Controlled symmetries and passive walking

IEEE Transactions on Automatic Control

Volumn 50, Issue 7, 2005, Pages 1025-1031

  Spong, Mark W ^a   Bullo, Francesco ^b  

^a University of Illinois at Urbana Champaign   (United States)

^b University of California   (United States)

Author keywords

Bipedal locomotion; Group action; Limit cycle; Nonlinear control; Passive walking; Potential energy shaping; Symmetry

Indexed keywords

ALGORITHMS; BIPED LOCOMOTION; CONTROL THEORY; DEGREES OF FREEDOM (MECHANICS); DYNAMICS; KINEMATICS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; THEOREM PROVING; VECTORS;

CONTROLLED SYMMETRY; GROUP ACTION; LIMIT CYCLE; PASSIVE WALKING; POTENTIAL ENERGY SHAPING;

NONLINEAR CONTROL SYSTEMS;

EID: 23144459310     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.851449     Document Type: Article

References (20)

1. T. McGeer, "Passive dynamic walking," Int. J. Robot. Res., vol. 9, no. 2, pp. 62-82, 1990.
2. A. Goswami, B. Espiau, and A. Keramane, "Limit cycles in a passive compass gait biped and passivity-mimicking control laws," Auton. Robot., vol. 4, no. 3, pp. 273-86, 1997.
3. M. Garcia, A. Chatterjee, A. Ruina, and M. Coleman, "The simplest walking model: Stability, complexity, and scaling," ASME J. Biomech. Eng., vol. 120, no. 2, pp. 281-288, 1998.
4. A. Goswami, B. Thuilot, and B. Espiau, "A study of the passive gait of a compass-like biped robot: Symmetry and chaos," Int. J. Robot. Res., vol. 17, no. 12, pp. 1282-301, 1998.
5. M. W. Spong, "Bipedal locomotion, robot gymnastics, and robot air hockey: A rapprochement," in Proc. TITech COE/Super Mechano-Systems Workshop, Tokyo, Japan, Feb. 1999, pp. 34-41.
6. M. W. Spong, "Passivity based control of the compass gait biped," in Proc. IFAC World Congr., vol. 3, Beijing, China, Jul. 1999, pp. 19-23.
7. H. Ohta, M. Yamakita, and K. Furuta, "From passive to active dynamic walking," in Proc. IEEE Conf. Decision and Control, Phoenix, AZ, Dec. 1999, pp. 3883-3885.
8. S. Suzuki, K. Furuta, Y. Pan, and S. Hatakeyama, "Biped walking robot control with passive walker model by new VSC servo," in Proc. Amer. Control Conf., Arlington, VA, Jun. 2001, pp. 107-112.
9. A. D. Kuo, "Stabilization of lateral motion in passive dynamic walking," Int. J. Robot. Res., vol. 18, no. 9, pp. 917-30, 1999.
10. S. H. Collins, M. Wisse, and A. Ruina, "A three-dimensional passive-dynamic walking robot with two legs and knees," Int. J. Robot. Res., vol. 20, no. 7, pp. 607-15, 2001.
11. M. Takegaki and S. Arimoto, "A new feedback method for dynamic control of manipulators," J. Dyna. Syst., Measure., Control, vol. 102, pp. 119-125, 1981.
12. D. E. Koditschek et al., "The application of total energy as a Lyapunov function for mechanical control systems," in Dynamics and Control of Multibody Systems, J. E. Marsden et al., Eds. Providence, RI: AMS, 1989, vol. 97, pp. 131-157.
13. N. E. Leonard, "Stabilization of underwater vehicle dynamics with symmetry-breaking potentials," IFAC Syst. Control Lett., vol. 32, no. 1, pp. 35-42, 1997.
14. R. Ortega et al., "Energy shaping revisited," in Proc. IEEE Conf. Control Applications, Anchorage, AK, Sep. 2000, pp. 121-126.
15. J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry, 2nd ed. New York: Springer-Verlag, 1999.
16. P. J. Olver, Application of Lie Groups to Differential Equations. New York: Springer-Verlag, 1993, vol. 107. GTM.
17. M. W. Spong and M. Vidyasagar, Robot Dynamics and Control. New York: Wiley, 1989.
18. Y. Hurmuzlu and D. Moskowitz, "The role of impact in the stability of bipedal locomotion," Dyna. Stability Syst., vol. 1, no. 3, pp. 217-234, 1986.
19. F. Bullo and M. Žefran, "Modeling and controllability for a class of hybrid mechanical systems," IEEE Trans. Robot. Autom., vol. 18, no. 4, pp. 563-573, Aug. 2002.
20. A. Goswami, "Postural stability of biped robots and the foot rotation indicator (FRI) point," Int. J. Robot. Res., vol. 18, no. 6, pp. 523-533, 1999.