Finding the rhythm: Humans exploit nonlinear intrinsic dynamics of compliant systems in periodic interaction tasks

Activities like ball bouncing and trampoline jumping showcase the human ability to intuitively tune to system dynamics and excite motions that the system prefers intrinsically. This human sensitivity to resonance has been experimentally supported for interactions with simple linear systems but remains a challenge to validate in more complex scenarios where nonlinear dynamics cannot be predicted analytically. However, it has been found that many nonlinear systems exhibit periodic orbits similar to the eigenmodes of linear systems. These nonlinear normal modes (NNM) are computable with a recently developed numerical mode tool. Using this tool, the present resarch compared the motions that humans excite in nonlinear systems with the predicted NNM of the energy-conservative systems. In a user study consisting of three experiment parts, participants commanded differently configured virtual double pendula with joint compliance through a haptic joystick. The task was to alternately hit two targets, which were either aligned with the NNM (Experiments 1 and 2) or purposefully arranged offset (Experiment 3). In all tested experiment variations, participants intuitively applied a control strategy that excited the resonance and stabilized an orbit close to the ideal NNM of the conservative systems. Even for increased task accuracy (Experiment 2) and targets located away from the NNM (Experiment 3), participants could successfully accomplish the task, likely by adjusting their arm stiffness to alter the system dynamics to better align the resonant motions to the task. Consequently, our experiments extend the existing research on human resonance sensitivity with data-based evidence to nonlinear systems. Our findings emphasize the human capabilities to apply control strategies to excite and exploit resonant motions in dynamic object interactions, including possibly shaping the dynamics through changes in muscle stiffness.Author summary: Without thinking about it, humans intuitively excite resonant motions in everyday object interactions, despite the complex and nonlinear nature of their dynamics. Computing these nonlinear dynamics is challenging, but it is essential to verify if the excited object motion matches the objects’ intrinsic dynamics. Using a new numerical tool, we could predict these intrinsic dynamics. In a human user study, participants were tasked with exciting a virtual double pendulum through a haptic joystick. The excited motions were then compared to the intrinsic nonlinear dynamics predicted by the tool. The experiments verified that participants intuitively excited the resonance frequency of the nonlinear system and stabilized motion trajectories close to the computed intrinsic ones. Experimental variations also indicated that humans shape the system dynamics by changing their arm stiffness to create resonances that better align with the task. These findings support existing research showing that humans are highly sensitive to resonance and exploit it intuitively for tasks when possible.