Dynamical stability and mechanical impedance are optimized when manipulating uncertain dynamically complex objects

Manipulating complex objects is ubiquitous in our daily activities, such as donning a jacket or carrying a cup of coffee. However, such non-rigid objects easily become unstable: When carrying a cup of coffee, the coffee could slosh unpredictably and spill out of the cup. It remains unclear what motor control strategies ensure stability, especially when the physical properties of the object, like the amount of liquid in the cup, are unknown. The task of transporting a 'cup of coffee' was simplified to transporting a virtual cup with a sliding ball inside, modeled as a cart-pendulum system. Participants were instructed to 'jiggle' the cup in one dimension to prepare the cup and ball states for the ensuing continuous rhythmic movement. To introduce uncertainty regarding the object's properties, the pendulum's length was manipulated either to 1) change randomly from trial to trial, or to 2) remain constant across trials. We measured the ball's angle at the end of preparation and the cup's oscillation frequency during the rhythmic portion of the trial. Grip force on the robot handle served as proxy for mechanical impedance of the arm. The results supported three predictions: 1) When dynamic uncertainty was high, object preparation was important to stabilize the transient dynamics; stability increased during preparation and humans prepared longer when the dynamics was uncertain. 2) Humans maximized dynamic stability by flexibly covarying system initialization and cup frequency; dynamic stability matched participant behavior better than magnitude or smoothness of force. 3) Humans increased their arm impedance to accommodate uncertain dynamics, while the net force applied on the cup remained the same. Feedforward simulations using an impedance controller and stochastic open-loop optimal control corroborated these findings, further revealing that participants' selection of preparation and interaction frequencies also minimized mechanical impedance. In sum, humans used preparation and interaction strategies to optimize the mechanical impedance and dynamic stability of the hand-object interactions. These results may inform approaches in robotic control and rehabilitation.