Extending the Cooperative Dual-Task Space in Conformal Geometric Algebra

TL;DR

This paper extends the cooperative dual-task space framework into conformal geometric algebra, enhancing geometric modeling capabilities for dual-arm robotic tasks and demonstrating its effectiveness through real-world experiments with model predictive control.

Contribution

It introduces a conformal geometric algebra extension of the CDTS, providing more tools for geometric modeling and seamless integration with optimal control frameworks.

Findings

Enhanced geometric expressiveness for dual-arm tasks.

Successful real-world implementation with Franka Emika robots.

Effective modeling of objectives and constraints using CGA-CDTS.

Abstract

In this work, we are presenting an extension of the cooperative dual-task space (CDTS) in conformal geometric algebra. The CDTS was first defined using dual quaternion algebra and is a well established framework for the simplified definition of tasks using two manipulators. By integrating conformal geometric algebra, we aim to further enhance the geometric expressiveness and thus simplify the modeling of various tasks. We show this formulation by first presenting the CDTS and then its extension that is based around a cooperative pointpair. This extension keeps all the benefits of the original formulation that is based on dual quaternions, but adds more tools for geometric modeling of the dual-arm tasks. We also present how this CGA-CDTS can be seamlessly integrated with an optimal control framework in geometric algebra that was derived in previous work. In the experiments, we demonstrate how to model different objectives and constraints using the CGA-CDTS. Using a setup of two Franka Emika robots we then show the effectiveness of our approach using model predictive control in real world experiments.