January  2015, 2(1): 25-50. doi: 10.3934/jcd.2015.2.25

Symmetry exploiting control of hybrid mechanical systems

1. 

Neuroscience and Robotics Laboratory, Northwestern University, Evanston, IL, United States

2. 

Chair of Applied Mathematics, University of Paderborn, Paderborn, Germany, Germany

Received  May 2014 Revised  April 2015 Published  August 2015

Symmetry properties such as invariances of mechanical systems can be beneficially exploited in solution methods for control problems. A recently developed approach is based on quantization by so called motion primitives. A library of these motion primitives forms an artificial hybrid system. In this contribution, we study the symmetry properties of motion primitive libraries of mechanical systems in the context of hybrid symmetries. Furthermore, the classical concept of symmetry in mechanics is extended to hybrid mechanical systems and an extended motion planning approach is presented.
Citation: Kathrin Flasskamp, Sebastian Hage-Packhäuser, Sina Ober-Blöbaum. Symmetry exploiting control of hybrid mechanical systems. Journal of Computational Dynamics, 2015, 2 (1) : 25-50. doi: 10.3934/jcd.2015.2.25
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show all references

References:
[1]

Addison-Wesley, 1987. Google Scholar

[2]

IEEE Transactions on Automatic Control, 45 (2000), 2253-2270. doi: 10.1109/9.895562.  Google Scholar

[3]

Springer, 2005. doi: 10.1007/978-1-4899-7276-7.  Google Scholar

[4]

in Modelling, Analysis, and Design of Hybrid Systems (eds. S. Engell, G. Frehse and E. Schnieder), vol. 279 of Lecture Notes in Control and Information Sciences, Springer, 2002, 311-335. doi: 10.1007/3-540-45426-8_18.  Google Scholar

[5]

MIT Press, 2005. Google Scholar

[6]

Journal of Nonlinear Science, 22 (2012), 599-629. doi: 10.1007/s00332-012-9140-7.  Google Scholar

[7]

PhD thesis, University of Paderborn, 2013. Google Scholar

[8]

PhD thesis, Massachusetts Institute of Technology, 2001. Google Scholar

[9]

in Proceedings of the 41st IEEE Conference on Decision and Control, 1 (2002), 817-823. doi: 10.1109/CDC.2002.1184606.  Google Scholar

[10]

in Proceedings of the 39th IEEE Conference on Decision and Control, 1 (2000), 821-826. doi: 10.1109/CDC.2000.912871.  Google Scholar

[11]

IEEE Transactions on Robotics, 21 (2005), 1077-1091. Google Scholar

[12]

vol. 200 of Progress in Mathematics, 2002. doi: 10.1007/978-3-0348-8167-8.  Google Scholar

[13]

PhD thesis, University of Paderborn, 2012. Google Scholar

[14]

PhD thesis, University of Southern California, USA, 2008. Google Scholar

[15]

IEEE Transactions on Automatic Control, 48 (2003), 2-17. doi: 10.1109/TAC.2002.806650.  Google Scholar

[16]

no. 174 in London Mathematical Society Lecture Note Series, Cambridge University Press, 1992. doi: 10.1017/CBO9780511624001.  Google Scholar

[17]

Communications in Mathematical Physics, 199 (1998), 351-395. doi: 10.1007/s002200050505.  Google Scholar

[18]

2nd edition, Springer, 1999. doi: 10.1007/978-0-387-21792-5.  Google Scholar

[19]

Journal of Mathematical Physics, 41 (2000), 3379-3429. doi: 10.1063/1.533317.  Google Scholar

[20]

Zeitschrift für angewandte Mathematik und Physik (ZAMP), 44 (1993), 17-43. doi: 10.1007/BF00914351.  Google Scholar

[21]

Acta Numerica, 10 (2001), 357-514. doi: 10.1017/S096249290100006X.  Google Scholar

[22]

Control, Optimisation and Calculus of Variations, 17 (2011), 322-352. doi: 10.1051/cocv/2010012.  Google Scholar

[23]

Springer, 2000. Google Scholar

[24]

Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications & Algorithms, 12 (2005), 649-687.  Google Scholar

[25]

Archive for Rational Mechanics and Analysis, 115 (1991), 15-59. doi: 10.1007/BF01881678.  Google Scholar

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