An Analytical Approach for Gait Study and Its Applications on Wave Gaits

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Abstract
In the past, the determination of the gait stability margins of legged locomotion systems depended mainly on numerical computation assisted by graphical methods. Although some of these results were expressed as empirically derived equa tions, analytical derivations were lacking. The only exception was the equation of the longitudinal stability margin for quadruped wave gaits derived by McGhee and Frank (1968). They applied a complicated, nonlinear programming ap proach to the derivation. In this paper, we describe an ana lytical approach that has proved to be more efficient than previous gait study techniques. This analytical approach de fines the foot positions by means of the concept of local phase, which is the fraction of a cycle period by which the current foot position follows the placement of that foot. Based on this concept, basic theorems that simplify the study of periodic gaits are developed. This analytical approach is then applied to derive a general equation for the longitudinal stability margin for the 2n-legged wave gait. Also, this ap proach is applied to study the effects on the stability margin of the wave gait by varying the stroke and the pitch of the leg.

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