Near–simultaneous footfalls lend stability to multi–legged gaits

Parsimonious dynamical models for legged locomotion are piecewise–defined. The state flows in continuous–time according to an ordinary differential equation (ODE) until a touchdown or liftoff event occurs, triggering an instantaneous reset at a discrete time instant [1]. We’ve shown that models for periodic gaits with footfalls isolated in time (e.g. bipedal walk or run, quadrupedal walk or gallop) reduce to classical dynamical systems—smooth ODEs on smooth manifolds [2]. However, footfalls are not isolated for general behaviors.