This paper develops a Bayesian optimal experimental design for robot kinematic calibration on ${\mathbb{S}^3 \!\times\! \mathbb{R}^3}$. Our method builds upon a Gaussian process approach that incorporates a geometry-aware kernel based on Riemannian Mat\'ern kernels over ${\mathbb{S}^3}$. To learn the forward kinematics errors via Bayesian optimization with a Gaussian process, we define a geodesic distance-based objective function. Pointwise values of this function are sampled via noisy measurements taken using fiducial markers on the end-effector using a camera and computed pose with the nominal kinematics. The corrected Denavit-Hartenberg parameters are obtained using an efficient quadratic program that operates on the collected data sets. The effectiveness of the proposed method is demonstrated via simulations and calibration experiments on NASA's ocean world lander autonomy testbed (OWLAT).

翻译：本文针对 ${\mathbb{S}^3 \!\times\! \mathbb{R}^3}$ 上的机器人运动学标定问题，提出了一种贝叶斯最优实验设计方法。我们的方法建立在高斯过程框架之上，该框架融合了一个基于 ${\mathbb{S}^3}$ 上黎曼 Mat\'ern 核的几何感知核函数。为了通过高斯过程贝叶斯优化来学习正向运动学误差，我们定义了一个基于测地距离的目标函数。该函数的逐点值通过使用末端执行器上的基准标记进行噪声测量来采样，测量使用相机并基于标称运动学计算位姿。校正后的 Denavit-Hartenberg 参数通过一个在收集的数据集上运行的高效二次规划程序获得。所提方法的有效性通过仿真以及在 NASA 海洋世界着陆器自主测试平台（OWLAT）上进行的标定实验得到了验证。