A Minimum-Jerk Approach to Handle Singularities in Virtual Fixtures

TL;DR

This paper addresses singularities in virtual fixtures for robot guidance by analyzing their geometric nature and proposing a minimum-jerk control solution to improve smoothness and robustness in human-robot interaction.

Contribution

It provides a geometric interpretation of Euclidean Distance Singularities and introduces a minimum-jerk based approach to handle these discontinuities effectively.

Findings

The proposed method reduces discontinuities in virtual fixtures.

Experimental validation shows improved smoothness in robot guidance.

The approach enhances robustness in human-robot interaction scenarios.

Abstract

Implementing virtual fixtures in guiding tasks constrains the movement of the robot's end effector to specific curves within its workspace. However, incorporating guiding frameworks may encounter discontinuities when optimizing the reference target position to the nearest point relative to the current robot position. This article aims to give a geometric interpretation of such discontinuities, with specific reference to the commonly adopted Gauss-Newton algorithm. The effect of such discontinuities, defined as Euclidean Distance Singularities, is experimentally proved. We then propose a solution that is based on a Linear Quadratic Tracking problem with minimum jerk command, then compare and validate the performances of the proposed framework in two different human-robot interaction scenarios.