Synchronous Transition in Complex Object Control

A complex object is a system with internal degrees of freedom, such as a cup of hot coffee hand-held by a human in walking. In spite of the natural ability of humans to handle complex objects, an understanding of how this is accomplished is lacking, yet the issue is fundamental to applied fields such as soft robotics. Recent virtual experiments on how humans handle a moving bowl with a mechanical ball inside have revealed that humans typically use two strategies to handle a complex object: a low-frequency strategy in which the motions of the bowl and ball synchronized in phase and a high-frequency strategy where antiphase synchronization occurs. Utilizing a nonlinear dynamical model of a pendulum attached to a moving cart, subject to external periodic forcing, we study the transition between in-phase and antiphase synchronization. We find that, in the weakly forcing regime, as the external driving frequency is varied, the transition is abrupt and occurs at the frequency of resonance, which can be fully understood using linear systems control theory. Beyond this regime, a transition region emerges in between in-phase and antiphase synchronization, where the motions of the cart and the pendulum are not synchronized. We also find that there is bistability in and near the transition region on the low-frequency side. Overall, our results indicate that humans are able to switch abruptly and efficiently from one synchronous attractor to another, a mechanism that can be exploited for designing smart robots to adaptively handle complex objects in a changing environment.