Robotic Grinding Skills Learning Based on Geodesic Length Dynamic Motion Primitives

TL;DR

The paper tackles the challenge of learning robotic grinding skills with high orientation accuracy and synchronized control of position, orientation, and force on free-form surfaces. It introduces Geo-DMPs, which use geodesic-length phase on the $S^3$ orientation manifold and surface-encoding strategies (2D weighted Gaussian kernels and intrinsic mean on the orientation manifold) to enable robust, time-independent orientation learning and cross-surface trajectory generation. A synchronized framework combines arc-length DMPs for position, Geo-DMPs for orientation, and Gaussian-force encoding to produce complete grinding trajectories between arbitrary surface points, validated on chamfer and free-form surface grinding with improved orientation accuracy and finish quality. The results demonstrate significant improvements over baseline DMPs and provide a practical path for deploying autonomous robotic grinding in industrial settings, with future work extending vision-based feedback and closed-loop skill refinement.

Abstract

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.

Figures (17)

• Figure 1: Example of robotic grinding skills: free-form surface and chamfer grinding.
• Figure 2: Robotic grinding skill learning framework. The purple area implements the encoding of surface skills from multiple demonstration trajectories, outputting a position-orientation-force reference trajectory between any two points on the surface. The blue area handles parameter estimation for a single trajectory and real-time generation of robot actions.
• Figure 3: Encoding surfaces with two-dimensional weighted Gaussian kernel function. The upper surface represents the free-form surface obtained from encoding, while the lower surface corresponds to the weighted Gaussian kernel functions.
• Figure 4: Intrinsic cluster center algorithm on the manifold illustration.
• Figure 5: The purple arrow represents the logarithmic and exponential mappings between the manifold $\mathcal{M}$ and the tangent space $\mathcal{T}_{\boldsymbol{p}}\mathcal{M}$. For a point $\boldsymbol{q}$ on the manifold needs to be mapped to the tangent space $\mathcal{T}_{\boldsymbol{p}}\mathcal{M}$ in order to perform linear operations.