Swarm Behavioral Sorting based on Robotic Hardware Variation

Beining Shang, Richard Crowder and Klaus-Peter Zauner

Electronics and Computer Science, Faculty of Physical Sciences and Engineering,

University of Southampton, Southampton, SO17 1BJ, U.K.

Keywords:

Swarm Robot Simulation, Hardware Variation, Sorting, Behavioral Heterogeneity.

Abstract:

Swarm robotic systems can offer advantages of robustness, ﬂexibility and scalability, just like social insects.

One of the issues that researchers are facing is the hardware variation when implementing real robotic swarms.

Identical software can not guarantee identical behaviors among all robots due to hardware differences between

swarm members. We propose a novel approach for sorting swarm robots according to their hardware differ-

ences. This method is based on the large number of interactions between robots and the environment. Indi-

vidual robot’s unique hardware circumstance determines its unique decision and reaction during each robotic

controlling step, and these unique local reactions accumulate and contribute to the robot’s global behavior.

Accordingly by separating these hardware-triggered global behaviors, swarm robots can be sorted according

to their hardware variations.

1 INTRODUCTION

Swarm robotic research is either simulation–based or

hardware–based. In hardware–based swarm robotics,

one of the issues’ researchers face is the hardware dif-

ferences between swarm members. Although such

differences are very small, identical software in ev-

ery member of the swarm, does not necessarily re-

sult in identical behavior due to the ampliﬁcation by

the non-linear controller, and interactions between the

robots and environment.

It has been argued that behaviors of identically

trained robots in the same environment are subject

to divergence due to hardware variations generated

by component manufacture, the assembly process

and wear–and–tear (Shang et al., 2013). It was

found out through simulated obstacle avoidance ex-

periments (Pugh and Martinoli, 2007) that both ge-

netic algorithms and particle swarm optimization can

not withstand different types of sensor variations in-

cluding offsets and scaling factors. It was further (El-

liott and Shadbolt, 2003) argued that although it is

very difﬁcult and not cost-effective, identical behav-

iors of hardware-based robots in a swarm is still pos-

sible, where the software is ﬁne-tuned to compen-

sate the inherent hardware differences. The retun-

ing process has to be repeated at regular intervals

due to constant wear–and–tear (Roth et al., 1987).

Although some researchers have focused on utiliz-

ing different hardware equipments to develop swarm

robotic systems which are heterogeneous on the hard-

ware level (Dorigo et al., 2013; Parker, 1994), still

it can not be ignored that hardware variation always

exist and inﬂuence robotic behaviors.

In this paper, we propose a novel approach to sort

swarm robots based on their behavioral differences

which are caused by hardware variations. The sort-

ing of robots is useful in two ways: the efﬁciency

of swarm can be increased by allocating tasks to

sorted robots, and expensive calibration process can

be avoided for low cost swarm robots by using this

self-sorting method.

To achieve the required sorting, we consider the

performance characteristics of a large number of sim-

ple robots suitable for operating in a swarm, that con-

tain variations of their component parameters. After a

large number of interactions with the environment, in-

dividual robots shows difference behaviors, it is found

that robots with similar behaviors have similar hard-

ware differences.

In Section 2, we discuss the source of hardware

variations, and presenting our argument that it is fea-

sible to separating robots against their hardware vari-

ations according to their behavioral differences. Fol-

lowing this discussion, we describe the design of the

simulation in Section 3 including modeling the robots

and testing methods. The results are presented and

discussed in Section 4, with the conclusions in Sec-

tion 5.

631

Shang B., Crowder R. and Zauner K..

Swarm Behavioral Sorting based on Robotic Hardware Variation.

DOI: 10.5220/0005111006310636

In Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH-2014),

pages 631-636

ISBN: 978-989-758-038-3

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

2 PROBLEM DESCRIPTION

Irrespective of the manufacturing and assemble pro-

cesses, real swarm robots come with hardware varia-

tions. even if they are built to the same design. Fig 1

illustrated some of the reasons which cause variations

at hardware level in in a swarm robot.

An example of components variation would be

that the same type of sensors on two robots have dif-

ferent sensitivity (Pugh and Martinoli, 2007). Actua-

tors and batteries can have individual characteristics.

For mobile robots, the tires of the wheels are often

made from rubber to improve traction, which makes

it rather difﬁcult to manufacture with exactly the same

diameter (Borenstein, 1996). Furthermore asymmet-

ric load distribution will make tire compress differ-

ently, resulting different wheel diameters in practice.

In the assembly phase, positions of components and

soldering parameters vary. For instance, sensors can

be placed with slightly different orientations during

soldering, or the quality of soldering joints inﬂuence

the maximum current, thus the driving ability of the

motors varies. In addition, alignment of sensors or

wheels may have minor difference. In use, the robots

experience differences in wear and tear, including

sensor aging, battery draining, mechanic deteriora-

tion, or even damage.

manufacture

use

Assembly

Variation

Components

Variation

Wear

and Tear

sensitivity

accuracty

motor

characteristics

components

position

soldering

deterioration

damage

Figure 1: The causes of hardware differences: reasons

which can cause robots different in their hardware are listed.

They are categorized based on robot’s timeline: when robot

is manufactured and used. During manufacture, variations

exist in components’ sensitivity, accuracy, driving ability

etc. During assembly, components’ placement and solder-

ing parameters varies. When using swarm robots, differ-

ent damage and deterioration situations are encountered by

robots. All of these circumstances are applied to robots’

hardware, which differentiate them. This list is not ex-

hausted.

In practice, it is very difﬁcult to get accurate val-

ues for each parameter within a complex robotic sys-

tem. In addition, all measurements have to be taken

on each of the robots within the swarm. Furthermore,

due to the constant wear and tear, this has to be re-

peated at regular intervals. Therefore it is not feasi-

ble to modify the performance manually according to

their hardware variations. Although it is difﬁcult to

get the values for all parameters, the behaviors of the

robot is related with its hardware circumstance. Both

the decisions and reactions of the robot are always de-

termined by its hardware circumstance. And these de-

cisions and reactions contributes to the robot’s global

behaviors. Therefore by categorizing robots’ behav-

iors, the sorting of robots according to their hardware

variations can be achieved.

3 SYSTEM MODELING

As discussed in the previous section, we consider a

conventional swarm robot prototype which can follow

a reﬂective line using two IR photoelectric sensors.

The modelling of this robot comprises two parts: a

model of the abstracted robot hardware and a model

of the expected deviation from the ideal prototype.

3.1 Modeling of the Robot

The basic features of the robot being simulated are

shown in Fig 2, it is a differentially steered, two

wheeled robot ﬁtted with casters to the front and rear.

leftwheel

Wheel

rmotor

Motor

lsensor

Sensor

Figure 2: Plan view of the robot and its controller arrange-

ment, showing two sensors in the front and two wheels on

each side. The diagram on the robot explains its control

mechanism: Voltage difference between outputs of the two

IR sensors are ampliﬁed by a PI ampliﬁer and then fed to

the motors after adding a constant voltage V

which keeps

the robot moving forward.

3.1.1 IR Sensor

The two IR sensors located at the front of the robot

point downwards to measure the reﬂected light from

the surface beneath the robot, including any reﬂective

track. The sensor’s response (Benet et al., 2002) as

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voltage is modeled using Eq. 1,

V = β + α

cosθdθ (1)

where α is the sensitivity of the sensor, and β mod-

els the sensor’s offset and the effect of ambient light.

The sensors response to individual reﬂective elements

within the sensor’s viewing angle ]v is a function of

the incidence angle of the reﬂective light θ and the

distance x between the sensor and the reﬂecting point

(Shang et al., 2013).

3.1.2 Controller

The robot uses a conventional PI (proportional and

integral) controller to control the robot position along

the reﬂective line. The control algorithm of the robot

can be expressed using Eq. 2. The schematic diagram

of the controller is illustrated in Fig 2.

δ(t) = V

(t) −V

(t)

out

(t) = p δ(t) + i

−∞

δ(t)dt

(t) = V

−V

out

(t)

(t) = V

out

(t)

(2)

The voltage difference δ between the left and right IR

sensor V

, V

is fed to the PI ampliﬁer, the result V

out

is used to offset the driving voltages for the left and

right motors.

3.1.3 Drivetrain

A conventional differential drivetrain system is used.

Output voltages from the controller power the left and

right motors. Eq. 3 shows the motor model used,

which includes any gearbox used.

(3)

where ω is the angular speed of the wheels. The mo-

tors are modeled as pure gain, m between the output

of the controller and the wheel speed to simplify the

model of the motor and any gearbox, hence.





˙x

˙y











−

sinφ

−

sinφ

cosφ

−











(4)

where d is the distance between the wheels, and r

and r

are the individual wheel’s radius. Based on the

wheels’ angular speed, the linear change of robotic

position (˙x and ˙y) and orientation (

φ) can be calcu-

lated.

3.2 Modeling of Hardware Variations

Sensors and actuators can remarkably inﬂuence the

performance of the swarm robots behavior. Consider-

ing each robot as an continuous robotic system, sen-

sors and actuators functions as its input and output.

Any tiny difference on these components propagated

through each of robot. Thus the robotic behaviors are

inﬂuenced, and was conﬁrmed in our earlier paper

(Shang et al., 2013). Therefore variations simulated

in this work are the robot’s IR sensors, motor gear

boxes and the two wheels.

Variation on IR sensor can normally be found on

its performance parameters including sensitivity α,

viewing angle ]v. In addition, when ﬁtting sensors

to the robot, variation can occurs due to misalignment

of sensor orientation. In general parameters on which

the assembly variation include sensor height (h), sen-

sor lateral offset (O

) and sensor sagittal offset (O

To effectively model the variation found on the motor

gearbox and wheel, the following parameters are con-

sidered: motor gearbox gain (m), wheel radius (r) and

the distance between two wheels (d). In total there

are 13 parameters. Apart from wheel separation, the

rest of the parameters appear twice as there are two

IR sensor and two drive train systems on one robot.

Hardware variation across individual robot in a

swarm are different, the values of the same parame-

ter on all the robots follow a Gaussian distribution.

In this case, a standard robot was ﬁrstly generated

with all its parameters values measured according to a

real robot. By varying the parameter values for a ran-

domly generated percentage, the rest of its kind were

then modeled.

Table 1: The parameters of the robot are varied with

Gaussian-distributed random numbers which have different

distributions. ‘L’, ‘M’, ‘S’ denote for large, medium, small

sigma values.

Component Parameter Description Sigma

IR sensor

α gain S

]v view angle S

h height M

lateral M

sagittal M

Drivetrain m gain L

Wheel d separation L

In reality the deviations for the values of the

robots’ parameters can be different. Therefore three

sigma values (large deviation σ = 0.05, medium de-

viation σ = 0.03, small deviation σ = 0.01) are used

to generate random number sequences with different

distributions. Sensor gain and viewing angle are mod-

eled with small sigma value due to more strict quality

SwarmBehavioralSortingbasedonRoboticHardwareVariation

633

control during manufacture. Sensor assembly varia-

tion (sensor height, lateral offset and sagittal offset)

are comparably small comparing with variations on

the motor and gearbox gain, and wheel separation.

Details of robotic parameters and the sigma values for

Gaussian process are summarized in Table 1.

3.3 Training

A total of approximately 210 different robots were

generated and then individually trained using a sim-

ple line-following task for the optimal coefﬁcients of

the PI controller using exhausted search method. A

single period sinusoid reﬂective line was used, as the

robot’s ability of both turning right and left would be

trained without any bias. During training all robots

have the same initial training condition: they all starts

with exactly the same position located at the begin-

ning of the sinusoid line with exactly the same orien-

tation. For every robot, this task will be repeated for a

number of times to test different sets of controller co-

efﬁcients. The controller parameters which help the

robot achieve the best accuracy in terms of following

the target line will be chosen as the optimal parame-

ters.

To evaluate the training results, the trajectory of

each robot which is achieved with the optimal param-

eters is nearly the same with the shape of one period

of sinusoid. Therefore, the uniform training method

has helps the robots to achieve almost the same trajec-

tories. In other words, the optimal parameters com-

pensate the hardware difference among robots and

similar behaviors have been generated.

3.4 Testing

After training, robots were then tested in the testing

arena illustrated in Fig 3. The testing arena is a long

rectangle shaped area. A large number of short re-

ﬂective lines are drawn in the arena with randomized

orientations. All lines sit on the grid, so that they do

not overlap each other. The initial condition for all

robots are the same: they all start on the left hand side

of the arena with the same location, same orientation.

While robots were doing the line-following task and

interacting with the reﬂective lines in the arena, the

following assumption was made. In the simulation we

consider that there is a constant “wind” from the left

to the right of the arena, which can inﬂuence a robot’s

speed and orientation. This is analogous to a small

sail on top of each robot. If there exists difference be-

tween the direction of the wind and orientation of the

robot, a force will be applied to the robot by the sail

so that the orientation of the robot will change to con-

form to the wind direction and also a subcomponent

of speed to the right will be applied to the robot.

Figure 3: A small square-shape region has been magniﬁed,

allowing the length of the line and robot compared. The

starting point of each robots and their orientation is denoted

by the arrow. The size of the robot is 10×10 in arbitrary

unit. The arenas dimension is in the same unit.

Within the model, if the orientation of the robot

and direction of the wind is different, the speed of

each robot at each simulation step is the vector addi-

tion of the robotic autonomous speed and a subcom-

ponent of speed which is due to the blowing wind, and

an angular speed is added to the robot which force the

robot to orientate to the right. The reason of making

this assumption is that in order to separate all robot as

loosely as possible, a tendency of moving to the right

of the arena for all robots has to be enforced.

To further reduce the complexity of the problem,

all robots will be separated based only on their po-

sition on the arena’s x axis. Therefore when the

robots go beyond either upper or lower boundary of

the arena, it is assumed that they will be picked up

and put into the arena from the other side which is

the lower or upper boundary accordingly with main-

tained orientation. In this case, the position of robots

with reference to the arena y axis will not matter any

more.

Given the size of the arena, robots are able to run

in the arena for extended periods of time, thus robots

can be separated along the x axis as loosely as possi-

ble.

4 RESULTS AND DISCUSSION

Approximately 210 robots have been simulated in two

arenas (Arena1 and Arena2). Results are shown in

Fig 4 and 5. The only difference between Arena1

and Arena2 is the orientation of the reﬂective patterns.

According to the results from both arenas, it is found

out that some robots consistently led in the front or

left behind in both arenas.

As shown in Fig 5, the rank of robots in terms of

x coordinates for their end points after a ﬁxed sim-

ulation period are almost consistent in both arenas.

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250

500

750

1000

1e+07 1.1e+07 1.2e+07 1.3e+07

Arena1 y

Arena1 x

(a) Farthest and Nearest 5 Robots Location in Arena2

250

500

750

1000

1e+07 1.1e+07 1.2e+07 1.3e+07

Arena2 y

Arena2 x

(b) These Robots Location in Arena2

Figure 4: The size of the arenas is in arbitrary unit. Dots in both ﬁgures denote the location of robots after the same time. In

Fig 4(a), dots with square markers are the fastest ﬁve robots in Arena1. These robots also ranked in the top ﬁve in Arena2

(square markers) in terms of their end point distance to the starting point. Robots which are near to the starting point in

Arena1(marked with diamond) also trail in Arena2(diamond markers).

1e+07

1.2e+07

1e+07 1.2e+07

Arena2 End Points x Value

Arena1 End Points x Value

Figure 5: The x axis values (in arbitrary unit) of the robots’

end points in Arena1 compared to those in Arena2. Robots

which were left behind in Arena1 were also left behind in

Arena2. It is the same for robots which run the fastest.

Therefore this approach is able to separate hardware-

varied robots according to their behavioral differences

regardless of the orientations of reﬂective elements in

the arenas.

After analysing the data, it is found out that all

robots which have travelled far had both strong drive

train system on the left and right, in Fig 6. This is

consistent with the experiment set-up that the wind

blowing effect applied on robots’ sail will force robot

to orientation to the right. In this case robots with

strong left and right motors ﬁnish their run the farthest

from the starting point.

However strong drive train system is only the nec-

essary condition for large distance between robots’

end points and the starting point: not all robots which

have large gain on their drive train system travelled

far. After analysing the hardware variation factors of

all robots with high gain on both their left and right

1.8

1.9

2.1

2.2

1e+07 1.2e+07

Sum[%]

Arena X

(a) Left and Right Motor Gain Sum

-0.01

0.01

1e+07 1.2e+07

Difference[%]

Arena X

(b) Left and Right Motor Gain Difference

Figure 6: The x axises of the two ﬁgures are in arbitrary

unit, the x coordinates of robots’ end points in the Arena1

is compared with robots’ motor gain variation factor (in per-

centage). It can be seen from the second ﬁgure that for all

robots, the gain difference between left and right drivetrain

system are very small. From the ﬁrst ﬁgure, all robots which

travelled far have large gain on both left and right drive train

system.

drive train system, there is no clear pattern on other

robotic parameters. In other words, the distance be-

tween robotic end points and the starting point does

not depend on one or two parameters of the robots,

instead it is determined by the combination of multi-

ple parameters of each robot. To prove this, the robots

which end up at both far and near locations have been

clustered in the multiple dimensional space of their

parameters. In total, each robot has 13 parameters:

eight sensor related parameters, three drivetrain sys-

SwarmBehavioralSortingbasedonRoboticHardwareVariation

635

tem parameters and two parameters for PI controller

coefﬁcients. Examples of clustering results are shown

in Fig 7. The sorting result shows that there are differ-

ent parameter settings for robots to travel either far or

near from the starting point. The x values of robotic

end points depend on the combination of all parame-

ters instead of individual parameter.

0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

x 10

200

400

600

800

1000

4 Clusters of Robots in Arena1

Figure 7: The size of the arena is in arbitrary unit. The

end points of the three robots with left-oriented triangles

are all very far from the starting point. They are also near

to each other in their parameter space. It is the same for

robots with circle and square markers. However the end

point for the robot marked with upper triangle is near to the

starting points and it is not near to any other robots in the

parameter space, its unique parameter setting makes it have

this behavior.

5 CONCLUSION

In this work, we propose a novel approach for sorting

swarm robot according to their hardware variations.

A set of robots is derived from a standard robot by

adding minor variations in their parameters to model

the intrinsic hardware difference that exists in real

robotic swarms and they are then simulated in per-

forming a line following task in the arenas covered

with randomly oriented IR-reﬂective patterns. Results

show that this approach is able to sort the group of

robots according to their hardware differences. The

method of differentiating the robots through the accu-

mulated effect of numerous interactions with the en-

vironment is analogous to separating chemical mix-

tures by chromatography. This method is robust that

the sorting of the robots does not depend on the ori-

entations of the reﬂective patterns in the arena, but

on the hardware characteristics of individual robots.

Furthermore it is found out that the behaviors of indi-

vidual robot is not determined by a single parameter

but by the combinations of multiple hardware factors.

Different combinations of hardware parameters can

help robots achieve similar behaviors.

We view the model system explore the possibil-

ity of sorting swarm robots according to their hard-

ware variations in order to tackle the inequality exists

in real homogeneous robotic swarms. Future work

will focus on improving swarm efﬁciency by auto-

matically assigning tasks according to their hardware-

variation-triggered behaviors.

ACKNOWLEDGEMENT

This work was supported by Panzhihua ChangNing

Co., Ltd. The authors also acknowledge the use of

the IRIDIS High Performance Computing Facility,

and associated support services at the University of

Southampton, in the completion of this work.

REFERENCES

Benet, G., Blanes, F., Sim

o, J., and P

erez, P. (2002). Using

Infrared Sensor for Distance Measurement in Mobile

Robots. Robotics and Autonomous Systems, 40:255–

266.

Borenstein, J. (1996). Measurement and Correction of Sys-

tematic Odometry Errors in Mobile Robots. IEEE

Transactions on Robotics and Automation, 12:6.

Dorigo, M. et al. (2013). Swarmanoid: a novel concept for

the study of heterogeneous robotic swarms. In Robotic

& Automation Magazine, IEEE, volume 20, pages 60–

71.

Elliott, T. and Shadbolt, N. R. (2003). Developmental

robotics: Manifesto and application. Philosophical

Transactions of the Royal Society of London, Series

A, 361:2187–2206.

Parker, L. (1994). Heterogeneous multi-robot cooperation.

PhD thesis, MIT.

Pugh, J. and Martinoli, A. (2007). Parallel Learning in Het-

erogeneous Multi-Robot Swarms. In IEEE Congress

on Evolutionary Computation, pages 3839–3846, Sin-

gapore.

Roth, Z., Mooring, B., and Bavani, B. (1987). An Overview

of Robot Calibration. IEEE Journal of Robotics and

Automation, 3(5):377–385.

Shang, B., Crowder, R., and Zauner, K.-P. (2013). Simu-

lation of Hardware Variations in Swarm Robots. In

IEEE International Conference on Systems, Man, and

Cybernetics, pages 4066–4071, Manchester.

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