  Classical approaches to grasp planning are deterministic, requiring perfect
knowledge of an object's pose and geometry. In response, data-driven approaches
have emerged that plan grasps entirely from sensory data. While these
data-driven methods have excelled in generating parallel-jaw and power grasps,
their application to precision grasps (those using the fingertips of a
dexterous hand, e.g, for tool use) remains limited. Precision grasping poses a
unique challenge due to its sensitivity to object geometry, which allows small
uncertainties in the object's shape and pose to cause an otherwise robust grasp
to fail. In response to these challenges, we introduce Probabilistic Object
Normals for Grasping (PONG), a novel, analytic approach for calculating a
conservative estimate of force closure probability in the case when contact
locations are known but surface normals are uncertain. We then present a
practical application where we use PONG as a grasp metric for generating robust
grasps both in simulation and real-world hardware experiments. Our results
demonstrate that maximizing PONG efficiently produces robust grasps, even for
challenging object geometries, and that it can serve as a well-calibrated,
uncertainty-aware metric of grasp quality.
