On the Certification of the Kinematics of 3-DOF Spherical Parallel Manipulators

TL;DR

This paper investigates the kinematics and singularity analysis of 3-DOF spherical parallel manipulators with unlimited rolling, incorporating uncertainties to identify safe control zones for stable operation.

Contribution

It introduces symbolic and semi-numerical methods to analyze singularities considering uncertainties, enabling the certification of safe operational zones.

Findings

Identified singularity-free zones in work and joint spaces.

Developed methods to account for parameter uncertainties.

Provided guidelines for stable control of the manipulator.

Abstract

This paper aims to study a specific kind of parallel robot: Spherical Parallel Manipulators (SPM) that are capable of unlimited rolling. A focus is made on the kinematics of such mechanisms, especially taking into account uncertainties (e.g. on conception & fabrication parameters, measures) and their propagations. Such considerations are crucial if we want to control our robot correctly without any undesirable behavior in its workspace (e.g. effects of singularities). In this paper, we will consider two different approaches to study the kinematics and the singularities of the robot of interest: symbolic and semi-numerical. By doing so, we can compute a singularity-free zone in the work- and joint spaces, considering given uncertainties on the parameters. In this zone, we can use any control law to inertially stabilize the upper platform of the robot.