Distributed Localization and Scene Reconstruction from RGB-D Data

Sergio Ayuso

, Carlos Sag

and Rosario Arag

2,3

Instituto de Investigaci

on en Ingenier

ıa de Arag

on, Universidad de Zaragoza,

Mar

ıa de Luna 1 E-50018, Zaragoza, Spain

Clermont Universite, Institut Pascal, BP 10448, F-63000, Clermont-Ferrand, France

CNRS, UMR 6602, IP, F-63171, Aubiere, France

Keywords:

Network Robots, RGB-D Sensing, Distributed Systems, 3D Mapping and Localization.

Abstract:

In this paper we present a method to make every robot of a team to compute a global 3D map of the scenarios

explored by all the members, obtaining also the trajectories of the team. Every robot has a RGB-D device on

board which gives RGB and depth data simultaneously and uses this information to build its own local map

in real time. Once all robots have formed their local maps, they start a communication process to transform

all maps to a common reference and merge them. The interest of this work is related to the establishment of

the global reference and the management of the local point clouds to get correspondences between local maps

which make possible to obtain the best possible transformation from the reference of every robot to the global

reference.

1 INTRODUCTION

The increasing interest in multi-robot applications is

motivated by the wealth of possibilities offered by

teams of robots cooperatively performing collective

tasks. The efﬁciency and robustness of these teams

goes beyond what individual robots can do. In these

scenarios, distributed strategies attract a high atten-

tion, especially in applications which are inherently

distributed in space, time or functionality. These dis-

tributed schemas do not only reduce the completion

time of the task due to the parallel operation, but also

present a natural robustness to failures due to the re-

dundancy. Our research is focused on distributed ap-

plications for perception tasks. Perception is of high

importance in robotics, since almost all robotic appli-

cations require the robot team to interact with the en-

vironment. Then, if a robot is not able to obtain an en-

vironmental representation from others, or an a priori

representation is not available, it must posses percep-

tion capabilities to sense its surroundings. Perception

has been long studied for single robot systems and a

lot of research has been carried out in the ﬁelds of lo-

calization, map building and exploration. Among the

different sensors that can be used to perceive the en-

vironment, we are interested in visual perception, and

the multiple beneﬁts of using cameras have motivated

the interest of many researchers. These beneﬁts in-

clude the property that cameras are able to sense quite

distant features so that the sensing is not restricted to a

limited range. An additional kind of cameras of high

interest are RGB-D devices (Fig. 1). They provide

both regular RGB (Fig. 2, ﬁrst row) and depth image

information (Fig. 2, second row). Thus, it is possible

to compute the landmark 3D position from a single

image (Fig. 2, third row).

Figure 1: Example of a RGB-D camera.

A general overview of the achieved results, and the

current and future research lines in distributed multi-

robot systems can be found in (Parker, 2000). Many

existent solutions for single robot perception have

been extended to multi-robot scenarios under cen-

tralized schemes, full communication between the

robots, or broadcasting methods. In (Fox et al., 2006)

maps are represented as constraint graphs, where

nodes are scans measured from a robot pose and edges

represent the difference between pairs of robot poses.

Robot to robot measurements are used to merge two

local maps into a single map.

Distributed estimation methods (Olfati-Saber,

2007) maintain a joint estimate of a system that

evolves with time by combining noisy observations

taken by the sensor network. Early approaches sum

377

Ayuso S., Sagüés C. and Aragüés R..

Distributed Localization and Scene Reconstruction from RGB-D Data.

DOI: 10.5220/0004485103770384

In Proceedings of the 10th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2013), pages 377-384

ISBN: 978-989-8565-71-6

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

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Figure 2: An example of the images obtained with the RGB-D sensor.

the measurements from the different agents in IF (In-

formation Filter) form. If the network is complete,

then the resulting estimator is equivalent to the cen-

tralized one. In general networks the problems of

cyclic updates or double counting information ap-

pear when nodes sum the same piece of data more

than once. Other approaches (Alriksson and Rantzer,

2006) use distributed consensus ﬁlters to average the

measurements taken by the nodes. A related scenario

with estimation is sensor fusion (Lynch et al., 2008;

Calaﬁore and Abrate, 2009), where measurements ac-

quired by several sensors are fused in a distributed

fashion. Distributed perception methods must address

speciﬁc challenges such as associating the elements

observed by the robots in a globally consistent way,

or computing the relative poses of the robots and es-

tablishing a common reference frame for the whole

robot team.

The data association problem consists of estab-

lishing correspondences between different measure-

ments or estimates of a common element. Traditional

data association methods, like the Nearest Neigh-

bor and Maximum Likelihood (Kaess and Dellaert,

2009), the Joint Compatibility Branch and Bound

(JCBB) (Neira and Tard

os, 2001), or the Combined

Constraint Data Association (Bailey et al., 2000) are

designed for single robot systems. Multi-robot ap-

proaches have not fully addressed the problem of data

association. Many methods rely on broadcasting con-

trols and observations or submaps, see e.g., (Gil et al.,

2009), and solve the data association using a cycle-

free order, thus essentially reducing the problem to

that of the single robot scenario.

The problem of estimating the common reference

frame for the team of robots is motivated by the fact

that, in general, the robots start at unknown locations

and do not know their relative poses. This informa-

tion can be recovered by comparing their local maps

and looking for overlapping regions. This approach,

known as map alignment, has been deeply investi-

gated and interesting solutions have been presented

for feature-based (Thrun and Liu, 2003) and occu-

pancy grid (Carpin, 2008) maps. However, it has

the inconvenience that its results depend on the accu-

mulated uncertainty in the local maps. Alternatively,

the relative poses between the robots can be explicitly

measured (Sagues et al., 2006).

In this work we propose a distributed solution to

compute the 3D global map. Each robot obtains ro-

bust matches based on descriptors of the features in

successive images, and it builds its 3D local map

based on this information. As it may happen that the

neighbor robots in communication have not common

3D maps, we search for robots in the network which

have observed common regions of the 3D scene. Fi-

nally, all our robots obtain the same global map,

which is composed of both individual and common

regions. The robot with the most common parts with

other robots is also selected as the reference robot.

2 ROBOT NETWORK

The multi-robot system is composed by N robots,

each one with one RGB-D sensor to acquire the infor-

mation from the scene. Additionally they can commu-

nicate with the other members of the team. The robots

are labeled by i ∈ V = {1, . . . , N} and each robot in

the team i ∈ V can be univocally identiﬁed, for ex-

ample, considering the IP addresses the robots use to

communicate.

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378

Figure 3: Two graphs with six robots. On the left is a com-

plete communication graph and on the right an incomplete

communication graph.

We assume that the limited communication capabil-

ities imply that not all the robots will be able to

directly exchange information with each other (Fig-

ure 3). These limitations can be modeled using a

graph G = {V , E}, where E ⊂ V × V contains the

pairs of robots that can directly communicate. We

say that there is a communication link between i and

j when they can directly exchange messages, which

happens if and only if (i, j) ∈ E. And we deﬁne the

neighbors of a robot i ∈ V as the set of robots that can

directly communicate with i,

= { j ∈ V | (i, j) ∈ E}. (1)

We will consider undirected communications. That

is, (i, j) ∈ E ⇔ ( j, i) ∈ E and j ∈ N

⇔ i ∈ N

. In

this paper, we assume that the graph G is ﬁxed over

the time.

We formally deﬁne the consensus problem and

present solutions to solve it using a distributed lin-

ear iteration. The consensus problem is formally de-

ﬁned as follows: Given initial conditions x

(0), i =

1, . . . , N, we deﬁne the consensus problem as the

problem of making the state of all the robots regard-

ing the quantity of interest reach the same value, com-

puted as a function, f , of the initial observations:

= x

= f (x

(0)), k = 1, . . . , N, for all i and j in V .

This problem has a great importance in many robotic

tasks such as sensor fusion and formation control. In

the ﬁrst case it is required for a proper representation

of the environment whereas in the second is relevant

to achieve a desired conﬁguration, e.g., to make all the

robots meet at a ﬁxed point or explore a some region.

The solutions we are interested in correspond with

distributed algorithms that follow a linear iteration

scheme. Linear iterations are very easy to implement,

as they only require to compute linear combinations

of different quantities. This simplicity makes them

very interesting to be used in a distributed setup. In

addition, they represent an important class of iterative

algorithms that ﬁnd applications in optimization or in

distributed decision making (Bullo et al., 2009). A

linear iteration computes weighted sums of the differ-

ent values to achieve this objective. Speciﬁcally, each

robot updates its value of the quantity of interest com-

puting a weighted sum of its previous value and that

of its direct neighbors,

(t + 1) = w

(t)x

(t) +

∑

j∈N

(t)

i j

(t)x

(t). (2)

In the previous equation w

i j

is the Metropolis weight

associated to the information given by the neighbor

j (Xiao et al., 2005). We refer to iteration (2) as

the standard discrete time distributed consensus algo-

rithm. The extension to quantities of the dimension

of the RGB-D data acquired by the robot is straight-

forward, applying the same iteration rule for each one

of the scalar components of the state vector indepen-

dently.

If we consider the update rule of all the robots

simultaneously, we can model the update as a N-

dimensional discrete-time linear dynamical system

with dynamics inherently related to the network struc-

ture,

x(t + 1) = W(t)x(t), (3)

with x(t) = (x

(t), . . . , x

(t))

the values of the data

acquired by the robots in vectorial form and W(t) =

i j

(t)] ∈ R

N×N

, the weight matrix generated using

all the individual weights.

In case of using a distributed linear iteration like

(2) then the algorithm is fully distributed because each

robot is only using the information provided by its

neighbors in the communication graph, and the robots

do not need to know the topology of the whole net-

work to execute these algorithms, they only require

the information about their direct neighbors.

On the other hand, the use of this kind of iter-

ations assume that the communications between the

robots are synchronous and uncorrupted. Neverthe-

less, some of the most standard issues in communi-

cation can be handled by a proper modeling of the

communication graph. For example, packet drops

and communication failures can be seen as regular

changes in the communication topology and asyn-

chronous communications can be modeled by consid-

ering a directed communication graph. Therefore, if

we design our algorithms in such a way that they can

handle these topologies, we can expect them to be ro-

bust to these communication issues.

One interesting point is to assign the appropriate

weights to the different elements so that different con-

sensus objectives are achieved. In the case of averag-

ing, we suppose that all the observations of all the

robots have the same importance because the average

weights all of them equally,

¯x =

∑

i∈V

(0). (4)

DistributedLocalizationandSceneReconstructionfromRGB-DData

379

The average of the initial information of the robots

can be achieved very easily using a linear iteration.

We consider that the communication graph remains

ﬁxed during the execution of the whole iteration, i.e.,

W(t) = W for all t in equation (3).

3 INDIVIDUAL MAPS

The camera on board of each robot gives RGB and

depth information simultaneously. From them we get

a point cloud having the 3D coordinates of each point

and its color information. The XY Z information can

be computed for each pixel [i, j] of the image as:

X = (i − c

)

depth(i, j)

Y = ( j − c

)

depth(i, j)

Z = depth[i, j]

(5)

being c

y c

the center of the image, depth(i, j) the

depth of the pixel and f the focal length of the camera.

The ﬁrst step to obtain the local map of each robot

is the search of common parts between the last point

clouds captured. However the matching process be-

tween successive frames using directly the 3D infor-

mation of the point cloud is not very robust. So, in a

preliminary stage, SURF (Bay et al., 2006) descrip-

tors are obtained from the 2D image of the scene

in grayscale. This descriptor is based on the Haar

wavelets responses and integral images in order to in-

crease the computation speed. It turns out to be in-

variant to rotation, translation, scaling and changes in

illumination.

Using these SURF descriptors, the process of

matching is carried out in two steps. Firstly, the

k − NearestNeighbor (Muja and Lowe, 2009) is ap-

plied to ﬁnd the most similar descriptors between the

current image and the following one. The process is

repeated, but this time starting with the second im-

age and comparing it with the current one. Only the

matches that appear in both directions are selected

(Cross Check Filter). Although this procedure is quite

robust, many outlier matches may remain, and we

propose in a second stage to apply the Fundamen-

tal Matrix constraint. The 2D coordinates of two

matched descriptors of two images, x

and x

, are re-

lated with the fundamental matrix F as,

= 0 (6)

To get better matches robust solutions have been

proposed in the literature and we propose to use

RANSAC (Fischler and Bolles, 1981) to compute the

fundamental matrix. This robust method also allows

to eliminate the correspondences which do not ﬁt to

the most voted solution in such a way that the result-

ing matches will (ideally) not have any outlier. In ﬁg-

ure 4 we can observe the resulting good matches and

the rejected matches using the RANSAC procedure.

Once good correspondences between images are

given, the 3D information of these correspondences

are recovered using the original point cloud. A test

is carried out to check that all the depths are coher-

ent being between 0.05 and 8 meters. Using that 3D

information of the valid correspondences, RANSAC

is applied again to obtain a preliminary 3D transfor-

mation between the last two frames. The ﬁgure 5 il-

lustrates this method labeling the correspondences as

inliers and outliers.

In order to obtain a more accurate transformation

matrix T between the last two frames the ICP (Itera-

tive Closest Point) (Besl and Mckay, 1992) algorithm

can be computed. This matrix T is a 4x4 matrix which

represents the translation and rotation that has to be

applied to one cloud to transform it to the reference

of another cloud. Two matched points x

↔ x

are

valid if they satisfy that the distance between x

a Tx

is smaller than a threshold. The ICP algorithm takes

two point clouds A = {a

} y B = {b

} and one initial

transformation T

from B to A, and tries to reduce it-

eratively the distance between the points of A and B

until the best transformation T that ﬁts B with A is

found. It must satisfy that the distance between corre-

sponding points is less than some threshold. In ﬁgure

6 we show the procedure for one iteration of the algo-

rithm.

As the point clouds obtained with the camera are

very big, the point clouds used in the ICP algorithm

are downsampled, using a 3D voxel grid with the

same leaf size for all directions, in order to make the

algorithm converge quickly. In ﬁgure 7 the process of

downsampling a point cloud is shown.

In this step, the transformation between the last

two frames (

i−1

) has been computed. As the refer-

ence between the previous image and the local refer-

ence is already computed (

i−1

), the transformation

from the last image to the initial can be computed as

(Figure 8),

i−1

(7)

This transformation is applied to all the points in the

original cloud to obtain all the points in the initial lo-

cal reference of the robot. As some of these points

may correspond to part of an already observed scene,

they are eliminated in such a way that only new points

are added to the local map. The criteria used to detect

and eliminate points that have been already observed

is based on the 3D Euclidean distance between points.

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380

Figure 4: Matches of 2D descriptors. The green lines join good correspondences and the red lines the matches rejected with

the Fundamental Matrix constraint and RANSAC.

Figure 5: Checking of outliers using the 3D matrix trans-

formation with the distance from p

to the transformed cor-

responding point pt

= Tp

. Left: the distance from p

the transformed point pt

is lower than the threshold (in-

lier). Right: the distance from p

to pt

is bigger than the

threshold (outlier).

Figure 6: K − th iteration of the ICP. The closest neighbor

is found with the T

k−1

of the previous cloud. From here

the T

is computed and the process is iteratively repeated to

compute the optimal solution.

Figure 7: Original point cloud (left) and corresponding

sampled point cloud (right)

The localization and orientation of the camera respect

the local reference can be computed using the infor-

Figure 8: With transformation computed, the points of the

last images are transformed and added to the local map. The

points already existing in the local map are eliminated.

mation provided by the transformation matrix

The 3D position is obtained directly from the trans-

lation vector p and the orientation is computed with

RPY angles using the information of the rotation ma-

trix R (Equation 8).

T =



3x3

3x1

1x3



(8)

If the motion of the camera between the last two poses

is less than a threshold, the last frame captured is

eliminated and not added to the local map.

4 DISTRIBUTED GLOBAL MAP

Once the robots have built their own local map, they

start the communication process to fuse their infor-

mation and create the global map. As commented in

the introduction, one issue of relevance in multi-robot

systems is the establishment of a common reference.

Although there are several solutions to select the ori-

gin of the common reference here a particular solution

is implemented.

In order to make the reading easier, we name i, j, k

the robots in the network and r, s, u the point clouds

of each robot. The r

point cloud captured by the i

DistributedLocalizationandSceneReconstructionfromRGB-DData

381

robot is denoted as c

. The number of clouds captured

by the i

robot is m

The robots are scattered forming a network with

the communications described with an undirected

graph G

com

= {V

com

, E

com

}. The robot i can di-

rectly exchange information with a set of neighbors

= { j ∈ V

com

| (i, j) ∈ E

com

}. If robot i has to

exchange information with robot j and they are not

neighbors, then robot i ﬁnds the shortest path to com-

municate with robot j through their neighbors. The

idea is that the robots try to ﬁnd the robots in the

network with whom they share common regions of

their local maps, although they are not neighbors in

the communication graph.

The communication between robots is established

using the ROS library (Quigley et al., 2009), in par-

ticular the messages are send through ROS topics re-

sulting in an unidirectional and streaming communi-

cation.

In the ﬁrst stage, the SURF features extracted

from the local maps are used to ﬁnd 2D correspon-

dences between the point clouds of all the robots in a

distributed fashion. Given robots i and j, they look for

matches between c

, r = 1..m

and c

, s = 1..m

estab-

lishing a ratio to represent the quality of the found

matches for each pair of point clouds. Each robot

stores the indexes of the point clouds r, s obtained.

One robot is selected to decide which is the robot

with the most and best ratios of correspondences,

which is chosen as the reference re f

. At the same

time it decides how the local maps will be combined

to obtain the global map. When the local associations

to be done are known, the corresponding transforma-

tion

of the local point clouds are computed with

RANSAC and ICP in a similar way as the used to

combine the point clouds in the local map. Addition-

ally as the local point clouds are referred to the local

reference re f

, re f

, this has to be considered in the

computation.

Figure 9: Transformations between the r, s point clouds of

the robots i and j and the references re f

, re f

of those

robots.

Robots have already computed the transformations of

their local point clouds to their local references,

re f

· p

re f

· p

(9)

As we want to compute

re f

, we use the above

equations,

re f

· p

re f

· p

re f

· (

re f

)

−1

· p

re f

(10)

In such a way that

re f

· (

re f

)

−1

(11)

Finally as the robots propagate the transformations

with their neighbors, all of them can transform their

maps to the global reference and also they can com-

pute the global map.

re f

(12)

which shows the situation where robot j has the trans-

formation

re f

and robot k has the transformation

to the global reference

re f

In case one robot cannot ﬁnd matches with any

other robot, its local map will not be added to the

global map, although the robot will be available for

the communications of the team, if necessary.

5 REAL EXPERIMENTS

Several experiments have been carried out with real

data. A RGB-D device in each robot is available to

get the local information. The experiments have been

accomplished in enclosed environments with different

number of robots and communication graphs. Fig-

ure 10 shows the 3D maps built by a team of ﬁve

robots. We also show the pose of the robots with

triangles in the localization where the robot has cap-

tured a RGB-D image. Once the robots have built

their own maps, they establish communication be-

tween them according to the communication graph

and then they choose as the global reference, the lo-

cal reference of the robot whose local map has the

most and best matches with the rest of maps. In this

experiment, the reference of the red robot has been

selected as the global reference frame. The next step

is to compute the transformation of each map to the

global reference as indicated in section 4. In ﬁgure 11

we show the global map obtained by the team of ﬁve

robots and their trajectories in the scene.

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382

Figure 10: Local 3D map built by each robot of a team that contains the environment explored. The lines in different colors

are the trajectories followed by robots, and the triangles represent the camera poses from which a RGB-D image has been

captured.

Figure 11: Global 3D map obtained by 5 robots visiting some rooms of a house. The trajectory of each robot is represented

in different colors (red, blue, green, yellow and magenta).

In the implementation, each local maps has approx-

imately 200.000 points and the global map 800.000

points. These maps are downsampled in order to de-

crease the memory use and the computation time of

the communication process. The time needed to add a

new point cloud to the local map is in average around

600 milliseconds, so the maps can be carried out in

real time. The computation of the global map is in av-

erage 60 seconds and it’s made once the robots have

constructed their local maps.

All the experiments have been carried out using

a computer with an Intel Core i7-3630QM processor

and 6 Gb of RAM.

6 CONCLUSIONS

In this work we have presented a distributed method

to make every robot in the network compute simulta-

neously the global map and the localization of every

robot.

Our method allows each robot to build its local

map and compute its trajectory in a robust and efﬁ-

cient way. After that, robots communicate with their

DistributedLocalizationandSceneReconstructionfromRGB-DData

383

neighbors and ﬁnd the best global reference frame.

All robots transform their maps to this global frame

and ﬁnally they obtain a common global map.

The information used is RGB-D data. This makes

possible to obtain accurate 3D information of the

scene. The huge amount of data managed introduces

the necessity of using 2D descriptors in some steps of

the matching process. The real results presented show

the goodness of the computed map.

ACKNOWLEDGEMENTS

This work was supported by projects Ministerio

de Econom

ıa y Competitividad / Uni

on Europea

DPI2009-08126, DPI2012-32100.

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