A Unified Calibration Framework for Coordinate and Kinematic Parameters in Dual-Arm Robots

2026-03-16

AI Summary

This work addresses the error accumulation inherent in conventional separate calibration of coordinate frames and kinematic parameters for dual-arm robotic visual collaborative tasks, which degrades overall system accuracy. To overcome this limitation, the paper presents the first unified calibration framework that jointly models and optimizes both sets of parameters within Lie algebra space, thereby eliminating artificial decoupling errors. The approach formulates an error model based on the product-of-exponentials formula, derives an analytical Jacobian matrix using Lie derivatives, and incorporates semidefinite relaxation to obtain a certifiably near-globally optimal initialization, ensuring parameter identifiability and well-posed optimization. Experimental results demonstrate that, under identical visual measurement conditions, the proposed method achieves significantly higher calibration accuracy than existing approaches, with stable and reliable initialization, thus providing robust support for high-precision collaborative manipulation.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Precise collaboration in vision-based dual-arm robot systems requires accurate system calibration. Recent dual-robot calibration methods have achieved strong performance by simultaneously solving multiple coordinate transformations. However, these methods either treat kinematic errors as implicit noise or handle them through separated error modeling, resulting in non-negligible accumulated errors. In this paper, we present a novel framework for unified calibration of the coordinate transformations and kinematic parameters in both robot arms. Our key idea is to unify all the tightly coupled parameters within a single Lie-algebraic formulation. To this end, we construct a consolidated error model grounded in the product-of-exponentials formula, which naturally integrates the coordinate and kinematic parameters in twist forms. Our model introduces no artificial error separation and thus greatly mitigates the error propagation. In addition, we derive a closed-form analytical Jacobian from this model using Lie derivatives. By exploring the Jacobian rank property, we analyze the identifiability of all calibration parameters and show that our joint optimization is well-posed under mild conditions. This enables off-the-shelf iterative solvers to stably optimize these parameters on the manifold space. Besides, to ensure robust convergence of our joint optimization, we develop a certifiably correct algorithm for initializing the unknown coordinates. Relying on semidefinite relaxation, our algorithm can yield a reliable estimate whose near-global optimality can be verified a posteriori. Extensive experiments validate the superior accuracy of our approach over previous baselines under identical visual measurements. Meanwhile, our certifiable initialization consistently outperforms several coordinate-only baselines, proving its reliability as a starting point for joint optimization.

Problem

• dual-arm robots
• system calibration
• kinematic parameters
• coordinate transformations
• error accumulation

Innovation

• unified calibration
• Lie algebra
• product-of-exponentials
• certifiable initialization
• dual-arm robots