Ruprecht-Karls-Universität Heidelberg
Optimization in Robotics and Biomechanics

Open-loop stable juggling

Katja Mombaur - IWR
Peter Giesl
- University of Sussex, Brighton
Heiko Wagner
- Universit√§t M√ľnster

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 in form of a Hill-type model.

As an example for a biological motion powered by muscles, we study 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.

Since the numerical techniques applied in this study are capable to solve much larger problems, we plan to extend the investigation of stable juggling to more complex problems involving both hands and more balls.



K. D. Mombaur, P. Giesl, H. Wagner - Stability Optimization of Juggling, , in H. G. Bock, E. Kostina, H. X. Phu and R. Rannacher (eds.): "Modeling, Simulation and Optimization of Complex Processes", Lecture Notes in Scientific Computing, Springer, 2008

K. Mombaur,
Last Update: 19.10.2011 - 16:03

The photographs in the header of this webpage have been taken at the Musee de l'Automate in Souillac, France