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

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 equations, 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 approach to the derivation. In this paper, we describe an analytical approach that has proved to be more efficient than previous gait study techniques. This analytical approach defines 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 approach is applied to study the effects on the stability margin of the wave gait by varying the stroke and the pitch of the leg.

Comparison of Alternative Gaits for Multiped Robots with Severed Legs

“…A key criterion of comparison is the gait stability, more precisely, the longitudinal stability margin sL as proposed by McGhee and Frank [17] and Song and Waldron [18], [19]. A plot of the movement of the legs and the robot body, as shown in Possible displacement ranges of the legs are shown by vertical lines in the figure.…”

Fault-Tolerant Gait Planning of Multi-Legged Robots

“…1 θ , 2 θ and 3 θ are values of each joint angle, and 1 l and 2 l are lengths of the upper and lower links, respectively. By adopting the major premise of gait study (Song & Waldron, 1987), we assume that the robot body remains parallel to the ground, and that the ground is flat over the region affecting the robot workspace. The dimension of the working area of each leg is thus kept the same throughout walking.…”

“…The leg sequence with which a quadruped gait can have the maximum longitudinal stability margin (Song & Waldron, 1987) in straight-line walking is known to be (2,5)-(3,4)-(1,6) when the hexapod robot has the prototype shown in Figure 1 (Yang, 1999). In other words, lifting two legs in the symmetric positions with respect to the center of gravity guarantees the maximum stability to the resulting support pattern.…”

“…In other words, lifting two legs in the symmetric positions with respect to the center of gravity guarantees the maximum stability to the resulting support pattern. The leg stroke, the distance through which the foot is translated relative to the body during the support phase (Song & Waldron, 1987), should be equal to the stride length if the gait is periodical. Therefore, if the stride length of the robot body is chosen, the leg stroke is determined equally.…”

A Measure of Stability for Mobile Manipulators With Application to Heavy-Duty Hydraulic Machines

“…Defi'n'ition /r. : Ã support pattern is a two-climensionalpoint set in a horizontal plane consisting of the convex hull of the vertical projection of all foot points in support phase [3].…”