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Dynamical stability and mechanical impedance are optimized when manipulating uncertain dynamically complex objects

Fig 6

Forward simulations to explain preparation and interaction choices.

A) A human-inspired controller with mechanical impedance was used to run forward simulations of the cart-pendulum model. The controller computed a force proportional to deviation from the desired states, related through the impedance gains K and B. The impedance gains were held constant at K = 40 and B = 70. B) One forward simulation for initial ball angle of and cup frequency . The relative phase hovered close to with a circular variability of 0.012. C) Heatmaps of relative phase variability for combinations of initial ball angles and cup frequencies plotted in grey shades in the background. Participant choices of initial ball angle and cup frequency from all trials are plotted as colored points in the foreground. Colors represent different participants. Participants’ choices fell into the dark regions of the heatmap, showing that they nonlinearly covaried preparation and interaction strategies to maximize relative phase stability. D) Heatmaps of absolute force, smoothness of force, and risk of ball escape plotted for the medium pendulum condition. Participant choices of initial ball angle and cup frequency from the random protocol plotted in the foreground. Kullback-Leibler divergence between the distributions of participant data and the underlying heatmaps were lowest for relative phase variability, i.e., stability, (random-medium plot in C) compared to the three alternative costs. Relative phase variability captures covariation of preparation and interaction strategies better than absolute force or smoothness of force.

doi: https://doi.org/10.1371/journal.pcbi.1013797.g006