Field and Service Robotics - Corke P. and Sukkarieh S.(Eds) Part 4 doc

The consistency model is described by an H c matrix equivalent to equation 4. This matrix is formed by iterating through each of the graph edges of the mesh structure, where each edge yields one row of H c . For each edge, where the edge is between nodes i and j : H c row,i = IH c row,j = − I (8) The consistency model observation becomes an addition to Y , as in equation 5. 5.4 Two Dimensional Angular Profiles Demonstration Figure 5 shows a demonstration of angular profiles from our flight vehicle and ground vehicle. The patterned cylinder object was characterised according to the metric area of the object as viewed from the (air or ground) borne image sensor. This is a preliminary observable for demonstration of the esti- mation structure. Figure 5(d) shows the separate contributions from the air and ground vehicle, which are separate due simply to their differing angles of elevation. The fusion of information from air and ground is simplified by the use of angular profiles because they allow explicit differences in value at viewing angles. Hence it is not required that features be absolutely identical from air and ground. Figures 5(a) and 5(b) are shown at the same orienta- tion. The peaks in profile information correspond to the groups of observation points where multiple observations have been fused. Regions without observa- tions take on an estimate obtained through the network of consistency models, causing those regions to have non-zero information. 5.5 Information Theoretic Properties of Two Dimensional Angular Profiles One application of angular profiles is in causing information theoretic control schemes [10] to explore multiple viewing angles of point features (in addi- tion to spatial exploration over multiple features). This section describes the properties of the determinants of the information matrices of angular profiles. The entropic information i of an n -dimensional Gaussian variable with Fisher information, Y and the mutual information I between two alternate information matrices Y a and Y b are given by: i = 1 2 log [(2πe) n | Y | ] I = 1 2 log  | Y a | | Y b |  (9) Angular profiles determinants have the followingproperties: • After application of theconsistencymodel but before observations, | Y | = 0. Thismeans that Y retains the properties of anon-informativeprior after application of the consistencymodel. • Asingleobservation causes the determinant, | Y b | ,tobenon-zero. Development of Angular Characterisation 113 114 P. Thompson and S. Sukkarieh Easting MGA (m) Northing MGA (m) Cyclinder and View positions 6.1675 6.1676 6.1677 6.1678 6.1679 x 10 6 2.297 2.2975 2.298 2.2985 2.299 2.2995 2.3 2.3005 x 10 5 Cylinder Ground Obs Air Obs (a)Cylinder Object location and air and groundviewing positions −1500−1000−500 0 500 1000 1500 2000 −1000 −500 0 500 1000 1500 2000 (b)Radius represents theprofile infor- mation(inverse covariance). Theorien- tation matches that of 5(a) −4 −2 0 2 −2 −1 0 1 2 3 4 (c) Radius representsthe profileestimate (Projected area of theobject, m 2 ) -1 500 -1000 -500 0 500 1000 15 00 20 00 -5 00 0 500 1000 1500 -1000 -500 0 Air vehicle contributed in fo rmatio n Ground vehicle contributed information (d) Radius representsthe profileinformation (in- verse covariance). Informationpeakscorrespond to air and ground observations Fig. 5. Angular Profiles Demonstration The mutualinformation properties of angular profiles are distinct from those of three dimensional bearing onlypointlocalisation [10].Given asingle observation,the next observationtomaximise information gain should be 180 degrees around theprofile. Asequence of adjacentobservations optimised for information gain exploresall angles. 5.6 Other Applications and Extensions Themethod of interpreting prediction modelsasdifferential observations used here to develop atechnique for developing the consistencymodels forangu- lar profiles can be applied to otherproblems in the estimation of spatially distributed states. In particular,itcouldbeapplied to the estimation of the trajectory of near-linearfeatures suchasfences, roads and rivers presented by our fieldsite. Interpreting prediction models as differential observations can also be ap- plied to temporal estimation. It is a subject of future investigation to compare this to other treatments of delayed and asequent data handling [11] and to other smoothing formulations of estimation. [12] Interpreting spatial consistency models and temporal prediction models as differential observations (in space a time respectively) allows one to describe consistency in space and time simultaneously. This provides a method for simultaneously estimating spatially distributed random fields and providing temporal smoothing (spatio-temporal estimation). This can be compared to the spatial Kalman filtering described in [13] and [14]. It will be necessary to describe temporal process models for the angular profiles, primarily to introduce uncertainty over time. There are difficulties involved with handling observations of the angular profile from uncertain angles. As described, the technique treats the angular states as fixed on a set of angles around the object and so observations must be subject to data association to choose the angle to update. 6 Conclusion and Future Work In this paper we introduced our project and approach, described the vision system and environment. We introduced a theory for the estimation of angular profiles with demonstrations from simulation and field data. In future developments we will be incorporating the image processing al- gorithms and observation models necessary to observe angular profiles as de- scribed here. We will be revising the decentralised data fusion system to allow greater flexibility in the choice of states associated with each feature in order to support the communication and fusion of angular profiles. Feedback from the angular profile states and localisation states will need to be used simultaneously for information theoretic decentralised control. As discussed in section 5.5, an angular profile of a single feature has well behaved properties in entropy and mutual information, causing decentralised control algorithms to explore not only different positions in space but different an- gles of view. However, implementing angular profiling alongside localisation presents many challenges. The technique of angular profiling is limited by the choice of the profiled observable. For general vision based applications it may be preferable to fo- cus on methods for estimating the three dimensional geometric structure and colour or itensity of regions, rather than relying upon low dimensional remote observables. However, the ability of angular profiles to provide an entropic measure of angular information coverage is a relevant and beneficial feature. Acknowledgments This project is supported by the ARC Centre of Excellence programme, funded by the Australian Research Council (ARC) and the New South Wales State Govern- ment. This project is supported by BAE Systems, Bristol, UK. Development of Angular Characterisation 115 116 P. Thompson and S. Sukkarieh References 1. Salah Sukkarieh, Eric Nettleton, Jong-Hyuk Kim, Matthew Ridley, Ali Gokto- gan, and Hugh Durrant-Whyte. The ANSER project: Data fusion across mul- tiple uninhabited air vehicles. The International Journal of Robotics Research, 22(7-8):505–539, 2003. 2. Nadine Gobron, Bernard Pinty, Michel M Verstraete, Jean-Luc Widlowski, and David J. Diner. Uniqueness of multiangular measurements. IEEE Transactions on Geoscience and Remote Sensing , 40(7):1574 – 1592, 2002. 3. Eric Nettleton. Decentralised Architectures for Tracking and Navigation with Multiple Flight Vehicles. PhD thesis, The University of Sydney, 2003. 4. Frank Dellaert, Steven M. Seitz, Charles E. Thorpe, and Sebastian Thrun. Struc- ture from motion without correspondence. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2:557 – 564, 2000. 5. D.T. Cole, S. Sukkarieh, A.H. Goktogan, H. Stone, and R. Hardwick-Jones. The development of a real-time modular architecture for the control of uav teams. In The 5th International Conference on Field and Service Robotics, July 2005. 6. Ed Waltz. Handbook of Multisensor Data Fusion. The Principles and Practice of Image and Spatial Data Fusion. CRC Press, 2001. 7. Peter S. Maybeck. Stochastic models, estimation, and control, volume 1 of Math- ematics in Science and Engineering. 1979. 8. Sebastian Thrun, Yufeng Liu, Daphne Koller, Andrew Y. Ng, Zoubin Ghahra- mani, and Hugh Durrant-Whyte. Simultaneous localization and mapping with sparse extended information filters. The International Journal of Robotics Re- search, 23(7-8):693–716, 2004. 9. Pen-Olof Persson and Gilbert Strang. A simple mesh generator in matlab. SIAM Review, 46(2):329 – 345, 2004. 10. Ben Grocholsky. Information-Theoretic Control of Multiple Sensor Platforms. PhD thesis, Australian Centre for Field Robotics Department of Aerospace, Mechatronic and Mechanical Engineering The University of Sydney, 2002. 11. Eric W. Nettleton and Hugh F. Durrant-Whyte. Delayed and asequent data in decentralised sensing networks. Proceedings of SPIE - The International Society for Optical Engineering, 4571:1 – 9, 2001. Decentralised sensing networks. 12. Robert F. Stengel. Optimal Control and Estimation. Dover, 1994. 13. K.V. Mardia, C. Goodall, E.J. Redfern, and F.J. Alonso. The kriged kalman filter. Test (Trabajos de Estadstica) , 7(2):217–285, December 1998. 14. Noel Cressie and Christopher K. Wikle. Space time kalman filter. Encyclopedia of Environmetrics, 2002. Topological Global Localization for Subterranean Voids David Silver, Joseph Carsten, and Scott Thayer Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA { dsilver,jcarsten,sthayer} @ri.cmu.edu Summary. The need for reliablemaps of subterranean spaces toohazardous for humans to occupyhas motivated the developmentofrobotic mapping tools. For suchsystemstobefully autonomous, they must be able to deal withall varietiesof subterranean environments, including those containing loops. This paper presents an approachfor an autonomous mobile robot to determine if the areacurrently being exploredhas been previously visited. Combined with other techniques in topological mapping, this approachwill allowfor the fully autonomous general exploration of subterranean spaces. Data collected from aresearchcoal mine is used to experimen- tally verify ourapproach. 1Introduction In many parts of the world, abandonedmines present asignificant environ- mental hazard. Toxic runoff, landslides,and subsidenceare just some of the dangerspresentedbythesestructures.Inthe U.S. alone, there are tens of thousands of abandoned mines [3] that threaten nearbysurfaceand subter- ranean operations.The first steptowards combating this problemistoobtain an accurate metric survey of the mine structure. Unfortunately,inmost cases an accuratesurvey of the mine has either been lostornever existed.Taking anew surveyofthe structure is oftenlimitedtoinspections via boreholes, as abandoned mines are usually toodangerous for peopletoenter. Forthis reason, robots have been proposed as amethod for mapping abandoned mines. The Carnegie MellonSubterranean Roboticsgroup has undertakenthe taskofdevelopingrobotic systems that can autonomously explore abandoned mines or other hazardous subterraneanvoids. Theinitial effort led to the developmentofasystem that canautonomously navigateand explore long stretches of asingle mine portal [2]. More recentwork has focussed on ex- panding mission profiles to include generalexplorationofmultipleintersect- ing corridors.This led to asystemwhichcan detect and traverse multiple corridors [13], but cannot determinewhen it has returned to apreviously P. Corke and S. Sukkarieh (Eds.): Field and Service Robotics, STAR 25, pp. 117–128, 2006. © Springer-Verlag Berlin Heidelberg 2006 118 D. Silver, J. Carsten, and S. Thayer Fig. 1. Left: Groundhog, the currentrobotic platform of the mine mapping project. Right:This map wasgeneratedfrom data acquired during experimentation and utilizes offline globally consistent mapping techniques. It shows the highly cyclic natureofroom-and-pillar mines. visited corridor intersection from adifferentdirection. This constraintlimited the environmentsexplored in [13]tothose whichdid not contain loops. Thispaper presents amethod by which an autonomousmobile robot can identify correspondences between intersections in subterranean environments, allowing for autonomous loop closure and more general exploration. Our ap- proachfor matching intersections is based on comparisons of both 2D and 3D range datalocal to eachintersection.The results of these comparisons are then fedtoabinaryclassifier, whichproducesthe probabilityofamatch. Such aclassifier can then be integrated into acompletesystemdesigned to trackmultiple topological maphypotheses. Theremainder of thispaper discusses therelevantdetails of our approach. Section 2provides background into subterraneantopological exploration. Sec- tion 3describesour technique, with experimental results presented in Section 4. We concludewithadiscussion and directions for future work. 2Subterranean TopologicalExploration 2.1Robotic Platform Ourcurrentmine mapping platform is Groundhog (Figure 1), a700 kg custom-builtATV-typerobot that is physicallytailoredfor operation in the harsh conditions of abandoned mines. Groundhog’sprimary sensing consists of 2SICK LMS-200 laserrange findersmountedinfrontand back. Eachhas a180 ◦ field of view,and is mounted on atilt mechanism with a60 ◦ range. Tilting each laser allows forthe acquisition of 3D range data. Groundhog has been used extensively in both testand abandoned mine environments, accruing hundreds of hours of mine navigation, including 8successful portal entry experiments in the abandonedMathiesmine outside of Pittsburgh, PA. Offline techniques have been used to generate globallyconsistent, large-scale maps based on log datafrom these experiments. Forathoroughoverview of the Groundhog system,see [2]. Topological Global Localization for Subterranean Voids 119 2.2 Topological Representations Topological representations coincide nicely with the inherent structure of room-and-pillar mines, which consist almost exclusively of narrow corridors and corridor intersections (see Figure 1). A topological map is a graph repre- sentation of an environment. The nodes of the graph correspond to distinct lo- cations in the environment, and the edges correspond to direct paths between two such locations. For mines, nodes and edges correspond to intersections and corridors, respectively. This approach was used in [10] to allow a robot to traverse known mine environments. Topological maps have also proven useful in robotic exploration tasks of unknown environments [9]. Unexplored edges in a topological map correspond to unexplored regions of the environment, thus providing a mechanism for determining which region of the environment to explore next. The key components of a system designed for autonomous topological exploration are: • A method for traversing an edge in the environment until a node is reached. • A method for detecting a node and its associated edges in the environment. • A method for determining whether the currently sensed node has been visited before, and if so which previously visited node it corresponds to (this is the problem our current work strives to solve). • A representation of the topological map and its associated uncertainty. The first two components have been previously developed and tested in sub- terranean environments, as described in the following sections. 2.3 Edge Traversal Edge traversal is the first necessary component for autonomous topological exploration. While traversing a single corridor, Groundhog utilizes the Sense- Plan-Act (SPA) framework. While stationary, Groundhog tilts one of its lasers to accumulate 3D range data from the space in front of it. This 3D point cloud is used to generate a 2.5D cost map. Next, a goal pose is chosen that will further Groundhog’s progress down the corridor (or turn it into a new corridor). A path is planned to the goal pose by feeding the cost map into a nonholonomic motion planner described in [13]. The planned path is then traversed by Groundhog, and the whole process repeated. For a more detailed description, see [2, 13]. 2.4 Node Detection A method for node detection is also critical to topological exploration. Groundhog detects intersections in its environment by searching for nodes of the generalized Voronoi diagram (GVD) [6]. Edges of the GVD represent sets of points equidistant from 2 objects. Nodes of the GVD represent points Fig. 2. Thedata collectedateachnode. Left: Groundhog approaching an inter- section. Center: the 2D range data collected, as well as the detected node location and radius. Right: the 3D range data collected. equidistantfrom 3objects. Whiletraversing an edge,potential GVD nodes are detectedusingaprocedure described in [15]. Each potential node is then trackeduntil Groundhogdrives throughthe intersection to whichthe node corresponds.The purposeofthis extra traverse is to obtain a2Dmap of the environmentaround the node with afull 360 ◦ coverage, as opposedtothe 180 ◦ field of view of Groundhog’s lasers. Suchcoverageisachieved by combining multiple laser scansfrom differentvantage points. This 360 ◦ coverageisnec- essary to determinewhetherthe intersectionjust traversedisworthexploring; if the end of acorridor is already withinsensor range from the intersection itself, it maynot be worth further exploration.This procedure alsoeliminates largeconcavities that can appear as intersections whenfirst detected. After anodehas been detected and verified,a3Dscan of theintersection is taken, and Groundhogcontinues its exploration. The Voronoiradius (equidistance value between thenodeand the objects that formed it), 2D map, and 3D scan (Figure 2) are all storedfor later use. 2.5 Framework for Topological Uncertainty Forsuccessful topological exploration, arobot must be abletodetermine if a given node has been previouslyvisited. This determination canbemadebased purely on the localtopology [7],orbycombining topological information with rangedata or dataonnearbyfeatures. The techniques described in this paper followthe latterapproach. Regardless of the specifics of the node matchingapproach, its output will be uncertain. There maybemultipleprevious nodes whichmatchthe current node closely enough to be considered apossiblematch, and thefact that the node maynever have been previously visited adds additionaluncertainty.A framework is necessary for dealing with this uncertainty until the ambiguity can be removed. Awidely adopted approach is to maintain multiple hypothe- sesastothe correcttopology of theenvironment [8, 11,16]. The robot can then either takeactions designed to explicityremove the ambiguity, or main- tainmultiple hypotheses until the natural explorationbehavior of therobot 120 D. Silver, J. Carsten, and S. Thayer Topological Global Localization for Subterranean Voids 121 produces enough additional information. In either case, the correct framework can add additional robustness on top of the chosen node matching scheme. 3Subterranean Node Matching We approachnodematching as atopological global localization problem. When arobot arrives at anode N i alongedge E i ,itcan localizeitself to adiscrete subset of all possible states in theworld(the set of states located at anode, oriented alonganedge). If the robot canproperly match N i and E i to apreviously visited N j and E j ,then it will have relocalized itself. If the robot canproperly determine that N i has not been visited before,itwill still have localized itself to the correct state, albeit astate thathas not previously been visited. To determine whether the current node N i matches aprevious node N j , we use ahybrid approach based on both localtopology and range data(Figure 3). Local topological dataisrarely descriptive enoughtodetermine explicitly whether twonodes match. However, it requiresessentially no preprocessing: it is computationally inexpensivetodetermine whether N i and N j are of the same degree. Forthis reason, localtopological dataisused to pare down the number of prospective matches. Forsimilarreasons, 2D as well as 3D range data is used. While 2D range data is usually not descriptiveenoughtomakeanexplicit determination, it is much cheaper to process than thefull 3D pointcloud,and can further pare down the number of prospective matches. 2D datahas anotheradvantageun- der our current setup: as described in Section 2.4,2Dinformation is collected afull 360 ◦ around theintersection. The additionalcoverage offered by 2D dataoften provesquite useful in determining final matches. Acommon approachfor determining whether arobot is revisiting alo- cation is to explicitly search for featuresinthe local environment, and try to matchthesefeatures to those that have been previously detected.How- ever, subterranean spaces provide aunique challenge for featureextraction. While suchspaces are oftenfeature rich,itishard to characterize thefeatures exhibited. Featurescan very greatly in both type and scale, and so amore robustapproach is needed. Forthis reason, our approachcompares nodes in a manner which does not require explicit extraction of predetermined features. 3.1Comparison of Topological Properties The first step of our node matching schemeistouse thetopological properties of thedetected node N i to eliminate as many nonmatching nodes N j as possi- ble. These topological properties are thedegree of the node and its associated Voronoiradius. Another property we explored wasthe relativeorientations of the edgesassociated withthe node. Previous work [12]has shown these relative orientations to be quite susceptible to noise. This lackofrobustness CompareNodes(N i ,N j ) : if N i . degree = N j . degree then return 0 d ← N i . degree if | N i . vRadius − N j . vRadius | >T d r then return 0 P 2 ← PositionOffsetBetweenNodes(N i ,N j ) R 2 ← MinimumErrorRotation(N i ,N j ,P 2 ) ( MSE 2 D ,P 2 ,R 2 ) ← TrICP2D(N i . 2 D, N j . 2 D, P 2 ,R 2 ) if MSE 2 D >T d e then return 0 ( MSE 3 D ,P 3 ,R 3 ) ← TrICP3D(N i . 3 D, N j . 3 D, P 2 ,R 2 ) E ← FormErrorVector(N i ,N j ,P 3 ,R 3 ) return LogisiticRegression(E, d ) Fig. 3. Pseudocode for our node matching procedure was also observed in our own experiments, and therefore this property was not used. Instead, if N j has a different degree than N i , or the difference in observed radii is more than a threshold T r , N j is eliminated as a candidate match. T r is set relatively high, so as to ensure that no correct matches are ever thrown out, while eliminating as many incorrect matches as possible in a computationally inexpensive manner. 3.2 2D Map Matching The next phase of node matching is to compare each node’s 2D local map. Before the 2D maps can be compared, they must be properly aligned. Align- ment of 2D point sets can be achieved using the Iterative Closest Point (ICP) algorithm [4]. ICP assumes that each point in the data set corresponds to the closest point in the model set. These correspondences are used to compute the transformation between the two sets that minimizes the Mean Squared Error (MSE). The correspondences are then recomputed, and the process iterates until convergence. Due to the manner in which our 2D maps are constructed, the assumption that every point in the data set has a corresponding point in the model set is often violated to a degree that degrades performance. Therefore, the Trimmed Iterative Closest Point algorithm (TrICP) [5] is used instead. The key differ- ence between ICP and TrICP is that TrICP assumes that only a proportion ξ of the points in the data set correspond to points in the model set. At each iteration, only ξK of the K points in the data set are used. The ξK points used are those with the smallest squared distance to their corresponding point in the model set. When unknown beforehand, ξ can be automatically set by minimizing the function ψ ( ξ ) = MSE ( ξ ) ξ − (1+λ ) (1) 122 D. Silver, J. Carsten, and S. Thayer [...]... the environment and does not compute any geometrical information While this work builds in part upon early experiments reported in [8] P Corke and S Sukkarieh (Eds.): Field and Service Robotics, STAR 25, pp 143 –1 54, 2006 © Springer-Verlag Berlin Heidelberg 2006 144 D Prasser, M Milford, and G Wyeth many aspects are new or greatly improved In particular the visual processing has been expanded to include... Driankov and A Saffiotti, editors Fuzzy Logic Techniques for Autonomous Vehicle Navigation Springer-Verlag, Berlin, Germany, 2001 3 E S Duff and J M Roberts Wall following with constrained active contours In 4th International Conference on Field and Service Robotics, July 1 4- 1 6 2003 4 E S Duff, J M Roberts, and P I Corke Automation of an underground mining vehicle using reactive navigation and opportunistic... Conference on Robotics and Automation, 2005 14 J Rossignac and P Borrel Multi-Resolution 3D Approximations for Rendering Complex Scenes., pages 45 5 46 5 Springer-Verlag, 1993 15 D Silver, D Ferguson, A Morris, and S Thayer Feature extraction for topological mine maps In IEEE/RSJ Conf on Intelligent Robots and Systems, 20 04 16 N Tomatis, I Nourbakhsh, and R Siegwart Hybrid simultaneous localization and map... tends to increase with tele-operation These facts have led to the desire to automate the whole P Corke and S Sukkarieh (Eds.): Field and Service Robotics, STAR 25, pp 129– 140 , 2006 © Springer-Verlag Berlin Heidelberg 2006 130 J Larsson, M Broxvall, and A Saffiotti Fig 1 Left: The ATRV-Jr research robot, carrying the two main sensors used in our experiments, the SICK laser scanner and the RFID tag reader... nextNode(j4) AND NOT oriented(t7) nextNode(j4) nextNode(j5) AND NOT oriented(t4) nextNode(j5) AND oriented(t4) nextNode() THEN THEN THEN THEN THEN THEN Avoid() Orient(t7) Follow(t7) Orient(t4) Follow(t4) Still() Avoid, Orient, Follow and Still are fuzzy behaviors, activated according to the fuzzy predicates obstacle near, nextNode and oriented j4, j5, t4 and t7 are control system representations of... In IEEE International Conference on Robotics and Automation, 20 04 12 B Lisien, D Morales, D Silver, G Kantor, I Rekleitis, and H Choset Hierarchical simultaneous localization and mapping In IEEE/RSJ Int Conference on Intelligent Robots and Systems, volume 1, pages 44 8 45 3, Oct 2003 13 A Morris, D Silver, D Ferguson, and S Thayer Towards topological exploration of abandoned mines In Proceedings of the... (ei ) = + N (ei , µ+ , σi ) i − + + N (ei , µi , σi ) + N (ei , µ− , σi ) i (4) + where µ+ and σi are the mean and standard deviation of the ith element i − of E over matches, µ− and σi are the mean and standard deviation over i non-matches, and N (e, µ, σ) is the Gaussian probability density function 4 Experimental Results 4. 1 Data Collection To test our node matching approach, data was collected from... 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