option (based on

some measure of fitness) at a local level,

optimization is not guaranteed. In addition, the

Linear Programming (LP) approach, which

guarantees optimality, cannot be applied to some of

the more complex MRTA problem types including

ST-SR-IA-OA, ST-SR-TA, ST-MR-IA, ST-MR-TA,

MT-SR-IA, MT-SR-TA, MT-MR-IA and MT-MR-

TA combinations, some of which are strongly NP-

hard (Gerkey and Mataric (2004)). There is thus a

need for heuristic approaches that are capable of

providing fitter solutions than those offered by

greedy algorithms, and much research effort has

been directed towards the development of heuristic

MRTA techniques. For example, auction-like

allocation mechanisms are described in Guerreor

and Oliver (2011), Nanjanath and Gini (2010) and

Gerkey and Mataric (2002). There have also been a

number of works published on market-based

techniques (for example Dias et al. (2005)),

coalition-formation methods (Shehory and Kraus

Whitbrook A., Gainham G. and Chen W..

AN IDIOTYPIC NETWORK APPROACH TO TASK ALLOCATION IN THE MULTI-ROBOT DOMAIN - Use of an Artiﬁcial Immune System to Moderate

the Greedy Solution.

DOI: 10.5220/0003709000050014

In Proceedings of the 4th International Conference on Agents and Artiﬁcial Intelligence (ICAART-2012), pages 5-14

ISBN: 978-989-8425-96-6

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

(1998)), self-organisation (Fukuda et al. (1988)) and

emergent systems (Liu et al. (2007) and Atay and

Bayazit (2007)).

This paper presents a set of equations based on

those developed by Farmer et al. (1986) that

represent an idiotypic immune system approach (see

Jerne (1974)) to solving the problem of task

allocation in the multi-robot domain. The equations

have been adapted to include 2-dimensional

stimulation and suppression and the use of affinity

rather than concentration levels to select antibodies.

This is a novel approach that allows each robot to

solve a separate task independently so that all tasks

can be completed simultaneously.

The paper describes the analogy between task

allocation and the idiotypic network theory of the

immune system and shows how the equations can be

applied to general ST-SR-IA problems with N robots

looking for one task to complete and L tasks

requiring one robot. It sets out how this approach

differs from previous idiotypic implementations of

MRTA and explains its advantages over them; in

particular, other idiotypic algorithms have only been

applicable to problems where many robots are

required to perform one task at a time using

swarming behaviours.

A set of experimental results on simulated

problems of this type is presented, initially where L

= N, N varies between 3 and 15, and robots are

required to organise mine diffusion tasks in a way

that minimizes travel costs. Some preliminary results

for the case where N ≠ L are also briefly discussed.

The results provide empirical evidence that the

Idiotypic Task Allocation Algorithm (ITTA)

described here is capable of outperforming the

greedy approach such that mean fitness is

significantly improved for these problem types.

2 BACKGROUND, PRIOR WORK

AND MOTIVATION

2.1 Background

The purpose of the immune system is to identify and

neutralize the molecules or cells that are dangerous

to the body (antigens) without damaging healthy

cells (Barra and Agliari (2007)). This is achieved

through the interaction of many different types of

immune cell, which each have specific roles. The

main constituents of the adaptive immune system are

B-lymphocytes (B-cells) and T-lymphocytes (T-

cells), which have particular protein molecules on

their surfaces called receptors. The receptors of B-

cells can bind to antigens that 'match' them, allowing

the B-cells to neutralize them.

The clonal selection theory of the immune

system (Burnet (1958)) states that lymphocytes

operate independently, and that once a match is

established, B-cells proliferate (increase in

concentration) by cloning and releasing free

receptors known as antibodies. Binding takes place

between a region of the antibody known as the

paratope and a region of the antigen known as the

epitope. In contrast, Jerne's idiotypic network theory

of the immune system (Jerne (1974)) postulates that

lymphocytes interact with each other so that the

immune system functions as a global network of

cells stimulated and suppressed by internal

recognition and matching between themselves. This

is because antibodies also serve as internal images of

certain antigens and are thus themselves being

detected and acted upon (Barra and Agliari (2007)),

which keeps the concentrations of antibodies at

appropriate levels. Antibody paratopes are thus not

only matched to antigen epitopes but also to epitope

regions on other antibodies, known as idiotopes.

Figure 1 below shows the structure of an antibody

and illustrates how antibody concentrations are

suppressed by other antibodies that recognise their

idiotope, and how concentrations are stimulated to

increase when they recognise another antibody's

idiotope.

Figure 1: Antibody paratope and idiotope regions.

2.2 Prior Work

The dynamics of antibody and antigen

concentrations are modelled computationally as

differential equations in Farmer et al. (1986). This

model is widely used for constructing Artificial

Immune System (AIS) implementations of idiotypic

networks, especially in navigational robotics, where

the method has demonstrated flexible behaviour-

mediation properties. However, in this field artificial

ICAART 2012 - International Conference on Agents and Artificial Intelligence

idiotypic networks have largely been confined to

single robot navigation problems, for example,

Watanabe et al. (1998), Vargas et al. (2003), Luh

and Liu (2004), and Whitbrook et al. (2007), where

the individual behaviours of single robots are

modelled as antibodies and environmental

information is modelled as antigens.

On the other hand, the application of idiotypic

principles to task allocation in the multi-robot

domain is somewhat more scarce, especially

utilization of the Farmer-based model, despite the

fact that its decentralized yet cooperative and

coordinated approach to problem solving lends itself

very elegantly to such systems. Sathyanath and

Sahin (2002) implement idiotypic mine detection but

use a simplistic analogy rather than the Farmer

model, i.e., idiotopes are not modelled and play no

role in determining the stimulation and suppression

levels of robots. Mitsumoto et al. (1995) implement

swarm behaviour by using a clonal selection-based

method rather than an idiotypic network; self-non-

self discrimination is modelled and tactics between

the robots are secreted and proliferated until

swarming behaviours emerge. Dioubate et al. (2008)

use a hybrid Farmer-based idiotypic network

coupled with clonal selection and genetic evolution

of lymphocytes to generate co-ordinated formation

of robots behind obstacles. Lee and Sim (1997) use

the Farmer model to develop idiotypic cooperative

strategies leading to swarm behaviours; robots

communicate their behaviours to each other on a

local level and the behaviour (antibody) that shows

the greatest stimulation is adopted by the whole

group. Jun, Lee and Sim (1999) and Sun, Lee and

Sim (2001) use an extended version of this model

that includes additional T-cell control of

concentrations to improve the adaptation capability.

Razali et al. (2009, 2010) use the same model as

Jun, Lee and Sim (1999), but also include memory

enhancement to achieve shepherding behaviour for

robot dogs managing robot sheep. Li et al. (2007)

solve the same problem, also using Farmer's

idiotypic model, but do not include T-cell control or

enhanced memory.

2.3 Motivation

In all of the examples cited above either the Farmer

model is not implemented or the goal is to adopt

majority behaviour patterns rather than assign

individual behaviours to individual tasks. The

general Lee and Sim approach is thus suited to

problems where a number of tasks that require many

robots to solve them are completed in sequence (ST-

MR-TE), but it is not applicable to the broader

spectrum of problems including those that require

instantaneous assignment (IA) of robots to different

tasks. In essence, the Lee and Sim analogy is the

same as for single robot navigation, i.e., behaviours

are modelled as antibodies, and only one behaviour

is adopted at a given time. If robots in the group are

required to adopt different behaviours at a given

time (as in IA problems), then a different model is

clearly needed. Furthermore, there is a real

requirement for IA-type assignment of

heterogeneous tasks to heterogeneous robots within

the military domain. In particular, it is envisaged

that within the next twenty-five years autonomous

military capabilities will undergo a major shift

toward joint, multi-mission, collaborative operations

between manned and unmanned vehicles (US

Department of Defence (DOD) (2009)). For

example, fleets of unmanned aerial vehicles (UAVs)

and unmanned ground vehicles (UGVs) will be

required to work together to accomplish

reconnaissance, surveillance, mine detection and

target-designation missions. Within such operations,

successful task allocation and coordination of the

many heterogeneous assets will be critical to mission

success, but will also impose a great burden on

central command and control as the number of assets

increases. For this reason, an autonomous,

decentralized, self-regulating coordination system in

which the assets are able to allocate tasks

independently of human control would be of great

value to the military. In addition, if progressed

through to use in theatre, a successful framework for

decentralized coordination and control of

heterogeneous, multi-agent, military systems would

represent a significant step forward for autonomy.

Indeed, the current US DOD Unmanned Air

Systems Roadmap (2005) cites “distributed control”

as the main criteria for achieving an autonomy level

of 8 in the DOD scale (range = 1 to 10) compared

with the remotely-operated systems that are typically

in place at present; these are measured as between

levels 1 and 3 on the same scale. This paper sets out,

describes and tests the Idiotypic Task Allocation

Algorithm (ITAA), which provides a potential

solution to the problem of autonomous,

decentralized, distributed task allocation for IA-type

assignment of heterogeneous tasks to heterogeneous

robots.

3 PROBLEM SPACE

A mine-clearance scenario has been selected as the

AN IDIOTYPIC NETWORK APPROACH TO TASK ALLOCATION IN THE MULTI-ROBOT DOMAIN - Use of an

Artificial Immune System to Moderate the Greedy Solution

test-bed for the ITAA as it has many properties that

make it ideal. In particular, there is sufficient

flexibility within the problem space to allow more

simple variations to be implemented in the early

stages of research, and to build and test more

complex instances as the work progresses, for

example beginning with ST-SR-IA experiments,

equal numbers of identical tasks (mines to diffuse)

and identical robots, incrementally building up to the

inclusion of online assignments (OA), time-extended

assignments (TE), unequal numbers of tasks and

robots, heterogeneous tasks and robots, multi-task

robots (MT), multi-robot tasks (MR), and real-time,

real-world implementations that require additional

features such as reactive obstacle avoidance

modules.

In this paper, research begins with the problem

of assigning a known number L of identical, un-

diffused mines to a known number N of

homogenous robots in simulation. Initially, it is

assumed that:

1. the robots have equal capabilities and travel at

the same, fixed speed;

2. the mines are equally accessible to all the

robots, i.e., there are no obstacles to negotiate;

3. the level of difficulty in diffusing a mine is

equal for all mines and constant throughout the

operation;

4. the number of mines L does not change at any

time during the operation;

5. the number of robots N does not change at any

time during the operation;

6. the number of robots available is always equal

to the number of mines needing diffusing, i.e., N

≡ L.

7. once assignment has taken place and the mines

are diffused, all work is done.

Note that assumptions 1 to 3 allow the distance

between robots and mines to be used as a measure of

affinity between them. If this were not the case, then

a more complex measure would be needed, i.e. one

that also considers the ability of each robot to

complete each individual task and the additional

time that would be needed to negotiate (possibly

moving) obstacles. This paper is chiefly concerned

with validating the theory set out in Section 4 so use

of the most simplistic case in the first instance

allows the essential theory of the ITTA model to be

tested independently of any real-world noise. The

results of a preliminary investigation into cases

where N ≠ L is also briefly discussed here but more

complex experiments will be conducted in the future

in order to establish whether the method stands up to

the problems associated with real-world

implementation.

4 THE IDIOTYPIC TASK

ALLOCATION ALGORITHM

(ITAA)

In the model presented here, antibodies are

analogous to possible robot-mine pairs, and the

affinity U of each antibody to the current antigen

(physical positioning of all robots and mines) is the

distance d between the robot and mine in the

antibody pair. This is the antibody pre-affinity,

before stimulation and suppression from other

antibodies are taken into consideration. The post-

affinity after stimulation and suppression is denoted

as T. Writing this more formally, U

is the pre-

affinity, T

is the post-affinity and d

is the distance

between robot i, i = 1, …, N and mine j, j = 1, …, L.

The pre-affinity is thus given by





=



(1)

After pre-affinities have been calculated, the

initial allocation of robots to mines is achieved by

executing a simple and intuitive greedy algorithm

where the antibody with the smallest affinity is

repeatedly selected as an allocation and then all pairs

that contain that robot and mine are eliminated from

future allocations until exactly one robot is allocated

to exactly one mine. This greedy algorithm is also

known as the Sequential Best-Pair Algorithm

(SBPA, see Oliver and Guerrero (2011)). Let 

represent the index of the robot allocated to mine j

based on pre-affinities. Under the ITTA model, this

is the antigenic robot to mine j, one of a set of L

antigenic robots (as exactly one robot is antigenic to

each of the L mines). Similarly, let represent the

index of the mine allocated to robot i based on pre-

affinities. This is the antigenic mine to robot i, one

of a set of N antigenic mines (as exactly one mine is

antigenic to each of the N robots). After the

antigenic robots and mines are known, the post-

affinity is calculated using





=



+







+







−



−



(2)

where:

• V corresponds to suppression from the

antibodies that represent robots competing for

the same mine (they may suppress the antigenic

ICAART 2012 - International Conference on Agents and Artificial Intelligence

robot if they have a higher fitness (lower

affinity) or are close in fitness to it).

• X corresponds to stimulation of antibodies that

represent robots competing for the same mine

(the antigenic robot may stimulate other robots

only if the other robots have a higher fitness

(lower affinity) than it).

• W corresponds to suppression from the

antibodies that represent mines competing for

use of the same robot (they may suppress the

antigenic mine if they have a higher fitness

(lower affinity) or are close in fitness to it).

• Y corresponds to stimulation of antibodies that

represent mines competing for use of the same

robot (the antigenic mines may stimulate other

mines only if the other mines have a higher

fitness (lower affinity) than it).

Equation (2) is similar to the original Farmer

equation but differs in two important respects. First,

concentrations of antibodies are not modelled, only

affinities, and second, there are two stimulation

terms and two suppression terms (rather than one of

each as in the original). This reflects the 2-

dimensional nature of the model used here, i.e.,

stimulation and suppression are considered between

robots and also between mines. To illustrate, if the

affinities between mine-robot pairs were set out as a

matrix, for example with each row representing a

unique mine and each column representing a unique

robot, then stimulation and suppression are

measured both across the columns in the x-direction

and down the rows in the y-direction, see Figure 2,

which shows an example of 2-dimensional

stimulation and suppression for the 3-robot, 3-mine

case. Note also that stimulation terms are subtracted

from the pre-affinity and suppression terms are

added to it. This is because, in this case, the affinity

is based on the distance the robot has to travel, and

thus, a reduction is seen as an improvement.

In this model the total inter-robot suppression on

antibody γj is given by the sum of the suppressions V

imposed by antibodies kj (j = 1 to L, k = 1 to N)

where

















−





∀ ≠ ⋀



−



<.

(3)

The inter-robot stimulation X on antibody ij is

imposed by antibody γj (i = 1 to N, j = 1 to L) and is

a single term given by





=





−









∀( ≠ ⋀



<



).

(4)

The total inter-mine suppression on antibody iγ is

given

by the sum of the suppressions W imposed by

antibodies ik (i = 1 to N, k = 1 to L) where

















−





∀ ≠ ⋀



−



<.

(5)

The inter-mine stimulation Y on antibody ij is

imposed by antibody iγ (i = 1 to N, j = 1 to L) and is

a single term given by









−









∀( ≠ ⋀



<



(6)

Figure 2: An example of 2-dimensional stimulation and

suppression for a 3-robot, 3-mine case.

In the above equations, 



is a scaling constant

that determines the overall level of stimulation and

suppression and  is a constant that governs how

closely antibodies have to match in affinity to

become stimulated. After post-affinities have been

calculated the SBPA is implemented again to

allocate the new antigenic antibodies. The post-

affinities then become the new pre-affinities and

stimulation and suppression are calculated again.

The algorithm proceeds in this way until some

stopping criteria is met. The final, overall,

theoretical fitness F of the task-allocation solution is

determined as

=

10,000

∑









(7)

where 

γj

is the distance between a final antigenic

robot and its allocated mine. Note that a different

measure of fitness, for example use of time taken t to

get to the mine (instead of d in the above equation)

should be used when attempting to demonstrate the

practical advantages of the ITTA, rather than the

theoretical. However, in the experiments described

here these measures are equivalent because of

assumptions 1 to 3.

The ITAA, as described above, is original in its

2-dimensional approach to stimulation and

suppression, its focus on affinities rather than

concentrations of antibodies, its novel suppression

and stimulation models, and its algorithmic

implementation, which results in the assignment of a

unique task to each robot, rather than the global

adoption of majority behaviours as in previous

AN IDIOTYPIC NETWORK APPROACH TO TASK ALLOCATION IN THE MULTI-ROBOT DOMAIN - Use of an

Artificial Immune System to Moderate the Greedy Solution

idiotypic research within the multi-robot domain.

Note that 1-dimensional models were trialled but

failed to guarantee converge to a solution. In

addition, a 2-dimensional model is a more accurate

reflection of an idiotypic system, where interactions

occur between all agents.

5 EXPERIMENTAL DETAILS

The ITTA was transcribed into MATLAB code and

was programmed to store the current fittest solution

after each iteration. The algorithm was stopped after

a maximum of 15 iterations had elapsed and the best

solution was accepted. In all cases, the initial

positions of the N robots and mines were generated

randomly on a square grid 30m by 30m in area, and

baseline comparisons were made for each problem

using the greedy (SBPA) algorithm (the solution

after the first iteration). Initially, the ITTA was

applied to 10,000 different mine diffusion problems

for N between 3 and 10 in order to determine

suitable values for parameters  and 



, i.e., the

above was repeated varying the parameter 



between 10 and 1,000 (values of 10, 50, 100, 150,

250, 500, 750 and 1,000 were trialled), and varying

the parameter  between 0.5m and 4m in steps of

0.5m. Once suitable values were found, the ITTA

was applied to a further 10,000 mine diffusion

problems for N ranging between 3 and 15, in order

to assess its performance against the baseline.

6 RESULTS

6.1 Parameter Selection

In all initial test cases 



values of 10 and 50 proved

superior in performance to the others, with 10

tending to work better for smaller numbers of robots

(3 to 7) and 50 tending to work better for larger

numbers (8 to 10). Figures 3a and 3b show how the

mean % improvement in fitness varies with 



Figure 3a summaries the results for the different 

values and Figure 3b does the same for the numbers

of robots N. Figure 3b also shows that mean %

improvement in fitness tends to increase steadily

with the number of robots; this is discussed more

fully in Section 6.2.

The  value was more robust, demonstrating

much less variation in performance than 



. This can

be seen in Figure 3a. Figures 4a and 4b also

summarise the preliminary results for ; the charts

show how mean % fitness improvement varies with

, with Figure 4a showing the results for each value

of N and Figure 4b showing the results for each

value of 



Figure 3a: Variation of mean % improvement in fitness

with p

for different  values.

Figure 3b: Variation of mean % improvement in fitness

with p

for different values of N.

Figure 4a also illustrates a clear trend for

increase in mean improvement in fitness as the

numbers of robots increases (see Section 6.2). In

general, there is a slight improvement as  rises, but

the differences are much less pronounced than for





. Figure 4b highlights the poorer performance

when higher values of 



are used. It shows that

values of either 10 or 50 are preferable and that

a



value of 50 has an almost constant performance

across the  spectrum, whereas a 



value of 10 tends

to work better for lower values of , between about

0.5 and 1.5.

As it showed a consistent performance for all

and worked well with higher numbers of robots, a





value of 50 was chosen for use in the performance

assessment, where N would rise to 15. Initially, 

values of 3.0m and 4.0m were selected, based on the

preliminary results, but the best overall performance

was obtained when  was set to 0.5m and 



was set

to 50.

1.5

2.5

3.5

4.5

5.5

6.5

0 100 200 300 400 500 600 700 800 900 1000

Mean % Improvement in Fitness

0.5

1.5

2.5

3.5

ζ (m)

0.5

1.5

2.5

3.5

4.5

5.5

6.5

7.5

0 100 200 300 400 500 600 700 800 900 1000

Mean % Improvement in Fitness

ICAART 2012 - International Conference on Agents and Artificial Intelligence

Figure 4a: Variation of mean % improvement in fitness

with 

for different values of N.

Figure 4b: Variation of mean % improvement in fitness

with 

for different values of p

6.2 Performance Assessment

Table 1 summarises the performance of the ITTA

(using the assigned parameters, 



= 50,  = 0.5)

compared with the baseline greedy SBPA algorithm.

For all N there is an increase in the mean fitness of

the solution, which ranges from about 3.5% (N = 3)

to 7.2% (N = 9 and N = 11). Moreover, paired t-tests

conducted on the mean fitness values show that

ITTA fitness is significantly higher (at the 95%

level) than the baseline for all values of N, for all

results and also for the sub-set of improved cases.

Figure 5 shows that the mean improvement in fitness

starts off by increasing almost linearly with N but

gradually reaches a plateau at about N = 9. This

may be explained as follows; the likelihood that the

initial, greedy solution may already be the optimal

one is higher for smaller N, and so there is less room

for improvement. This explanation is validated by

examination of the % of improved cases, which also

increases steadily with N up until reaching a plateau

at about N = 10, see Figure 6. In addition, when the

improved cases are examined in isolation, as

expected, the % improvement is greater for all N, but

this

is more pronounced for smaller N, for example,

Table 1: Performance summary for ITTA and baseline.

the difference is 8.25% for N = 3, but only about

1.30% at plateau values of N, see Figure 5.

For all N the maximum % improvement in

solution is considerably higher than the mean, for

example, for N = 3 it is about 76% and for N = 12 it

is about 46%. This variable tends to oscillate

locally, but has a general downward trend with

increased N, see Figure 6. For all results, the mean

number of iterations ranges from about 2.0 for N = 3

to about 6.5 for plateau values of N, see Figure 7,

which is intuitive given the earlier explanation for

plateau behaviour. For improved cases only this

variable is much more consistent, tending to about

7.0 iterations.

Figure 5: Variation of mean % improvement in fitness

with N.

The above results suggest that the ITTA is able

to make significant improvements over greedy

strategies, and that, as the number of robots

increases, an improvement in the solution is more

likely. For the particular parameters used here there

is approximately an 85% chance of generating a

1.5

2.5

3.5

4.5

5.5

0.511.522.533.54

Mean % Improvement in Fitness

ζ (m)

1.5

2.5

3.5

4.5

5.5

6.5

0.511.522.533.54

Mean % Improvement in Fitness

ζ (m)

100

150

250

500

750

1000

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Mean % Improvement in Fitness

Improved cases only All results

AN IDIOTYPIC NETWORK APPROACH TO TASK ALLOCATION IN THE MULTI-ROBOT DOMAIN - Use of an

Artificial Immune System to Moderate the Greedy Solution

Figure 6: Variation of max % improvement in fitness and

% of improved cases with N.

Figure 7: Variation of mean iterations with N.

better solution for N greater than 8. For N greater

than 6, a mean increase in fitness of about 7% is

expected, although individual increases of up to

about 70% are possible. The ITTA has also proved

to be a fast algorithm as the mean number of

iterations for convergence is always below eight.

In addition, a further set of experiments that

varied 



between 50 and 150 across the suppression

and stimulation equations (3), (4), (5) and (6) has

also been conducted for N = 4. The use of 



= 50 in

all equations except (3) (which used 90 instead)

increased the overall performance by a further 0.7%.

These results demonstrate the potential of the

ITTA method and show that it is a good candidate

for further investigation involving more complex

problems (as described fully in Section 3), real-

world implementations and more rigorous parameter

tuning. Preliminary investigations have already

shown that the method is easily adapted to cases

where L > N and N > L. Where there are more robots

than mines (N > L) robots are simply marked as

redundant when the SBPA part of the algorithm does

not allocate them to a mine. In addition, ITTA

consistently outperforms SBPA and, as N increases

for a fixed number of L, performance improves.

Conversely, when L > N absolute performance

drops, with the algorithm having to run repeatedly as

robots change position, but ITTA still performs

better than the greedy algorithm. Thus, relatively

speaking, there is no noticeable drop in ITTA's

performance when L > N.

7 FUTURE WORK

Future work will aim to develop an optimum

stopping criteria and to test the algorithm in more

complex scenarios, where online and time-extended

assignments are required, there are heterogeneous

tasks and robots, multi-task robots and multi-robot

tasks. Real-world implementations that require

additional features such as reactive obstacle

avoidance modules will also be carried out in an

outdoor environment. Further work also needs to be

done to compare performance of the ITTA with

state-of-the-art task allocation methods (for example

market-based approaches) and linear optimization

techniques such as Mixed Integer Linear

Programming (MILP).

Note that in real-life implementations the

algorithm would need to run independently on each

robot in order to constitute a truly decentralized

system. The robots would also need to communicate

reliably in order to transmit their locations to one

another, and there would need to be a level of

assurance that each robot was receiving all the

available information and compiling the same

solution to the problem. Maintaining and sharing an

accurate intelligence picture within an ad-hoc

network has been the subject of a research program

within BAE Systems Advanced Technology Centre

(ATC), and the outputs have already produced a

prototype data sharing framework. Future work will

thus aim to integrate the ideas presented in this paper

with the outputs of the data sharing programme in

order to demonstrate decentralized multi-robot task-

allocation in a real-world environment. In addition,

the ATC has also been working on Consensus-Based

Bundle Algorithms (CBBA) and Max-Sum task

allocation mechanisms (Mathews et al. (2010)), so

work will be undertaken to assess the feasibility of

integrating the ITTA approach with those methods

(see also Stranders et al. (2009)).

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40.00

50.00

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100.00

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Max % improvement % of improved cases

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3.00

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4.00

4.50

5.00

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7.00

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3 4 5 6 7 8 9 101112131415

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Improved cases only All results

ICAART 2012 - International Conference on Agents and Artificial Intelligence

8 CONCLUSIONS

This paper has described an idiotypic AIS algorithm

(ITAA) for solving task allocation problems in the

multi-robot domain. The algorithm is novel since

other idiotypic approaches have only been

applicable to problems where many robots are

required to perform one task at a time using

swarming behaviours; in contrast ITTA is suited to

problems that require members of a multi-robot team

to act individually so that different tasks can be

solved simultaneously. The algorithm is also original

in its implementation of the Farmer equation, which

ignores concentrations of antibodies and uses novel,

2-dimensional models for stimulation and

suppression of the antibody affinities.

A series of initial tests have been carried out on

the algorithm using simulated mine diffusion

problems in MATLAB. These tests have helped to

establish suitable parameter values for the

stimulation and suppression terms and have

provided statistical evidence that the ITTA is

capable of out-performing the greedy Sequential

Best-Pair Assignment (SBPA) algorithm in about

85% of cases for numbers of robots N exceeding 8.

For smaller N the likelihood of outperforming the

greedy solution rises almost linearly as N increases.

The ITTA has also shown fast convergence to a

solution; for N of 8 and above the mean number of

iterations for arrival at the best solution is about 5,

i.e., the solution can be produced almost

instantaneously.

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