Characterizing Error in Noncommutative Geometric Gait Analysis

TL;DR

This paper analyzes the errors in displacement estimates for robotic gait optimization, focusing on how low and high order terms affect accuracy and how parameter choices can mitigate these errors.

Contribution

It formulates existing displacement estimates, quantifies the impact of higher order terms, and shows how parameter variation can control these effects in gait analysis.

Findings

Low order terms significantly influence displacement estimates.

Parameter choices like body coordinate and gait diameter affect higher order effects.

Variation of parameters can effectively manage third order contributions.

Abstract

A key problem in robotic locomotion is in finding optimal shape changes to effectively displace systems through the world. Variational techniques for gait optimization require estimates of body displacement per gait cycle; however, these estimates introduce error due to unincluded high order terms. In this paper, we formulate existing estimates for displacement, and describe the contribution of low order terms to these estimates. We additionally describe the magnitude of higher (third) order effects, and identify that choice of body coordinate, gait diameter, and starting phase influence these effects. We demonstrate that variation of such parameters on two example systems (the differential drive car and Purcell swimmer) effectively manages third order contributions.