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Dynamical stability and mechanical impedance are optimized when manipulating uncertain dynamically complex objects
Fig 8
Predictions of open-loop optimal control on mechanical impedance.
A) State space variables from one simulation run with the medium pendulum, and low noise simulating the blocked protocol, setting the desired initial ball angle to 
, and cup frequency to 
. The desired cup trajectories and initial ball angle are highlighted in red. The stiffness K rises monotonously in the preparation stage and plateaus in the rhythmic stage. B) Stiffness and applied force plotted against time for the blocked (low noise) and random (high noise) conditions, for the same desired initial ball angle and cup frequency as in A. Predicted stiffness values are higher in the random protocol in comparison to the blocked protocol, similar to the experimentally reported grip forces. In contrast, applied forces are similar between the protocols. C) Average stiffness and applied force from all runs with combinations of desired initial ball angles and cup frequencies. Stiffness values are higher in the random protocol compared to the blocked protocol. In contrast, the applied forces are of similar magnitude between the two protocols. D) Model predicted stiffness (K) for various combinations of initial ball angle and cup frequency plotted in the background. Participant choices from different trials from either the blocked protocol or random protocol are plotted in the foreground. Colors represent different participants. Participants covaried their choice of preparation and interaction to minimize mechanical impedance in both the random and the blocked protocol. E) Model predicted average absolute feedforward force (Fff) for various combinations of initial ball angle and cup frequency plotted in the background. There are some regions of overlap between low average absolute forces and low stiffness.
doi: https://doi.org/10.1371/journal.pcbi.1013797.g008