Dealing With Instability

We encounter unexpected and unpredictable forces acting upon our bodies every day. Whether it’s a sudden bump on the subway or picking up an empty bottle you thought was full, we move in highly unpredictable environments. Through experience, we learn to anticipate some of these disturbances. For example, we estimate an object’s weight before we pick it up to properly counter the force. This process occurs almost imperceptibly—you probably only notice when your internal calculations are off and you’re suddenly raising that empty bottle above your head.

This educated-guess-and-check approach, however, will only work in predictable, stable situations. Many tasks are inherently unstable. Imagine using a screwdriver. If you don’t push perfectly straight, the screwdriver slips off of the screw head. You don’t know these interaction forces in advance, and you fail the task without compensating for them. Yet, humans use screwdrivers (and a host of other tools) every day without grievous injury. We’re impressively dexterous, all things considered.

How does our nervous system accomplish such an impressive feat? One obvious possibility is by using reflexes. By sensing unwanted or potentially harmful changes in our joint positions and quickly opposing them, we overcome unexpected forces to continue on our way. But these compensation mechanisms only go so far. As information travels from sensory receptors in muscles and joints, up to the spinal cord to compute the necessary motor response, and back out to the muscles, relay delays build up. For highly unstable environments, like using a screwdriver, reflexes aren’t enough. By the time they’ve kicked in, the screwdriver has slipped and is scratching your nice wood desk.

Etienne Burdet, Reiko Osu and colleagues explored how humans navigate highly unstable environments in their 2001 Nature paper (“The Central Nervous System Stabilizes Unstable Dynamics by Learning Optimal Impedance”). The group simulated screwdriver-like dynamics in the lab by applying an unstable force field to human subjects’ arms. They asked subjects to make center-out reaches (starting close to their body, and reaching straight ahead of them to a peripheral target) while holding onto the handle of a robotic device used to implement the force field. The researchers applied a divergent force field (DF), which enhanced movement errors perpendicular to the subjects’ movement. If the subjects reached perfectly straight, no forces were applied to their limb. If their hand drifted away from the straight path, however, the DF would expand these errors and push the subject’s hand away—just like the slip of a screwdriver.

The researchers asked subjects to make reaches with and without the force field. Initial reaches in the DF were unsuccessful; their hands were quickly pushed away. Over time, though, subjects were able to complete reaches in the DF despite its unpredictable dynamics. What had changed in their motor strategy?

Burdet et al hypothesized that limb impedance was a likely mechanism for overcoming this challenging DF. Though it is a familiar concept in electronics, impedance can be a bit difficult to grasp in the context of your limbs. Consider the difference between writing your signature, a well-practiced task that most of us are rather sloppy about, and printing on your tax forms, something that requires careful precision. One major difference between these two writing tasks is the impedance of your arm. In the former case, you’re very relaxed; in the latter, you’re more tense. Limb impedance describes the limb’s ability to resist external forces; a limb with a high impedance will move very little when pushed. So, to increase the accuracy of your writing, you ‘stiffen’ your arm, giving you more control. Furthermore, since our limbs move in a three-dimensional space, impedance is a 3D quantity. Your arm can be stiff in one direction, while remaining loose in others.

One way we can control our limb impedance is by contracting/relaxing agonist-antagonist muscle pairs. Our muscles are rather similar to springs; the shorter (i.e. more contracted) they are the more force it takes to change their length. By contracting muscles that have equal and opposite effects on the limb (e.g. your biceps that flex your elbow and triceps which extend them), the limb won’t move—equal and opposite forces—but the muscles will be shorter, and thus stiffer. The net effect is an increase in the stiffness of the limb. The interesting aspect of limb impedance is that it can be changed independent of your movement kinematics. I can reach for my coffee cup with a stiff or loose arm. The position and velocity of my joints will be the same in both cases, but the dynamics (my limb’s response to external forces) will be very different. This property of limb impedance makes it a likely candidate for dealing with unstable dynamics like the DF. By increasing the impedance of their arms, subjects can make their arms less sensitive to the perturbing forces of the DF while still making the same center-out reaches.

To test their hypothesis that impedance plays a key role in navigating unstable dynamics, Burdet et al measured subjects’ limb impedance during their normal reaches and those made after they’d learning to navigate the DF*. They found that, indeed, subjects’ arms were stiffer during movements in the DF compared to free movements. Interestingly, their limb impedance only increased significantly in the direction of the environmental instability (i.e. the direction that DF forces were applied). Since the DF only causes instability along one direction, changes in limb impedance along other axes are not necessary to successfully complete the task. The researchers showed that subjects were able to optimize their limb impedance to match the specific task requirements.

Stiffening your limb requires a lot of energy since it involves contracting many muscles. Your arm quickly tires after only a page or two of filling out tax forms for precisely this reason—your muscles are in over-drive. Considering its high metabolic cost, Burdet’s finding that subjects optimize limb impedance as much as possible isn’t shocking. The intrigue of this result is that the central nervous system appears to have incredibly precise control of limb impedance. Indeed, this group later replicated the experiment using DFs with other orientations (e.g. pushing the hand along a 35 degree angle relative to the direction of motion) and found that subjects’ limb stiffness again changed to closely match the DF instability [See D.W. Franklin et al Journal of Neuroscience 2007]. This precision impedance control requires manipulation of a myriad of muscle pairs. Given our complex limb geometry, this optimization is not trivial. The CNS solves this computationally intensive problem with apparent ease.

This research demonstrates one way our motor system deals with the unpredictability of the world. However, how the CNS implements such exacting control remains to be explored. Do spinal cord reflexes primarily govern impedance control, or is the motor cortex also involved? If the cortex plays a role, how is impedance represented and encoded? Our brains are solving problems that an engineer with several computers might be able to solve in a few hours in a matter of milliseconds. Its methods remain an exciting mystery.


* Measuring limb impedance is a non-trivial and rather technical problem, the details of which are not particularly interesting from a neuroscience perspective. As such, I’ve omitted them here. See Burdet et al Journal of Biomechanics 2000 for details of the stiffness measurement methods used in these experiments.