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Rhythmic Manipulation of Objects with Complex Dynamics: Predictability over Chaos

Figure 2

Examples of force profiles and task kinematics in simulation and experiment, with corresponding definitions of the main variables.

The left column of panels shows the simulations: the cup kinematics is defined as a pure sine wave with fixed amplitude and frequency ; ball angle and angular velocity are fully defined by their initial values and . The force F is found by solving the inverse dynamics for these kinematic profiles ( = 1.0 Hz, = 0.2 m, = 1.0rad, = 0 rad). The right column shows the experimental kinematics: cup position , ball angle and ball angular velocity are used to estimate the frequency , amplitude , initial ball angle , and initial ball angular velocity at each cycle of the trajectories. Red dots and vertical red lines indicate the location and time of the peak cup positions, at which the initial ball angle and angular velocity values for each cycle were determined, and , marked by blue dots. The experimental force profile is the net force applied by the subject to the manipulandum.

doi: https://doi.org/10.1371/journal.pcbi.1003900.g002