On the Comparative Analysis of Locomotory Systems with Vertical Travel

Abstract

This paper revisits the concept of specific resistance, a dimensionless measure of locomotive efficiency often used to compare the transport cost of vehicles (Gabrielli & von Karman 1950), and extends its use to the vertical domain. As specific resistance is designed for comparing horizontal locomotion, we introduce a compensation term in order to offset the gravitational potential gained or lost during locomotion. We observe that this modification requires an additional, experimentally fitted model estimating the efficiency at which a system is able to transfer energy to and from gravitational potential. This paper introduces a family of such models, thus introducing methods to allow fair comparisons of locomotion on level ground, sloped, and vertical surfaces, for any vehicle which necessarily gains or loses potential energy during travel. AbstractThis paper revisits the concept of specific resistance, ε, a dimensionless measure of locomotive efficiency often used to compare the transport cost of vehicles [6], and extends its use to the vertical domain. As specific resistance is designed for comparing horizontal locomotion, we introduce a compensation term in order to offset the gravitational potential gained or lost during locomotion. We observe that this modification requires an additional, experimentally fitted model estimating the efficiency at which a system is able to transfer energy to and from gravitational potential. This paper introduces a family of such models, thus introducing methods to allow fair comparisons of locomotion on level ground, sloped, and vertical surfaces, for any vehicle which necessarily gains or loses potential energy during travel.

Autonomous legged hill ascent

“…For the first set of experiments, where we seek the steady state performance with no obstacles, both P avg and v avg are computed over a portion of the trial where the translational velocity command applied to the 15 Our measurements do not take the work done against gravity into account. For more accurate specific resistance measurements and thus fair comparisons of locomotion between level, sloped, and vertical surfaces, (Haynes and Koditschek, 2010) proposes a model containing the original equation ( 58) plus an experimentally fitted correction term. Since our goal is to compare two different control laws over the same hill patches with the same initial and final elevations (an thus, with the same work against gravity), we chose to utilize the original specific resistance measurement.…”

Legged Self-Manipulation

“…This notion of fighting an external force and relaxing the internal force has been used before on legged robots, usually without stating it in this way. For example, prior work on RHex pushes the body uphill to be centered over the legs while climbing steep terrain [43], and separately regulate individual leg torques such that no one leg pushes harder than the rest [44]. These ideas were further developed on RiSE [45], [46] whose reactive gait phase adjustments were designed to balance forces within and between the sides.…”

“…From Section II-D, the active components a k of the base kinematic constraint are shown in ( 41)- (43), which combine to form a in each contact mode,…”

Standing self-manipulation for a legged robot

“…Extrapolating these ideas into a walking task introduces a variety of new issues and we only briefly sketch our preliminary adaptations and experiments as motivation for future work. A full extension to a walking controller will have to consider the problem of providing enough propulsive power while ascending slopes [4,5], and problem of "combinatorial obstacles" [26] required to maintain enough legs on the ground at all times. Thus a full walking version of this controller is outside the scope of this paper.…”

“…This notion of fighting an external force and relaxing the internal force has been used before on legged robots, usually without stating it in this way. For example, on RHex there has been past work to push the body uphill and be centered over the legs while climbing steep terrain [4,5], as well as approaches that regulate individual leg torques such that no one leg pushes much harder than the rest [6]. These ideas were further developed by research on RiSE [7,8] whose reactive gait phase adjustments were designed to balance forces within and between the sides with the goal of evenly distributing ground reaction forces.…”