, Volume 51, Issue 5, pp 1227–1243 | Cite as

Dynamic single actuator robot climbing a chute

Period-doubling bifurcations: analysis and experiments


The planar mechanism analyzed in this paper, called DSAC for Dynamic, Single Actuated Climber, comprises only two links connected by a single oscillating actuator. This simple open loop motion propels the robot stably between two vertical walls. We explore the local orbital stability of the DSAC mechanism. Using the Poincaré map, we reduce the analyzed dimension and find the stable regions while varying the control inputs and mechanism’s parameters. Moreover, in response to a continuous change of a parameter of the mechanism, the symmetric and steady stable gait of the mechanism gradually evolves through a regime of period doubling bifurcations. This investigation includes numerical approximation of the local stability, and basin of attraction. Finally, the paper reports experimental results of open-loop, stable climbing in a planar, reduced gravity environment undergoing bifurcations which correlate well to the numerical analysis.


Stance Phase Period Doubling Period Doubling Bifurcation Zero Moment Point Wall Width 
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.



The author would like to thank Matthew T. Mason, Howie Choset, Kevin Lynch, and Andy Ruina for their guidance and suggestions and Siyuan Feng for his help with the design and experiments.

Supplementary material

11012_2015_286_MOESM1_ESM.mpg (15.5 mb)
Supplementary material 1 (MPG 15836 kb)


  1. 1.
    Autumn K, Buehler M, Cutkosky M, Fearing R, Full RJ, Goldman D, Groff R, Provancher W, Rizzi AA, Saranli U, Saunders A, Koditschek DE (2005) Robotics in scansorial environments. In: Proceedings of SPIE vol 5804 unmanned ground vehicle technology VII, pp 291–302Google Scholar
  2. 2.
    Berkemeier MD, Fearing RS (1998) Sliding and hopping gaits for the underactuated acrobot. IEEE Trans Robot Autom 14(4):629–634CrossRefGoogle Scholar
  3. 3.
    Bretl T (2006) Motion planning of multi-limbed robots subject to equilibrium constraints: the free-climbing robot problem. Int J Robot Res 25(4):317–342CrossRefGoogle Scholar
  4. 4.
    Canny J, Goldberg K (1995) A RISC approach to sensing and manipulation. J Robot Syst 12(6):351–363Google Scholar
  5. 5.
    Colett JS, Hurst JW (2012) Artificial restraint systems for walking and running robots: an overview. Int J Hum Robot 9:1250001. doi: 10.1142/S0219843612500016
  6. 6.
    Collins SH, Wisse M, Ruina A (2001) A three-dimensional passive-dynamic walking robot with two legs and knees. Int J Robot Res 20(7):607–615CrossRefGoogle Scholar
  7. 7.
    Degani A, Choset H, Mason MT (2010) DSAC—dynamic, single actuated climber: local stability and bifurcations. In: Robotics and automation (ICRA), 2010 IEEE international conference on, pp 2803–2809Google Scholar
  8. 8.
    Degani A, Shapiro A, Choset H, Mason MT (2007) A dynamic single actuator vertical climbing robot. In: Proceedings of IEEE/RSJ international conference on intelligent robots and systems (IROS’07)Google Scholar
  9. 9.
    Dullin H (1994) Melnikov’s method applied to the double pendulum. Zeitschrift fur Phys B Condens Matter 93(4):521–528ADSCrossRefGoogle Scholar
  10. 10.
    Erdmann MA, Mason MT (1988) An exploration of sensorless manipulation. IEEE Trans Robot Autom 4(4):369–379CrossRefGoogle Scholar
  11. 11.
    Garcia M, Chatterjee A, Ruina A, Coleman M (1998) The simplest walking model: stability, complexity, and scaling. J Biomech Eng 120(2):281–288CrossRefGoogle Scholar
  12. 12.
    Goswami A, Thuilot B, Espiau B (1998) A study of the passive gait of a compass-like biped robot: symmetry and chaos. Int J Robot Res 17(12):1282CrossRefGoogle Scholar
  13. 13.
    Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer, New YorkCrossRefMATHGoogle Scholar
  14. 14.
    Hsu C (1997) Cell-to-cell mapping: a method of global analysis for nonlinear systems. Springer, New YorkGoogle Scholar
  15. 15.
    Kato I, Ohteru S, Kobayashi H, Shirai K, Uchiyama A (1974) Information-power machine with senses and limbs. In: First CISM-IFToMM symposium on theory and practice of robots and manipulators. Springer-VerlagGoogle Scholar
  16. 16.
    Longo D, Muscato G (2006) The Alicia\(^3\) climbing robot. IEEE Robot Autom Mag 13:2–10CrossRefGoogle Scholar
  17. 17.
    Lynch GA, Clark JE, Lin PC, Koditschek DE (2012) A bioinspired dynamical vertical climbing robot. Int J Robot Res 31(8):974–996Google Scholar
  18. 18.
    Lynch KM, Mason MT (1999) Dynamic nonprehensile manipulation: controllability, planning, and experiments. Int J Robot Res 18(1):64–92Google Scholar
  19. 19.
    McGeer T (1990) Passive dynamic walking. Int J Robot Res 9(2):62–82CrossRefGoogle Scholar
  20. 20.
    Moon JS, Spong MW (2011) Classification of periodic and chaotic passive limit cycles for a compass-gait biped with gait asymmetries. Robotica 29:967–974CrossRefGoogle Scholar
  21. 21.
    NaturalPoint\(^{\rm TM}\): optitrack camera system. Retrieved from (2014)
  22. 22.
    Nayfeh A, Balachandran B (1995) Applied nonlinear dynamics. Wiley, New YorkCrossRefMATHGoogle Scholar
  23. 23.
    Provancher W, Jensen-Segal S, Fehlberg M (2011) ROCR: an energy-efficient dynamic wall-climbing robot. Mech IEEE/ASME Trans 16(5):897–906CrossRefGoogle Scholar
  24. 24.
    Raibert MH (1986) Legged robots balance. The MIT Press, CambridgeMATHGoogle Scholar
  25. 25.
    Schwab A, Wisse M (2001) Basin of attraction of the simplest walking model. In: Proceedings of the ASME design engineering technical conference 6:531–539Google Scholar
  26. 26.
    Takanishi A, Naito G, Ishida M, Kato I (1985) Realization of plane walking by the biped walking robot WL-10R. In: Morecki A, Bianchi G, Kȩdzior K (eds) Theory and practice of robots and manipulators. Springer, pp 383–393. doi: 10.1007/978-1-4615-9882-4_40
  27. 27.
    M, D A contribution to the synthesis of biped gait. In: IFAC symposium technical and biological problem on control. Erevan, USSRGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Faculty of Civil and Environmental EngineeringTechnion - Israel Institute of TechnologyHaifaIsrael

Personalised recommendations