Modeling and Control of Robots on Rough Terrain

  • Keiji Nagatani
  • Genya Ishigami
  • Yoshito Okada
Part of the Springer Handbooks book series (SHB)


In this chapter, we introduce modeling and control for wheeled mobile robots and tracked vehicles. The target environment is rough terrains, which includes both deformable soil and heaps of rubble. Therefore, the topics are roughly divided into two categories, wheeled robots on deformable soil and tracked vehicles on heaps of rubble.

After providing an overview of this area in Sect. 50.1, a modeling method of wheeled robots on a deformable terrain is introduced in Sect. 50.2. It is based on terramechanics, which is the study focusing on the mechanical properties of natural rough terrain and its response to off-road vehicle, specifically the interaction between wheel/track and soil. In Sect. 50.3, the control of wheeled robots is introduced. A wheeled robot often experiences wheel slippage as well as its sideslip while traversing rough terrain. Therefore, the basic approach in this section is to compensate the slip via steering and driving maneuvers. In the case of navigation on heaps of rubble, tracked vehicles have much advantage. To improve traversability in such challenging environments, some tracked vehicles are equipped with subtracks, and one kinematical modeling method of tracked vehicle on rough terrain is introduced in Sect. 50.4. In addition, stability analysis of such vehicles is introduced in Sect. 50.5. Based on such kinematical model and stability analysis, a sensor-based control of tracked vehicle on rough terrain is introduced in Sect. 50.6. Sect. 50.7 summarizes this chapter.


Mobile Robot Slip Ratio Rough Terrain Visual Odometry Terrain Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



center of gravity


discrete element method


Deutsches Zentrum für Luft- und Raumfahrt


degree of freedom


energy stability margin


finite element method


inertial measurement unit


Japan Aerospace Exploration Agency


light detection and ranging


Massachusetts Institute of Technology


normalized ESM




soil contact model


simultaneous localization and mapping


unmanned ground vehicle


  1. 50.1
    M. Jurkat, C. Nuttall, P. Haley: The AMC' 74 Mobility Model, Tech. Rep. 11921 (US Army Tank Automotive Command, Warren, 1975)Google Scholar
  2. 50.2
    R.B. Ahlvin, P.W. Haley: NATO Reference Mobility Model Edition II, NRMM User's Guide, Tech. Rep. GL-92-19 (US Army WES, Vicksburg, 1992)Google Scholar
  3. 50.3
    A. Gibbesch, B. Schäfer: Multibody system modelling and simulation of planetary rover mobility on soft terrain, 8th Int. Symp. Artif. Intell. Robotics Autom. Space (i-SAIRAS), Munich (2005)Google Scholar
  4. 50.4
    R. Krenn, A. Gibbesch, G. Hirzinger: Contact dynamics simulation of rover locomotion, Proc. 9th Int. Symp. on Artif. Intell., Robotics Autom. Space, Los Angeles (2007)Google Scholar
  5. 50.5
    D. Holz, A. Azimi, M. Teichmann, J. Kövecses: Mobility prediction of rovers on soft terrain: Effects of wheel- and tool-induced terrain deformations, Proc. 15th Int. Conf. Climbing Walk. Robots Support Technol. Mob. Mach. (CLAWAR) (2012)Google Scholar
  6. 50.6
    J.Y. Wong: Theory of Ground Vehicles (Wiley, New York 1978)Google Scholar
  7. 50.7
    M. Buehler, K. Iagnemma, S. Singh (Eds.): The 2005 DARPA Grand Challenge: The Great Robot Race Springer Tracts Adv. Robotics Ser, Vol. 36 (Springer, Berlin, Heidelberg 2005)Google Scholar
  8. 50.8
    M. Buehler, K. Iagnemma, S. Singh (Eds.): The DARPA Urban Challenge: Autonomous Vehicles in City Traffic, Springer Tracts Adv. Robotics, Vol. 56 (Springer, Berlin, Heidelberg 2009)Google Scholar
  9. 50.9
    C. Li, T. Zhang, D.I. Goldman: A terradynamics of legged locomotion on granular media, Science 339, 1408–1412 (2013)CrossRefGoogle Scholar
  10. 50.10
    C. de Wit, H. Khennouf, C. Samson, O. Sordalen: Nonlinear control design for mobile robots. In: Recent Trends in Mobile Robots, World Scientific Series in Robotics and Automated System, Vol. 11, ed. by Y. Zheng (World Scientific, Singapore 1993)Google Scholar
  11. 50.11
    A. Luca, G. Oriolo, C. Samson: Feedback control of nonholonomic car-like robots. In: Robot Motion Planning and Control, ed. by J. Laumond (Springer, Berlin, Heidelberg 1998) pp. 171–254CrossRefGoogle Scholar
  12. 50.12
    F. Rio, G. Jimenez, J. Sevillano, S. Vicente, A. Balcells: A generalization of path following for mobile robots, Proc. 1999 IEEE Int. Conf. Robotics Autom. (ICRA), Detroit (1999) pp. 7–12Google Scholar
  13. 50.13
    S. Rezaei, J. Guivant, E. Nebot: Car-like robot path following in large unstructured environments, Proc. IEEE Int. Conf. Intell. Robots Syst. (IROS) (2003) pp. 2468–2473Google Scholar
  14. 50.14
    P. Coelho, U. Nunes: Path-following control of mobile robots in presence of uncertainties, IEEE Trans. Robotics 21(2), 252–261 (2005)CrossRefGoogle Scholar
  15. 50.15
    D. Helmick, Y. Cheng, D. Clouse, L. Matthies, S. Roumeliotis: Path following using visual odometry for a Mars rover in high-slip environments, Proc. 2004 IEEE Aerosp. Conf., Big Sky (2004) pp. 772–789Google Scholar
  16. 50.16
    D. Helmick, S. Roumeliotis, Y. Cheng, D. Clouse, M. Bajracharya, L. Matthies: Slip-compensated path following for planetary exploration rovers, Adv. Robotics 20(11), 1257–1280 (2006)CrossRefGoogle Scholar
  17. 50.17
    G. Ishigami, K. Nagatani, K. Yoshida: Slope traversal controls for planetary exploration rover on sandy terrain, J. Field Robotics 26(3), 264–286 (2009)CrossRefGoogle Scholar
  18. 50.18
    D.A. Messuri, C.A. Klein: Automatic body regulation for maintaining stability of a legged vehicle during rough-terrain locomotion, IEEE J. Robotics Autom. 1(3), 132–141 (1985)CrossRefGoogle Scholar
  19. 50.19
    S. Hirose, H. Tsukagoshi, K. Yoneda: Normalized energy stability margin and its contour of walking vehicles on rough terrain, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2001) pp. 181–186Google Scholar
  20. 50.20
    E. Magid, T. Tsubouchi, E. Koyanagi, T. Yoshida, S. Tadokoro: Controlled balance losing in random step environment for path planning of a teleoperated crawler-type vehicle, J. Field Robotics 28(6), 932–949 (2011)CrossRefGoogle Scholar
  21. 50.21
    A. Jacoff, E. Messina, B.A. Weiss, S. Tadokoro, Y. Nakagawa: Test arenas and performance metrics for urban search and rescue robots, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS), Las Vegas (2003) pp. 3396–3403Google Scholar
  22. 50.22
    K. Ohno, V. Chun, T. Yuzawa, E. Takeuchi, S. Tadokoro, T. Yoshida, E. Koyanagi: Rollover avoidance using a stability margin for a tracked vehicle with sub-tracks, IEEE Int. Workshop Saf. Sec. Rescue Robotics (2009)Google Scholar
  23. 50.23
    N. Vandapel, D. Huber, A. Kapuria, M. Hebert: Natural terrain classification using 3-D ladar data, Proc. IEEE Int. Conf. Robotics Autom. (ICRA), Vol. 5 (2004) pp. 5117–5122Google Scholar
  24. 50.24
    M. Onosato, S. Yamamoto, M. Kawajiri, F. Tanaka: Digital gareki archives: An approach to know more about collapsed houses for supporting search and rescue activities, IEEE Int. Symp. Saf. Secur. Rescue Robotics (SSRR) (2012) pp. 1–6Google Scholar
  25. 50.25
    A. Lacaze, K. Murphy, M. Del Giorno: Autonomous mobility for the demo III experimental unmanned vehicles, AUVS Int. Conf. Unnanned Veh. (2002)Google Scholar
  26. 50.26
    K. Ohno, T. Suzuki, K. Higashi, M. Tsubota, E. Takeuchi, S. Tadokoro: Classification of 3-D point cloud data that includes line and frame objects on the basis of geometrical features and the pass rate of laser rays, Proc. 8th Int. Conf. Field Serv. Robotics (2012)Google Scholar
  27. 50.27
    M. Onosato, T. Watasue: Two attempts at linking robots with disaster information: InfoBalloon and gareki engineering, Adv. Robotics 16(6), 545–548 (2002)CrossRefGoogle Scholar
  28. 50.28
    M. Onosato: Digital GAREKI modeling for exploring knowledge of disaster-collapsed houses, IEEE Int. Workshop Saf. Secur. Rescue Robotics (SSRR) (2006)Google Scholar
  29. 50.29
    L. Woosub, K. Sungchul, K. Munsang, P. Mignon: ROBHAZ-DT3: Teleoperated mobile platform with passively adaptive double-track for hazardous environment applications, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2004) pp. 33–38Google Scholar
  30. 50.30
    B. Yamauchi: Packbot: A versatile platform for military robotics, Proc. SPIE 5422, 228–237 (2004)CrossRefGoogle Scholar
  31. 50.31
    D. Inoue, K. Ohno, S. Nakamura, S. Tadokoro, E. Koyanagi: Whole-body touch sensors for tracked mobile robots using force-sensitive chain guides, IEEE Int. Workshop Saf. Secur. Rescue Robotics (SSRR) (2008) pp. 71–76Google Scholar
  32. 50.32
    A. Jain, J. Balaram, J. Cameron, J. Guineau, C. Lim, M. Pornerantz, G. Sohl: Recent developments in the ROAMS planetary rover simulation environment, Proc. 2004 IEEE Aerosp. Conf., Big Sky (2004) pp. 861–876Google Scholar
  33. 50.33
    K. Iagnemma, C. Senatore, B. Trease, R. Arvidson, A. Shaw, F. Zhou, L. Van Dyke, R. Lindemann: Terramechanics modeling of mars surface exploration rovers for simulation and parameter estimation, ASME Int. Des. Eng. Tech. Conf. (2011)Google Scholar
  34. 50.34
    R. Bauer, W. Leung, T. Barfoot: Development of a dynamic simulation tool for the exomars rover, Proc. 8th Int. Symp. Artif. Intell., Robotics Autom. Space, Munich (2005)Google Scholar
  35. 50.35
    M.G. Bekker: Theory of Land Locomotion (Univ. Michigan Press, Ann Arbor 1956)Google Scholar
  36. 50.36
    M.G. Bekker: Introduction to Terrain-Vehicle Systems (Univ. Michigan Press, Ann Arbor 1969)Google Scholar
  37. 50.37
    J.Y. Wong: Theory of Ground Vehicles, 4th edn. (Wiley, Hoboken 2008)Google Scholar
  38. 50.38
    J.Y. Wong, A.R. Reece: Prediction of rigid wheel performance based on the analysis of soil-wheel stresses – Part I: Performance of driven rigid wheels, J. Terramechanics 4(1), 81–98 (1967)CrossRefGoogle Scholar
  39. 50.39
    J.Y. Wong, A.R. Reece: Prediction of rigid wheel performance based on the analysis of soil-wheel stresses – Part II: Performance of towed rigid wheels, J. Terramechanics 4(2), 7–25 (1967)CrossRefGoogle Scholar
  40. 50.40
    I.C. Schmid: Interaction of vehicle and terrain results from 10 years research at IKK, J. Terramechanics 32(1), 3–25 (1995)CrossRefGoogle Scholar
  41. 50.41
    L. Ding, Z. Deng, H. Gao, K. Nagatani, K. Yoshida: Planetary rovers' wheel-soil interaction mechanics: New challenges and applications for wheeled mobile robots, Intell. Serv. Robotics 4(1), 17–38 (2010)CrossRefGoogle Scholar
  42. 50.42
    H. Nakashima, H. Fujii, A. Oida, M. Momozu, Y. Kawase, H. Kanamori, S. Aoki, T. Yokoyama: Parametric analysis of lugged wheel performance for a lunar microrover by means of DEM, J. Terramechanics 44, 153–162 (2007)CrossRefGoogle Scholar
  43. 50.43
    H. Nakashima, H. Fujii, A. Oida, M. Momozu, H. Kanamori, S. Aoki, T. Yokoyama, H. Shimizu, J. Miyasaka, K. Ohdoi: Discrete element method analysis of single wheel performance for a small lunar rover on sloped terrain, J. Terramechanics 47, 307–321 (2010)CrossRefGoogle Scholar
  44. 50.44
    W. Li, Y. Huang, Y. Cui, S. Dong, J. Wang: Trafficability analysis of lunar mare terrain by means of the discrete element method for wheeled rover locomotion, J. Terramechanics 47, 161–172 (2010)CrossRefGoogle Scholar
  45. 50.45
    K. Iagnemma: A Laboratory single wheel testbed for studying planetary rover wheel-terrain interaction, Tech. Rep. 01-05-05 (MIT, Cambridge 2005)Google Scholar
  46. 50.46
    S. Wakabayashi, H. Sato, S. Nishida: Design and mobility evaluation of tracked lunar vehicle, J. Terramechanics 46(3), 105–114 (2009)CrossRefGoogle Scholar
  47. 50.47
    N. Patel, R. Slade, J. Clemmet: The ExoMars rover locomotion subsystem, J. Terramechanics 47, 227–242 (2010)CrossRefGoogle Scholar
  48. 50.48
    G. Ishigami, A. Miwa, K. Nagatani, K. Yoshida: Terramechanics-based model for steering maneuver of planetary exploration rovers on loose soil, J. Field Robotics 24(3), 233–250 (2007)CrossRefGoogle Scholar
  49. 50.49
    R. Lindemann, D. Bickler, B. Harrington, G. Ortiz, C. Voorhees: Mars exploration rover mobility development, IEEE Robotics Autom. Mag. 13(2), 19–26 (2006)CrossRefGoogle Scholar
  50. 50.50
    G. Ishigami, A. Miwa, K. Nagatani, K. Yoshida: Terramechanics-based analysis on slope traversability for a planetary exploration rover, Proc. 25th Int. Symp. Space Technol. Sci. (2006) pp. 1025–1030Google Scholar
  51. 50.51
    S. Michaud, L. Richter, T. Thueer, A. Gibbesch, T. Huelsing, N. Schmitz, S. Weiss, A. Krebs, N. Patel, L. Joudrier, R. Siegwart, B. Schäfer, A. Ellery: Rover chassis evaluation and design optimisation using the RCET, Proc. 9th ESA Workshop Adv. Space Technol. Robotics Autom. (ASTRA) (2006)Google Scholar
  52. 50.52
    K. Nagatani, A. Ikeda, K. Sato, K. Yoshida: Accurate estimation of drawbar pull of wheeled mobile robots traversing sandy terrain using built-in force sensor array wheel, Proc. 2009 IEEE/RSJ Int. Conf. Robots Syst. (IROS), St. Loius (2009) pp. 2373–2378CrossRefGoogle Scholar
  53. 50.53
    G. Meirion-Griffith, M. Spenko: A Modified pressure-sinkage model for small, rigid wheels on deformable terrains, J. Terramechanics 48(2), 149–155 (2011)CrossRefGoogle Scholar
  54. 50.54
    C. Senatore, K. Iagnemma: Direct shear behaviour of dry, granular soils for low normal stress with application to lightweight robotic vehicle modeling, 17th Conf. Terrain-Veh. Syst. (ISTVS), Blacksburg (2011)Google Scholar
  55. 50.55
    K. Iagnemma, S. Kang, H. Shibly, S. Dubowsky: Online terrain parameter estimation for wheeled mobile robots with application to planetary rovers, IEEE Trans. Robotics 20(5), 921–927 (2004)CrossRefGoogle Scholar
  56. 50.56
    S. Hutangkabodee, Y. Zweiri, L. Seneviratne, K. Althoefer: Soil parameter identification for wheel-terrain interaction dynamics and traversability prediction, Int. J. Autom. Comput. 3(3), 244–251 (2006)CrossRefGoogle Scholar
  57. 50.57
    D. Helmick, A. Angelova, L. Matthies, C. Brooks, I. Halatci, S. Dubowsky, K. Iagnemma: Experimental results from a terrain adaptive navigation system for planetary rovers, Proc. 9th Int. Symp. Artif. Intell., Robotics Autom. Space (i-SAIRAS), Hollywood (2008)Google Scholar
  58. 50.58
    G. Ishigami, G. Kewlani, K. Iagnemma: A statistical approach to mobility prediction for planetary surface exploration rovers in uncertain terrain, IEEE Robotics Autom. Mag. 16(4), 61–70 (2009)CrossRefGoogle Scholar
  59. 50.59
    O. Yoshito, K. Nagatani, K. Yoshida, S. Tadokoro, T. Yoshida, E. Koyanagi: Shared autonomy system for traversing and turning tracked vehicles on rough terrain based on continuous three-dimensional terrain scanning, J. Field Robotics 28(6), 875–893 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Aerospace Engineering, Graduate School of EngineeringTohoku UniversitySendaiJapan
  2. 2.Department of Mechanical EngineeringKeio UniversityYokohamaJapan

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