Rhythmic Manipulation of Objects with Complex Dynamics: Predictability over Chaos

Abstract

The study of object manipulation has been largely confined to discrete tasks, where accuracy, mechanical effort, or smoothness were examined to explain subjects' preferred movements. This study investigated a rhythmic manipulation task, which involved continuous interaction with a nonlinear object that led to unpredictable object behavior. Using a simplified virtual version of the task of carrying a cup of coffee, we studied how this unpredictable object behavior affected the selected strategies. The experiment was conducted in a virtual set-up, where subjects moved a cup with a ball inside, modeled by cart-and-pendulum dynamics. Inverse dynamics calculations of the system showed that performing the task with different amplitudes and relative phases required different force profiles and rendered the object's dynamics with different degrees of predictability (quantified by Mutual Information between the applied force and the cup kinematics and its sensitivity). Subjects (n = 8) oscillated the virtual cup between two targets via a robotic manipulandum, paced by a metronome at 1 Hz for 50 trials, each lasting 45 s. They were free to choose their movement amplitude and relative phase between the ball and cup. Experimental results showed that subjects increased their movement amplitudes, which rendered the interactions with the object more predictable and with lower sensitivity to the execution variables. These solutions were associated with higher average exerted force and lower object smoothness, contradicting common expectations from studies on discrete object manipulation and unrestrained movements. Instead, the findings showed that humans selected strategies with higher predictability of interaction dynamics. This finding expressed that humans seek movement strategies where force and kinematics synchronize to repeatable patterns that may require less sensorimotor information processing.

Velocity-Curvature Patterns Limit Human–Robot Physical Interaction

“…Finally, even if not physically tiring, the incompatible and possibly unpredictable changes in velocities lead to discomfort and cognitive fatigue. A recent study showed that in complex object control, predictability of the object dynamics was a major determinant for human movement generation that outweighed the minimization of force [26]. Hence, complex interactions may introduce additional costs that are absent in unconstrained movements.…”

Predictability and Robustness in the Manipulation of Dynamically Complex Objects

“…To quantitatively test this hypothesis, predictability must be operationalized. One possible measure is the mutual information (MI) between the applied force and the motion of the object, which characterizes the long-term predictability of the object’s dynamics (Cover and Thomas 2006; Nasseroleslami et al 2014). MI is a nonlinear correlation measure defined between two probability density distributions of two random variables and quantifies the information shared between the two.…”

“…Our recent study provided evidence that subjects increase the predictability of object dynamics with practice and favor predictable solutions over those that minimize expended force and smoothness, criteria that are widely supported criteria for free movements (Nasseroleslami et al 2014). In this study, subjects (n = 8) oscillated the virtual cup between two targets with a robotic manipulandum, paced by a metronome at 1 Hz for 50 trials, each lasting 45 s. They were free to choose their movement amplitude and relative phase between the ball and cup.…”

“…To evaluate Hypothesis 1 , that subjects seek predictable object interactions, MI , and the alternative costs mean squared force MSF , and mean squared jerk MSJ were calculated for each measured strategy ${\overline{A}}_k,{\overline{f}}_k,{\overline{\theta }}_k,{\overline{\dot{\theta }}}_k$. Calculation of MI followed the same procedure as in the simulated MI , except that probability density functions were estimated experimentally (for more details see (Nasseroleslami et al 2014). To calculate MSF , the continuous force profile of each trial was squared and averaged, analogous to the simulated data.…”

“…The schematic below visualizes the applied force as arrows in accelerating and decelerating directions. Figure modified from Nasseroleslami et al (2014) with permission under Creative Commons Attribution (CC BY) license…”