Optimal Uncertainty-Aware Calibration for the AX=YB Problem

This article proposes a general optimization framework for solving hand-eye calibration problem. Unlike traditional methods, an iterative algorithm based on Lie algebra that achieves approximately global optimal solutions is developed. During the optimization process, the method strictly preserves the structural constraints of the calibration parameters and enables synchronized updates between calibration parameters. Recognizing that data used in real-word hand-eye calibration often contain uncertainty, especially in over-loading and large workspace industrial robot scenarios, which can significantly degrade accuracy, and accurately modeling such uncertainty is inherently difficult, this article avoids explicit uncertainty modeling. Instead, an uncertainty metric to evaluate the relative uncertainty between data sources is introduced and used to dynamically refine the iterative process. To further enhance convergence efficiency, an effective initial solution generation method that improves overall stability and accuracy is designed. Numerical simulations and real-world experiments validate the effectiveness of the proposed approach, and in synthetic datasets, the proposed approach improves the estimation accuracy by at least 67\% under high-uncertainty conditions compared with the existing methods.

Robotic Grinding Skills Learning Based on Geodesic Length Dynamic Motion Primitives

Learning grinding skills from human craftsmen via imitation learning has become a key research topic in robotic machining. Due to their strong generalization and robustness to external disturbances, Dynamical Movement Primitives (DMPs) offer a promising approach for robotic grinding skill learning. However, directly applying DMPs to grinding tasks faces challenges, such as low orientation accuracy, unsynchronized position-orientation-force, and limited generalization for surface trajectories. To address these issues, this paper proposes a robotic grinding skill learning method based on geodesic length DMPs (Geo-DMPs). First, a normalized 2D weighted Gaussian kernel and intrinsic mean clustering algorithm are developed to extract geometric features from multiple demonstrations. Then, an orientation manifold distance metric removes the time dependency in traditional orientation DMPs, enabling accurate orientation learning via Geo-DMPs. A synchronization encoding framework is further proposed to jointly model position, orientation, and force using a geodesic length-based phase function. This framework enables robotic grinding actions to be generated between any two surface points. Experiments on robotic chamfer grinding and free-form surface grinding validate that the proposed method achieves high geometric accuracy and generalization in skill encoding and generation. To our knowledge, this is the first attempt to use DMPs for jointly learning and generating grinding skills in position, orientation, and force on model-free surfaces, offering a novel path for robotic grinding.