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Minimalistic control of biped walking in rough terrain

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Abstract

Toward our comprehensive understanding of legged locomotion in animals and machines, the compass gait model has been intensively studied for a systematic investigation of complex biped locomotion dynamics. While most of the previous studies focused only on the locomotion on flat surfaces, in this article, we tackle with the problem of bipedal locomotion in rough terrains by using a minimalistic control architecture for the compass gait walking model. This controller utilizes an open-loop sinusoidal oscillation of hip motor, which induces basic walking stability without sensory feedback. A set of simulation analyses show that the underlying mechanism lies in the “phase locking” mechanism that compensates phase delays between mechanical dynamics and the open-loop motor oscillation resulting in a relatively large basin of attraction in dynamic bipedal walking. By exploiting this mechanism, we also explain how the basin of attraction can be controlled by manipulating the parameters of oscillator not only on a flat terrain but also in various inclined slopes. Based on the simulation analysis, the proposed controller is implemented in a real-world robotic platform to confirm the plausibility of the approach. In addition, by using these basic principles of self-stability and gait variability, we demonstrate how the proposed controller can be extended with a simple sensory feedback such that the robot is able to control gait patterns autonomously for traversing a rough terrain.

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References

  • Adamczyk, P. G., Collins, S. H., & Kuo, A. D. (2006). The advantages of a rolling foot in human walking. Journal of Experimental Biology, 209, 3953–3963.

    Article  Google Scholar 

  • Aoi, S., & Tsuchiya, K. (2005). Locomotion control of biped robot using nonlinear oscillators. Autonomous Robots, 19, 219–232.

    Article  Google Scholar 

  • Aoi, S., & Tsuchiya, K. (2006). Stability analysis of a simple walking model driven by an oscillator with a phase reset using sensory feedback. IEEE Transactions on Robotics, 22(2), 391–397.

    Article  Google Scholar 

  • Aoi, S., & Tsuchiya, K. (2007). Self-stability of a simple walking model driven by a rhythmic signal. Nonlinear Dynamics, 48(1), 1–16.

    Article  MATH  MathSciNet  Google Scholar 

  • Asano, F., Yamakita, M., & Furuta, K. (2000). Virtual passive dynamic walking and energy-based control laws. In IEEE/RSJ international conference on intelligent robots and systems (IROS 2000) (pp. 1149–1154).

  • Asano, F., Yamakita, M., Kamamichi, N., & Luo, Z.-W. (2004). A novel gait generation for biped walking robots based on mechanical energy constraint. IEEE Transactions on Robotics and Automation, 20(3), 565–573.

    Article  Google Scholar 

  • Asano, F., Hayashi, T., Luo, Z. W., Hirano, S., & Kato, A. (2007). Parametric excitation approaches to efficient dynamic bipedal walking. In Proc. of the IEEE/RSJ int. conf. on intelligent robots and systems (pp. 2210–2216).

  • Byl, K., & Tedrake, R. (2008a). Approximate optimal control of the compass gait on rough terrain. In Proceedings IEEE international conference on robotics and automation (ICRA) (pp. 1258–1263).

  • Byl, K., & Tedrake, R. (2008b). Metastable walking machines. International Journal of Robotics Research, 28(8), 1040–1064.

    Google Scholar 

  • Collins, S. H., Wisse, M., & Ruina, A. (2001). A three-dimensional passive-dynamic walking robot with two legs and knees. International Journal of Robotics Research, 20, 607–615.

    Article  Google Scholar 

  • Collins, S. H., Ruina, A., Tedrake, R., & Wisse, M. (2005). Efficient bipedal robots based on passive-dynamic walkers. Science, 307, 1082–1085.

    Article  Google Scholar 

  • Garcia, M., Chatterjee, A., Ruina, A., & Coleman, M. (1998). The simplest walking model: stability, complexity, and scaling. Journal of Biomechanical Engineering. Transactions of the ASME, 120(2), 281–288.

    Article  Google Scholar 

  • Goswami, A., Espiau, B., & Keramane, A. (1997). Limit cycles in a passive compass gait biped and passivity-mimicking control laws. Autonomous Robots, 4, 273–286.

    Article  Google Scholar 

  • Goswami, A., Thuilot, B., & Espiau, B. (1998). A study of the passive gait of a compass-like biped robot: symmetry and chaos. International Journal of Robotics Research, 17(12), 1282–1301.

    Article  Google Scholar 

  • Harata, Y., Asano, F., Luo, Z. W., Taji, K., & Uno, Y. (2007). Biped gait generation based on parametric excitation by knee-joint actuation. In Proc. of the IEEE/RSJ int. conf. on intelligent robots and systems (pp. 2198–2203).

  • Hass, J., Herrmann, J. M., & Geisel, T. (2006). Optimal mass distribution for passivity-based bipedal robots. International Journal of Robotics Research, 25(11), 1087–1098.

    Article  Google Scholar 

  • Hobbelen, D. G. E., & Wisse, M. (2008). Swing-leg retraction for limit cycle walkers improves disturbance rejection. IEEE Transactions on Robotics, 24(2), 377–389.

    Article  Google Scholar 

  • Iida, F., & Tedrake, R. (2009). Minimalistic control of a compass gait robot in rough terrain. In International conference on robotics and automation (ICRA 09) (pp. 1985–1990).

  • Iida, F., Rummel, J., & Seyfarth, A. (2008). Bipedal walking and running with spring-like biarticular muscles. Journal of Biomechanics, 41, 656–667.

    Article  Google Scholar 

  • Ijspeert, A. J. (2008). Central pattern generators for locomotion control in animals and robots: a review. Neural Networks, 21(4), 642–653.

    Article  Google Scholar 

  • Kajita, S., & Espiau, B. (2008). Legged robots. In B. Siciliano & O. Khatib (Eds.), Springer handbook of robotics (pp. 361–389). Berlin: Springer.

    Chapter  Google Scholar 

  • Kim, J., Choi, C., & Spong, M. (2007). Passive dynamic walking with symmetric fixed flat feet. In International conference on control and automation (pp. 24–30).

  • Kinugasa, T., Miwa, S., & Yoshida, K. (2008). Frequency analysis for biped walking via leg length variation. Robotics and Mechatronics, 20(1), 98–104.

    Google Scholar 

  • Kuo, A. D. (1999). Stabilization of lateral motion in passive dynamic walking. International Journal of Robotics Research, 18(9), 917–930.

    Article  Google Scholar 

  • Kuo, A. D. (2002). Energetics of actively powered locomotion using the simplest walking model. Journal of Biomechanical Engineering, 124, 113–120.

    Article  Google Scholar 

  • Kurz, M. J., & Stergiou, N. (2005). An artificial neural network that utilizes hip joint actuations to control bifurcations and chaos in a passive dynamic bipedal walking model. Biological Cybernetics, 93, 213–221.

    Article  MATH  Google Scholar 

  • Kwan, M., & Hubbard, M. (2007). Optimal foot shape for a passive dynamic biped. Journal of Theoretical Biology, 248, 331–339.

    Article  Google Scholar 

  • Manchester, I. R., Mettin, U., Iida, F., & Tedrake, R. (2009, in press). Stable dynamic walking over rough terrain: theory and experiment. In Proceedings of the international symposium on robotics research (ISRR2009).

  • Manoonpong, P., Geng, T., Kulvicius, T., Porr, B., & Wörgötter, F. (2007). Adaptive, fast walking in a biped robot under neuronal control and learning. PLoS Computational Biology, 3(7), 1305–1320.

    Article  Google Scholar 

  • McGeer, T. (1988). Stability and control of two-dimensional bipedal walking. Simon Fraser University CSS-ISS TR 88-01.

  • McGeer, T. (1990). Passive dynamic walking. International Journal of Robotics Research, 9(2), 62–82.

    Article  Google Scholar 

  • Miyakoshi, S., & Cheng, G. (2004). Examining human walking characteristics with a telescopic compass-like biped walker model. In Proceedings of the IEEE international conference on systems, man and cybernetics (SMC2004) (pp. 1538–1543).

  • Ono, K., Furuichi, T., & Takahashi, R. (2004). Self-excited walking of a biped mechanism with feet. International Journal of Robotics Research, 23(1), 55–68.

    Article  Google Scholar 

  • Pekarek, D., Ames, A. D., & Marsden, J. E. (2007). Discrete mechanics and optimal control applied to the compass gait biped. In Proceedings of IEEE conference on decision and control (pp. 5376–5382).

  • Pratt, J., Chew, C.-M., Torres, A., Dilworth, P., & Pratt, G. (2001). Virtual model control: an intuitive approach for bipedal locomotion. International Journal of Robotics Research, 20(2), 129–143.

    Article  Google Scholar 

  • Spong, M. W. (2003). Passivity based control of the compass gait biped. In IFAC world congress (pp. 19–24).

  • Spong, M. W., & Bhatia, G. (2003). Further results on control of the compass gait biped. In Proceedings of the IEEE international conference on intelligent robots and systems (IROS) (pp. 1933–1938).

  • Su, J. L.-S., & Dingwell, J. B. (2007). Dynamic stability of passive dynamic walking on an irregular surface. ASME Journal of Biomechanical Engineering, 129(6), 802–810.

    Article  Google Scholar 

  • Taga, G., Yamaguchi, Y., & Shimizu, H. (1991). Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment. Biological Cybernetics, 65, 147–159.

    Article  MATH  Google Scholar 

  • Tedrake, R. (2004). Applied optimal control for dynamically stable legged locomotion. PhD thesis, Massachusetts Institute of Technology.

  • Tedrake, R., Zhang, T. W., & Seung, H. S. (2004). Stochastic policy gradient reinforcement learning on a simple 3D biped. In Proceedings of the IEEE international conference on intelligent robots and systems (IROS) (Vol. 3, pp. 2849–2854).

  • van der Linde, R. Q. (1999). Passive bipedal walking with phasic muscle contraction. Biological Cybernetics, 81, 227–237.

    Article  MATH  Google Scholar 

  • Wisse, M., & van Frankenhuyzen, J. (2003). Design and construction of MIKE: a 2D autonomous biped based on passive dynamic walking. In Proceedings of international symposium of adaptive motion and animals and machines (AMAM03).

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Authors and Affiliations

  1. Institute of Robotics and Intelligent Systems, Swiss Federal Institute of Technology Zurich, LEO D 9.2, Leonhardstrasse 27, 8092, Zurich, Switzerland

    Fumiya Iida

  2. Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, 32 Vassar Street, Cambridge, MA, 02139, USA

    Russ Tedrake

Authors
  1. Fumiya Iida
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  2. Russ Tedrake
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Correspondence to Fumiya Iida.

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Iida, F., Tedrake, R. Minimalistic control of biped walking in rough terrain. Auton Robot 28, 355–368 (2010). https://doi.org/10.1007/s10514-009-9174-3

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  • DOI: https://doi.org/10.1007/s10514-009-9174-3

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