Dynamic Stability of Passive Bipedal Walking on Rough Terrain:A Preliminary Simulation Study

doi:10.1016/S1672-6529(11)60139-X

摘要/Abstract

摘要：

A simplified 2D passive dynamic model was simulated to walk down on a rough slope surface defined by deterministic profiles to investigate how the walking stability changes with increasing surface roughness. Our results show that the passive walker can walk on rough surfaces subject to surface roughness up to approximately 0.1% of its leg length. This indicates that bipedal walkers based on passive dynamics may possess some intrinsic stability to adapt to rough terrains although the maximum roughness they can tolerate is small. Orbital stability method was used to quantify the walking stability before the walker started to fall over. It was found that the average maximum Floquet multiplier increases with surface roughness in a non-linear form. Although the passive walker remained orbitally stable for all the simulation cases, the results suggest that the possibility of the bipedal model moving away from its limit cycle increases with the surface roughness if subjected to additional perturbations. The number of consecutive steps before falling was used to measure the walking stability after the passive walker started to fall over. The results show that the number of steps before falling decreases exponentially with the increase in surface roughness. When the roughness magnitude approached to 0.73% of the walker’s leg length, it fell down to the ground as soon as it entered into the uneven terrain. It was also found that shifting the phase angle of the surface profile has apparent affect on the system stability. This is probably because point contact was used to simulate the heel strikes and the resulted variations in system states at heel strikes may have pronounced impact on the passive gaits, which have narrow basins of attraction. These results would provide insight into how the dynamic stability of passive bipedal walkers evolves with increasing surface roughness.

关键词: bipedal walking, rough terrain, dynamic stability, human locomotion

Abstract:

Key words: bipedal walking, rough terrain, dynamic stability, human locomotion

Parsa Nassiri Afshar, Lei Ren. Dynamic Stability of Passive Bipedal Walking on Rough Terrain:A Preliminary Simulation Study[J]. J4, 2012, 9(4): 423-433.

参考文献

[1] Pfeiffer F, Inoue H. Walking: technology and biology. Philosophical Transactions of the Royal Society A - Mathematical Physical & Engineering Sciences, 2006, 365, 3–9.

[2] Hirose M, Ogawa K. Honda humanoid robots development. Philosophical Transactions of the Royal Society A - Mathematical Physical & Engineering Sciences, 2006, 365, 11–19.

[3] McMahon T A. Mechanics of locomotion. International Journal of Robotics Research, 1984, 3, 4–28.

[4] Fujita M. How to make an autonomous robot as a partner with humans: design approach versus emergent approach. Philosophical Transactions of the Royal Society A - Mathematical Physical & Engineering Sciences, 2006, 365, 21–47.

[5] Lim H O, Takanishi A. Biped walking robots created at Waseda University: WL and WABIAN family. Philosophical Transactions of the Royal Society A - Mathematical Physical & Engineering Sciences, 2006, 365, 49–64.

[6] McGeer T. Passive dynamic walking. International Journal of Robotics Research, 1990, 9, 62–82.

[7] McGeer T. Dynamics and control of bipedal locomotion. Journal of Theoretical Biology, 1993, 163, 277–314.

[8] Coleman M J, Ruina A. An uncontrolled walking toy that cannot stand still. Physical Review Letters, 1998, 80, 3658–3661.

[9] Collins S, Ruina A, Tedrake R, Wisse M. Efficient bipedal robots based on passive-dynamic walkers. Science, 2005, 307, 1082–1085.

[10] Mochon S, McMahon T A. Ballistic walking. Journal of Biomechanics, 1980, 13, 49–57.

[11] Mochon S, McMahon T A. Ballistic walking: an improved model. Mathematical Bioscience, 1981, 52, 241–260.

[12] Collins S H, Wisse M, Ruina A. A 3D passive-dynamic walking robot with two legs and knees. International Journal of Robotics Research, 2001, 20, 607–615.

[13] Narukawa T, Yokoyama K, Takahashi M, Yoshida K. Design and construction of a simple 3D straight legged passive walker with flat feet and ankle springs. Journal of System Design and Dynamics, 2009, 3, 1–12.

[14] Wisse M, Schwab A L, van der Helm F C T. Passive dynamic walking model with upper body. Robotica, 2004, 22, 681–688.

[15] Wisse M, Schwab A L, van der Linde R Q, van der Helm F C T. How to keep from falling forward: elementary swing leg action for passive dynamic walkers. IEEE Transaction on Robotics, 2005, 21, 393–401.

[16] Wisse M. Three additions to passive dynamic walking; actuation, an upper body, and 3D stability. International Journal of Humanoid Robotics, 2005, 2, 459–478.

[17] Kuo A D. A simple model of bipedal walking predicts the preferred speed-step length relationship. Journal of Biomechanical Engineering, 2001, 123, 264–269.

[18] Kuo A D. Energetics of actively powered locomotion using the simplest walking model. Journal of Biomechanical Engineering, 2002, 124, 113–120.

[19] Garcia M, Chatterjee A, Ruina A, Coleman M. The simplest walking model: stability, complexity, and scaling. Journal of Biomechanical Engineering, 1998, 120, 281–288.

[20] Goswami A, Espiau B, Keramane A. Limit cycle in a passive compass gait and passivity-mimicking control laws. Autonomous Robots, 1997, 4, 273–286.

[21] Su J L, Dingwell J B. Dynamic stability of passive dynamic walking on an irregular surface. Journal of Biomechanical Engineering, 2007, 129, 1–11.

[22] Hurmuzlu Y, Basdogan C, Stoianovici D. Kinematics and dynamic stability of the locomotion of post-polio patients. Journal of Biomechanical Engineering, 1996, 118, 405–411.

[23] Hurmuzlu Y, Basdogan C. On the measurement of dynamic stability of human locomotion. Journal of Biomechanical Engineering, 1994, 116, 30–36.

[24] Dingwell J B, Kang H G, Marin L C. The effects of sensory loss and walking speed on the orbital dynamic stability of human walking. Journal of Biomechanics, 2007, 40, 1723–1730.

[25] Dingwell J B, Kang H G. Differences between local and orbital dynamic stability during human walking. Journal of Biomechanical Engineering, 2007, 129, 586–593.

[26] Strogatz S H. Nonlinear Dynamics and Chaos. Cambridge, Westview Press, Boulder, Colorado, USA, 1994.

[27] McGeer T. Passive dynamic biped catalogue. In: Chatila R, Hirzinger G (eds). Experimental Robotics II. Springer- Verlag, London, UK, 1993.

[28] Goswami A, Thuilot B, Espiau B. A study of the passive gait of a compass-like biped robot: symmetry and chaos. International Journal of Robotic Research, 1998, 17, 1282–1301.

[29] Schwab A L, Wisse M. Basin of attraction of the simplest walking model. Proceedings of ASME Design Engineering Technical Conferences, Pittsburgh, PA, USA, 2001, DETC2001/VIB-21363.

[30] Amaraporn B, Ren L. The human ankle-foot complex as a multi-configurable mechanism during the stance phase of walking. Journal of Bionic Engineering, 2010, 7, 211–218.

[31] Ren L, Howard D, Ren L Q, Nester C, Tian L M. A generic analytical foot rollover model for predicting translational ankle kinematics in gait simulation studies. Journal of Biomechanics, 2010, 43, 194–202.

[32] Ren L, Jones R, Howard D. Predictive modelling of human walking over a complete gait cycle. Journal of Biomechanics, 2007, 40, 15671574.

[33] Manoonpong P, Geng T, Kulvicius T, Porr B, Worgotter, F. Adaptive, fast walking in a biped robot under neuronal control and learning. PLoS Computational Biology, 2007, 3, e134.

[34] Luo X, Li W, Zhu C. Planning and control of CoP-switch- based planar biped walking. Journal of Bionic Engineering, 2011, 8, 33–48.

[35] Maxwell D, Kram R, Kuo A D. Simultaneous positive and negative external mechanical work in human walking. Journal of Biomechanics, 2002, 35, 117–124.

[36] Bauby C E, Kuo A D. Active control of lateral balance in human walking. Journal of Biomechanics, 2000, 33, 1433–1440.

[37] Kuo A D. Stabilization of lateral motion in passive dynamic walking. International Journal of Robotics Research, 1999, 18, 917–930.