Stability Optimization of Juggling

Katja Mombaur (), Peter Giesl () and Heiko Wagner ()
Additional contact information
Katja Mombaur: Universität Heidelberg, IWR
Peter Giesl: University of Sussex, Department of Mathematics
Heiko Wagner: Universität Münster, Institut für Sportwissenschaft

A chapter in Modeling, Simulation and Optimization of Complex Processes, 2008, pp 419-432 from Springer

Abstract: Abstract 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.

Keywords: Optimal Control Problem; Muscle Force; Spectral Radius; Contact Phase; Periodic Trajectory (search for similar items in EconPapers)
Date: 2008
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-79409-7_29

Ordering information: This item can be ordered from
http://www.springer.com/9783540794097

DOI: 10.1007/978-3-540-79409-7_29

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().