Low-cost control of repetitive gait in passive bipedal walkers

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 15, Issue 6, 2005, Pages 1959-1973

  Piiroinen, Petri T ^a   Dankowicz, Harry J ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b State University   (United States)

Author keywords

Control; Passive walkers; Piecewise smooth systems; Stability analysis

Indexed keywords

EID: 23944513305     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127405013083     Document Type: Article

References (32)

1. Adolfsson, J., Dankowicz, H. & Nordmark, A. [1999] "3-d stable gait in passive bipedal mechanisms," Proc. European Mechanics Colloquium, Euromech 372, pp. 253-259.
2. Adolfsson, J. [2001] Passive Control of Mechanical Systems - Bipedal Walking and Autobalancing, PhD thesis, Royal Institute of Technology, Department of Mechanics, Sweden.
3. Adolfsson, J., Dankowicz, H. & Nordmark, A. [2001] "3d passive walkers: Finding periodic gaits in the presence of discontinuities," Nonlin. Dyn. 24, 205-229.
4. Aizerman, M. A. & Gantmakher, F. R. [1958] "On the stability of periodic motions," J. Appl. Math. Mech. 22, 1065-1078, (translated from Russian).
5. Basmajian, J. V. & Tuttle, R. [1973] "EMG of locomotion in gorilla and man," in Control of Posture and Locomotion (Plenum Press, NY), pp. 599-609.
6. Chatterjee, A. & Garcia, M. [1998] "Small slope implies low speed in passive dynamic walking," Dyn. Stab. Syst. 15, 139-157.
7. Chew, C.-M. & Pratt, G. A. [1999] "A minimum model adaptive control approach for a planar biped," Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems, Kyongju, Korea.
8. Coleman, M. & Ruina, A. [1998] "An uncontrolled toy that can walk but cannot stand still," Phys. Rev. Lett. 80, 3658-3661.
9. Collins, S., Wisse, M. & Ruina, A. [2001] "A 3-d passive-dynamic walking robot with two legs and knees," Int. J. Robot. Res. 20, 607-615.
10. Dankowicz, H. J., Adolfsson, J. & Nordmark, A. B. [2001a] "Repetetive gait of passive bipedal mechanisms in a three-dimensional environment," J. Biomech. Eng. 123, pp. 40-46.
11. Dankowicz, H. J., Piiroinen, P. T. & Nordmark, A. B. [2001b] "Grazing bifurcation of initially quasi-periodic system attractors," ASME 2001 DETC'01, Pennsylvania.
12. Dankowicz, H. J. & Piiroinen, P. T. [2002] "Exploiting discontinuities for stabilization of reccurrent motions," Dyn. Syst. 17, 317-342.
13. Formal'sky, A. M. [1996] Ballistic Locomotion of a Biped. Design and Control of Two Biped Machines, CISM Advanced School on Modelling and Simulation of Human and Walking Robots Locomotion, Udine.
14. Fredriksson, M. H. & Nordmark, A. B. [2000] "On normal form calculations in impact oscillators," Proc. Roy. Soc. A456, 315-329.
15. Garcia, M., Chatterjee, A. & Ruina, A. [2000] "Efficiency, speed, and scaling of passive dynamical bipedal walking," Dyn. Stab. Syst. 15, 75-99.
16. Garcia, M., Chatterjee, A., Ruina, A. & Coleman, M. [1998] "The simplest walking model: Stability, complexity, and scaling," ASME J. Biomech. Engin. 120, 281-288.
17. Goswami, A., Espiau, B. & Keramane, A. [1997] "Limit cycles in a passive compass gait biped and passivity-mimicking control laws," J. Auton. Rob. 4, 273-286.
18. Goswami, A., Thuilot, B. & Espiau, B. [1998] "A study of the passive gait of a compass-like biped robot: Symmetry and chaos," Int. J. Rob. Res. 17, 1282-1301.
19. Howell, G. W. & Baillieul, J. [1998] "Simple controllable walking mechanism which exhibit bifurcations," Proc. 37th IEEE Conf. Decision and Control, pp. 3027-3032.
20. Kuo, A. D. [1999] "Stabilization of lateral motion in passive dynamic walking," Int. J. Rob. Res. 10, 917-930.
21. Leine, R. [2000] Bifurcations in Discontinuous Mechanical Systems of Filippov-Type, PhD thesis, Teknische Universiteit Eindhoven, The Netherlands.
22. McGeer, T. [1990a] "Passive dynamic walking," Int. J. Rob. Res. 9, 62-82.
23. McGeer, T. [1990b] "Passive walking with knees," Proc. IEEE Conf. Robotics and Automation, Vol. 2, pp. 1640-1645.
24. McGeer, T. [1993] "Dynamics and control of bipedal locomotion, " J. Theoret. Biol. 163, 277-314.
25. Müller, P. C. [1995] "Calculations of lyapunov exponents for dynamical systems with discontinuities," Chaos Solit. Fract. 5, 1671-1681.
26. Mochon, S. & McMahon, T. [1980] "Ballistic walking: An improved model," Math. Biosci. 52, 241-260.
27. Nordmark, A. B. [1997] "Universal limit mapping in grazing bifurcations," Phys. Rev. E55, 266-270.
28. Parker, T. S. & Chua, L. O. [1989] Practical Numerical Algorithms for Chaotic Systems (Springer-Verlag, NY), pp. 118-127.
29. Piiroinen, P. T. [2000] "Passive walking: Transition from 2d to 3d," Licetiate thesis, Department of Mechanics, Royal Institute of Technology.
30. Piiroinen, P. T., Dankowicz, H. J. & Nordmark, A. B. [2001] "On a normal-formal analysis for a class of passive bipedal walkers," Int. J. Bifurcation and Chaos 11, 2411-2425.
31. Piiroinen, P. T., Dankowicz, H. J. & Nordmark, A. B. [2003] "Breaking symmetries and constraints: Transitions from 2d to 3d in passive walkers," Multibody Syst. Dyn. 10, 147-176.
32. Wisse, M., Schwab, A. L. & van der Linde, R. Q. [2001] "A 3d passive dynamic biped with yaw and roll compensation," Robotica 19, 275-284.