Advanced LMI based analysis and design for Acrobot walking |
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| Authors: | Milan Anderle Sergej Čelikovský Didier Henrion Jiří Zikmund |
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| Affiliation: | 1. Faculty of Electrical Engineering, Department of Control Engineering , Czech Technical University in Prague , Technická 2, 166 27 Prague, Czech Republic;2. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic , Pod Vodárenskou vě?í 4, 182 08 Prague, Czech Republic anderle@utia.cas.cz;4. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic , Pod Vodárenskou vě?í 4, 182 08 Prague, Czech Republic;5. LAAS-CNRS , University of Toulouse , 7 avenue du colonel Roche, 31077 Toulouse, France;6. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic , Pod Vodárenskou vě?í 4, 182 08 Prague, Czech Republic |
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| Abstract: | This article aims to further improve previously developed design for Acrobot walking based on partial exact feedback linearisation 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 three time-varying entries only, the remaining entries being either zero or one. In such a way, exponentially stable tracking can be obtained by quadratically stabilising a linear system with polytopic uncertainty. The current improvement is based on applying linear matrix inequalities (LMI) methods to solve this problem numerically. This careful analysis significantly improves previously known approaches. Numerical simulations of Acrobot walking based on the above-mentioned LMI design are demonstrated as well. |
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| Keywords: | linear matrix inequalities underactuated mechanical systems walking robots |
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