ICRA Conference 2025 Conference Paper
Patch Tree: Exploiting the Gauss Map and Principal Component Analysis for Robotic Grasping
- Yan-Bin Jia
- Yuechuan Xue
- Ling Tang
Grasp planning must consider an object's local geometry (at the finger contacts), for the range of applicable wrenches under friction, and its global geometry, for force closure and grasp quality. Most everyday objects have curved surfaces unamenable to a pure combinatorial approach but treatable with tools from differential geometry. Our idea is to “discretize” such a surface in a top-down fashion into elementary patches (e-patches), each consisting of points that would yield close enough wrenches. Preprocessing based on Gaussian curvature decomposes the surface into strictly convex, strictly concave, ruled, and saddle patches. The Gauss map guides the subdivision of any patch with a large variation in the contact force direction, with the aid of a Platonic solid. The principal component analysis (PCA) further subdivides any patch that has a large variation in torque. The final structure is called a patch tree, which stores e-patches at its leaves, and force or torque ranges at its internal nodes. Grasp synthesis and optimization operates on the patch tree with a stack to efficiently prune away non-promising finger placements. Simulation and experiment with a Shadow Hand have been conducted over everyday items. The patch tree exhibits different levels of surface granularity. It has a good promise for efficient planning of finger gaits to carry out grasping and tool manipulation.