ROBOT BEHAVIOR ADAPTATION FOR FORMATION

MAINTENANCE

Maite L

opez-S

anchez

WAI Volume Visualization and Artiﬁcial Intelligence Research Group, MAiA Dep

Universitat de Barcelona. Gran Via de les Corts Catalanes 585, Barcelona, Spain

Keywords:

Autonomous robotics, behavior-based robots, simulation.

Abstract:

The autonomous robot formation maintenance problem can be approached by considering local information

only. This approach is more realistic than using global information, but presents a troop deformation draw-

back. This paper performs a step forward in local information usage for formation maintenance by analyzing a

parameterization of different basic behaviors. Formation maintenance emerges from the combination of these

simple behaviors, and its overall accuracy is empirically optimized by tuning behavior parameters. In particu-

lar, we study and characterize three different formations: queue or column (as for ants), inverted V or wedge

(as for birds or planes) and rectangle (for manipulus an tique roman troop formations). This paper describes

simulated robots that incorporate a unique set of basic behaviors from which formation maintenance emerges.

These simple behaviors provide formation robustness and are parameterized in order to minimize deformation

while following a trajectory.

1 INTRODUCTION

In this paper simulated robots implement a series of

basic behaviors that use local information to allow

the emergence of a global behavior that maintains the

group formation without having the notion of it em-

bedded in the individuals. In particular, we consider

an autonomous maintenance of three different well-

known formations in motion (see ﬁgure 1): queue,

also known as line or column, is the simplest; wedge –

or inverted V-formation– has aerodynamic advantages

so it is usually adopted by birds and planes; and rec-

tangle, which is much more condensed, corresponds

to the ‘manipulus’ antique roman troop formation in

military operations.

Most early work in formation control of robots

(Bekey, 2005) has assumed global knowledge. Balch

and Arkin identiﬁed tree approaches to formation

control (Balch and Arkin, 1998): unit centre ref-

erenced, leader referenced and neighbor reference.

They differ in the information that each robot requires

to compute its desired position. Every robot in a unit

centre referenced formation uses as reference the cen-

troid position of the whole robot group, so robots re-

quire global information. Similarly, for leader refer-

enced formations, robots always know the position of

the leader regardless its position, thus this formation

also entails a global scope. On the contrary, neighbor

reference is the only that is considered to use local in-

formation since a robot can take as reference a robot

in its vicinity and gather information about it (such as

its position or distance to it) by using its own sensors.

Although simulations usually have access to global

information, it is much more realistic to use local in-

formation when modeling physical formations such

as robotic or biological groups, where the access to

the overall information is hardly possible mainly due

to sensing capabilities and to limitations on commu-

nication.

Therefore, our formation simulations consider lo-

cal information only, assuming a neighbor reference

approach. Furthermore, our pure local information

approach lacks of a “formation notion”. In this man-

ner, a robot only knows about its neighbors and does

not have the concept of group nor the group ability

to keep the formation (since its measurement would

require some sort of global information).

Unfortunately, local information presents the prob-

lem of error propagation among robots in the forma-

tion, whose main consequence is the deformation of

the troop. This is an important issue that we tackle

by parameterising the basic behaviors and perform-

ing experiments to study how these parameter val-

ues inﬂuence in the whole performance. In order

to facilitate the set up and comparison of different

settings, experiments have been conducted by sim-

283

López-Sánchez M. (2006).

ROBOT BEHAVIOR ADAPTATION FOR FORMATION MAINTENANCE.

In Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics, pages 283-288

DOI: 10.5220/0001211502830288

 SciTePress

Figure 1: Robot’s references (black arrows) in our three dif-

ferent formations.

ulation, based on the open source OpenSteer (Steer,

2004) C++ library.

2 BASIC BEHAVIORS

We consider formations as speciﬁc distributions of ro-

bots with regular relative positions. Additionally, if

formations are to be maintained while moving, they

require a robust adaptation in order to keep these local

relations as constant as possible. Simplicity is often

related to robustness, and therefore, we propose that

all robots in the troop do rely on a reduced set of basic

behaviors to maintain formations.

Brieﬂy, these simple behaviors are: “Reaching

a target position”; “Reference neighbor following”;

“Reactivity”; “Waiting for the follower”; and “Pri-

ority respect”. The former is the one that actually

moves the robot towards a target position that is com-

puted by the “Reference neighbor following” behav-

ior based on the reference robot’s position. Neverthe-

less, one robot lacks of reference so that it is given a

trajectory to follow and it is said to be the leader or

conductor. Additionally, “Reactivity” behavior deter-

mines the degree of sensitivity of a robot regarding

its reference. Finally, “Waiting for the follower” and

“Priority respect” behaviors implement what could be

interpreted as social courtesy.

This section describes these simple behaviors in-

dividually, giving a hint of their different complex-

ity degrees and how can they be parameterized. Next

section will afterwards show how three different for-

mations are composed by deﬁning different relative

positions.

We propose the following basic behaviors:

Reference neighbor following: Robots follow the

trajectories of their reference neighbors keeping ﬁxed

angles α and distances d (see Figure 2). Different for-

mations require different angles and reference robots

(see ﬁgure 1), so they can be treated as ﬁxed forma-

tion properties. On the contrary, the separation dis-

tance depends on other factors such as robot visibility

range, speed or reaction capabilities, so it has been

used as a parameter to tune the overall performance.

Reactivity: Reference neighbor following im-

plies the propagation and ampliﬁcation of movements

along the formation. Noisy movements must there-

fore be ﬁltered. This is done by this “Reactivity” ba-

Figure 2: Reference neighbour following behaviour: a

white robot follows the orange one.

Figure 3: Tolerance for reaching a target position.

sic behavior, which establishes a minimum movement

distance the reference robot must move before the fol-

lower reacts and follows it. Small values for this pa-

rameter do not avoid noise and emergence of many

oscillations. On the contrary, large values introduce

delays in the formation.

Reaching a target position: When a robot tries

to reach a position, it must get to the target position

and stop there, and therefore, it must reduce its veloc-

ity when approaching the target position at a certain

braking distance (i.e. a parameter). If this distance is

too large, robot separation distances are never accom-

plished, since the follower robot moves signiﬁcantly

slower than the reference robot. On the other hand, if

this braking distance is too small, the inertia of a ro-

bot moving at high speed causes the robot to surpass

the target position and to include loops in the trajec-

tory that are afterwards propagated to following ro-

bots. Similarly, reaching an exact position may be too

demanding for robots without much accuracy. This

requires a tolerance parameter (see ﬁgure 3) so to en-

large the target position point up to a circle without

loosing much accuracy in maintaining the formation.

Waiting for the follower: This behavior forces the

reference robot to reduce its velocity when its fol-

lower robot exceeds a threshold distance (that is, be-

fore it can be lost). Figure 4 shows this maximum

separation distance as the radius of blue circumfer-

ences centered on each reference robot. Obviously,

this threshold distance should be larger than the sepa-

ration distance parameter.

Priority respect: Leader’s trajectories can have

loops that force following robots to cross their ways.

Robots should thus avoid to collision with crossing

ones. As ﬁgure 5 shows, this behavior has two pa-

rameters: a critical stopping distance that makes the

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284

Figure 4: Waiting for the follower behavior.

Figure 5: Priority respect behavior.

robot to stop in order to avoid an imminent collision

and a larger precautionary distance that only requires

a speed reduction (the critical braking distance). Both

distances have an angle of inﬂuence and there is a

priority system that establishes a total order relation

among robots, so that when a robot encounters in its

neighborhood area another robot, it detects its order-

ing and, and decides to give it the priority in order to

avoid waiting deadlocks.

3 FORMATION MAINTENANCE

AS EMERGENT BEHAVIOR

From the combination of previous basic behaviors we

can obtain complex behaviors that allow the robots to

maintain different formations. Each type of formation

just emerges by specifying reference robots and the

angle to form with them. Here we study three of them.

Queue: when having a queue of robots, the refer-

ence robot is the foregoer and the angle is zero de-

grees. The only exception is the leader, positioned on

the ﬁrst place, which follows its own trajectory. As

a consequence of the “Reference neighbor following”

behavior, the formation propagates the movement of

the leader. In this manner, all robots in the queue pass

eventually through the same positions. Figure 6 a)

shows a snapshot of the formation in movement when

the leader follows trajectories that are rectilinear (a),

curved (b) or crossed (c).

Inverted V: birds and planes usually adopt in-

verted V-formations due to its aerodynamic advan-

tages. Leaders are located at the centre of the for-

mation and angles must be +/-45 degrees for those

robots on the left/right side. As before, the reference

a) b)

Figure 6: Queue formation in movement: a) The troop

leader follows a rectilinear trajectory, b) a curved path, and

c) a trajectory with a loop (white lines clarify successor re-

lations).

a) b)

Figure 7: Inverted-V formation in movement. a) The troop

leader follows a rectilinear trajectory, b) leader turns left.

robot is the foregoer. Rectilinear trajectories do not

deform formations (see Figure 7 a)). On the contrary,

deformations appear for turnings. Figure 7 b) shows

the consequences of a left turn (right turns perform

analogously): right-side robots must follow a wider

trajectory so that distances between robots increase

before robots can adapt whilst left-side robots must

move slower because foregoers become closer to fol-

lowers.

Rectangle: This formation comes from the ‘manip-

ulus’ antique roman troop formation in military oper-

ations and is characterized by its density of individu-

als. Figure 8 a) illustrates a formation with its leader

located on the top left position. This facilitates left

turns such as the one depicted in ﬁgure 8 b). Rectan-

gle formations require robots to have two reference

robots: the one in front and the robot on the left hand

side. Therefore, angles are 0 degrees and -90 degrees

respectively. As we can see, the deformation during

turns becomes obvious, since robots on the right side

of the formation must cover much longer distances,

whereas robots behind the leader behave quite simi-

larly to robots in a queue. Finally, just mention that,

for right turns, the robot on the top right position

should become the leader, just as soldier troops do

in real settings.

Although queue formations adapt to trajectory

ROBOT BEHAVIOR ADAPTATION FOR FORMATION MAINTENANCE

285

Figure 8: Rectangle formations a) 16 robots at its initial

positions b) 25 robots when the leader has turned left.

changes faster than inverted-V and these faster than

rectangles (we could say they present an increasing

‘rigidity’), all three formation distributions do recover

from deformations, especially when the leader fol-

lows a rectilinear trajectory for some time. They are

also able to restore their topology once the leader

stops. They do it naturally in an ordered manner:

since changes propagate trough the formation, the

successors of the leader are the ﬁrst ones in reach-

ing their target position, which, corresponds to their

target position in the static formation. And this same

process propagates until the last robot in the forma-

tion reaches its target position, so that the whole for-

mation topology is recovered.

Nevertheless, formations are not kept exactly.

Some delays are introduced due to the propagation of

the movement and robots’ errors do propagate with an

accumulative effect. Next section presents some ex-

periments we have performed with the aim of study-

ing how basic behavior parameters can be set so that

the error keeps as small as possible.

4 PERFORMANCE EVALUATION

In order to evaluate the formation maintenance per-

formance of our different formations, we have consid-

ered an error measure that provides the maximum dis-

tance between robot actual trajectories and the ones

that should have followed instead.

More concretely, for the queue case, every robot

should follow the leader trajectory, and thus we mea-

sure, for each robot, the maximum distance between

its trajectory and the leader’s trajectory. Furthermore,

robots can return to previously visited positions so

Figure 9: Trace of the trajectories of 5 robots in a queue

formation. Leader’s red trajectory is the reference one. Last

robot (veh. 4) has the larger deviation.

that distance measures among trajectories are per-

formed taking time into account. Therefore, we mea-

sure the distance between a robot’s position and the

equivalent position in the leader’s trajectory for this

speciﬁc instant.

5 RESULTS

Considering error measurements and behavior para-

meters described in previous sections, we have per-

formed a series of tests about the formation mainte-

nance performance in terms of the resulting error. We

have done it by changing a single parameter for each

test so that we can isolate its inﬂuence in the overall

performance.

Figure 9 plots an example of how does perform a

queue formation of 5 robots. In this case, the leader

follows a trajectory that starts with a rectilinear move-

ment, performs a right turning, and ends with a new

straightforward movement. Consecutive robots (veh.

1 to veh. 4) do deviate along the turning and recover

during the second rectilinear movement. For this spe-

ciﬁc example, the maximum error is performed by

robot 4 at position (14.6, 29.9) where there is a dis-

tance of 5.37 to the reference leader position (14.03,

24.6). The average error for each of the 4 robots is

0.19, 0.50, 0.85, and 1.5 respectively.

By tuning some parameters, it is possible to re-

duce these performance errors empirically. Due to

the lack of space we cannot present all conducted

studies. Nevertheless, we exemplify error reduction

by presenting the case shown in ﬁgure 10. We con-

sider a queue formation composed by 5 robots where

leader performs two consecutive turnings (right turn

ﬁrst, and left turn afterwards). Accuracy in following

the trajectory (and thus, in maintaining the formation)

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286

Figure 10: Trajectory traces in a 5- robot queue formation

with braking distance parameter = 2.0.

has visibly increased. In fact, the average error for

each of the 4 robots is 0.03, 0.04, 0.05, and 0.07 re-

spectively. These values can be considered especially

accurate considering that a robot is simulated as a cir-

cle of diameter 1 in OpenSteer environment units.

Getting into more detail, this error reduction has

been accomplished by setting the separation distance

to 4.0 for the “Reference neighbor following” behav-

ior. Although this distance could be thought as a for-

mation parameter rather than a behavior parameter,

our tests have proven that the performance drops con-

siderably when this distance is smaller than 4 times

the size of the robot. This is mainly due to the fact

that, if robots do not have enough maneuverability,

their turns generate oscillations that propagate errors.

Nevertheless, in order to avoid robot losses, sepa-

ration distance values should be proportional to the

maximum separation distance parameter in the “Wait-

ing for the follower” behavior. In our case, this last

parameter has been set to 4.5 so that robots do not

move at high speeds when its successors cannot fol-

low them.

On the other hand, minimum movement distance

parameter has been set to 2.0 for the “Reactivity”

behavior. In general, being this value twice the ro-

bot’s size is enough to prevent for small local oscilla-

tions that do propagate along the formation. Values

higher than that do introduce undesired delays that

result in the deformation of the formation (usually,

elongation). Another parameter that helps in reduc-

ing local oscillations is tolerance. Similarly, it should

be kept small (it has been set to 0.1 in the example) to

avoid global deformation. “Priority respect” behav-

ior does also have parameters that help in the avoid-

ance of undesired situations such as robot losses or

collisions. These parameters are critical stopping and

critical braking distances, which have been set to 2.0

and 3.5 respectively. These values, which must be

Figure 11: Trajectory traces in a 5- robot queue formation

with braking distance parameter = 1.0.

correlated, are applied within an inﬂuence angle that

has been set to 90 degrees in order to implement the

right side priority trafﬁc norm.

Finally, braking distance from “Reaching a target

position” behavior has been set to 2.0 in the case

shown in ﬁgure 10. This is a key parameter that af-

fects three signiﬁcant factors. Firstly, braking dis-

tance values do have an overall effect in the forma-

tion that is inversely proportional to the formation ve-

locity: large braking distance values slow down the

whole formation advance (robots start reducing its ve-

locity unnecessary early) whilst small values allow

the formation to advance faster. Secondly, its val-

ues introduce a divergence between the separation

distance that should be kept between robots during

formation displacements and the one that is actually

kept. And thirdly, and most important, braking dis-

tance values do also affect into the accuracy in fol-

lowing the trajectory. On one hand, small values po-

sition robots so near to their target position that they

are not able to react smoothly to turnings, and there-

fore, local oscillations are propagated and ampliﬁed

among robots in the formation. On the other hand,

large braking distance values enlarge target positions

distances to an extent that causes robots to perform

rectilinear shortcuts in tunings, and therefore, the ac-

curacy in following the trajectory (and thus, maintain-

ing the formation) is reduced.

Additional experiments have been performed for

this braking distance parameter. In this manner, ﬁg-

ure 11 shows the trace for a formation of 5 robots hav-

ing value equal to 1.0 for this parameter and keeping

those values mentioned before for the remaining para-

meters. In this case, the average error has increased up

to 0.04, 0.07, 0.11, 0.18 for each of the four follower

robots. As mentioned before, if we increase braking

distance values up to 2.0, then errors decrease (ﬁg-

ure 10: 0.03, 0.04, 0.05, 0.07), but it is a minimum,

ROBOT BEHAVIOR ADAPTATION FOR FORMATION MAINTENANCE

287

because if we keep increasing it, accuracy decreases

again. In this case, for example, a breaking distance

value of 3.0 involves average errors of 0.04, 0.5, 0.9,

0.1.

6 RELATED WORK

Multi-agent robotic systems have been intensively

studied by the scientiﬁc community over the past

decade ((Brooks et al., 1990) (Johnson and Bay,

1995)). The main reason for this is that, despite the

limitations of single robots for accomplishing general

tasks such as foraging, transportation, construction or

surveillance, these tasks can be successfully achieved

by coordinated groups of robots. Furthermore, some

of these tasks can be outperformed when the group of

robots form speciﬁc spatial distributions (Fredslung

and Mataric, 2002a), what it is usually known as ro-

bot formations.

This paper presents a parameterization of basic be-

haviors whose combination yields to the emergence

of a more complex global behavior that consists on

formation maintenance while following a trajectory.

In particular, robots have proven to be able to main-

tain three different formations just by using local in-

formation and without having the concept of forma-

tion explicitly. Local information refers to reference

robots in the neighborhood, similarly to friend ro-

bots in (Fredslung and Mataric, 2002b). Our “Pri-

ority respect” behavior is also analogous to its robot

ID ordering. Nevertheless, following its ‘friendship’

nomenclature, the “Waiting for the follower” behav-

ior results in a more tight double-linked chain (i.e.,

reciprocal-friendship) than the single-linked chain of

friendships of Fredslund and Mataric.

On the other hand, this “Waiting for the follower”

behavior is related to the unsupervised formation

maintenance work by Yamaguchi et al. (Yamaguchi

et al., 2001), where attractions between robots are

symmetrical. As in our case, the validity of their re-

sults was supported by computer simulations, but they

study mathematically the stabilization of the forma-

tion by means of formation vectors that do apply in

the formation creation rather than in the formation

maintenance in movement. These formation vectors

are also related to the attractive and repulsive gradi-

ent forces implemented by Feddema et al. (Feddema

et al., 2004). Their work has a system control per-

spective that focuses on stability rather than, as in our

case, in following accurately a trajectory while main-

taining the formation.

7 CONCLUSIONS AND FUTURE

WORK

Our work is based on the parameterization of basic

behaviors to optimize the performance of robot for-

mations empirically. Despite the potential loss of gen-

erality, this tuning strategy applies for different queue,

inverted V and rectangle formations, and tries to pose

a step forward in the solution of the formation main-

tenance problem when using local information. Fu-

ture work will focus on the way adaptation can be

achieved automatically: since we work on simula-

tions, we envision genetic algorithms as an alterna-

tive, were the set of parameters codify the population

and the error measure can be used as objective func-

tion to be optimized.

ACKNOWLEDGEMENTS

Bernat Grau’s implementation has been key for this

work.

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