A note on synthesizing geodesic based contact curves

TL;DR

This paper presents a method for synthesizing geodesic-based contact curves to ensure rolling constraints between bodies, with modifications to handle disturbances, demonstrated through in-hand manipulation simulations.

Contribution

It introduces a novel approach to generate contact curves on surfaces using geodesic equations that guarantee rolling constraints and disturbance rejection.

Findings

Geodesic contact curves ensure proper rolling constraints.

Modified geodesic equations can reject disturbances.

Simulations demonstrate effectiveness in in-hand manipulation.

Abstract

The paper focuses on synthesizing optimal contact curves that can be used to ensure a rolling constraint between two bodies in relative motion. We show that geodesic based contact curves generated on both the contacting surfaces are sufficient conditions to ensure rolling. The differential geodesic equations, when modified, can ensure proper disturbance rejection in case the system of interacting bodies is perturbed from the desired curve. A corollary states that geodesic curves are generated on the surface if rolling constraints are satisfied. Simulations in the context of in-hand manipulations of the objects are used as examples.