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World Modeling

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Springer Handbook of Robotics

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Abstract

In this chapter we describe popular ways to represent the environment of a mobile robot. For indoor environments, which are often stored using two-dimensional representations, we discuss occupancy grids, line maps, topological maps, and landmark-based representations. Each of these techniques has its own advantages and disadvantages. Whilst occupancy grid maps allow for quick access and can efficiently be updated, line maps are more compact. Also landmark-based maps can efficiently be updated and maintained, however, they do not readily support navigation tasks such as path planning like topological representations do.

Additionally, we discuss approaches suited for outdoor terrain modeling. In outdoor environments, the flat-surface assumption underling many mapping techniques for indoor environments is no longer valid. A very popular approach in this context are elevation and variants maps, which store the surface of the terrain over a regularly spaced grid. Alternatives to such maps are point clouds, meshes, or three-dimensional grids, which provide a greater flexibility but have higher storage demands.

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Abbreviations

2-D:

two-dimensional

2.5-D:

two-and-a-half-dimensional

3-D:

three-dimensional

EKF:

extended Kalman filter

EM:

expectation maximization

SLAM:

simultaneous localization and mapping

References

  1. H.P. Moravec, A.E. Elfes: High resolution maps from wide angle sonar, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (1985)

    Google Scholar 

  2. H. Choset, K. Lynch, S. Hutchinson, G. Kantor, W. Burgard, L. Kavraki, S. Thrun: Principles of Robot Motion: Theory, Algorithms and Implementation (MIT Press, Cambridge 2005)

    MATH  Google Scholar 

  3. D.H. Douglas, T.K. Peucker: Algorithms for the reduction of the number of points required to represent a line or its caricature, Cdn. Cartogr. 10(2), 112–122 (1973)

    Article  Google Scholar 

  4. D. Sack, W. Burgard: A comparison of methods for line extraction from range data, Proc. IFAC Symp. Intell. Auton. Veh. (IAV) (2004)

    Google Scholar 

  5. P. Beeson, N.K. Jong, B. Kuipers: Towards autonomous topological place detection using the extended Voronoi graph, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2005)

    Google Scholar 

  6. M. Montemerlo, S. Thrun, D. Koller, B. Wegbreit: FastSLAM: A factored solution to the simultaneous localization and mapping problem, Proc. Nat. Conf. Artif. Intell. (AAAI) (2002)

    Google Scholar 

  7. B.J. Kuipers, Y.-T. Byun: A robust qualitative method for spatial learning in unknown environments, Proc. Nat. Conf. Artif. Intell. (AAAI) (1988)

    Google Scholar 

  8. H. Choset, K. Nagatani: Topological simultaneous localization and mapping (SLAM): Toward exact localization without explicit localization, IEEE Trans. Robotics Autom. 17(2), 125–137 (2001)

    Article  Google Scholar 

  9. S. Thrun: Robotic mapping: A survey. In: Exploring Artificial Intelligence in the New Millenium, ed. by G. Lakemeyer, B. Nebel (Morgan Kaufmann, San Diego 2003)

    Google Scholar 

  10. M. Maimone, P. Leger, J. Biesiadecki: Overview of the Mars exploration rovers’ autonomous mobility and vision capabilities, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2007)

    Google Scholar 

  11. S. Lacroix, A. Mallet, D. Bonnafous, G. Bauzil, S. Fleury, M. Herrb, R. Chatila: Autonomous rover navigation on unknown terrains: functions and integration, Int. J. Robotics Res. 21(10-11), 917–942 (2002)

    Article  Google Scholar 

  12. R. Olea: Geostatistics for Engineers and Earth Scientists (Kluwer, Boston 1999)

    Book  Google Scholar 

  13. A. Kelly, A. Stentz, O. Amidi, M. Bode, D. Bradley, A. Diaz-Calderon, M. Happold, H. Herman, R. Mandelbaum, T. Pilarki, P. Rander, S. Thayer, N. Vallidi, R. Warner: Toward reliable off road autonomous vehicles operating in challenging environments, Int. J. Robotics Res. 25(5-6), 449–483 (2006)

    Article  Google Scholar 

  14. I.S. Kweon, T. Kanade: High-resolution terrain map from multiple sensor data, IEEE Trans. Pattern Anal. Mach. Intell. 14(2), 278–292 (1992)

    Article  Google Scholar 

  15. M. Montemerlo, S. Thrun: A multi-resolution pyramid for outdoor robot terrain perception, Proc. AAAI Nat. Conf. Artif. Intel., San Jose (2004)

    Google Scholar 

  16. R. Triebel, P. Pfaff, W. Burgard: Multi-level surface maps for outdoor terrain mapping and loop closing, Proc. IEEE/RSJ Int. Conf. Intell. Robotics Syst. (IROS) (2006)

    Google Scholar 

  17. C. Wellington, A. Courville, A. Stentz: A generative model of terrain for autonomous navigation in vegetation, Int. J. Robotics Res. 25(12), 1287–1304 (2006)

    Article  Google Scholar 

  18. P. Pfaff, R. Triebel, W. Burgard: An efficient extension to elevation maps for outdoor terrain mapping and loop closing, Int. J. Robotics Res. 26(2), 217–230 (2007)

    Article  Google Scholar 

  19. D.M. Cole, P.M. Newman: Using laser range data for 3D SLAM in outdoor environments, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2006)

    Google Scholar 

  20. A. Nüchter, K. Lingemann, J. Hertzberg, H. Surmann: 6D SLAM – 3D mapping outdoor environments: Research articles, J. Field Robotics 24(8–9), 699–722 (2007)

    Article  MATH  Google Scholar 

  21. J. Elseberg, D. Borrmann, A. Nüchter: Efficient processing of large 3D point clouds, Proc. 23rd Int. Symp. Infor. Commun. Autom. Technol. (ICAT) (2011)

    Google Scholar 

  22. R.B. Rusu, S. Cousins: 3D is here: Point cloud library (PCL), Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2011)

    Google Scholar 

  23. N. Fairfield, G. Kantor, D. Wettergreen: Real-time SLAM with octree evidence grids for exploration in underwater tunnels, J. Field Robotics 24(1), 3–21 (2007)

    Article  Google Scholar 

  24. A. Foessel: Scene Modeling from Motion-Free Radar Sensing, Ph.D. Thesis (Carnegie Mellon Univ., Pittsburgh 2002)

    Google Scholar 

  25. K.M. Wurm, A. Hornung, M. Bennewitz, C. Stachniss, W. Burgard: OctoMap: A probabilistic, flexible, and compact 3D map representation for robotic systems, Proc. ICRA Workshop Best Pract. 3D Percept. Model. Mob. Manip. (2010)

    Google Scholar 

  26. J.-F. Lalonde, N. Vandapel, M. Hebert: Data structure for efficient processing in 3-D, Proc. Robotics Sci. Syst., Vol. I (2005) p. 48

    Google Scholar 

  27. A. Hornung, K.M. Wurm, M. Bennewitz, C. Stachniss, W. Burgard: OctoMap: An efficient probabilistic 3D mapping framework based on octrees, Auton. Robots 34(3), 189–206 (2013)

    Article  Google Scholar 

  28. K.M. Wurm, D. Hennes, D. Holz, R.B. Rusu, C. Stachniss, K. Konolige, W. Burgard: Hierarchies of octrees for efficient 3D mapping, Proc. IEEE/RSJ Int Conf. Intell. Robots Syst. (IROS) (2011)

    Google Scholar 

  29. L. Heng, L. Meier, P. Tanskanen, F. Fraundorfer, M. Pollefeys: Autonomous obstacle avoidance and maneuvering on a vision-guided MAV using on-board processing, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2011)

    Google Scholar 

  30. S. Oßwald, A. Hornung, M. Bennewitz: Improved proposals for highly accurate localization using range and vision data, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2012)

    Google Scholar 

  31. M. Ciocarlie, K. Hsiao, E.G. Jones, S. Chitta, R.B. Rusu, I.A. Sucan: Towards reliable grasping and manipulation in household environments, Int. Symp. Exp. Robotics (ISER) (2010)

    Google Scholar 

  32. A. Hornung, M. Phillips, E.G. Jones, M. Bennewitz, M. Likhachev, S. Chitta: Navigation in three-dimensional cluttered environments for mobile manipulation, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2012)

    Google Scholar 

  33. J. Leal: Stochastic Environment Representation, Ph.D. Thesis (Univ. of Sydney, Sydney 2003)

    Google Scholar 

  34. P. Heckbert, M. Garland: Optimal triangulation and quadric-based surface simplification, J. Comput. Geom. Theory Appl. 14(1-3), 49–65 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  35. A. Akbarzadeh: Towards urban 3d reconstruction from video, Proc. Int. Symp. 3D Data Vis. Transm. (2006)

    Google Scholar 

  36. C. Frueh, S. Jain, A. Zakhor: Data processing algorithms for generating textured 3d building facade meshes from laser scans and camera images, Int. J. Comput. Vis. 61(2), 159–184 (2005)

    Article  Google Scholar 

  37. I. Stamos, P. Allen: Geometry and texture recovery of scenes of large scales, Comput. Vis. Image Underst. 88, 94–118 (2002)

    Article  MATH  Google Scholar 

  38. D. Gennery: Traversability analysis and path planning for a planetary rover, Auton. Robotics 6, 131–146 (1999)

    Article  Google Scholar 

  39. D. Ferguson, A. Stentz: The delayed D* algorithm for efficient path replanning, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2005)

    Google Scholar 

  40. D. Ferguson, A. Stentz: Field D*: An interpolation-based path planner and replanner, Proc. Int. Symp. Robotics Res. (ISRR) (2005)

    Google Scholar 

  41. M. Likhachev, D. Ferguson, G. Gordon, A. Stentz, S. Thrun: Anytime dynamic A*: An anytime, replanning algorithm, Proc. Int. Conf. Autom. Plan. Sched. (ICAPS) (2005)

    Google Scholar 

  42. B. Sofman, E. Lin, J. Bagnell, J. Cole, N. Vandapel, A. Stentz: Improving robot navigation through self-supervised online learning, J. Field Robotics 23(12), 1059–1075 (2006)

    Article  Google Scholar 

  43. D. Stavens, S. Thrun: A self-supervised terrain roughness estimator for off-road autonomous driving, Uncertainty Artif. Intell., Boston (2006)

    Google Scholar 

  44. A. Angelova, L. Matthies, D. Helmick, P. Perona: Slip prediction using visual information, Robotics Sci. Syst., Philadelphia (2006)

    Google Scholar 

  45. D. Kim, J. Sun, S. Oh, J. Rehg, A. Bobick: Traversability classification using unsupervised on-line visual learning for outdoor robot navigation, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2006)

    Google Scholar 

  46. S. Thrun, M. Montemerlo, A. Aron: Probabilistic terrain analysis for high-speed desert driving, Robotics Sci. Syst. (2005)

    Google Scholar 

  47. R. Murrieta-Cid, C. Parra, M. Devy: Visual navigation in natural environments: From range and color data to a landmark-based model, Auton. Robotics 13(2), 143–168 (2002)

    Article  MATH  Google Scholar 

  48. D. Asmar, J. Zelek, S. Abdallah: Tree trunks as landmarks for outdoor vision SLAM, Proc. Conf. Comp. Vis. Pattern Recogn. Workshop (2006)

    Google Scholar 

  49. I. Posner, D. Schroeter, P. Newman: Using scene similarity for place labelling, Int. Symp. Exp. Robotics (2006)

    Google Scholar 

  50. A. Torralba, K.P. Murphy, W.T. Freeman, M.A. Rubin: Context-based vision system for place and object recognition, Proc. IEEE Int. Conf. Comput. Vis. (ICCV) (2003)

    Google Scholar 

  51. D. Bradley, S. Thayer, A. Stentz, P. Rander: Vegetation Detection for Mobile Robot Navigation, Tech. Rep. CMU-RI-TR-04-12 (Carnegie Mellon Univ., Pittsburgh 2004)

    Google Scholar 

  52. S. Kumar, J. Guivant, H. Durrant-Whyte: Informative representations of unstructured environments, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2004)

    Google Scholar 

  53. S. Kumar, F. Ramos, B. Douillard, M. Ridley, H. Durrant-Whyte: A novel visual perception framework, Proc. 9th Int. Conf. Control Autom. Robotics Vis. (ICARCV) (2006)

    Google Scholar 

  54. F. Ramos, S. Kumar, B. Upcroft, H. Durrant-Whyte: Representing natural objects in unstructured environments, NIPS Workshop Mach. Learn. Robotics (2005)

    Google Scholar 

  55. C. Pantofaru, R. Unnikrishnan, M. Hebert: Toward generating labeled maps from color and range data for robot navigation, Proc. IEEE/RSJ Int. Conf. Intell. Robotics Syst. (2003)

    Google Scholar 

  56. D. Anguelov, B. Taskar, V. Chatalbashev, D. Koller, D. Gupta, G. Heitz, A. Ng: Discriminative learning of Markov random fields for segmentation of 3D scan data, Proc. Conf. Comp. Vis. Pattern Recogn. (CVPR) (2005)

    Google Scholar 

  57. R. Triebel, K. Kersting, W. Burgard: Robust 3D scan point classification using associative Markov networks, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2006)

    Google Scholar 

  58. J.F. Lalonde, N. Vandapel, D. Huber, M. Hebert: Natural terrain classification using three-dimensional ladar data for ground robot mobility, J. Field Robotics 23(10), 839–861 (2006)

    Article  Google Scholar 

  59. M. Devy, R. Chatila, P. Fillatreau, S. Lacroix, F. Nashashibi: On autonomous navigation in a natural environment, Robotics Auton. Syst. 16(1), 5–16 (1995)

    Article  Google Scholar 

  60. R. Manduchi, A. Castano, A. Talukder, L. Matthies: Obstacle detection and terrain classification for autonomous off-road navigation, Auton. Robotics 18(1), 81–102 (2005)

    Article  Google Scholar 

  61. D. Huber, M. Hebert: 3D modeling using a statistical sensor model and stochastic search, Proc. IEEE Conf. Comput. Vision Pattern Recogn. (CVPR) (2003) pp. 858–865

    Google Scholar 

  62. S. Balakirsky, A. Lacaze: World modeling and behavior generation for autonomous ground vehicles, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2000)

    Google Scholar 

  63. A. Lacaze, K. Murphy, M. Delgiorno: Autonomous mobility for the demo III experimental unmanned vehicles, Proc. AUVSI Int. Conf. Unmanned Veh. (2002)

    Google Scholar 

  64. P. Bellutta, R. Manduchi, L. Matthies, K. Owens, A. Rankin: Terrain perception for demo III, Proc. Intell. Veh. Symp. (2000)

    Google Scholar 

  65. J.F. Lalonde, R. Unnikrishnan, N. Vandapel, M. Hebert: Scale selection for classification of point-sampled 3D surfaces, Proc. 5th Int. Conf. 3-D Digital Imaging Model. (3DIM) (2005)

    Google Scholar 

  66. J. Macedo, R. Manduchi, L. Matthies: Ladar-based discrimination of grass from obstacles for autonomous navigation, Proc. 7th Int. Symp. Exp. Robotics (ISER) (2000)

    Google Scholar 

  67. H. Chen, P. Meer, D. Tyler: Robust regression for data with multiple structures, Proc. IEEE Int. Conf. Comput. Vis. Pattern Recogn. (CVPR) (2001)

    Google Scholar 

  68. R. Unnikrishnan, M. Hebert: Robust extraction of multiple structures from non-uniformly sampled data, Proc. IEEE/RSJ Int. Conf. Intell. Robotics Syst. (IROS) (2003)

    Google Scholar 

  69. D. Wolf, G. Sukhatme, D. Fox, W. Burgard: Autonomous terrain mapping and classification using hidden Markov models, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2005)

    Google Scholar 

  70. C. Olson, L. Matthies, J. Wright, R. Li, K. Di: Visual terrain mapping for Mars exploration, Comput. Vis. Underst. 105, 73–85 (2007)

    Article  Google Scholar 

  71. J. Nieto, J. Guivant, E. Nebot: The hybrid metric maps (hymms): A novel map representation for denseSLAM, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2004)

    Google Scholar 

  72. F. Ramos, J. Nieto, H. Durrant-Whyte: Recognising and modelling landmarks to close loops in outdoor SLAM, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2007)

    Google Scholar 

  73. D. Hähnel, D. Schulz, W. Burgard: Mobile robot mapping in populated environments, Adv. Robotics 17(7), 579–598 (2003)

    Article  Google Scholar 

  74. C.-C. Wang, C. Thorpe, S. Thrun: Online simultaneous localization and mapping with detection and tracking of moving objects: Theory and results from a ground vehicle in crowded urban areas, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2003)

    Google Scholar 

  75. P. Biber, T. Duckett: Dynamic maps for long-term operation of mobile service robots, Proc. Robotics Sci. Syst. (2005)

    Google Scholar 

  76. D. Meyer-Delius, J. Hess, G. Grisetti, W. Burgard: Temporary maps for robust localization in semi-static environments, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS), Taipei (2010)

    Google Scholar 

  77. C. Stachniss, W. Burgard: Mobile robot mapping and localization in non-static environments, Proc. Nat. Conf. Artif. Intell. (AAAI), Pittsburgh (2005)

    Google Scholar 

  78. D. Hähnel, R. Triebel, W. Burgard, S. Thrun: Map building with mobile robots in dynamic environments, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2003)

    Google Scholar 

  79. R. Siegwart, I. Nourbakhsh: Introduction to Autonomous Mobile Robots (MIT Press, Cambridge 2001)

    Google Scholar 

  80. S. Thrun, W. Burgard, D. Fox: Probabilistic Robotics (MIT Press, Cambridge 2005)

    MATH  Google Scholar 

  81. H. Samet: Foundations of Multidimensional and Metric Data Structures (Elsevier, Amsterdam 2006)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Freiburg, Georges-Koehler-Allee 79, 79110, Freiburg, Germany

    Wolfram Burgard

  2. The Robotics Institute, Carnegie Mellon University, 5000 Forbes Avenue, PA 15213, Pittsburgh, USA

    Martial Hebert

  3. Institute for Computer Science VI, University of Bonn, Friedrich-Ebert-Allee 144, 53113, Bonn, Germany

    Maren Bennewitz

Authors
  1. Wolfram Burgard
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  2. Martial Hebert
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  3. Maren Bennewitz
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Corresponding author

Correspondence to Wolfram Burgard .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Naples Federico II, Via Claudio 21, 80125, Naples, Italy

    Bruno Siciliano

  2. Department of Computer Sciences, Artificial Intelligence Laboratory, Stanford University, 450 Serra Mall, CA 94305, Stanford, USA

    Oussama Khatib

Video-References

Video-References

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OctoMap visualization available from http://handbookofrobotics.org/view-chapter/45/videodetails/79

:

3-D textured model of urban environments available from http://handbookofrobotics.org/view-chapter/45/videodetails/269

:

Service robot navigation in urban environments available from http://handbookofrobotics.org/view-chapter/45/videodetails/270

:

Learning navigation cost grids available from http://handbookofrobotics.org/view-chapter/45/videodetails/271

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Burgard, W., Hebert, M., Bennewitz, M. (2016). World Modeling. In: Siciliano, B., Khatib, O. (eds) Springer Handbook of Robotics. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-319-32552-1_45

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