[论文解读] A Unified Calibration Framework for Coordinate and Kinematic Parameters in Dual-Arm Robots

Tianyu Huang, Bohan Yang+5 more|arXiv (Cornell University)|Mar 16, 2026

Robotic Mechanisms and Dynamics被引用 0

一句话总结

该论文提出一个统一的Lie代数校准框架，联合估计双臂机器人两臂的坐标变换和运动学参数，使用整合的PoE基误差模型并提供可证正确的初始化。

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.

研究动机与目标

• 需要精确的双臂协作以实现相对定位和系统校准，超越仅仅基于坐标的方法的局限。
• 提出一个统一优化问题，联合估计坐标变换和两臂的运动学参数，以减少误差传递。
• 通过闭式雅可比矩阵与雅可比秩分析，确保联合估计的可识别性与数值稳定性。
• 提供一种鲁棒的初始化策略，通过SDP松弛得到可证正确性，从而提高联合优化的收敛性。

提出的方法

• 基于指派的Lie代数误差模型，采用乘积指数（PoE）公式，将坐标参数和运动学参数耦合在SE(3)中。
• 通过Lie导数推导闭式解析雅可比，将参数增量映射到残差，在每次迭代中实现线性最小二乘子问题。
• 通过检查雅可比的秩进行可识别性分析，在温和的激励条件下确立良定性。
• 通过求解一个QCQP并将其松弛为SDP，提出一个可证正确的坐标初始化，并提供事后接近全局最优的证据。
• 使用现成求解器在SE(3)流形上迭代优化所有参数，更新通过指数映射应用。

Figure 1: Illustration of a canonical dual-arm robot system. The sensor-side robot is equipped with a camera. The tool-side robot holds a calibration tool (e.g., a chessboard). The closed-loop pose chain in the dual-arm system can be defined by $\boldsymbol{A}\boldsymbol{X}\boldsymbol{B}=\boldsymbol

实验结果

研究问题

• RQ1 在不解耦的情况下，是否可以用单一统一的PoE基误差模型同时识别两臂的坐标变换和运动学参数？
• RQ2 在实际激励条件下联合优化是否是良定的且可识别的？
• RQ3 与仅坐标基线相比，基于SDP的可证正确初始化是否改善收敛性和精度？
• RQ4 在相同视觉测量下，该框架相对于基线在标定精度方面的表现如何？

主要发现

• 统一框架在相同视觉测量下对比基线具有更高的精度。
• 基于PoE的系统级模型避免了误差源的人工分离，从而降低误差传播。
• 闭式雅可比使在SE(3)流形上的优化稳定高效，线性子问题具有良好条件。
• 可识别性分析表明在温和激励条件下联合优化是良定的。
• 通过SDP实现的可证正确初始化提供一个可靠起点，初始化质量持续优于仅坐标基线。

Figure 2: Pipeline of the proposed unified calibration algorithm. Given a set of measurements under multiple dual-arm postures, we construct a consolidated Lie-algebraic error model and iteratively refine the coordinate and kinematic parameters on the $\mathrm{SE}(3)$ manifold. Before our iterative