The M-Space Feature Representation for SLAM

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<ul><li><p>1024 IEEE TRANSACTIONS ON ROBOTICS, VOL. 23, NO. 5, OCTOBER 2007</p><p>The M-Space Feature Representation for SLAMJohn Folkesson, Member, IEEE, Patric Jensfelt, Member, IEEE, and Henrik I. Christensen, Member, IEEE</p><p>AbstractIn this paper, a new feature representation for si-multaneous localization and mapping (SLAM) is discussed. Therepresentation addresses feature symmetries and constraintsexplicitly to make the basic model numerically robust. In previousSLAM work, complete initialization of features is typically per-formed prior to introduction of a new feature into the map. Thisresults in delayed use of new data. To allow early use of sensorydata, the new feature representation addresses the use of featuresthat initially have been partially observed. This is achieved by ex-plicitly modelling the subspace of a feature that has been observed.In addition to accounting for the special properties of each featuretype, the commonalities can be exploited in the new representationto create a feature framework that allows for interchanging ofSLAM algorithms, sensor and features. Experimental results arepresented using a low-cost web-cam, a laser range scanner, andcombinations thereof.</p><p>Index TermsFeature representation, localization, mapping,mobile tobots, simultaneous localization and mapping (SLAM),navigation.</p><p>I. INTRODUCTION</p><p>THE PROBLEM of simultaneous localization and mappinghas been widely studied. Central to the problem is howthe estimation algorithm represents the map. Dense represen-tations1 that store partially processed sensor data give a verydetailed map [1][7]. As more data is retained, this can be an ad-vantage when, for instance, a robot needs to match sensor read-ings from a totally unknown location with the map. A drawbackof this approach is that the amount of data stored in the map be-comes very large.</p><p>An alternative is to use the sensor data to form a hypothesisabout the existence and location of features in the environment.Only the features and the accumulated evidence about them isstored. This leads to an abstraction of the environment that ide-ally will capture the essential information gathered from the sen-sors. Thus, a feature map can be considered a form of data com-pression. The abstraction of the environment could also lead to</p><p>Manuscript received March 14, 2006; revised October 29, 2006. This paperwas recommended for publication by Associate Editor G. Sukhatme and EditorL. Parker upon evaluation of the reviewers comments. This work was supportedby the Swedish Foundation for Strategic Research through the Centre for Au-tonomous Systems.</p><p>J. Folkesson is with the Department of Mechanical Engineering, MassacusettsInstitute of Technology, Cambridge, MA 02139 USA (e-mail: johnfolk@mit.edu).</p><p>P. Jensfelt is with the Center for Autonomous Systems, Numerical AnalysochDatalogi, Kungliga Tekniska Hgskolan, S-100 44 Stockholm, Sweden (e-mail:patric@nada.kth.se).</p><p>H. I. Christensen is with the College of Computing, Georgia Institute of Tech-nology, Atlanta, GA 30332 USA (e-mail: hic@cc.gatech.edu).</p><p>Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.</p><p>Digital Object Identifier 10.1109/TRO.2007.903807</p><p>1SLAM methods that employ dense representation include scan matching,image matching, and occupancy grid methods.</p><p>an understanding of the data on a deeper level. It is preferred,even if not necessary, for the features to be landmarks recogniz-able by humans.</p><p>One advantage of the data reduction is that the resources thatwould have been used to store and manage the large data cannow be used to better interpret the data. Thus, algorithms ofgreater complexity can be applied to try to estimate the map.</p><p>The selection of features is based on the task, the sensors, andthe environment. One task that is fundamental to a SLAM map isthe task of localization. Without the ability to localize the robot,using the map, it would be impossible to combine new sensordata with older information.</p><p>As a result, one requirement of a map feature is that it be ableto constrain some of the pose dimensions of the robot. For thecase of a wheeled robot operating in a planar environment, thedistance to the floor is useless as a feature measurement sincethe robot is already constrained to a level surface. On the otherhand, a doorway is a useful feature.</p><p>A single feature will partially constrain the robot pose in thefull space of robot poses. In general, a combination of severalfeatures are required to fully constrain the pose. For example, in2-D, three differing bearing angles to points are sufficient.</p><p>The feature selection is also driven by the need to extract in-formation about the geometry of the features from the sensordata. This then is a requirement that the sensor measurementscan constrain some of the geometry of features.</p><p>Thus, the available sensors limit the feature selection. More-over, just as a single feature may not fully constrain the robotpose, a single sensor reading may not be enough to fully con-strain the geometry of the feature. This leads to the situation ofpartially observed features. In some cases, the partial observ-ability depends on the frame of reference of the sensor data. Asthe robot moves around it can more fully observe the features.For example, the angle of a wall might be measured first. Then,as the robot travels along the wall the length of the wall is ob-served. Any single measurement might only observe a subspaceof the complete feature description.</p><p>This partial observability is a fundamental property of mapfeatures. Coming back to representations of features, the repre-sentation of the evidence gathered about features should be ableto represent the lack of evidence for the unobserved parts of thefeatures as well as the evidence for the observed parts.</p><p>The observable subspace needs to be explicitly representedfor a practical reason. Simultaneous localization and mapping(SLAM) estimation might process different parts of the datausing different estimated states. Without explicit representa-tion, the observable subspace might shift in the full featurespace throughout the calculation. This can lead to inconsistentestimates.</p><p>Another factor in feature selection is the environment itself.It can be a drawback of feature-based mapping that features</p><p>1552-3098/$25.00 2007 IEEE</p></li><li><p>FOLKESSON et al.: M-SPACE FEATURE REPRESENTATION FOR SLAM 1025</p><p>Fig. 1. Here, we illustrate how inconsistency can arise. The left pair of figures shows a line feature. The information gathered on the line is only perpendicular tothe line. At a later stage of SLAM the line has rotated but the information has not. This then incorrectly indicates some information tangent to the line. By explicitlyrepresenting the observable subspace, we are able to have the information rotate with the feature (right pair of figures).</p><p>are normally selected for a specific environment based on priorknowledge of that environment. For a park, trees might be used[8], for an office building walls are more appropriate. Using vi-sion some rather general image features can be employed [9],[10]. Some of the really early work on SLAM used features,e.g., [11][13].</p><p>One other issue regarding features is the initialization of thefeatures in the map. If the features are initialized too quicklypoor features may be used resulting in worse navigation. Theuse of delayed initialization was investigated in [14].</p><p>A. Outline</p><p>As pointed out in [15] most feature representations use com-pletely different parameterizations for each type of feature. Theresult is a representation that lacks generality. The motivationfor our work is to look for a representation that can: 1) use theinformation from the measurements of the features to improvethe estimated feature coordinates while not changing the unob-served parts of the feature (preserving invariants); 2) representboth size and position information; 3) represent connections be-tween features such as a corner between two walls; and 4) rep-resent uncertainties in a frame attached to the feature.</p><p>In Section II, we introduce the basic mathematical analysisof using features to do SLAM. In Section III, we survey someof the different feature representations that have been used. InSection IV, we describe the basis for our new representationand provide some feature examples in Section IV-D. Section Voutlines a SLAM EKF implementation using the new represen-tation. Section VI deals with the cases of connected featuressuch as when two walls form a corner. To highlight some of thebenefits of the representation, we present experimental resultsin Section VII. Finally, we summarize and draw conclusions inSection VIII.</p><p>II. FEATURE MATH</p><p>In Section I, we discussed how the feature measurements con-strain the robot pose and parts of the feature coordinates. Here,we formalize the problem. The sensors provide data from whicha vector of measurements is extracted, denoted by . At thesame time there are features that have given rise to these mea-surements. These features will have some parameterization oftheir geometry,2 which we will denote by . Finally, the robotpose coordinates are denoted by .3</p><p>2By feature geometry we mean location, orientation, and spacial extent.3The robot pose here could contain offsets to the various sensors and the</p><p>number of coordinate dimensions could thus be greater than 6.</p><p>To make inferences about the feature and robot coordinatesbased on the measurements, we need to define a vector functionthat relates all three. We refer to this function as an innovation,</p><p>. The Jacobian matrix of this innovation is</p><p>(1)</p><p>We can now be more formal about what we mean by measure-ments constraining the robot pose. The measurements will con-strain the robot pose coordinates on the subspace of spannedby . In other words, if there are directions that the robot posecan change without causing any change to the innovation, thenthese directions are not constrained by the measurement. Suchdirections are characterized by being in the null space of .Similarly, the observable subspace of the feature coordinatesis spanned by . We will now show how these two matricesare related to one another by the transformation properties ofthe feature coordinates.</p><p>The sensor measurements are taken in a reference frame at-tached to the robot. Thus, the innovation function in this framewill depend on the transformed feature coordinates only</p><p>(2)</p><p>where are the feature coordinates transformed tothe sensor frame of reference. It is the Jacobians of this trans-formation that give us the relationship between and</p><p>(3)</p><p>The approximations used by SLAM estimation algorithms ofteninvolve linearization of these Jacobians with respect to the fea-ture and robot pose coordinates. Consistency problems occurwhen the Jacobians used at an earlier iteration of a SLAM algo-rithm no longer lie in the observable subspace of the features.This situation can arise when these features are rotated with re-spect to their earlier orientations, see Fig. 1. We have shownhow the constrained subspace of robot poses and the observablesubspace of features are related to one another by the transfor-mation of the feature coordinates. Both this central importanceof transformation rules and the existence of an observable sub-space will guide us in defining our feature representation.</p><p>III. FEATURE REPRESENTATIONS</p><p>A number of different types of features have been used formapping. Depending on the type of application the model ofthe environment is 2-D or 3-D. For most indoor applicationsa 2-D representation is used. Navigation in cluttered environ-ments often requires a 3-D representation. When taking the step</p></li><li><p>1026 IEEE TRANSACTIONS ON ROBOTICS, VOL. 23, NO. 5, OCTOBER 2007</p><p>outdoors the world is less structured and it becomes increasinglylikely that the ground is not flat which also calls for a 3-D model.Some commonly used features are as follows.</p><p> Point: The point is probably the most commonly used fea-ture. It is simple to work with, yet powerful. When workingin 2-D, vertical edges become points. In outdoor applica-tions, point features have successfully been used to repre-sent, e.g., tree trunks [8].</p><p> Line: In indoor man-made environments there are typicallymany walls. These appear as lines when measured with 2-Drange sensors. These line segments are, therefore, naturalto use as features. Vertical edges are also common in man-made environments. This type of line feature is typicallyextracted using visual information as in [16].</p><p> Plane: When taking the step from 2-D to 3-D what was aline in 2-D often becomes a plane in 3-D. Planes have beenused in, for example, [17] and [18].</p><p>A. Wall Feature Representations</p><p>In this section, we will look closer at the wall feature as it canbe used to illustrate some of the good and bad aspects of the nu-merous different representations that have been suggested in theliterature. To limit the scope we concentrate on representationsfor the 2-D case in which a wall appears as a line segment in the</p><p> plane.Before listing different representations some characteristics</p><p>of the wall are given. Four parameters are needed to fully specifythe line segment. One key issue of a wall is that the sensors maynot be able to detect its end points. Even if the end points arewithin the range of the sensors they are often hard to detect dueto occlusions. This implies that a measurement typically onlyconstrains the position of the sensor to a certain distance andrelative angle w.r.t. the wall. In other words, all dimensions ofa wall are typically not constrained by one single measurement.</p><p>1) Slope and Intersection: The slope and intersection repre-sentation is the first that comes to mind. How-ever, it suffers from a major disadvantage in that the parameter</p><p>has a hyperbolic dependence on the rotation angle of theline. This nonlinear and singular behavior must be dealt with inan ad hoc manner and adds complications and approximationsto the SLAM estimate. The extent of the wall is not representedeither.</p><p>2) End Points: The most straight forward representation isto use the two end points to parameterize the wall. One disad-vantage with this is that one typically does not measure the endpoints of a wall but rather the distance to and orientation of thewall. This means that all four dimensions of the wall cannot beproperly initialized. An ad hoc solution to this using very largeuncertainty for the end-points along the wall will not behavewell during estimation.</p><p>3) Distance and Direction : Starting from the measure-ments, one of the most natural representations is to use the per-pendicular distance to the wall and the orientation of the wall.This results in a description of an infinite line. This has beenused in, for example, [16]. There are two main problems withthis representation. The first one is that walls are not infinitein reality. This becomes a problem in large areas where therewill be lines everywhere. The second problem is the so called</p><p>lever-arm effect [19] that results from...</p></li></ul>

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