Cooperative Task Spaces for Multi-Arm Manipulation Control based on Similarity Transformations

TL;DR

This paper introduces a geometric algebra-based framework for controlling multi-arm robotic systems through cooperative task spaces, simplifying complex multi-robot coordination by representing systems similarly to single-arm robots.

Contribution

It develops a theoretical foundation using conformal geometric algebra to model cooperative task spaces, enabling straightforward control and integration with existing operational space control methods.

Findings

Successfully applied to bimanual manipulators, humanoids, and multi-fingered hands.

Demonstrated in optimal control and teleoperation experiments.

Embedded nullspace structures for secondary objectives.

Abstract

Many tasks in human environments require collaborative behavior between multiple kinematic chains, either to provide additional support for carrying big and bulky objects or to enable the dexterity that is required for in-hand manipulation. Since these complex systems often have a very high number of degrees of freedom coordinating their movements is notoriously difficult to model. In this article, we present the derivation of the theoretical foundations for cooperative task spaces of multi-arm robotic systems based on geometric primitives defined using conformal geometric algebra. Based on the similarity transformations of these cooperative geometric primitives, we derive an abstraction of complex robotic systems that enables representing these systems in a way that directly corresponds to single-arm systems. By deriving the associated analytic and geometric Jacobian matrices, we then show the straightforward integration of our approach into classical control techniques rooted in operational space control. We demonstrate this using bimanual manipulators, humanoids and multi-fingered hands in optimal control experiments for reaching desired geometric primitives and in teleoperation experiments using differential kinematics control. We then discuss how the geometric primitives naturally embed nullspace structures into the controllers that can be exploited for introducing secondary control objectives. This work, represents the theoretical foundations of this cooperative manipulation control framework, and thus the experiments are presented in an abstract way, while giving pointers towards potential future applications.