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

2025-10-30

AI Summary

Modeling motion coordination in high-degree-of-freedom multi-arm robotic systems remains challenging due to complex inter-arm kinematic coupling and geometric constraints. Method: This paper proposes a conformal geometric algebra (CGA)-based cooperative task-space framework. It leverages CGA to represent geometric primitives and their similarity transformations, mapping the multi-arm system onto an equivalent single-arm abstraction for motion decoupling and geometric abstraction. The formulation inherently embeds null-space structure, enabling hierarchical optimization—primary task tracking in the task space and secondary objectives (e.g., obstacle avoidance, joint limit avoidance) in the null space—via integrated analytical/geometry-based Jacobian derivation, operational-space control, and differential optimal control. Results: Experiments on dual-arm manipulators, humanoid robots, and multifingered hands demonstrate high-precision geometric target tracking and robust teleoperation performance under dynamic constraints.

Technology Category

• Intelligent Robots: Multi-Robot Systems
• Computer Vision: Motion & Tracking
• Multiagent Systems: Coordination and Collaboration

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Modeling coordination for multi-arm robotic systems with high degrees of freedom
• Developing geometric abstractions for complex collaborative manipulation tasks
• Integrating cooperative task spaces into classical operational space control

Innovation

• Multi-arm control using geometric algebra primitives
• Similarity transformations abstract complex robotic systems
• Analytic Jacobian matrices integrate with classical control