Human Control of Underactuated Objects: Adaptation to Uncertain Nonlinear Dynamics Ensures Stability

Abstract

Humans frequently interact with objects that have dynamic complexity, like a cup of coffee. Such systems are nonlinear and underactuated, potentially creating unstable dynamics. Instabilities generate complex interaction forces that render the system unpredictable. And yet, humans interact with these objects with ease. Nonlinear dynamic analysis shows that the initial conditions and frequencies of input forces determine the system’s stability. Taking inspiration from carrying a cup of coffee, participants rhythmically moved a cup with a ball rolling inside which was modeled as a cart-pendulum system. They were encouraged to prepare the cup-and-ball system by ‘jiggling’ the cup before moving it back and forth on a horizontal line. We tested the hypothesis that humans initialize the system and choose interaction frequencies that stabilize their interactions. To create uncertainty about the specific cup-and-ball system, the pendulum length was varied without providing cues to the participant. Stability was quantified by variability of relative phase between cup and ball. Results showed that participants nonlinearly co-varied the initial ball angle at the end of preparation and the cup frequency during the rhythmic phase. Mapping participants’ choices onto the highly nonlinear manifold of stable solutions generated by forward-simulations verified that they indeed achieved stable solutions.