Rhythmic gymnasts train for years to guide their long ribbons into intricate swirls without tangling them. But most able-bodied adults handle similarly complex objects every day, often without even thinking. Walking with a cup of coffee without spilling it may not sound like a daunting task. But the coffee has infinitely many degrees of freedom, the brain lacks the computing power to predict the dynamics of the fluid in real time, and the nervous system is far too slow to notice and compensate for each individual slosh.
A few researchers in the movement-science community have explored the idea that our extraordinary dexterity in handling objects comes from our ability to exploit their dynamic stability. In certain regions of an object’s phase space, perturbations die away over time instead of being amplified, and trajectories are thus largely insensitive to external noise or uncertainty. Over our years of life experience, the theory goes, we unconsciously learn to guide objects toward regions of stability to make them easier to control.
The idea has passed some experimental tests, but so far only for periodic motions such as walking or bouncing a ball on a racket. Now Dagmar Sternad of Northeastern University in Boston, her postdoc Salah Bazzi, and their colleagues have turned to a different way of evaluating stability that’s applicable to transient motions like moving a cup of coffee from one point to another. Rather than analyzing perturbations about a steady-state closed orbit in phase space, they applied a method that considers pairs of closely spaced trajectories and how the distance between them evolves in time. A region of phase space is deemed stable if the trajectories converge exponentially.
To test that mathematical framework, the researchers created a robotic simulation of a simplified cup of sloshing coffee: a shallow bowl containing a freely rolling ball. After mapping the system’s phase space, they instructed volunteer test subjects to guide the bowl quickly along a one-dimensional track without losing the ball. Midway along the track was a bump that jerked the bowl either forward or back. Sure enough, as the subjects repeated the experiment, they consistently learned to maneuver the system into a stable region of phase space right before the bowl hit the bump. Although more work is needed to explore just how broadly applicable the analysis is to other transient movements, the results could have implications for robotics, prosthetics, and the design of everyday objects that are easier for motor-impaired individuals to control. (S. Bazzi et al., Chaos, in press; photo by AYakovlev/iStock/Thinkstock.)
