vivek a. sujan efﬁcient steven dubowsky information-based...

Vivek A. SujanSteven DubowskyDepartment of Mechanical EngineeringMassachusetts Institute of TechnologyCambridge, MA 02139, [email protected]

EfficientInformation-basedVisual RoboticMapping inUnstructuredEnvironments

Abstract

In field environments it is often not possible to provide robot teamswith detailed a priori environment and task models. In such un-structured environments, robots will need to create a dimensionallyaccurate three-dimensional geometric model of its surroundings byperforming appropriate sensor actions. However, uncertainties inrobot locations and sensing limitations/occlusions make this diffi-cult. A new algorithm, based on iterative sensor planning and sensorredundancy, is proposed to build a geometrically consistent dimen-sional map of the environment for mobile robots that have artic-ulated sensors. The aim is to acquire new information that leadsto more detailed and complete knowledge of the environment. Therobot(s) is controlled to maximize geometric knowledge gained ofits environment using an evaluation function based on Shannon’sinformation theory. Using the measured and Markovian predictionsof the unknown environment, an information theory based metric ismaximized to determine a robotic agent’s next best view (NBV) ofthe environment. Data collected at this NBV pose are fused usinga Kalman filter statistical uncertainty model to the measured envi-ronment map. The process continues until the environment mappingprocess is complete. The work is unique in the application of infor-mation theory to enhance the performance of environment sensingrobot agents. It may be used by multiple distributed and decentralizedsensing agents for efficient and accurate cooperative environmentmodeling. The algorithm makes no assumptions of the environmentstructure. Hence, it is robust to robot failure since the environmentmodel being built is not dependent on any single agent frame, butis set in an absolute reference frame. It accounts for sensing uncer-tainty, robot motion uncertainty, environment model uncertainty andother critical parameters. It allows for regions of higher interest re-

The International Journal of Robotics ResearchVol. 24, No. 4, April 2005, pp. 275-293,DOI: 10.1177/0278364905051774©2005 Sage Publications

ceiving greater attention by the agents. This algorithm is particularlywell suited to unstructured environments, where sensor uncertaintyand occlusions are significant. Simulations and experiments showthe effectiveness of this algorithm.

KEYWORDS—visual mapping, information theory, unstruc-tured environments

1. Introduction

An important goal of robotics research is to develop mobilerobot teams that can work cooperatively in unstructured fieldenvironments (Baumgartner et al. 1998; Huntsberger, Ro-driguez, and Schenker 2000); see Figure 1. Potential tasksinclude explosive ordinance removal, de-mining and haz-ardous waste handling, exploration/development of space, en-vironment restoration, and construction (Shaffer and Stentz1992; Baumgartner et al. 1998; Huntsberger, Rodriguez, andSchenker 2000). For example, space and planetary roboticmissions will require robot scouts to lead the way, by explor-ing, mapping, seeking or extracting soil and rock samples, andeventually constructing facilities in complex terrains. Multi-ple cooperating robots will be required to set up surface fa-cilities in challenging terrain forin situ measurements, com-munications, and to pave the way for human exploration ofplanetary surfaces. This will require the handling of relativelylarge objects, such as deploying of solar panels and sensor ar-rays, anchoring of deployed structures, movement of rocks,and clearing of terrain.

The control of such systems typically requires models ofthe environment and task. In unstructured field environmentsit is often not possible to have such a priori models. In suchcases, the robot needs to construct these from sensory infor-mation usually from vision systems. A number of problemscan make this non-trivial. These include the uncertainty of the

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276 THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / April 2005

Fig. 1. Representative physical system.

task in the environment, location and orientation uncertaintyin the individual robots, and occlusions (due to obstacles, workpiece, other robots). If the systems are equipped with cam-eras mounted on articulated mounts, intelligent planning ofthe camera motion can alleviate problems of the occlusions,providing an accurate geometrical model of the task and envi-ronment. If the system consists of more than one robot, plan-ning the behavior of these multi-information sharing systemscan further improve the system performance.

Environment mapping by mobile robots falls into the cat-egory of simultaneous localization and mapping (SLAM). InSLAM a robot is localizing itself as it maps the environment.Researchers have addressed this problem for well-structured(indoor) environments and have obtained important results(Asada 1990; Kuipers and Byun 1991; Leonard and Durrant-Whyte 1991; Pito and Bajcsy 1995; Kruse, Gutsche, and Wahl1996; Burschka, Eberst, and Robl 1997; Castellanos et al.1998; Thrun, Fox, and Burgard 1998; Yamauchi, Schultz,and Adams 1998; Anousaki and Kyriakopoulos 1999; Vic-torino, Rives, and Borrelly 2000; Choset and Nagatani 2001;Tomatis, Nourbakhsh, and Siegwar 2001). These algorithmshave been implemented for several different sensing meth-ods, such as camera vision systems (Pito and Bajcsy 1995;Hager et al. 1997; Castellanos et al. 1998; Park, Jiang, andNeumann 1999), laser range sensors (Yamauchi, Schultz, andAdams 1998; Tomatis, Nourbakhsh, and Siegwar 2001), andultrasonic sensors (Leonard and Durrant-Whyte 1991; Ya-mauchi 1998; Anousaki and Kyriakopoulos 1999; Choset andNagatani 2001). Sensor movement/placement is usually per-formed sequentially (raster scan type approach), by followingtopological graphs or using a variety of “greedy” algorithmsthat explore regions only on the extreme edges of the knownenvironment (Kuipers and Byun 1991; Leonard and Durrant-Whyte 1991;Yamauchi, Schultz, and Adams 1998; Anousakiand Kyriakopoulos 1999; Rekleitis, Dudek, and Milios 2000;Victorino, Rives, and Borrelly 2000; Choset and Nagatani

2001). Geometric descriptions of the environment are mod-eled in several ways, including generalized cones, graph mod-els and Voronoi diagrams, occupancy grid models, segmentmodels, vertex models, convex polygon models (Kuipers andByun 1991; Choset and Nagatani 2001). The focus of theseworks is accurate mapping. They do not address mapping ef-ficiency. Researchers have addressed mapping efficiency to alimited amount (Kruse, Gutsche, and Wahl 1996). However,sensing and motion uncertainties are not taken into account.They also generally assume that the environment is effec-tively flat (e.g., the floor of an office or a corridor) and readilytraversable (i.e., obstacles always have a route around them;Lumelsky, Mukhopadhyay, and Sun 1989; Kuipers and Byun1991; Yamauchi, Schultz, and Adams 1998; Anousaki andKyriakopoulos 1999; Thrun, Burgard, and Fox 2000; Chosetand Nagatani 2001) and have not been applied to robot teamsworking in rough planetary environments. Also, prior workhas not addressed optimizing the communication betweenagents for both multi-agent planning and cooperative mapbuilding.

To achieve the localization function, landmarks and theirrelative motions are monitored with respect to the vision sys-tems. Several localization schemes have been implemented,including topological methods such as generalized Voronoigraphs and global topological maps (Kuipers and Byun 1991;Victorino, Rives, and Borrelly 2000; Choset and Nagatani2001; Tomatis, Nourbakhsh, and Siegwar 2001), extendedKalman filters (Leonard and Durrant-Whyte 1991; Anousakiand Kyriakopoulos 1999; Park, Jiang, and Neumann 1999),Bayesian filters (Howard, Matari´c, and Sukhatme 2003), androbust averages (Park, Jiang, and Neumann 1999). Althoughnovel natural landmark selection methods have been proposed(Yeh and Kriegman 1995; Hager et al. 1997; Simhon andDudek 1998), most SLAM architectures rely on identifyinglandmarks as corners or edges in the environment (Kuipersand Byun 1991; Leonard and Durrant-Whyte 1991; Castel-lanos et al. 1998; Anousaki and Kyriakopoulos 1999; Vic-torino, Rives, and Borrelly 2000; Choset and Nagatani 2001).This often limits the algorithms to structured indoor-type en-vironments. Others have used human intervention to identifylandmarks (Thrun, Burgard, and Fox 2000).

Some studies have considered cooperative robot mappingof the environment (Thrun, Fox, and Burgard 1998;Yamauchi1998; Jennings, Murray, and Little 1999; Rekleitis, Dudek,and Milios 2000). Novel methods of establishing/identifyinglandmarks, identifying relative robot poses and dealing withcyclic environments have been introduced for indoor envi-ronments (Thrun, Fox, and Burgard 1998; Jennings, Murray,and Little 1999; Howard, Matari´c, and Sukhatme 2003). Insome cases, observing robot team members as references todevelop accurate maps are required (Rekleitis, Dudek, andMilios 2000). While the work done in this field has had sig-nificant impact on robot control architectures, these resultslargely do not address the problem of cooperative sensing in

Sujan and Dubowsky / Efficient Information-based Visual Robotic Mapping 277

the context of mobile robots in unknown, unstructured envi-ronments. In simple terms, the conventional approach for thecontrol of robotic systems is to use sensory information asinput to the control algorithms. System models are then usedto determine control commands. The methods developed todate generally rely on assumptions that include simple well-known terrains, accurate knowledge of the environment, lit-tle or no task uncertainty, sufficient sensing capability, andsufficient communication capabilities. For real field environ-ments, a number of these assumptions are often not valid. Ingeneral, current research has not solved the problem of con-trolling multiple mobile robots performing cooperative tasksin unknown environments, where uncertainty, limited sens-ing capabilities, and incomplete physical models of the sys-tem(s)/environment dominate the problem.

In this paper we propose an environment and task modelbuilding algorithm based on information theory. The objec-tive is to efficiently build a geometrically consistent dimen-sional model of the environment and target, available to therobot(s), to allow it (them) to perform its (their) tasks, whileovercoming the uncertainties in robot and camera location andorientation, for robots or robot teams cooperatively workingin an unstructured field environment. It is assumed that thesystem consists of one (or more) mobile robots working inan unknown environment (such as constructing a planetarystructure; see Figure 2). There are no physical interactionsbetween the robots. The target is static. Each has a three-dimensional (3D) vision system mounted on an articulatedarm. Sensing and sensor placement are limited, resulting inocclusions and uncertainties. It is assumed that dimensionalgeometric information is relevant and required for robots toperform their tasks, such as the construction of field facili-ties. The robot(s) is controlled to maximize geometric knowl-edge gained of its environment using an evaluation functionbased on Shannon’s information theory. Using the measuredand Markovian predictions of the unknown environment, aninformation theory based metric is maximized to determinethe robotic agent’s next best view (NBV) of the environment.Data collected at this NBV pose are fused using a Kalman fil-ter statistical uncertainty model to the measured environmentmap. The process continues until the environment mappingprocess is complete. For multi-agent teams, each robot mayshare its model with the other agents providing knowledge ofregions not visible by all robots (Sujan et al. 2003). For suchscenarios, the NBV is determined using the entire fused mapavailable to each agent. Each agent must account for the po-sition of all the other agents in determining its NBV to avoidcollisions. The details of the algorithm are presented next.

2. Algorithm Description

2.1. Overview

The first step in environment map building is to visually con-struct a model of the local environment, including the loca-

Mobile vehicles

with suspensions

Independently

mobile camera

Inter-system

communication

Fig. 2. Cooperative mapping by robots.

tions of the task elements and other robots (if necessary). The3D map is modeled as a probabilistic discretized occupancygrid. Every voxel in the map has a value for probability-of-occupancy that ranges from 0 (empty) to 1 (occupied).A valueof 0.5 indicates maximum uncertainty in occupancy of thevoxel. We assume that only the geometry of the task elements(such as parts of a solar panel that is to be assembled; Hunts-berger, Rodriguez, and Schenker 2000) and the robot(s) arewell known. Obstacles and robot positions are unknown untilmeasured/mapped.

The algorithm may be broken down as follows. First, the ar-ticulated vision sensors cooperatively scan the region arounda target, generating a local 3D geometric model. This allowsthe robots to locate themselves and the obstacles in the targetreference frame. This is achieved by “looking around” andmatching the known target element geometric CAD modelwith visual data (Lara, Althoefer, and Seneviratne 1998).Next, these models are used to find optimum environmentviewing poses for the multiple vision systems (NBV), bydefining and optimizing a rating function (RF) over the pos-sible sensor positions, subject to kinematic constraints of thesensor placement mechanisms for the individual robots. ThisRF aims to acquire as much new information (NI) about theenvironment as possible with every sensing cycle, while main-taining or improving the map accuracy, and minimizing theexploration time. The process is constrained by selecting goalpoints that are not occluded and that can be reached by acollision-free traversable path. The sensors then move to theirnew poses and acquire 3D data. Based on the sensor mountkinematics, the motion of the sensor is known. However, smallmotions of the robot base (due to suspension compliance) anderrors in sensor mounts lead to additional uncertainties. Theseare accounted for by measuring common features during thevision sensor motion. Finally, the new data and their associ-ated uncertainties are fused with the current environment map,resulting in an updated probabilistic environment map, whichmay then be shared with the other sensing agents. Each agentuses the updated probabilistic environment map to generate itsNBV. The process continues until the environment is mappedto the predefined extent necessary. In general, for each sens-


Start

Initialize robot system

Select new vision system configuration

for robot based on information, distance to goal,

and improvement to map accuracy

End criteria:

Is expanse and resolution sufficient

for task requirements?

Move system into desired state

and Rectify true motion

N

Y

Stop

Transmit data to team

Acquire and merge new data

(a) stereo map

(b) uncertainty evaluation

Parameterize critical terrain features

Step 1

Step 2

Step 3

Step 4

Fig. 3. Outline of model building and placement algorithm.

ing agent the algorithm consists of four steps, described asfollows (see Figure 3; Sujan et al. 2003).

2.2. System Initialization

As described above, a common target must be located to es-tablish a common inertial reference frame between the robotsand the environment. All robots contributing to or requiringuse of the map are localized with respect to the initial map.Localization may be achieved by either of the following:

(a) absolute localization, which is achieved by mapping acommon environment landmark that is visible by allrobots;

(b) relative localization, which is performed by mappingfiducials on all robots by other robot team memberswhere one robot is selected as the origin (Howard,Mataric, and Sukhatme 2003).

Absolute localization is used in this application, althoughrelative localization has been applied in the past (Howard,Mataric, and Sukhatme 2003; Sujan et al. 2003). Searchingfor the target (which forms the absolute origin) by movingthe robot sensors can be carried out in many ways (Luo andKay 1989; Tarabanis, Allen, and Tsai 1995). In this study,sensor placement for target searching is performed in the same

way as sensor placement for environment model building.The absolute origin target is located by matching the knowntarget element geometric CAD model with visual data (Lara,Althoefer, and Seneviratne 1998). Template matching for keyfiducials in matching a CAD model would takeO(n6) timefor each fiducial (wheren is the number of mapped points).However, this operation is only performed once during theentire process resulting in a one-time computational load. Atthis stage, the environment model is considered empty (i.e.,no points are known). The first stereo range map (includingthe common target and all objects within the field of view)is taken by each agent. We assume that only the geometryof the task elements (such as parts of a solar panel that is tobe assembled; Huntsberger, Rodriguez, and Schenker 2000)and the robot(s) are well known. The first stereo range map(including the common target and all objects within the fieldof view) is taken and fused to the model. This is describednext.

2.3. Data Modeling and Fusion

At any time, the cameras on each mobile robot can onlyobserve a small part of their environment. However, mea-surements obtained from multiple viewpoints can provide re-duced uncertainty, improved accuracy, and increased toler-ance in estimating the location of observed objects (Smith andCheeseman 1986). To fuse multiple range measurements of a


Probabilistic

Geometrical

World

Map

Sensor Measurements

Sensor Uncertainty

Model

Previous 3-D

Measurements &

Uncertainty

Updated world model

Fig. 4. 3D range measurement fusion with sensor uncertainty.

feature by sensors, a statistical model of sensor uncertaintyis employed (see Figure 4). Current and previous range sen-sor measurements and their uncertainty models can be inte-grated to give an updated probabilistic geometric model of theenvironment.

A single range observation of a point (x) is modeled as a3D Gaussian probability distribution centered atx, based ontwo important observations. First, the use of the mean andcovariance of a probability distribution function is a reason-able form to model sensor data and is a second-order linearapproximation (Smith and Cheeseman 1986). This linear ap-proximation corresponds to the use of a Gaussian (having allhigher moments of zero). Secondly, from the central limittheorem, the sum of a number of independent variables hasa Gaussian distribution regardless of their individual distri-butions. The standard deviations along the three axes of thedistribution correspond to estimates of the uncertainty in therange observation along these axes. These standard deviationsare a function of intrinsic sensor parameters (such as cameralens shape accuracy) as well as extrinsic sensor parameters(such as the distance to the observed point or feature).

For most range sensing systems, this model can be approx-imated as (Sujan and Dubowsky 2002)

σx,y,z = f (extrinsic parameters, intrinsic parameters)

≈ S · Tx,y,z · Ln

(1)

whereS is an intrinsic parameter uncertainty constant,Tx,y,z isan extrinsic parameter uncertainty constant,L is the distanceto the feature/environment point, andn is a constant (typi-cally 2). Provided two observations are drawn from a normaldistribution, the observations can be merged into an improved

estimate by multiplying the distributions. Because the resultof multiplying two Gaussian distributions is another Gaus-sian distribution, the operation is symmetric, associative, andcan be used to combine any number of distributions in anyorder. The canonical form of the Gaussian distribution inn

dimensions depends on the standard distributions,σx,y,z, a co-variance matrix (C) and the mean (x) (Smith and Cheeseman1986; Stroupe, Martin, and Balch 2000):

p(x ′|y) = 1

(2π)n/2

√|C|exp

(−1

2

(y − x ′)T

C−1(y − x ′))

whereC = σ 2

xρxyσxyσxy ρzxσzxσzx

ρxyσxyσxy σ 2y

ρyzσyzσyz

ρzxσzxσzx ρyzσyzσyz σ 2z

. (2)

Here, the exponent is called the Mahalanobis distance. Foruncorrelated measured dataρ = 0. The formulation in eq. (2)is in the spatial coordinate frame. However, all measurementsare made in the camera (or sensor) coordinate frame. Thisproblem is addressed through a transformation of parametersfrom the observation frame to the spatial reference frame asfollows

Ctransf ormed = R(−θ )T · C · R(−θ ) (3)

whereR(θ ) is the rotation matrix between the two coordi-nate frames. The angle of the resulting principal axis can beobtained from the merged covariance matrix

Cmerged = C1

(I − C1 (C1 + C2)

−1)

(4)

whereCi is the covariance matrix associated with theith mea-surement. Additionally, a translation operation is applied tothe result from eq. (2), to bring the result into the spatial ref-erence frame. Determining this transformation matrix is de-scribed in Section 2.5. To contribute to the probabilistic occu-pancy environment model, all measured points correspondingto obstacles are merged. That is, all measured points fallingin a particular grid voxel contribute to the error analysis asso-ciated with that voxel. Note that grid voxels falling within thefield of view of the vision system that correspond to emptyspace result in no contribution to the uncertainty model (sincethese are not measured). However, these points are tabulatedas measured (or known) points. This will be used to select thenext pose for the vision system. The data fusion process issummarized in Figure 5.

2.4. Vision System Pose Selection

A RF is used to determine the next pose of the camera fromwhich to look at the unknown environment. The aim is toacquire as much NI about the environment as possible withevery sensing cycle, while maintaining or improving the mapaccuracy, and minimizing the exploration time. The process isconstrained by selecting goal points that are not occluded and


Start

Given:

Environment model: Probabilistic Occupancy Geometric Environment Map (POGEM)

Sensor model: measurement + uncertainty

Acquire stereo image

Coordinate transformation

to align vision data with

global reference frame

Stop

For points coinciding with earlier measured points:

Multiply Gaussian covariance matrices

to get a merged covariance matrix

For environment model:

Add all Gaussian distributions that have been

contributed by each measured point

Fig. 5. Flowchart for data fusion using known vision system motion.

that can be reached by a collision-free traversable path. Fromthe probabilistic geometric environment model, (x, y, z) lo-cations withPx,y,z < Pempty = 0.05 (2σ) are considered asunoccupied. Such points form candidate configuration spacecamera pose coordinates.

The NI is equal to the expected information of the un-known/partially known region viewed from the camera poseunder consideration. This is based on the known obstaclesfrom the current environment model, the field of view of thecamera (see Figure 6) and a framework for quantifying infor-mation. Shannon (1948) showed that the information gainedby observing a specific event among an ensemble of possibleevents may be described by the following function

H (q1, q2, ..., qn) = −n∑

k=1

qk log2 qk (5)

whereqk represents the probability of occurrence for thekthevent. This definition of information may also be interpretedas the minimum number of states (bits) needed to fully de-scribe a piece of data. Shannon’s emphasis was in describingthe information content of one-dimensional signals. In twodimensions the gray-level histogram of an ergodic image can

be used to define a probability distribution

qi = fi/N for i = 1...Ngray (6)

wherefi is the number of pixels in the image with gray-level i, N is the total number of pixels in the image, andNgray is the number of possible gray levels. With this defi-nition, the information of an image for which all theqi arethe same—corresponding to a uniform gray-level distributionor maximum contrast—is a maximum. The less uniform thehistogram, the lower the information.

It is possible to extend this idea of information to a 3Dsignal—the environment model. In such an instance, the sceneprobability distribution for information analysis is still givenby eq. (6). However,N is the maximum number of voxelsvisible by the vision system (limited by the depth of fieldand the field of view), andfi is the number of voxels in thescene with gray-leveli. The equation is evaluated separatelyfor mapped verses unmapped regions:

H (q) =−((

n∑k=1

qk log2 qk

)known

+(

n∑k=1

qk log2 qk

)unknown

).

(7)


Viewed region

Obstacle

Unknown region

Depth of

Field

Field of View

3-D

vision

system

Fig. 6. Evaluation of expected NI.

The possible gray-level values are defined as follows.For all unknown/unsampled voxels, an occupancy valuep(x)unknown may be defined in the form of a Markovian chain,i.e., p(x) of a particular voxel is the average value ofp(x)

of the neighboring voxels. Intuitively, this results in unknownregions that are mapped as averages of closest known regions.Thus, for all spatial voxels, a gray (probabilistic) occupancyvalue between 0 and 1 is found. Next, the values forp(x) aremodified as follows

stretching:p′(x) ={ 1

1−p(x)· 1

dvoxel∀ p(x) < 0.5

1p(x)

· 1dvoxel

∀ p(x) � 0.5

+ scaling:p′′(x) ={

p′(x)−12

∀ p(x) < 0.51 − p′(x)−1

2∀ p(x) � 0.5

(8)

wheredvoxel is the Euclidean distance of the voxel from thecamera coordinate frame. This process causes regions withprobability densities closer to 0 or 1 (regions of most cer-tainty) to have a reduced effect on the NI expected. Regionsthat have a probability density closer to 0.5 (regions of leastcertainty of occupancy) are “stretched out” in the scene prob-ability distribution, thus increasing the new expected informa-tion associated with those regions. A uniform discretizationof this range ofp′′(x) values may be performed to define thegray-level valuesi, fi , Ngray andN (eq. (7)). With these defi-nitions,qk (eq. (6)) is evaluated and the results applied to eq.(8) resulting in a metric for NI. Alternatively, and possiblya better choice is a uniform discretization ofp(x) to definethe gray-level valuesi, fi , Ngray andN . To increase the con-tribution of regions with higher occupancy uncertainty to theinformation metric, the termqk log2 qk of eq. (7) is premul-tiplied by − (pk log2 pk + (1 − pk) log2 (1 − pk)

)reflecting

the greater expected information available in such regions:

H (q) = −

(n∑

k=1

(− (pk log2 pk + (1 − pk)

log2 (1 − pk))) (

qk log2 qk

) )known

+(

n∑k=1

(− (pk log2 pk + (1 − pk)

log2 (1 − pk))) (

qk log2 qk

) )unknown

. (9)

This definition for NI does behave in an intuitively correctform. For example, for a given camera pose, if the field ofview is occluded, then NI decreases. If every point in the fieldof view is known and is empty then NI = 0. NI increases as thenumber of unknowns in the field of view increases. Further,eq. (9) increases the NI expected with regions that are knownwith median probabilistic values (i.e., values that indicate withleast amount of certainty whether a voxel is occupied or not).On the other hand, regions with high probabilistic values foroccupancy result in reduced associated information.

In addition to maximizing information acquisition, it is alsodesirable to minimize travel distance and maintain/improvethe map accuracy, while being constrained to move alongpaths that are not occluded. A Euclidean metric in config-uration space, with individual weightsαi on each degree offreedom of the camera posec, is used to define the distancemoved by the camera

d =(

n∑i=1

αi(ci − c′i)2

)1/2

, (10)

where c and c′ are vectors of the new and current cameraposes, respectively.Although in this paperαi is set to unity, forgeneral systems this parameter reflects the ease/difficulty inmoving the vision system in the respective axis. Map accuracyis based on the accuracy of localization of each sensing agent.This may be obtained by adding the localization error of theagent along the path to the target (LE). Paths containing morepromising fiducials for localization result in higher utility indetermining both the goal location and the path to the goal.The NI, the travel distance, and the net improvement of mapaccuracy are combined into a single utility function that maybe optimized to select the next view pose

RF = (wNI · NI − wd · d − wLE · LE) · (1 − Px,y,z),

(11)

wherewNI , wd , andwLE are scaling constants. This RF canbe evaluated and optimized to find the next camera configura-tion from which to make future measurements of the environ-ment. This choice for RF is a simple standard weighted linearcombination. Other constraints (application-dependent) maybe readily integrated. For example, when multiple robots are


D

Given:

A probabilistic occupancy geometric environment map (POGEM)

A binary occupancy geometric environment map (BOGEM)

A C-space map of expanded points w.r.t. robot base

Evaluate rating function (RF1)

at point i in POGEM

Is i > number of

points in POGEM

E

i = 1

i = i + 1

Is point i in

BOGEM free?

To

incr

ease

com

pu

tati

on

al

effi

cien

cy

Rank the evaluated RF1 values

Is point i in

POGEM near the

periphery or near an

obstacle?

N

Y

Y

N

Y

N

Select best ranked point in list

Is the

selected point

within manipulator

workspace?

Generate C-space map of

expanded points w.r.t. entire

robot and desired arm config.

Is the

selected point in

un-separated free

C-space?

Delete current point from list

Use C-space map to generate robot path:

(a) complex methods such as tree searches

(b) simple small motion method--straight line

Plan vehicle path with constraints:

1. Path must be in contact with ground

2. Contact must be stable

3. Path must be traversable

Path found?

Define robot base path:

From: current base point

To: Camera target point projected up/down

till contact with C-space points

Set desired manipulator kinematics

Set desired manipulator kinematics

Is the

selected point

within manipulator

workspace

now?

Ign

ore

ifsm

all

mo

tions

and

toin

crea

seef

fici

ency

Generate C-space map of

expanded points w.r.t. entire

robot and desired arm config.

Is the

selected point in

un-separated free

C-space?

Ign

ore

ifsm

all

mo

tions

and

toin

crea

seef

fici

ency

N

Y

N

Y

Y

Y

N

N

Y

N

Fig. 7. Flowchart for vision system pose selection of environment mapping algorithm.

cooperatively mapping the environment, a weighted depen-dence on proximity to another robot can be added to pre-vent collisions. Selecting an optimum form for RF may notbe possible, as an infinite array of more complex linear andnonlinear combinations can be made. However, the standardlinear combination yields promising results, with significantimprovements in mapping efficiency over conventional meth-ods. The vision system pose selection algorithm is outlined inFigure 7. Note that the movement of the vision system mayrequire motions by the mobile robot (in addition to manipu-lator motions). The flowchart in Figure 7 includes a simplepath planning approach based on the principle of convex hulls(Sujan et al. 2003).

2.5. Camera Motion Correction

A final step in environment map building is to identify themotion of the camera. This process eliminates manipulatorend-point positioning errors and vehicle suspension motions,and allows for accurate data fusion. A single spatial point inthe reference frame,ri , is related to the image point (ui , vi)

by the 4× 4 transformation matrixg01 (see Figure 8).For motion calibration, we need to identifyg01:

kiui

kivi

kif

1

= g01 · ri =

[[R01]3x3 X3x1

0 1

]·

rxi

ry

i

rzi

1

. (12)


g01

Reference

frameCamera base

frame x

y

z

xy

z

rk(u,v,f)

(u,v)

f

Spatial point

Fig. 8. Relationship of camera and target frames.

Here,R01 is the rotational matrix,X is the translation vec-tor, f is the camera focal length, andki is a scaling constant.For computational reasons it is more convenient to treat thenine rotational components ofR01 as independent, rather thana trignometric relation of three independent parameters. Eachspatial point gives three algebraic equations, but also intro-duces a new variable,ki—a multiplicative constant to extendthe ith image point vector (u, v, f )i to the ith spatial pointin the camera coordinate frame.ki may be found from thedisparity pair of the stereo images. Forn points we have

u = g01r ⇒

k1u1

k1v1

k1f

1

k2u2

k2v2

k2f

1

· · ·knun

knvn

knf

1

= g01

rx1

ry

1

rz1

1

rx2

ry

2

rz2

1

· · ·rxn

ryn

rzn

1

. (13)

This set of linear equations can be readily solved using theleast-mean-square error solution:

g01 = u(rTr)−1

rT. (14)

The rotation matrix,R01, and the translation vector,X, of thecamera frame with respect to the base frame are extracteddirectly from this solution ofg01. However, for real measureddata and associated uncertainty, a larger number of spatialpoints are required to more correctly identify the geometrictransformation matrix,g01. Given the (i+1) spatial and imagepoint, from eq. (14),Ri+1 andXi+1 can be obtained.A recursivemethod can be used to determine the mean and covariance ofX andR01 based on the previousi measurements as follows:

ˆXi+1 =(i ˆXi+Xi+1

)i+1

CXi+1 = iCX

i+[Xi+1− ˆXi+1

][Xi+1− ˆXi+1

]T

i+1

R(l,m)

i+1 =(iR

(l,m)i

+R(l,m)i+1

)i+1

CR(l,m)

i+1 = iCR(l,m)i

+[R

(l,m)i+1 −R

(l,m)i+1

][R

(l,m)i+1 −R

(l,m)i+1

]T

i+1.

(15)

This essentially maintains a measure on how certain thecamera motion is with respect to its original configuration(assuming the original configuration is known very preciselywith respect to the common reference frame). This camerapose uncertainty must be accounted for to obtain an estimateon the position uncertainty of a measured point in the envi-ronment. Let the measurementz be related to the state vector(actual point position)x by a non-linear function,h(x). Themeasurement vector is corrupted by a sensor noise vectorv

of known covariance matrix,R:

z = h(x) + v. (16)

Assume that the measurement of the state vectorx is per-formed multiple times. In terms of the current measurement,a Jacobian matrix of the measurement relationship evaluatedat the current state estimate is defined as

Hk = ∂h(x)

∂x

∣∣∣∣x=xk

. (17)

The state (or positition) may then be estimated as follows:

Kk = PkHTk

[HkPkH

Tk

+ Rk

]−1

ˆxk+1 = ˆxk + Kk [zk − h(xk)]

Pk+1 = [1 − KkHk] Pk.

(18)

This estimate is known as the extended Kalman filter (Gelb1974). Using this updated value for both the measured pointx and the absolute uncertaintyP, the measured point maythen be merged with the current envrionment model usingeqs. (2) and (4). Note that combining noisy measurementsleads to a noisier result. For example, the camera pose un-certainty increases as the number of camera steps increase.With every new step, the current uncertainty is merged withthe previous uncertainty to obtain an absolute uncertainty incamera pose. However, merging redundant measurements (fil-tering) leads to a less noisy result (e.g., the environment pointmeasurements).

Obtaining appropriate spatial points is now addressed. Spa-tial points are a visible set of fiducials that are tracked dur-ing camera motion. As the camera moves, the fiducials moverelative to the camera, eventually moving out of the camera


view. This requires methods to identify and track new fidu-cials. Fiducials are selected from the probabilistic environ-ment model based on three criteria: the degree of certaintywith which a sampled point is known, the visual contrast ofthe sampled point with its surroundings, and depth contrast ofthe sampled point with its surroundings. These are combinedinto a single fiducial evaluation function:

F.E.F.= f (P (x)) + g (C (u, v)) + h (H (x)) . (19)

Fiducial certainty:f (P (x)) ∼ P(x)/r, wherer is the radiusof a sphere centered at the potential fiducial within whichneighboring voxels have decending certainty levels. Outsidethis sphere, voxel certainty levels increase. Lower values forr suggest that the region surrounding a potential fiducial iswell known, which is a desirable property.

Fiducial visual contrast:g(C(u,v))∼contrast (C) * windowsize (w). Contrast is defined as

C(u, v) = I (x) − Iw

Iw

(20)

whereI (x) is the two-dimensional image intensity value ofthe potential fiducial atx, Iw is the average intensity of a win-dow centered at the potential fiducial in the two-dimensionalimage, andw is the maximum window size after which thecontrast starts to decrease.

Fiducial depth contrast:h(H(x)) ∼ H(x) * window size(w), whereH(x) is the maximum spatial frequency (from a3D Fourier transform) at the potential fiducial within a win-dow, andw is the maximum window size after which thepower spectrum (of the 3D Fourier transform) starts shiftingto higher frequencies. To simplify computation, this may beapproximated with some heuristics.

Additionally, a penalty is added if a potential fiducial istoo close to other identified fiducials. Using the identifiedfiducials, camera motion can be identified. Fiducials can betracked with simple methods such as region growing or imagedisparity correspondence. This algorithm is summarized inFigure 9.

3. Results

3.1. Simulation Studies

Here we give the results using the RF for vision system poseselection to develop a probabilistic model of a planar envi-ronment. Two simulation results are presented: single cam-era/robot modeling of an unstructured environment and twocooperative cameras/robots modeling of an unstructured envi-ronment. Five camera pose selection methods are compared:

1. Random pose selection—the next camera pose is se-lected randomly within the known environment;

2. Sequential/raster pose selection—the next camera poseis selected as the next free location in the known envi-ronment from which measurements have not yet beenmade;

3. Pose with maximum expected unmapped (new) re-gion—the next camera pose is selected as the locationwith the largest expected new region while accountingfor known occlusions;

4. Pose with minimum mapped (old) region (also known asthe Frontier strategy)—the next camera pose is selectedas the location that will map the smallest previouslymapped region;

5. Pose with maximum expected information.

The RF cannot be optimized analytically. In practice, find-ing an optimum value for the RF requires exhaustive search-ing although the entiren-point configuration space takes 0(n)

time. This process to determine the true maxima may rapidlybecome intractable (as was evident in some of our initial tests).There are several methods around this. For example, a setof uniformly distributed randomly placed candidate points inthe environment may be selected and evaluated which is rep-resentative of the “behavior” of points in its neighborhood.Clearly, end-effector positioning errors will prohibit us fromtruly reaching the exact point, and hence it would be morevaluable to evaluate a representative point in a region ratherthan every point in the region. Determining region size or thenumber of points to evaluate is currently a topic of research.A small twist to this selection process is to employ a finite set(m-points) of goal configurations located uniformly but ran-domly near the current position. This process takes 0(m) time,wherem is a constant. Thus, while the best goal configurationwould be that maximizing the RF, any configuration chosenusing the method above with a high value for the RF wouldbe necessarily be in the neighborhood of the maxima. Sucha configuration may be found with reasonable effort. Otherways to reduce search time include search space reductionusing binning and decimation, finite neighborhood searches,etc.

Figure 10 shows an unknown environment (100× 100 m2)

with occlusions (black) to be mapped/modeled. It is assumedthat all mobile mapping sensing agents start at the center ofthis environment. Figure 11 shows the fraction of the envri-onment mapped (Figure 11(a)) and the net distance moved bythe vision system for the five mapping methods, using a singlemobile vision system (with 90◦ field of view, 15 m depth offield). The energy consumption by the system is proportionalto the net distance moved by the vision system. Hence, it isdesirable to have a large fraction of the environment mappedwith small net displacements. Figure 12 shows the fractionof the envrionment mapped in Figure 10 and the net distancemoved by the vision system for the five mapping methods,


Start

Stop

Track fiducials:

Region growing

Identify fiducials:

Score is based on

1. How well the point is known {P(x,y,z) + neighboring uncertainty}

2. How distinct is the point in physical space {dH(x,y,z)}

3. How distinct is the point in image space {dC(u,v)}

Solve g01 to localize camera

w.r.t. global coordinate frame

Is camera

localization uncertainty

small enough?

Does the system

need more/new

fiducials?

Have wheels

moved as much as

needed?

Has camera

reached target?

Move wheels

Move arm

Y

N

Y

N

Y N Y

N

Fig. 9. Flowchart for vision system motion identification using scene fiducials.

Fig. 10. Unknown planar environment.


0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Vision scan number

Fra

ction o

f w

orld

vie

wed

Random walk (area viewed)Sequential Min. knowns Max. expected unknowns Max. info.

(a)

0 10 20 30 40 50 60 70 80 90 1000

500

1000

1500

2000

2500

3000

3500

Vision scan number

To

tal d

ista

nce

mo

ved


(b)

Fig. 11. Results of single vision system modeling an unknown environment: (a) fraction of environment modeled as a functionof scan number; (b) distance moved by vision system as a function of scan number.


0 5 10 15 20 25 30 35 400

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Vision scan number

Fra

ction o

f w

orld

vie

wed


(a)

0 5 10 15 20 25 30 35 400

200

400

600

800

1000

1200

1400

1600

Vision scan number

To

tal d

ista

nce

mo

ved


(b)

Fig. 12. Results of two vision systems modeling an unknown environment: (a) fraction of environment modeled as a functionof scan number; (b) distance moved by vision system as a function of scan number.


using two cooperating mobile vision systems (with 75◦ fieldof view, 10 m depth of field). These results show the effective-ness of the information theroretic approach to vision systempose selection in environment modeling.

Figures 13–15 show the results of exploring this environ-ment with a single robot (with a 90◦ field of view, 15 mdepth of field). Figures 13 and 14 show examples of the areamapped and the path taken by the vision system using map-ping/modeling methods (i) and (v). Figure 15 shows the av-erage accumulated motion error of the vision system as itexplores the environment as a function of traveled distance.Comparing Figures 15(a) and (b), it is seen that this error de-creases substantially with redundancy of fiducials as well aswith proximity of the fiducials. The energy consumption bythe system is proportional to the net distance moved by thevision system. Hence, it is desirable to have a large fraction ofthe environment mapped with small net displacements. Thisis significantly more noticeable in Figure 14 where the robotpath based on the amount of information obtained from itsmotion appears to criss-cross over itself far less frequently ascompared to the random walk (with some heuristics). The for-mer path (Figure 14(b)) is substantially shorter than the latter(Figure 14(a)) whereas the amount of the environment ex-plored/mapped is greater in the former. The quantified resultis seen in Figure 11.

3.2. Experimental Studies

As described above and demonstrated in simulation, the algo-rithm developed in this paper is equally applicable to a singlerobot mapping agent as it is to a team of multiple mappingagents. The difference is in the RF, where one must accountfor the presence of other agents to avoid collisions. Addi-tionally, the presence of body parts of other robot agents inthe maps taken must be accounted for and deleted from themap, as they are not natural occurrences in the environment.This is accomplished using CAD models of the agents com-bined with the current environment measurement along withan estimate of the agents’ current pose. This process is notvery computationally expensive, as it is being carried out on asmall single sensor scan of the environment rather than on thewhole environment map. Due to resource limitations, experi-mental validation was limited to a single mapping agent. Fig-ure 16 shows a single vision system (stereo pair) mounted on amobile manipulator. The experimental platform consists of afour-wheeled robot with a four-degrees-of-freedom (4-DOF)manipulator arm mounted on a six-axis force/torque sensor.Figure 16(a) shows the system’s dimensions. On-board sen-sors also include a two-axis inclinometer. An off-board com-puter system (Pentium 166 MHz) is used for real-time control,data acquisition, and data processing. All programs are writ-ten in C++ operating on Windows NT. The robot was set ina rough unstructured Mars-type environment and is focusedon mapping the environment around a mock solar panel ar-

ray (representing a real system requiring service by a robotagent). Mapping is performed by breaking up the world intoa grid of voxels of specified resolution. All measured pointsfalling in a particular voxel contribute to the error analysis as-sociated with that voxel.Voxels corresponding to empty spacefalling in the field of view of the vision system are tabulatedas known, but with no contribution to the uncertainty model.The desired voxel resolution is a function of the task. For thistest, the resolution is set at 1mm.

Figure 17 shows the number of points mapped in the en-vironment for two pose selection methods: sequential/rasterscan and maximum information based pose selection. The se-quential/raster scan process is a common mapping processoften applied by researchers and has been included here forcomparison (Asada 1990; Kuipers and Byun 1991; Burschka,Eberst, and Robl 1997; Castellanos et al. 1998; Rekleitis,Dudek, and Milios 2000;Victorino, Rives, and Borrelly 2000;Choset and Nagatani 2001). Once again, the effectivenessof the information based pose selection process, seen as therate of development of the environment map, is significantlygreater using the algorithm developed in this work as com-pared to the sequential mapping process. Figure 18 shows theregions mapped using sequential camera pose selection andmaximum information based camera pose selection. There isalmost a factor of 6 increase in the region mapped for the samenumber of imaging steps when using the maximum informa-tion theory based approach as compared to the raster mappingmethod.

Due to the very rough nature of its surroundings, it wasoften difficult for the robot to find paths to its desired pose.As seen in Figure 16(b), the agent finds itself unable to movearound to the rear of the target due to obstructing boulders andvertical “hill” sides. It was noted that if the desired pose toview the environment was a substantial distance away fromthe current pose, then the computational time for the map-ping step was dominated by the process of determining a saferoute to the target pose. To minimize this effect, greater weightwas added to the term relating distance to target in the RF(eq. (11)). Future research will focus on determining the ef-fect of a large number of team members and their influenceon the mapping or scouting process of their environment. Co-operative robot control architectures for mapping may alsoexploit the added freedom associated with physical interac-tions to traverse more complex terrains.

4. Conclusions

In field environments it is often not possible to provide roboticteams with detailed a priori environment and task models. Insuch unstructured environments, cooperating robots will needto create a dimensionally accurate 3D geometric model byperforming appropriate sensor actions. The performance ofcooperative robots in field environments is limited by model


World X Dimension World X Dimension

Mapped World Mapped World

Wo

rld Y

Dim

ensi

on

Wo

rld Y

Dim

ensi

on

Fig. 13. Mapped area by a single vision system (gray = empty space; black = obstacle; white = unknown): (a) random walkpose selection; (b) maximum information pose selection.

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Camera X position

Cam

era

Y p

ositio

n

Random walk (viewed area)

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Camera X position

Cam

era

Y p

ositio

n

Maximum information

(a) (b)

Camera X DimensionCamera X Dimension

Random walk Maximum information

Cam

era

Y D

imen

sio

n

Cam

era

Y D

imen

sio

n

Fig. 14. Path taken by a single vision system: (a) random walk pose selection; (b) maximum information pose selection.

0 5 10 15 20 25 30 35 40 45 500

2

4

6

8

10

12

14

16

18

20

Scan step number

Po

sitio

n u

nce

rtain

ty (

mm

)

Camera positioning uncertainty - Average landmark distance: 1100 mm

No unnecessary landmarks Double the necessary landmarks Quadruple the necessary landmarks

0 5 10 15 20 25 30 35 40 45 500

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Scan step number

Po

sitio

n u

nce

rtain

ty (

mm

)

Camera positioning uncertainty - Average landmark distance: 350 mm

No unnecessary landmarks Double the necessary landmarks Quadruple the necessary landmarks

(a) (b)

Camera positioning uncertainty – Average landmark distance: 350 mmCamera positioning uncertainty – Average landmark distance: 1100 mm

Scan step numberScan step number

Posi

tion u

nce

rtai

nty

(m

m)

Posi

tion u

nce

rtai

nty

(m

m)

Fig. 15. Accumulated root-mean-square translation error of vision system: (a) average fiducial distance 1100 mm; (b) averagefiducial distance 350 mm.


344.2mm

228.6mm

159.1mm

159.1mm

138.2mm

76.2mm

101.6mm

89.3mm

(a) (b)

Fig. 16. Experimental mobile vision system modeling an unstructured environment: (a) schematic diagram of the physicalsystem; (b) physical system implementation.

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

2.5x 10

5

Camera scan number

Num

be

r o

f uniq

ue

envi

ronm

ent p

oin

ts s

ee

n

Maximum information scanSequential/raster scan

Fig. 17. Number of mapped environment points as a function of scan number.

uncertainties and on-board sensor limitations. In this paper wehave developed sensing and estimation algorithms to enablemultiple mobile robots to compensate for geometric modeluncertainties and to successfully perform interacting cooper-ative manipulation tasks in highly unstructured/unknown fieldenvironments using optimal information gathering methods.A new algorithm based on iterative sensor planning and sen-sor redundancy has been presented to build a geometricallyconsistent dimensional map of the environment for mobilerobots that have articulated sensors. This algorithm is uniquein that it uses a metric of the quality of information previ-

ously obtained by the sensors to find new viewing positionsfor the cameras. The aim is to acquire NI that leads to moredetailed and complete knowledge of the environment. Con-trolling robots to maximize knowledge is performed usingShannon’s information theory based evaluation functions.Thealgorithm is initialized by a scan of the region around a tar-get by all individual agents, to generate a local 3D geometricmodel of the origin reference frame. Next, these models areused to find optimum environment viewing poses for the mul-tiple vision systems by defining and optimizing a RF over thepossible sensor positions, subject to kinematic constraints of


(i) region mapped in 41 steps (ii) environment point cloud

(a)

(i) region mapped in 18 steps (ii) environment point cloud

(b)

Region

mapped in (a)

Fig. 18. Environment mapped/modeled: (a) sequential camera pose selection; (b) maximum information based camera poseselection.


the sensor placement mechanisms for the individual robots.This RF aims to acquire as much NI about the environmentas possible with every sensing cycle, while maintaining orimproving the map accuracy, and minimizing the explorationtime. The process is constrained by selecting goal points thatare not occluded and that can be reached by a collision-freetraversable path. The sensors then move to their new posesand acquire 3D data. Based on the sensor mount kinematics,the motion of the sensor is known. However, small motions ofthe robot base (due to suspension compliance) and errors insensor mounts lead to additional uncertainties. These are ac-counted for by measuring common features during the visionsensor motion. Finally, the new data and its associated uncer-tainty are fused with the current environment map, resultingin an updated probabilistic environment map, which may thenbe shared with the other sensing agents. Each agent uses theupdated probabilistic environment map to generate its NBV.The process continues until the environment is mapped to thepredefined extent necessary.

The algorithm may be used by multiple distributed anddecentralized sensing agents for efficient and accurate envi-ronment modeling. The algorithm makes no assumptions ofthe environment structure. Hence, it is robust to robot fail-ure since the environment model being built is not dependenton any single agent frame, but is set in an absolute referenceframe. It accounts for sensing uncertainty, robot motion un-certainty, environment model uncertainty, and other criticalparameters. It allows for regions of higher interest obtainingmore attention by the agents. Simulations and experimentsshow promising results.

Acknowledgments

The authors would like to acknowledge the support of theJet Propulsion Laboratory, NASA in this work (in particularDr. Paul Schenker and Dr. Terry Huntsberger). The authorsalso acknowledge the help of Grant Kristofek, MIT, for thefabrication of the experimental system used in this work.

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