Finding the rhythm: Humans exploit nonlinear intrinsic dynamics of compliant systems in periodic interaction tasks
Authors: Schmidt Annika , Forano Marion , Sachtler Arne , Calzolari Davide , Franklin David , Albu-Schäffer Alin 
Published: September 2023

Everyday activities, like jumping on a trampoline or using a swing-stick, show that humans seemingly effortless support systems in their intrinsically preferred motions. Although this observation seems obvious, data-based evidence proving that humans indeed match system dynamics has been lacking, since everyday objects usually exhibit complex, nonlinear dynamics, which are in general not analytically solvable. Recent insights in the field of nonlinear mode theory and the development of a tool to compute modes for nonlinear systems enabled us to investigate human strategies to excite periodic motions in the interaction with nonlinear systems. In the setup of a high score game, participants interacted with differently configured virtual compliant double pendulum systems through a haptic joystick. Through the joystick, the user could command positions to a motor link connected to the pendulum by a spring and received resulting spring forces in return to convey the feeling of holding a flexible stick. The participants were asked to alternately hit two targets located on the computed nonlinear mode of the system as often as possible. All participants intuitively exploited the elasticity of the system by choosing aholding strategyof the motor link and only compensate for energy losses with small motions. In this way, the intrinsic dynamics of the double pendulum system were exploited leading to the predicted fast motions along the nonlinear modes. The human strategy stayed consistent when decreasing the target size or increasing the mass of the lower pendulum link, i.e., changing the dynamics. Consequently, the presented research provides data-based evidence that humans can indeed estimate the nonlinear dynamics of system and intuitively exploit these. Additionally, the introduction to nonlinear modes and ways to compute them could be a powerful tool for further investigations on human capabilities and strategies in periodic interactions with nonlinear systems.

Author summary

Without thinking about it, humans interact with a wide variety of objects in everyday life. This includes objects with very complex nonlinear dynamics such as flexible rods or ropes. Since it is not trivial to enforce trajectories far away from the system’s intrinsic motions and frequencies, it is likely that humans explore and, whenever possible, exploit the natural dynamics of the system. By using a tool to predict the trajectories of systems with nonlinear dynamics, we collected human user data to validate this hypothesis for repetitive tasks with a virtual double pendulum. Indeed our research showed that humans supported mechanical systems in their respective intrinsic motions and were able to intuitively match the systems’ eigenfrequencies. In doing so, only little control effort and motion was needed from the users, which could aids to save energy and mental resources. Since both these aspects are limiting factors in continuous tasks, it seems to have an evolutionary benefit that humans are very capable in estimating and exploiting the natural dynamics of compliant systems and tune their own control strategy to be be synchronized to the controlled system.