GEOMETRIC FORMATIONS FOR A TEAM OF MOBILE ROBOTS

Odometric-based Maintenance Method for Heterogeneous Teams of Robots

Patricio Nebot and Enric Cervera

Robotic Intelligence Lab, Universitat Jaume I, E-12071 Castell´o de la Plana, Spain

Keywords:

Maintenance of formations, Heterogeneous team of mobile robots, Cooperation among robots.

Abstract:

One of the most important topics in multirobot formations is how to maintain the initial formations while the

robots are moving or navigating through the environment. This paper presents a new approach based on the

cooperation among a team of heterogeneous robots for the maintenance of multirobot formations. The robots

must cooperate among them in order to get that all the robots, despite their sensory power, can maintain the

formation while they are moving. To get that, the robots only have available the communication among them

and their own odometry information. One of the robots, the conductor, is in charge to drive the formation and

the rest of robots must follow it maintaining the formation. To do that, the use of “virtual points” and Bezier

curves are introduced.

1 INTRODUCTION

A considerable amount of research has been focused

on the problem of coordinated motion and cooper-

ative control of multiple autonomous robots. Re-

searchers have been trying to understand how a group

of moving robots can perform collective tasks. In fact,

this is one of the most popular ﬁelds of study in multi-

robot systems in the last years, with some applications

that are well understood including multirobot path

planning (Yamashita et al., 2000), formation genera-

tion (Arai et al., 1989), and formation keeping (Balch

and Arkin, 1998).

Coordination among a group of robots can be very

useful for many applications. One of the most impor-

tant tasks is, in motion coordination, how to move a

team of robots in an ordered way, such as maintaining

a predeﬁned formation. One of the ﬁrst approxima-

tions to multirobot formations is the leader-follower

approach (Das et al., 2002; Liu et al., 2005) where

one robot is selected as the leader and must be fol-

lowed by the rest of robots.

In this ﬁeld, two works (Chiem and Cervera, 2004;

Renaud et al., 2004) were developed at the Robotic

Intelligence Lab in Castell´on. These works were use-

ful as the basis for the work explained in this paper.

The application described in this paper is a contin-

uation of the previous ones but extended to multiple

types of formations by using virtual points. The main

idea is to make it feasible for a heterogeneous team of

four robots to navigate through an environment in

such a way that the robots with sensory power help

the robots without it, that is, cooperating among them.

The control for the maintenance of the formation

is performed using a decentralized process, where

each follower robot decides which movements must

be performed in order to follow the movements of the

conductor robot, which is specialized in navigation

because it is using a laser range-ﬁnder and is ahead

in the formation. Its actual position while it is mov-

ing is sent to every follower robot. When receiving

the position, each follower robot calculates the virtual

point that it must follow. This virtual point consists of

a displacement in the position of the conductor robot

that allows it to create different formations, not only

the leader-follower line formation.

Once the virtual point is calculated, the follower

robot computes the trajectory it must follow in order

to arrive from the current position to the estimated

conductor robot relative position. For the calculation

of this trajectory, Bezier curves are considered, as in

(Chiem and Cervera, 2004; Renaud et al., 2004).

2 MAINTENANCE OF THE

FORMATION

In this section it is described how a formation can be

maintained while the robots are moving in the envi-

399

Nebot P. and Cervera E. (2010).

GEOMETRIC FORMATIONS FOR A TEAM OF MOBILE ROBOTS - Odometric-based Maintenance Method for Heterogeneous Teams of Robots.

In Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics, pages 399-402

DOI: 10.5220/0002943403990402

 SciTePress

ronment. The formation is composed of a maximum

of four robots, where one of them, the conductor, is

equipped with a laser range-ﬁnder that allows it to

navigate in buildings and follow a path determined

from the map of the building, the goal point, and the

obstacles. The rest of robots have limited visibility,

that is, they only know their actual position.

Each robot determines its position in order to

maintain the formation with respect to the leader or

a displacement of the position of the leader, with a

“virtual” point. Also, they use a relative frame of ref-

erence, that is, they do not use an absolute positioning

system, only the robot with the laser uses an absolute

system in relation with the map that it uses to nav-

igate. And in relation with the communication capa-

bilities, the robots can share local and global informa-

tion to compensate for their limited visibility, in fact,

the global information shared among the robots is the

actual position of the robot with the laser, and the lo-

cal information is the actual position of each robot.

In the formation, the position of the robot follow-

ers can be controlled by the position of the conductor

if all the robots are arranged in a line formation. In

other cases, when the followers are positioned to the

right or left of the conductor, virtual points are added

to the system, as explained in (Chiem and Cervera,

2004). These virtual points are calculated by apply-

ing a displacement in the conductor position to the

left or to the right, depending on the desired forma-

tion. The followers, in this case, instead of following

the conductor must follow these virtual points. This

arrangement is shown in Figure 1.

In the approach here proposed to achieve the

maintenance of the formation, it is desired that robots

could perform the task using only the odometry in

conjunction with communication to estimate the po-

sition of the conductor with respect to each follower.

The conductor, by means of the localization task is

Figure 1: Formation using virtual points as reference for

followers.

Figure 2: Calculation of the local position of the conductor.

always correctly localized in the map, and it is as-

sumed that it will follow a predeﬁned trajectory, with

a constant, known linear velocity. In order for another

robot to follow the conductor, the linear and angular

velocities need to be computed at each time step. It

must be noted that the linear velocity of the follower

robots is not constant, due to the different radius of

their respective trajectories or because their position

may be relatively further back or further forward in

the formation.

In order to calculate the linear and angular veloc-

ities that allow the followers to move following the

movement of the conductor and maintaining the for-

mation, it is necessary to construct the corresponding

Bezier curve that deﬁnes the trajectory to be followed

by the robot. To compute the Bezier curve two posi-

tions are needed, the current position of the follower

and the current position of the conductor in relation to

the follower.

The conductor, at each step sends its own posi-

tion to the followers. The conductor is always local-

ized in the map by means of the localization task, so,

when it requires information about its position, this is

done with the coordinates of the map. The followers

are not localized on the map, so the only information

they have available is their position on their own lo-

cal system which is determined by the origin that is

ﬁxed by their initial position. So, the conductor must

transform their global position into a position in its

local system. In Figure 2, the necessary relationships

to transform the global position into a local position

can be seen.

From the ﬁgure, it can be deducted that to calcu-

late the position in the local system it is necessary to

know the origin of the trajectory in the global system

and the actual position of the robot in the global sys-

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400

tem.





−1

(1)

where

is the actual position of the conductor

in the local system,

is the origin of the trajectory

in the global system, and

is the actual position

of the conductor in the global system. This last posi-

tion is updated continuously by the localization task

so that the robot have always its current position on

the map.

The conductor sends its current position calcu-

lated in this way to each follower. When the follow-

ers receive the position of the conductor, they need to

calculate the position of the conductor in relation to

themselves in order to usethat information to generate

the Bezier curve necessary to calculate the velocities

which allow them to move maintaining the formation.

Each follower knows its original displacement in

the formation. This information in conjunction with

the current position of the follower and the current po-

sition of the conductor allows the robots to calculate

the relative position of the conductor in relation with

the follower. In Figure 3, the necessary relationships

to compute the conductor position are shown.

In this case, from the ﬁgure, the following equa-

tion to calculate the conductor position in relation

with the follower

can be obtained,





−1

(2)

where

is the position of the follower in its

local system,

is the position of the origin of the

conductor’s trajectory in relation to the origin of the

follower’s trajectory. This value is indicated by the

displacements assigned to the position of each robot

Figure 3: Calculation of the conductor’s position in relation

to the followers.

in the creation of the formation. And ﬁnally,

the position of the conductor in its local system. This

is the position that the conductor sends every step to

the followers.

Once this position is calculated, it is possible to

compute the Bezier curve between the current posi-

tion of the follower and the position calculated for the

conductor. It is at this moment when the virtual points

are calculated, if applicable, applying the following

formulas,

x = x− sin(δ) · dy

y = y+ cos(δ)· dy

(3)

where (x, y, δ) is the position of the conductor in

relation to the follower, and dy is the displacement in

the y axis to be applied. This generates a new point,

the virtual point, which will be used to compute the

Bezier curvethat drives the movement of the follower.

From the Bezier curve computed, the linear and

angular velocities can be obtained. The angular veloc-

ity can be computed from the curvature of the curve,

and the linear velocity is computed in order to main-

tain the distance from the conductor, applying a gain

factor proportional to the current distance from the

conductor robot. If the robots is nearer than a pre-

deﬁned distance in the formation, it will move slower,

and if the robot is further than the predeﬁned distance,

it will move faster.

3 TESTING AND RESULTS

The approach presented in this paper has been

tested simulating a team of robots consisting of

four Pioneer-2 mobile robots with different features

mounted on them, constituting therefore a heteroge-

neous group. In particular, only one robot is equipped

with a laser range-ﬁnder sensor and the rest of robots

do not have any type of exteroceptive sensors.

The formation control is developed in Acromovi

(Nebot and Cervera, 2005), a framework specially de-

signed for the development of distributed applications

for a team of heterogeneous mobile robots. The soft-

ware architecture gives us the ease of development of

cooperative tasks among robots, using an agent-based

platform.

In Figure 4, some examples executed for different

formations shapes are presented together with the for-

mation in which the robots are organized. Formations

from two robots up to four robots can be used.

As it can be seen, the odometry-based approach

is suitable for the development of applications using

multirobot formations. From the examples, it can be

infered that the behaviour of the robots is as desired,

GEOMETRIC FORMATIONS FOR A TEAM OF MOBILE ROBOTS - Odometric-based Maintenance Method for

Heterogeneous Teams of Robots

401

Figure 4: Results in simulation for formations with different number of robots.

and all the follower can follow the movements of the

conductor by the utilization of virtual points.

4 CONCLUSIONS

The paper describes a new method for a team of het-

erogenous robots to navigate maintaining any type of

formation by the introduction of “virtual points”. In

this application, the robots without sensory power get

support for the navigation from the robot with nav-

igation and localization facilities. In this way, all

the robots are able to follow a predeﬁned path get-

ting help from others if necessary, that is, cooperating

among them.

Results in simulation have demonstrated that the

presented approach, where robots maintain the forma-

tion only using communication and odometry, is suit-

able for getting the maintenance of formations with

any number of robots.

ACKNOWLEDGEMENTS

Support for this research is provided by the Gener-

alitat Valenciana under project GV/2010/087, and the

Fundaci´o Caixa Castell´o - Bancaixa under project P1-

1A2008-12.

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