Predictability, force, and (anti)resonance in complex object control.

Manipulation of complex objects as in tool use is ubiquitous and has given humans an evolutionary advantage. This study examined the strategies humans choose when manipulating an object with underactuated internal dynamics, such as a cup of coffee. The dynamics of the object renders the temporal evolution complex, possibly even chaotic, and difficult to predict. A cart-and-pendulum model, loosely mimicking coffee sloshing in a cup, was implemented in a virtual environment with a haptic interface. Participants rhythmically manipulated the virtual cup containing a rolling ball; they could choose the oscillation frequency, whereas the amplitude was prescribed. Three hypotheses were tested: 1) humans decrease interaction forces between hand and object; 2) humans increase the predictability of the object dynamics; and 3) humans exploit the resonances of the coupled object-hand system. Analysis revealed that humans chose either a high-frequency strategy with antiphase cup-and-ball movements or a low-frequency strategy with in-phase cup-and-ball movements. Counter to hypothesis 1, they did not decrease interaction force; instead, they increased the predictability of the interaction dynamics, quantified by mutual information, supporting hypothesis 2. To address hypothesis 3, frequency analysis of the coupled hand-object system revealed two resonance frequencies separated by an antiresonance frequency. The low-frequency strategy exploited one resonance, whereas the high-frequency strategy afforded more choice, consistent with the frequency response of the coupled system; both strategies avoided the antiresonance. Hence, humans did not prioritize small interaction forces but rather strategies that rendered interactions predictable. These findings highlight that physical interactions with complex objects pose control challenges not present in unconstrained movements. NEW & NOTEWORTHY Daily actions involve manipulation of complex nonrigid objects, which present a challenge since humans have no direct control of the whole object. We used a virtual-reality experiment and simulations of a cart-and-pendulum system coupled to hand movements with impedance to analyze the manipulation of this underactuated object. We showed that participants developed strategies that increased the predictability of the object behavior by exploiting the resonance structure of the object but did not minimize the hand-object interaction force.