Control lyapunov functions and hybrid zero dynamics

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2012, Pages 6837-6842

  Ames, Aaron D ^a   Galloway, Kevin ^b   Grizzle, J W ^b  

^a Texas A and M University   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIPED LOCOMOTION; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS;

BIPEDAL WALKING ROBOT; CONTINUOUS FLOWS; CONTROL LYAPUNOV FUNCTION; HYBRID ZERO DYNAMICS; INPUT OUTPUT LINEARIZATION; OUTPUT FUNCTIONS; STABILIZING CONTROLLERS; SYSTEM WITH IMPULSE EFFECTS;

DYNAMICS;

EID: 84874282999     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2012.6426229     Document Type: Conference Paper

References (28)

1. A. D. Ames. First steps toward automatically generating bipedal robotic walking from human data. In Robotic Motion and Control, volume 422 of LNICS, pages 89-116. Springer, 2012.
2. A. D. Ames. First steps toward underactuated human-inspired bipedal robotic walking. In IEEE International Conference on Robotics and Automation, St. Paul, MN, 2012.
3. D.D. Bainov and P.S. Simeonov. Systems with Impulse Effects : Stability, Theory and Applications. Ellis Horwood Limited, Chichester, 1989.
4. A. Banaszuk and J. Hauser. Feedback linearization of transverse dynamics for periodic orbits. In Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on, volume 2, pages 1639 -1644 vol.2, 1994.
5. S.P. Bhat and D.S. Bernstein. Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Transactions on Automatic Control, 43(5):678-682, 1998.
6. R. A. Freeman and P. V. Kokotović. Robust Nonlinear Control Design. Birkhäuser, 1996.
7. R. Goebel, R. Sanfelice, and A. Teel. Hybrid dynamical systems. IEEE Control Systems Magazine, 29(2):28-93, 2009.
8. J. W. Grizzle, G. Abba, and F. Plestan. Asymptotically stable walking for biped robots: Analysis via systems with impulse effects. IEEE Transactions on Automatic Control, 46(1):51-64, 2001.
9. J. W. Grizzle, C. Chevallereau, A. D. Ames, and R. W. Sinnet. 3D bipedal robotic walking: models, feedback control, and open problems. In 8th IFAC Symposium on Nonlinear Control Systems, Bologna, Italy, 2010.
10. W. M. Haddad, V. S. Chellaboina, and S. G. Nersesov. Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control. Princeton University Press, Princeton, NJ, 2006.
11. A. Isidori. Nonlinear Control Systems. Springer-Verlag, Berlin, third edition, 1995.
12. A. Isidori. Nonlinear Control Systems: An Introduction. Springer- Verlag, Berlin, Germany, 3rd edition, 1995.
13. A. Isidori and C. Moog. On the nonlinear equivalent of the notion of transmission zeros. In Byrnes C. and A. Kurzhanski, editors, Proc. of the IIASA Conference: Modeling and Adaptive Control, pages 146- 157, Berlin, 1988. Springer-Verlag.
14. B. Morris and J. W. Grizzle. Hybrid invariant manifolds in systems with impulse effects with application to periodic locomotion in bipedal robots. IEEE Transactions on Automatic Control, 54(8):1751-1764, 2009.
15. B. Morris and J.W. Grizzle. A restricted Poincaré map for determining exponentially stable periodic orbits in systems with impulse effects: Application to bipedal robots. In IEEE Conf. on Decision and Control, Seville, Spain, 2005.
16. S. Sastry. Nonlinear Systems: Analysis, Stability and Control. Springer-Verlag, 1999.
17. A. Shiriaev, J.W. Perram, and C. Canudas-de Wit. Constructive tool for orbital stabilization of underactuated nonlinear systems: Virtual constraints approach. Automatic Control, IEEE Transactions on, 50(8):1164-1176, 2005.
18. A.S. Shiriaev, L.B. Freidovich, and S.V. Gusev. Transverse linearization for controlled mechanical systems with several passive degrees of freedom. Automatic Control, IEEE Transactions on, 55(4):893-906, 2010.
19. G. Song and M. Zefran. Underactuated dynamic three-dimensional bipedal walking. In IEEE International Conference on Robotics and Automation, pages 854-859, Orlando, Florida, 2006.
20. E. Sontag. A 'universal' contruction of Artstein's theorem on nonlinear stabilization. Systems & Control Letters, 13:117-123, 1989.
21. K. Sreenath, H.W. Park, I. Poulakakis, and J. W. Grizzle. A compliant hybrid zero dynamics controller for stable, efficient and fast bipedal walking on MABEL. IJRR, 30(9):1170-1193, 2011.
22. D. Sun. A further result on an implicit function theorem for locally Lipschitz functions. Operations Research Letters, 28(4):193-198, 2001.
23. E. Wendel and A. D. Ames. Rank deficiency and superstability of hybrid systems. Nonlinear Analysis: Hybrid Systems, 6:787-805, 2012.
24. E. Westervelt, J.W. Grizzle, and D.E. Koditschek. Hybrid zero dynamics of planar biped walkers. IEEE Transactions on Automatic Control, 48(1):42-56, 2003.
25. E. R. Westervelt, G. Buche, and J. W. Grizzle. Experimental validation of a framework for the design of controllers that induce stable walking in planar bipeds. International Journal of Robotics Research, 24(6):559-582, 2004.
26. E. R. Westervelt, J. W. Grizzle, C. Chevallereau, J. H. Choi, and B. Morris. Feedback Control of Dynamic Bipedal Robot Locomotion. CRC Press, Boca Raton, 2007.
27. H. Ye, A. N. Michel, and L. Hou. Stability theory for hybrid dynamical systems. IEEE Transactions on Automatic Control, 43(4):461-474, 1998.
28. W. Zhang, A. Abate, J. Hu, and M. Vitus. Exponential stabilization ofdsicrete-time switched linear systems. Automatica, 45(11):2526-2536, 2009.