Journal of Intelligent & Robotic Systems

, Volume 93, Issue 3–4, pp 461–494 | Cite as

Towards Autonomous Planetary Exploration

The Lightweight Rover Unit (LRU), its Success in the SpaceBotCamp Challenge, and Beyond
  • Martin J. SchusterEmail author
  • Sebastian G. Brunner
  • Kristin Bussmann
  • Stefan Büttner
  • Andreas Dömel
  • Matthias Hellerer
  • Hannah Lehner
  • Peter Lehner
  • Oliver Porges
  • Josef Reill
  • Sebastian Riedel
  • Mallikarjuna Vayugundla
  • Bernhard Vodermayer
  • Tim Bodenmüller
  • Christoph Brand
  • Werner Friedl
  • Iris Grixa
  • Heiko Hirschmüller
  • Michael Kaßecker
  • Zoltán-Csaba Márton
  • Christian Nissler
  • Felix Ruess
  • Michael Suppa
  • Armin Wedler
Open Access


Planetary exploration poses many challenges for a robot system: From weight and size constraints to extraterrestrial environment conditions, which constrain the suitable sensors and actuators. As the distance to other planets introduces a significant communication delay, the efficient operation of a robot system requires a high level of autonomy. In this work, we present our Lightweight Rover Unit (LRU), a small and agile rover prototype that we designed for the challenges of planetary exploration. Its locomotion system with individually steered wheels allows for high maneuverability in rough terrain and stereo cameras as its main sensors ensure the applicability to space missions. We implemented software components for self-localization in GPS-denied environments, autonomous exploration and mapping as well as computer vision, planning and control modules for the autonomous localization, pickup and assembly of objects with its manipulator. Additional high-level mission control components facilitate both autonomous behavior and remote monitoring of the system state over a delayed communication link. We successfully demonstrated the autonomous capabilities of our LRU at the SpaceBotCamp challenge, a national robotics contest with focus on autonomous planetary exploration. A robot had to autonomously explore an unknown Moon-like rough terrain, locate and collect two objects and assemble them after transport to a third object – which the LRU did on its first try, in half of the time and fully autonomously. The next milestone for our ongoing LRU development is an upcoming planetary exploration analogue mission to perform scientific experiments at a Moon analogue site located on a volcano.


Autonomous mobile robots Planetary exploration Robotic challenge Navigation Manipulation Autonomous task execution 

Mathematics Subject Classification (2010)

68T40 70B15 93C85 68T45 



We thank the members of the Mobile Robots Group at DLR-RMC, especially Annika Maier, Bertram Willberg, Florian Schmidt and Philipp Lutz as well as our system administrators, in particular Stefan Engelhardt and Stefan von Dombrowski for their assistance. We thank Dr. Máximo A. Roa, Prof. Michael Beetz PhD, PD Dr. habil. Rudolph Triebel and Prof. Dr. Alin Albu-Schäffer for their support and many valuable discussions. We thank the anonymous reviewers for their insightful comments and suggestions.

Funding Information

This work was supported by the Helmholtz Association, project alliance ROBEX (contract number HA-304) and partially funded by the DLR Space Administration.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.

Supplementary material

(MP4 292 MB)


  1. 1.
    ROBEX - Robotic Exploration of Extreme Environments. Accessed 30 Aug 2016
  2. 2.
    DLR SpaceBot Camp. (2015). Accessed 31 Aug 2016
  3. 3.
    DLR SpaceBot Camp 2015 - Weltraumroboter live erleben. (2015). Accessed 30 Aug 2016
  4. 4.
    DARPA Robotics Challenge. (2016). Accessed 30 Aug 2016
  5. 5.
    Demo-Missions - ROBEX. (2016). Accessed 24 Aug 2016
  6. 6.
    Google Lunar XPRIZE. (2016). Accessed 30 Aug 2016
  7. 7.
    Lunar Reconnaissance Orbiter Camera. (2016). Accessed 24 Aug 2016
  8. 8.
    Manipulation - Kinova. (2016). Accessed 30 Aug 2016
  9. 9.
    Mission to the Moon. (2016). Accessed 30 Aug 2016
  10. 10.
    Mosh: the mobile shell. (2016). Accessed 30 Aug 2016
  11. 11.
    Products - F&P. (2016). Accessed 30 Aug 2016
  12. 12.
    ROBEX Field Trip - ROBEX. (2016). Accessed 24 Aug 2016
  13. 13.
    Albu-Schäffer, A., Ott, C., Hirzinger, G.: A unified passivity-based control framework for position, torque and impedance control of flexible joint robots. Int. J. Robot. Res. 26(1), 23–39 (2007)CrossRefzbMATHGoogle Scholar
  14. 14.
    Avsar, C., Frese, W., Meschede, T., Brieß, K.: Developing a planetary rover with students: Space education at TU Berlin. J. Autom. Mob. Robot. Intell. Syst., 8 (2014)Google Scholar
  15. 15.
    Beetz, M., Jain, D., Mȯsenlechner, L., Tenorth, M., Kunze, L., Blodow, N., Pangercic, D.: Cognition-enabled autonomous robot control for the realization of home chore task intelligence. Proc. IEEE 100(8), 2454–2471 (2012)CrossRefGoogle Scholar
  16. 16.
    Brand, C., Schuster, M.J., Hirschmüller, H., Suppa, M.: Stereo-vision based obstacle mapping for indoor/outdoor SLAM. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1846–1853. IEEE, Chicago (2014),
  17. 17.
    Brand, C., Schuster, M.J., Hirschmüller, H., Suppa, M.: Submap matching for stereo-vision based indoor/outdoor SLAM. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 5093–5100. IEEE, Hamburg (2015),
  18. 18.
    Brooks, R.A.: Intelligence without representation. Artif. Intell. 47(1-3), 139–159 (1991)CrossRefGoogle Scholar
  19. 19.
    Brunner, S.G., Steinmetz, F., Belder, R., Doemel, A.: RAFCON: A graphical tool for engineering complex, robotic tasks. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Deajeon (2016)Google Scholar
  20. 20.
    Brunner, S.G., Steinmetz, F., Belder, R., Dömel, A.: RAFCON: A graphical tool for task programming and mission control. In: RoboCup 2016: Robot Soccer World Cup XX, Lecture Notes in Computer Science. Springer, Leipzig (2016)Google Scholar
  21. 21.
    Büttner, S., Márton, Z.C., Hertkorn, K.: Automatic scene parsing for generic object descriptions using shape primitives. Robot. Auton. Syst. 76, 93–112 (2016). CrossRefGoogle Scholar
  22. 22.
    Byrne, C.: The Moon’s Near Side Megabasin and Far Side Bulge, 1st edn. Springer-Verlag, New York (2013)CrossRefGoogle Scholar
  23. 23.
    Czeluschke, A., Knapmeyer, M., Sohl, F., Bamberg, M., Lange, C., Luther, R., Margonis, A., Rosta, R., Schmitz, N.: Robex Asn study team: The ROBEX-ASN - a concept study for an active seismic network on the moon. In: European Planetary Science Congress 2014 (EPSC), vol. 9, pp. EPSC2014–728. Cascais, (2014)Google Scholar
  24. 24.
    Diankov, R., Kuffner, J.: OpenRAVE: A Planning Architecture for Autonomous Robotics. Robotics Institute, Pittsburgh. Tech. Rep. CMU-RI-TR-08-34, Pittsburgh (2008)Google Scholar
  25. 25.
    Dietrich, A., Wimböck, T., Albu-Schäffer, A., Hirzinger, G.: Reactive whole-body control: Dynamic mobile manipulation using a large number of actuated degrees of freedom. IEEE Robot. Autom. Mag. 19(2), 20–33 (2012)CrossRefGoogle Scholar
  26. 26.
    Eich, M., Hartanto, R., Kasperski, S., Natarajan, S., Wollenberg, J.: Towards coordinated multirobot missions for lunar sample collection in an unknown environment. J. Field Robot. R. 31(1). (2014)
  27. 27.
    Gonzalez-Banos, H.H., Latombe, J.C.: Navigation strategies for exploring indoor environments. Int. J. Robot. Res. 21(10–11), 829–848 (2002)CrossRefGoogle Scholar
  28. 28.
    Grotzinger, J.P., et al.: Mars science laboratory mission and science investigation. Space Sci. Rev. 170(1), 5–56 (2012)CrossRefGoogle Scholar
  29. 29.
    Haarmann, R., Hofmann, P., Richter, L., Claasen, F., Apfelbeck, M., Klinkner, S., Schwendner, J.: Mobile Payload Element (MPE): concept study for a sample fetching rover for the ESA Lunar Lander Mission. Planet. Space Sci. 74(1), 283–295 (2012)CrossRefGoogle Scholar
  30. 30.
    Hellerer, M., Bellmann, T., Schlegel, F.: The DLR visualization library - recent development and applications. In: Proceedings of the 10th International Modelica Conference, pp. 899–911. Linköping University Electronic Press; Linköpings universitet, Lund (2014),
  31. 31.
    Hellerer, M., Schuster, M.J., Lichtenheldt, R.: Software-in-the-loop simulation of a planetary rover. In: The International Symposium on Artificial Intelligence, Robotics and Automation in Space (i-SAIRAS). Beijing (2016)Google Scholar
  32. 32.
    Heppner, G., Roennau, A., Oberländer, J., Klemm, S., Dillmann, R.: Laurope - six legged walking robot for planetary exploration participating in the spacebot cup. In: International Conference on Automation and Robotics in Space (ASTRA). Noordwijk (2015)Google Scholar
  33. 33.
    Hirschmüller, H.: Stereo processing by semiglobal matching and mutual information. IEEE Trans. Pattern Anal. Mach. Intell. (TPAMI) 30(2), 328–341 (2008)CrossRefGoogle Scholar
  34. 34.
    Hirschmüller, H., Innocent, P.R., Garibaldi, J.M.: Fast, unconstrained camera motion estimation from stereo without tracking and robust statistics. In: International Conference on Control, Automation, Robotics and Vision (ICARCV). Singapore. (2002)
  35. 35.
    Hirzinger, G., Sporer, N., Albu-Schaffer, A., Hahnle, M., Krenn, R., Pascucci, A., Schedl, M.: Dlr’s torque-controlled light weight robot III-are we reaching the technological limits now?. In: IEEE International conference on robotics and automation (ICRA), vol. 2, pp. 1710–1716. IEEE (2002)Google Scholar
  36. 36.
    Holz, D., Basilico, N., Amigoni, F., Behnke, S.: Evaluating the efficiency of frontier-based exploration strategies. In: International Symposium on Robotics (ISR) and the German Conference on Robotics (ROBOTIK). VDE, Munich (2010)Google Scholar
  37. 37.
    Holz, D., Behnke, S.: Registration of non-uniform density 3D point clouds using approximate surface reconstruction. In: International Symposium on Robotics (ISR) and the German Conference on Robotics (ROBOTIK), Munich (2014)Google Scholar
  38. 38.
    Hornung, A., Wurm, K.M., Bennewitz, M., Stachniss, C., Burgard, W.: OctoMap: An efficient probabilistic 3D mapping framework based on octrees. Auton. Robot. Software available at (2013)
  39. 39.
    Jennings, E., Seguí, J., Gao, J., Clare, L., Abraham, D.: The impact of traffic prioritization on deep space network mission traffic. In: IEEE Aerospace Conference (2011)Google Scholar
  40. 40.
    Kaess, M., Johannsson, H., Roberts, R., Ila, V., Leonard, J.J., Dellaert, F.: iSAM2 : Incremental smoothing and mapping using the Bayes tree. Int. J. Robot. Res. 31, 217–236 (2012)CrossRefGoogle Scholar
  41. 41.
    Klem, S.M., Henriksen, M.R., Stopar, J., Boyd, A., Robinson, M.S.: Controlled LROC narrow angle camera high resolution mosaics. In: Lunar Planetary Science Conference. The Woodlands (2014)Google Scholar
  42. 42.
    Kriegel, S., Rink, C., Bodenmüller, T., Suppa, M.: Efficient next-best-scan planning for autonomous 3D surface reconstruction of unknown objects. J. Real-Time Image Process. 10(4), 611–631 (2015). CrossRefGoogle Scholar
  43. 43.
    Kubota, T., Otsuki, M., Shimada, T., Kuroda, Y., Kunii, Y.: Test-beds rovers for planetary surface exploration. In: International Symposium on Artificial Intelligence, Robotics and Automation in Space (i-SAIRAS). Turin (2012)Google Scholar
  44. 44.
    LaValle, S.M., Kuffner, J.J. Jr: Rapidly-exploring random trees: Progress and Prospects. Algorithmic and Computational Robotics: New Directions pp. 293—308 (2000)Google Scholar
  45. 45.
    Lichtenheldt, R., Hellerer, M., Barthelmes, S., Buse, F.: Heterogeneous , multi-tier wheel ground contact simulation for planetary exploration. In: ECCOMAS Thematic Conference on Multibody Dynamics. Barcelona (2015)Google Scholar
  46. 46.
    Maimone, M., Johnson, A., Cheng, Y., Willson, R., Matthies, L.E.M.H., Khatib, O.: Experimental Robotics IX, chap. Autonomous Navigation Results from the Mars Exploration Rover (MER) Mission, pp. 3–13. Springer, Berlin (2006)Google Scholar
  47. 47.
    Ott, C.: Cartesian Impedance Control of Redundant and Flexible-Joint Robots, Spr. Tra. Adv. Robot, vol. 49. Springer, Berlin (2008)Google Scholar
  48. 48.
    Porges, O., Stouraitis, T., Borst, C., Roa, M.A.: Reachability and capability analysis for manipulation tasks. In: ROBOT2013: First Iberian Robotics Conference, pp. 703–718. Springer, Madrid (2014)Google Scholar
  49. 49.
    Quigley, M., Conley, K., Gerkey, B., Faust, J., Foote, T., Leibs, J., Wheeler, R., Ng, A.Y.: ROS: An open-source robot operating system. In: Workshop on Open Source Software (ICRA), vol. 3, p. 5. Kobe, Japan (2009)Google Scholar
  50. 50.
    Reill, J., Sedlmayr, H.J., Kuß, S., Neugebauer, P., Maier, M., Gibbesch, A., Schäfer, B., Albu-Schäffer, A.: Development of a mobility drive unit for low gravity planetary body exploration. In: Symposium on Advanced Space Technologies in Robotics and Automation (ASTRA). Noordwijk (2013)Google Scholar
  51. 51.
    Reill, J., Sedlmayr, H.J., Neugebauer, P., Maier, M., Krämer, E., Lichtenheldt, R.: MASCOT - asteroid lander with innovative mobility mechanism. In: Symposium on Advanced Space Technologies in Robotics and Automation (ASTRA). Noordwijk (2015)Google Scholar
  52. 52.
    Rusu, R.B., Cousins, S.: 3D is here: Point Cloud Library (PCL). In: IEEE International Conference on Robotics and Automation (ICRA). Shanghai (2011)Google Scholar
  53. 53.
    Schadler, M., Stückler, J., Behnke, S.: Data set Spacebot Arena. Accessed 30 Aug 2016 (2014)
  54. 54.
    Schaub, A., Hellerer, M., Bodenmu̇ller, T.: Simulation of artificial intelligence agents using Modelica and the DLR visualization library. In: International Modelica Conference. Fu̇rstenfeldbruck (2012)Google Scholar
  55. 55.
    Schmid, K., Ruess, F., Burschka, D.: Local reference filter for life-long vision aided inertial navigation. In: International Conference on Information Fusion (FUSION). IEEE, Madrid (2014)Google Scholar
  56. 56.
    Schmid, K., Ruess, F., Suppa, M., Burschka, D.: State estimation for highly dynamic flying systems using key frame Odometry with varying time delays. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Vilamoura (2012)Google Scholar
  57. 57.
    Schneider, F.E., Wildermuth, D., Wolf, H.L.: ELROB and EURATHLON: Improving search & rescue robotics through real-world robot competitions. In: International Workshop on Robot Motion and Control (RoMoCo), pp. 118–123. IEEE, Poznan (2015)Google Scholar
  58. 58.
    Schuster, M.J., Brand, C., Brunner, S.G., Lehner, P., Reill, J., Riedel, S., Bodenmüller, T., Bussmann, K., Büttner, S., Dömel, A., Friedl, W., Grixa, I., Hellerer, M., Hirschmüller, H., Kassecker, M., Márton, Z.C., Nissler, C., Ruess, F., Suppa, M., Wedler, A.: The LRU rover for autonomous planetary exploration and its success in the SpaceBotCamp challenge. In: IEEE International Conference on Autonomous Robot Systems and Competitions (ICARSC). Bragança (2016)Google Scholar
  59. 59.
    Schuster, M. J., Brand, C., Hirschmüller, H., Suppa, M., Beetz, M.: Multi-Robot 6D graph SLAM connecting decoupled local reference filters. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Hamburg (2015)Google Scholar
  60. 60.
    Schwendner, J., Röhr, T., Haase, S., Wirkus, M., Manz, M., Arnold, S., Machowinski, J.: The artemis rover as an example for model based engineering in space robotics. In: Workshop Proceedings of the IEEE International Conference on Robotics and Automation (ICRA). Hong Kong (2014)Google Scholar
  61. 61.
    Senarathne, P.G.C.N., Wang, D: Frontier based exploration with task cancellation. In: IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), pp. 1–6. IEEE, Toyako-cho (2014)Google Scholar
  62. 62.
    Sentis, L., Khatib, O.: Synthesis of whole-body behaviors through hierarchical control of behavioral primitives. Int. J. Hum. Robot. 2(4), 505–518 (2005)CrossRefGoogle Scholar
  63. 63.
    Shreiner, D.: OpenGL programming guide: The official guide to learning openGL, Versions 3.0 and 3.1, 7th edn. Addison-Wesley Professional (2009)Google Scholar
  64. 64.
    Strobl, K.H., Hirzinger, G.: Optimal hand-eye calibration. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Beijing (2006)Google Scholar
  65. 65.
    Stückler, J., Schwarz, M., Schadler, M., Topalidou-Kyniazopoulou, A., Behnke, S.: NimbRo Explorer: Semi-autonomous exploration and mobile manipulation in rough terrain. J. Field Robot. (2015)Google Scholar
  66. 66.
    Sünderhauf, N., Neubert, P., Truschzinski, M., Wunschel, D., Pöschmann, J., Lange, S., Protzel, P.: Phobos and Deimos on mars - two autonomous robots for the DLR SpaceBot cup. In: Proceedings of International Symposium on Artificial Intelligence, Robotics and Automation in Space (iSAIRAS). Montreal (2014)Google Scholar
  67. 67.
    Thrun, S., Montemerlo, M., Dahlkamp, H., Stavens, D., Aron, A., Diebel, J., Fong, P., Gale, J., Halpenny, M., Hoffmann, G.: Stanley: The robot that won the DARPA grand challenge. J. Field Robot. 23(9), 661–692 (2006)CrossRefGoogle Scholar
  68. 68.
    Tran, T., Rosiek, M.R., Beyer, R.A., Mattson, S., Howington-Kraus, E., Robinson, M.S., Archinal, B.A., Edmundson, K., Harbour, D., Anderson, E.: Generating digital terrain models using LROC NAC images. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences (ISPRS Archives), 38 (2010)Google Scholar
  69. 69.
    Washington, R., Golden, K., Bresina, J., Smith, D., Anderson, C., Smith, T.: Autonomous rovers for mars exploration. In: IEEE Aerospace Conference, vol. 1. Snowmass at Aspen (1999)Google Scholar
  70. 70.
    Wedler, A., Chalon, M., Landzettel, K., Gȯrner, M., Krȧmer, E., Gruber, R., Beyer, A., Sedlmayr, H.J., Willberg, B., Wieland, B., Reill, J., Grebenstein, M., Schedl, M., Albu-Schȧffer, A., Hirzinger, G.: DLR’s dynamic actuator modules for robotic space applications. In: Aerospace Mechanisms Symposium. Passadena - Hilton -JPL (2012)Google Scholar
  71. 71.
    Wedler, A., Maier, A., Reill, J., Brand, C., Hirschmüller, H., Schuster, M.J., Suppa, M., Beyer, A., Lii, N.Y., Maier, M., Sedlmayr, H.J., Haarmann, R.: Pan/Tilt-Unit as a perception module for extra-terrestrial vehicle and landing systems. In: Symposium on Advanced Space Technologies in Robotics and Automation (ASTRA). Noordwijk (2013)Google Scholar
  72. 72.
    Wedler, A., Rebele, B., Reill, J., Suppa, M., Hirschmüller, H., Brand, C., Schuster, M., Vodermayer, B., Gmeiner, H., Maier, A., Willberg, B., Bussmann, K., Wappler, F., Hellerer, M., Lichtenheldt, R.: LRU - lightweight rover unit. In: Symposium on Advanced Space Technologies in Robotics and Automation (ASTRA). Noordwijk (2015)Google Scholar
  73. 73.
    Wettergreen, D., Wagner, M., Jonak, D., Baskaran, V., Deans, M., Heys, S., Pane, D., Smith, T., Teza, J., Thompson, D.R., Tompkins, P., Williams, C.: Long-distance autonomous survey and mapping in the robotic investigation of life in the atacama desert. In: Proceedings of International Symposium on Artificial Intelligence, Robotics and Automation in Space (iSAIRAS). Hollywood (2008)Google Scholar
  74. 74.
    Yamauchi, B.: Frontier-based exploration using multiple robots. In: Int. Conf. Autonom. Agents, pp. 47–53. ACM, Minuenpolis (1998)Google Scholar
  75. 75.
    Zacharias, F., Borst, C., Hirzinger, G.: Capturing robot workspace structure: Representing robot capabilities. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 3229–3236, San Diego (2007),
  76. 76.
    Ziegler, J., Bender, P., Schreiber, M., Lategahn, H., Strauss, T., Stiller, C., Dang, T., Franke, U., Appenrodt, N., Keller, C.G., Kaus, E., Herrtwich, R.G., Rabe, C., Pfeiffer, D., Lindner, F., Stein, F., Erbs, F., Enzweiler, M., Knöppel, C., Hipp, J., Haueis, M., Trepte, M., Brenk, C., Tamke, A., Hanaat, M. G., Braun, M., Joos, A., Fritz, H., Mock, H., Hein, M., Zeeb, E.: Making bertha drive - an autonomous journey on a historic route. IEEE Intell. Transp. Syst. Mag. 6(2), 8–20 (2014)CrossRefGoogle Scholar

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Authors and Affiliations

  • Martin J. Schuster
    • 1
    Email author
  • Sebastian G. Brunner
    • 1
  • Kristin Bussmann
    • 1
  • Stefan Büttner
    • 1
  • Andreas Dömel
    • 1
  • Matthias Hellerer
    • 2
  • Hannah Lehner
    • 1
  • Peter Lehner
    • 1
  • Oliver Porges
    • 1
  • Josef Reill
    • 1
  • Sebastian Riedel
    • 1
  • Mallikarjuna Vayugundla
    • 1
  • Bernhard Vodermayer
    • 1
  • Tim Bodenmüller
    • 1
  • Christoph Brand
    • 1
  • Werner Friedl
    • 1
  • Iris Grixa
    • 1
  • Heiko Hirschmüller
    • 3
  • Michael Kaßecker
    • 1
  • Zoltán-Csaba Márton
    • 1
  • Christian Nissler
    • 1
  • Felix Ruess
    • 3
  • Michael Suppa
    • 3
  • Armin Wedler
    • 1
  1. 1.Robotics and Mechatronics Center (RMC), Institute of Robotics and MechatronicsGerman Aerospace Center (DLR)WeßlingGermany
  2. 2.Robotics and Mechatronics Center (RMC), Institute of System Dynamics and ControlGerman Aerospace Center (DLR)WeßlingGermany
  3. 3.Roboception GmbHMünchenGermany

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