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Journal of Computational Dynamics (JCD)
 

Symmetry exploiting control of hybrid mechanical systems

Pages: 25 - 50, Volume 2, Issue 1, June 2015      doi:10.3934/jcd.2015.2.25

 
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Kathrin Flasskamp - Neuroscience and Robotics Laboratory, Northwestern University, Evanston, IL, United States (email)
Sebastian Hage-Packhäuser - Chair of Applied Mathematics, University of Paderborn, Paderborn, Germany (email)
Sina Ober-Blöbaum - Chair of Applied Mathematics, University of Paderborn, Paderborn, Germany (email)

Abstract: 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.

Keywords:  Symmetry, mechanical systems, hybrid systems, optimal control, motion planning.
Mathematics Subject Classification:  37C80, 93C30, 70H33.

Received: May 2014;      Revised: April 2015;      Available Online: August 2015.

 References