  Humans experience small fluctuations in their gait when walking on uneven
terrain. The fluctuations deviate from the steady, energy-minimizing pattern
for level walking, and have no obvious organization. But humans often look
ahead when they walk, and could potentially plan anticipatory fluctuations for
the terrain. Such planning is only sensible if it serves some an objective
purpose, such as maintaining constant speed or reducing energy expenditure,
that is also attainable within finite planning capacity. Here we show that
humans do plan and perform optimal control strategies on uneven terrain. Rather
than maintain constant speed, they make purposeful, anticipatory speed
adjustments that are consistent with minimizing energy expenditure. A simple
optimal control model predicts economical speed fluctuations that agree well
with experiments with humans (N = 12) walking on seven different terrain
profiles (correlated with model ro=0.55+-0.11, P<0.05 all terrains).
Participants made repeatable speed fluctuations starting about six to eight
steps ahead of each terrain feature (up to +-7.5 cm height difference each
step, up to 16 consecutive features). Nearer features matter more, because
energy is dissipated with each succeeding step collision with ground,
preventing momentum from persisting indefinitely. A finite horizon of
continuous look ahead and motor working space thus suffice to practically
optimize for any length of terrain. Humans reason about walking in the near
future to plan complex optimal control sequences.
