A Galloping Horse Model

Abstract

A two-dimensional numerical model of a horse is presented that predicts the locomotory behaviors of galloping horses, including how stride frequency, stride length, and metabolic rate change from a slow canter to a fast gallop. In galloping, each limb strikes the ground sequentially, one after the other, with distinct time lags separating hind and forelimb footfalls. In the model, each stance limb is represented as an ideal linear spring, and both feed-forward and feedback control strategies determine when each limb should strike the ground. In a feed-forward strategy, the first hindlimb and the first forelimb to strike the ground are phase-locked such that the time separating their adjacent footfalls is held constant by the controller. In distinction, in a feedback strategy, the footfalls of the second hindlimb and the second forelimb begin when the first hindlimb and the first forelimb are perpendicular to the model’s trunk, respectively. While any limb is in contact with the ground, the controller also employs a feedback control to move each stance foot at a constant tangential velocity relative to the model’s trunk. With these control schemes, the galloping model remains balanced without sensory knowledge of its postural orientation relative to vertical. This work suggests that a robot will exhibit behavior that is mechanically similar to that of a galloping horse if it employs spring-like limbs and simple feed-forward and feedback control strategies for which postural stabilization is an emergent property of the system.