Nonlinear techniques for the Acrobot tracking with application to robot walking

Dr. Sergej Celikovsky (Academy of Sciences of the Czech Republic )

DATE: 2009-11-27
TIME: 11:00:00 - 12:00:00
LOCATION: RSISE Seminar Room, ground floor, building 115, cnr. North and Daley Roads, ANU

ABSTRACT:
This talk aims to compare the performance of various techniques for the stabilization of the error dynamics of the Acrobot's walking like reference trajectory. Both the walking reference planning and the tracking feedback design are based on the Acrobot's model partial exact feedback linearization of order 3. Namely, such an exact system transformation leads to an almost linear system where error dynamics along trajectory to be tracked is a 4 dimensional linear time varying system having 3 time varying entries only, the remaining entries are either zero or equal to one.

Three techniques to stabilize asymptotically such an error dynamics are presented and compared. All of them are based on the robust control approaches viewing the above mentioned time-dependent terms as some partially unknown disturbances. First technique combines high-gain feedback with Lyapunovs analysis, the latter one enables to obtain some reasonable gain values, yet resulting in an unrealistically large actuator torque. The second technique relies on the fact that the desirable exponentially stable tracking can be obtained by solving quadratic stability of a linear system with polytopic uncertainty. To do so, LMI methods are engaged to solve this problem numerically. The results of this careful analysis are shown to be a significant improvement of previously known approaches, especially in the case of nonrectangular convex polytopic uncertainty set. Here, the advantage is taken of the fact that "uncertainty" is, in fact, a triple of the known scalar time functions, so that one can find significantly smaller bounding convex set than just a large rectangular box. The last technique uses the time-dependent transformation of the error dynamics resulting in much better results when the high-gain approach is applied. Similarly as with the first technique, the corresponding results are in a closed form, rather than in a numerical one. Again, the advantage is taken of the fact that the time dependent error dynamics parameters are, in fact, known and differentiable.

Numerical simulations and animations of the Acrobot walking based on all above mentioned techniques will be demonstated as well. Finally, some outlooks will be presented to extend these ideas to the walking design for the general n-link systems with n-1 actuators, underactuated at the pivot point.

BIO:
Prof. Sergej Celikovsky was graduated in 1984 from Faculty of Numerical Mathematics and Cybernetics of the Moscow State University, Department of Optimal Control, chaired by L.S. Pontryagin. In 1985 he received RNDr. degree (Rerum Naturalium Doctoris) from the Mathematical and Physical Faculty of Charles University in Prague and in 1989 he received PhD in technical cybernetics from the Institute of Information Theory and Automation of the Czechoslovak Academy of Sciences. Prof. Sergej Celikovsky has been with the Institute of Information Theory and Automation since 1989, currently, he is the chief researcher and the head of the Control Theory Department of this Institute. He took half year visiting position as the research associate at the Chinese University of Hong Kong in 1998 and the visiting professorship in CINVESTAV-IPN, Mexico during 1998-2000. Sergej Celikovsky has been also with the Department of Control Engineering, Faculty of Electrical Engineering, Czech Technical University in Prague since 2003, where he was promoted as Associatte Professor in 2008. Prof. Sergej Celikovsky is the Senior Member of IEEE, the member of IFAC TC on Nonlinear Systems, the Associate Editor of IEEE Transaction on Automatic Control and the member of the EB of Kybernetika journal. His research is focused on nonlinear systems theory and its applications, especially in robotics, resulting in 40 papers in the international peer-reviewed journals, more then 50 papers at the top international events proceedings and co-authoring the monograph published by Prentice Hall. SCI registers more than 200 citations of his scientific works.

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