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A Dynamical Approach to Create Different Juggling Patterns Using Chaos

Author(s):

T. Sutter
Conference/Journal:

Bachelor Thesis, FS10
Abstract:

A bouncing ball on a vibrating plate is a canonical example of a dynamic system, exhibiting nonlinear phenomena, such as chaos and it is easy to study experimentally. We present two strategies to create different juggling patterns for a blind juggling robot that juggles four balls at the same time. An algorithm to realize four desired periodic orbits is introduced starting with four balls in the P1-orbit, where the paddle’s trajectory is used as control input. The key idea is to use two different paddle modes and to switch it at an appropriate time. The first mode has the goal to ’break the symmetry’ of the four balls, i.e. we separate their trajectories from each other. This is done by a paddle trajectory that produces chaotic motion of the balls. Then, suitable ball’s states have to be induced such that the paddle’s trajectory can be switched to the second mode and the desired combination of four periodic orbits results. As a basic requirement for this approach we need to know what suitable ball’s states are. Therefore, the basin of attraction for each periodic orbit is determined by numerical simulation. Using the basin of attraction, each ball’s state at a potential switching point can be classified whether it leads to the desired periodic orbit or not.

Year:

2010
Type of Publication:

(13)Semester/Bachelor Thesis
Supervisor:

R. D' Andrea

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2010:IFA_5495
}
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