Multiple walking speed-frequency relations are predicted by constrained optimization

A person constrained to walk at a given speed v on a treadmill, chooses a p articular step frequency f and step length d = v/f. Testing over a range of speeds generates a speed-frequency (v-f) relationship. This relationship i s commonly posited as a basic feature of human gait. It is often further po sited that this curve follows from minimum energy cost strategy. We observe d that individuals walking under different constraint circumstances-walking to a range of fixed metronome frequencies (fixed f) or over a range of spa ced markers (fixed d)-produce speed-frequency relations distinct from the c onstrained v relation. We show here that three distinct speed-frequency cur ves, similar to those observed, are predicted by the assumption that a walk ing person optimizes an underlying objective function F(v,f) that has a min imum at the preferred gait. Further, the metabolic cost of transport is a r easonable approximate candidate for the function F. (C) 2001 Academic Press .