Planar Symmetric Juggling of a Devil-Stick

Nilay Kant, Ranjan Mukherjee

The problem of juggling a devil-stick is investigated. Assuming that the stick remains confined to the vertical plane, the task is to juggle between two symmetric configurations. Impulsive forces are applied to the stick intermittently and the impulse of the force and its point of application are modeled as inputs to the system. The dynamics of the devil-stick due to the impulsive forces and gravity is described by half-return maps between two Poincare sections; the symmetric configurations are fixed points of these sections. A coordinate transformation is used to convert the juggling problem to that of stabilization of one of the fixed points. Inclusion of the coordinate transformation into the dynamics results in a nonlinear discrete-time model. A dead-beat design for one of the inputs simplifies the problem and results in a linear discrete-time system. To achieve symmetric juggling, linear quadratic regulator and model predictive control based designs are proposed and validated through simulations.

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