This work examined how subjects learn to control balance and its relation to dynamic stability. We used a pendulum model to analyze a standing task that required subjects to abruptly pull on a handle to different target forces while maintaining balance and keeping their feet flat. Prior studies of this task have shown that subjects’ center of mass (CM) motion resembles an inverted pendulum.

The first study experimentally tested the hypothesis that, with practice, subjects simplify controls so that CM motion better resembles an inverted pendulum with constant ankle torque. Results indicated that the pendulum was less appropriate after practice mainly because ankle torque varied more with time during balance recovery.

The second study developed a theoretical model of stability limits to better understand ankle torque during balance recovery. This pendulum and foot model combined the equations of motion with constraints on friction, centripetal acceleration, strength, and the center of pressure (COP). The intersection of the constraints yielded permission of the copyright owner. Further reproduction prohibited without permission. torque boundaries, which define where the feet begin to move. An optimization algorithm used the torque boundaries to determine state boundaries, which define where balance recovery is not possible.

The third study empirically evaluated the torque and state boundaries. All of the trials from the pulling task fell within the theoretical limits defined by the torque boundaries, and 95% of the trials fell within the limits defined by the state boundaries. This supported using the nearest distance to a boundary (the safety margin) as a measure of relative stability. Because torque boundaries were heavily influenced by the COP constraint, we also found that relative stability was highly correlated with the COP’s nearest distance to the heel or toe.

The final study tested the hypothesis that relative stability improves over five days of practice on the pulling task. We measured the COP’s nearest distance to the heel or toe and also its shortest time to the heel or toe, and found that they increased with practice. The variability of the COP’s nearest distance decreased with practice. These results suggest that the nervous system may control balance using nearest distance and shortest time calculations.