用贝叶斯优化提升机器人运动学标定精度，结合几何感知核函数。
Bayesian Optimal Experimental Design for Robot Kinematic Calibration
- 基于黎曼马特恩核的高斯过程，融合球面空间几何特性建模误差。
- 通过相机测量末端执行器位姿，最小化测得与名义值间的测地距离。
- 在NASA海洋世界探测车测试平台验证，显著提升标定精度。
本文针对 ${\mathbb{S}^3 \! imes\! \mathbb{R}^3}$ 空间上的机器人运动学标定问题，提出一种贝叶斯最优实验设计方法。该方法基于高斯过程，采用基于黎曼马特恩核的几何感知核函数，以测地距离为优化目标，利用安装于末端执行器上的标记点通过相机获取的噪声测量值与名义运动学计算出的姿态进行误差建模。通过收集数据并求解高效的二次规划问题，获得修正后的Denavit-Hartenberg参数。在NASA的海洋世界登陆器自主性测试平台（OWLAT）上进行了仿真与实验验证，结果表明该方法能有效提升标定精度。
原文摘要 · Abstract (English)
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 Matérn 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).
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