Efficient sliding locomotion of three-link bodies with inertia

TL;DR

This paper optimizes the movement patterns of a three-link body for sliding locomotion, revealing that body inertia significantly affects efficiency especially under certain friction conditions, and that optimal motions converge with increased frequency components.

Contribution

It introduces the inclusion of body inertia in the optimization of three-link sliding locomotion, showing its importance and effects on efficiency and optimal movement patterns.

Findings

Optimal inertia is significant at low transverse friction.

Efficiency drops dramatically when inertia is reduced to zero in some motions.

Optimal motions converge as the number of frequency components increases.

Abstract

Many previous studies of sliding locomotion have assumed that body inertia is negligible. Here we optimize the kinematics of a three-link body for efficient locomotion and include among the kinematic parameters the temporal period of locomotion, or equivalently, the body inertia. The optimal inertia is non-negligible when the coefficient of friction for sliding transverse to the body axis is small. Inertia is also significant in a few cases with relatively large coefficients of friction for transverse and backward sliding, and here the optimal motions are less sensitive to the inertia parameter. The optimal motions seem to converge as the number of frequencies used is increased from one to four. For some of the optimal motions with significant inertia we find dramatic reductions in efficiency when the inertia parameter is decreased to zero. For the motions that are optimal with zero inertia, the efficiency decreases more gradually when we raise the inertia to moderate and large values.