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The effects of parameter variation on the gaits of passive walking models: simulations and experiments

Published online by Cambridge University Press:  01 July 2009

Liu Ning ,
Li Junfeng  and
Wang Tianshu
Liu Ning
Affiliation:
School of Aerospace, Tsinghua University, Beijing, China
Li Junfeng
Affiliation:
School of Aerospace, Tsinghua University, Beijing, China
Wang Tianshu*
Affiliation:
School of Aerospace, Tsinghua University, Beijing, China
*
*Corresponding author. E-mail: [email protected]
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Summary

We have made a systematic study of the gait of a straight leg planar passive walking model through simulations and experiments. Three normalised parameters, which represent the foot radius, the position of the mass centre and the moment of inertia, are used to characterise the walking model.

In the simulation, we have obtained the fixed points and the basins of attraction of the walking models with different parameter combinations by the aid of the cell mapping method. With the results of fixed points, we investigated the effects of parameter variations on the gait descriptors, including step length, period, average speed and energy inefficiency. A model that has a large basin of attraction has been obtained, and it can start walking far from its fixed point. However, the size of the basin of attraction is not a good measurement of robustness. Thus, we proposed floors with random slope angles or stairs with random heights to test robustness. Five hundred times of simulations with 100 non-dimensional time units were implemented for each parameter combination. The times that the walker failed to arrive at the end were recorded. The simulation results showed that the model with a larger foot radius and higher position of mass centre has a lower possibility of falling on uneven floors. A large moment of inertia is helpful for walking on a random slope angle floor, while low values of moment of inertia are good for navigating random stairs.

Prototype experiments have validated the simulation results, which showed that models with larger feet have a longer step length and high speed. However, period differences were difficult to obtain in the experiments since the differences were very small. We have tested the sensitivity with the initial conditions of the models with different foot radii on a flat floor, and have also tested the robustness of the models on a floor with random slope angles. The times that the model reached the end of the floor were recorded. The experimental results showed that a large foot radius is good for improving the basin of attraction and robustness on uneven floors. Finally, the exceptions of the experiment are explained.

Keywords

Passive dynamic walkingCell mapping methodRandom perturbationExperimentBasins of attractionRobustness
Type
Article
Information
Robotica , Volume 27 , Issue 4 , July 2009 , pp. 511 - 528
Copyright
Copyright © Cambridge University Press 2008

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References

1.McGeer, T., “Passive dynamic walking,” Int. J. Rob. Res. 9, 62–82 (Apr., 1990).CrossRefGoogle Scholar
2.Collins, S., Wisse, M. and Ruina, A., “A three-dimensional passive-dynamic walking robot with two legs and knees,” Int. J. Rob. Res. 20, 607–615 (Jul. 2001).CrossRefGoogle Scholar
3.Garcia, M., “Stability, Scaling, and Chaos in Passive Dynamic Gait Models,” Ph.D. Thesis (Cornell University, 1999).Google Scholar
4.Goswami, A., Thuilot, B. and Espiau, B., “A study of the passive gait of a compass-like biped robot: Symmetry and chaos,” Int. J. Rob. Res. 17, 1282–1301 (Dec. 1998).CrossRefGoogle Scholar
5.Kuo, A. D., “Stabilization of lateral motion in passive dynamic walking,” Int. J. Robot. Res. 18, 917–930 (Sep. 1999).CrossRefGoogle Scholar
6.Adolfsson, J., Dankowicz, H. and Nordmark, A., “3D passive walkers: Finding periodic gaits in the presence of discontinuities,” Nonlin. Dyn. 24, 205–229 (2001).CrossRefGoogle Scholar
7.Collins, S., Ruina, A., Tedrake, R. and Wisse, M., “Efficient bipedal robots based on passive-dynamic walkers,” Science 307, 1082–1085 (2005).CrossRefGoogle ScholarPubMed
8.Wisse, M., “Essentials of Dynamic Walking: Analysis and Design of Two-Legged Robots,” Ph.D. Thesis (Delft University, 2005).Google Scholar
9.Tedrake, R. L., “Applied Optimal Control for Dynamically Stable Legged Locomotion,” Ph.D. Thesis (MIT, 2004).Google Scholar
10.Garcia, M.. Chatterjee, A., Ruina, A. and Coleman, M. J., “The simplest walking model: Stability, complexity, and scaling,” ASME J. Biomech. Eng. 120, 281–288 (Apr. 1998).CrossRefGoogle ScholarPubMed
11.Wisse, M., Schwab, A. L., van der Linde, R. Q. and van der Helm, F. C. T., “How to keep from falling forward; elementary swing leg action for passive dynamic walkers,” IEEE Trans. Rob. 21, 393–401 (2005).CrossRefGoogle Scholar
12.Wisse, M., Schwab, A. L. and van der Helm, F. C. T., “Passive dynamic walking model with upper body,” Robotica 22(Part 6), 681–688 (2004).CrossRefGoogle Scholar
13.Wisse, M., Schwab, A. L. and van der Linde, R. Q., “A 3D passive dynamic biped with yaw and roll compensation,” Robotica 19(Part 3), 275–284 (2001).CrossRefGoogle Scholar
14.Schwab, A. and Wisse, M., “Basin of Attraction of the Simplest Walking Model,” Proceedings of International Conference on Noise and Vibration, ASME, Pennsylvania (2001).CrossRefGoogle Scholar
15.Asano, F. and Luo, Z.-W., “On Energy-Efficient and High-Speed Dynamic Biped Locomotion with Semicircular Feet,” Proceedings of 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems (2006) pp. 5901–5906.Google Scholar
16.Hass, J., Herrmann, J. M. and Geisel, T., “Optimal mass distribution for passivity-based bipedal robots,” Int. J. Rob. Res. 25, 1087–1098 (Nov. 2006).CrossRefGoogle Scholar
17.Wu, Q. and Sabet, N., “An experimental study of passive dynamic walking,” Robotica 22(Part 3), 251–262 (2004).CrossRefGoogle Scholar
18.Byl, K. and Tedrake, R., “Stability of Passive Dynamic Walking on Uneven Terrain,” Dynamic Walking 2006, Ann Arbor, MI (2006).Google Scholar
19.Su, J. L. and Dingwell, J. B., “Orbital Stability of Passive Dynamic Walking on a Bumpy Surface,” Proceedings of 30th Annual Meeting of the American Society of Biomechanics, Blacksburg, VA (2006).CrossRefGoogle Scholar
20.Daan Hobbelen, G. E. and Wisse, M., “Limit Cycle Walking,” In: Humanoid Robots Human-like Machines (Hackel, Matthias, ed.) (I-Tech Education and Publishing, Vienna, Austria, 2007) pp. 277–294.Google Scholar
21.Hsu, C. S., Cell-to-Cell Mapping: A Method of Global Analysis for Nonlinear Systems. Applied Mathematical Sciences 64 (Springer, New York, 1987).CrossRefGoogle Scholar
22.Safa, A. T., Mohammad Ghaffari, Saadat and Naraghi, Mahyar, “Passive dynamic of the simplest walking model: Replacing ramps with stairs” Mech. Mach. Theory 42, 1314–1325 (2007).CrossRefGoogle Scholar