Camera pose estimation is key to the proper functioning of robotic systems, supporting critical tasks such as robot navigation, target tracking, camera calibration, etc.Whilemultiple algorithms solving this problem have been proposed, their correctness has rarely been validated using formal techniques. This is true despite the fact that the adoption of formal verification is essential for the reliability of safety-critical systems, and for their certification to high assurance levels. In this article, we present an effort in formally verifying an algorithm for camera pose estimation in an interactive theorem prover. The algorithm leverages the power of Rodrigues formula to solve the pose estimation problem under conditions for which existing solutions cannot be applied. The technical ingredients include (but are not limited to) mechanized proofs of the Rodrigues formula (along with its Cayley decomposition form) and the least squares method for fitting data. Based on the formalization of the algorithm, we formally derive and verify its general solution and unique solution.

中文翻译：

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基于Rodrigues公式的相机位姿估计算法形式化

相机位姿估计是机器人系统正常运行的关键，支持机器人导航、目标跟踪、相机校准等关键任务。虽然已经提出了多种解决这个问题的算法，但它们的正确性很少使用正式技术进行验证。尽管采用形式验证对于安全关键系统的可靠性及其高保证水平的认证至关重要，但事实确实如此。在本文中，我们提出了在交互式定理证明器中正式验证相机姿态估计算法的努力。该算法利用 Rodrigues 公式的强大功能来解决无法应用现有解决方案的情况下的位姿估计问题。技术成分包括（但不限于）Rodrigues 公式的机械化证明（连同其 Cayley 分解形式）和拟合数据的最小二乘法。基于算法的形式化，我们正式推导并验证了它的通解和唯一解。