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Open‐loop stable solutions of periodic optimal control problems in robotics
Author(s) -
Mombaur K.D.,
Bock H.G.,
Schlöder J.P.,
Longman R.W.
Publication year - 2005
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310190
Subject(s) - classification of discontinuities , stability (learning theory) , monodromy matrix , control theory (sociology) , mathematics , spectral radius , robotics , set (abstract data type) , inverted pendulum , computer science , robot , control (management) , eigenvalues and eigenvectors , mathematical analysis , artificial intelligence , physics , quantum mechanics , machine learning , programming language , nonlinear system
We present a numerical method that optimizes the open‐loop stability of solutions of periodic optimal control problems. We consider general periodic processes that may have several phases, each characterized by its own set of differential equations, and discontinuities of the state variables and the right hand side between phases. Stability is measured in terms of the spectral radius of the monodromy matrix which results in a nonsmooth optimization criterion. We have applied this method to design walking robots that can perform stable periodic gaits without any sensors or feedback; three such examples are presented in this paper.