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.

翻译：基于视觉的双臂机器人系统实现精确协作需要准确的系统标定。近期的双机器人标定方法通过同时求解多个坐标变换取得了优异性能。然而，这些方法要么将运动学误差视为隐式噪声，要么通过分离的误差模型进行处理，导致产生不可忽略的累积误差。本文提出一种新颖的框架，用于统一标定两个机械臂的坐标变换与运动学参数。我们的核心思想是将所有紧密耦合的参数统一在单一的李代数表达式中。为此，我们基于指数积公式构建了一个统一的误差模型，该模型以旋量形式自然地整合了坐标参数与运动学参数。我们的模型未引入人为的误差分离，从而极大缓解了误差传播。此外，我们利用李导数从该模型推导出闭式解析雅可比矩阵。通过探究雅可比矩阵的秩特性，我们分析了所有标定参数的可辨识性，并证明在温和条件下我们的联合优化问题是适定的。这使得现成的迭代求解器能够在流形空间上稳定地优化这些参数。此外，为确保联合优化的鲁棒收敛性，我们开发了一种可证明正确的算法来初始化未知坐标。该算法基于半定松弛，能够产生可靠的估计值，其近全局最优性可在后验中得到验证。大量实验证明，在相同的视觉测量条件下，我们的方法相比先前基线具有更高的精度。同时，我们的可验证初始化算法持续优于多个仅标定坐标的基线方法，证明了其作为联合优化起点的可靠性。