Workspace and Singularity analysis of a Delta like family robot

TL;DR

This paper uses algebraic tools to analyze the workspace and singularities of delta-like parallel robots, providing visualizations and complexity metrics to aid in robot configuration selection.

Contribution

It introduces an algebraic approach using Gröbner bases and Cylindrical Algebraic Decomposition for detailed singularity and workspace analysis of delta-like robots.

Findings

Certified 3D visualizations of workspace and joint space shapes.

Tabulated parameters indicating singularity complexity.

Guidelines for selecting robot configurations based on singularity analysis.

Abstract

Workspace and joint space analysis are essential steps in describing the task and designing the control loop of the robot, respectively. This paper presents the descriptive analysis of a family of delta-like parallel robots by using algebraic tools to induce an estimation about the complexity in representing the singularities in the workspace and the joint space. A Gr{\"o}bner based elimination is used to compute the singularities of the manipulator and a Cylindrical Algebraic Decomposition algorithm is used to study the workspace and the joint space. From these algebraic objects, we propose some certified three dimensional plotting describing the the shape of workspace and of the joint space which will help the engineers or researchers to decide the most suited configuration of the manipulator they should use for a given task. Also, the different parameters associated with the complexity of the serial and parallel singularities are tabulated, which further enhance the selection of the different configuration of the manipulator by comparing the complexity of the singularity equations.