Stability Optimization of Juggling

Mombaur, Katja, Giesl, Peter and Wagner, Heiko (2008) Stability Optimization of Juggling. In: Bock, HG, Kostina, E, Hoang, XP and Rannacher, R (eds.) Modeling, Simulation and Optimization of Complex Processes. Springer Berlin Heidelberg, pp. 419-432. ISBN 978-3-540-79408-0

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Biological systems like humans or animals have remarkable stability properties allowing them to perform fast motions which are unparalleled by corresponding robot configurations. The stability of a system can be improved if all characteristic parameters, like masses, geometric properties, springs, dampers etc. as well as torques and forces driving the motion are carefully adjusted and selected exploiting the inherent dynamic properties of the mechanical system. Biological systems exhibit another possible source of self-stability which are the intrinsic mechanical properties in the muscles leading to the generation of muscle forces. These effects can be included in a mathematical model of the full system taking into account the dependencies of the muscle force on muscle length, contraction speed and activation level. As an example for a biological motion powered by muscles, we present periodic single-arm self-stabilizing juggling motions involving three muscles that have been produced by numerical optimization. The stability of a periodic motion can be measured in terms of the spectral radius of the monodromy matrix. We optimize this stability criterion using special purpose optimization methods and leaving all model parameters, control variables, trajectory start values and cycle time free to be determined by the optimization. As a result we found a self-stable solution of the juggling problem.

Item Type: Book Section
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Peter Giesl
Date Deposited: 06 Feb 2012 20:28
Last Modified: 11 Apr 2012 12:19
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