Meeting Abstract
Horses walk at slow speeds, trot at intermediate speeds, and gallop at high speeds. Other quadrupeds, including trained horses, can perform a variety of other gaits, such as an amble, pace, canter, tolt, etc. Here, we use a series of simple computer models of a quadrupedal animal to examine the metabolic energetic differences between these gaits. First, we considered perhaps the simplest model with the upper body consisting of a single extended rigid body and four ideal massless legs: for this quadruped, an inverted pendulum-like walking gait was energetically optimal a slow speeds and a perfect trotting gait is optimal at all higher speeds; galloping was never optimal. The walking gait was the exact analog a bipedal inverted pendulum walking motion: so that the front two legs were in synchrony with the rear two legs, so that the quadrupedal upper body moves without any rotation (no pitch or roll). Next, we considered a more realistic quadrupedal model, with a back that can bend and a neck attached to the body in a compliant manner: for this quadruped, a walking gait was optimal at slow speed, a trotting gait at intermediate speeds, and a more asymmetric gait reminiscent of galloping at high speeds. For our quadrupeds, we also found that other gaits such tolt and pace were sub-optimal. All these calculations were performed using large-scale numerical optimization, which attempted to obtain the energy optimal body motions and muscle (leg) force profiles for a given footfall sequence while systematically and simultaneously optimizing the footfall sequences from among a large set of possible footfall sequences. We will show how we obtain different gaits as we change some body size parameters. These methods could be generalized to other multipedal animals, say cockroaches and other insects, perhaps including other goal including other goal criteria than just energy minimization, e.g., improving stability.
