  Task-oriented grasping of unfamiliar objects is a necessary skill for robots
in dynamic in-home environments. Inspired by the human capability to grasp such
objects through intuition about their shape and structure, we present a novel
zero-shot task-oriented grasping method leveraging a geometric decomposition of
the target object into simple, convex shapes that we represent in a graph
structure, including geometric attributes and spatial relationships. Our
approach employs minimal essential information - the object's name and the
intended task - to facilitate zero-shot task-oriented grasping. We utilize the
commonsense reasoning capabilities of large language models to dynamically
assign semantic meaning to each decomposed part and subsequently reason over
the utility of each part for the intended task. Through extensive experiments
on a real-world robotics platform, we demonstrate that our grasping approach's
decomposition and reasoning pipeline is capable of selecting the correct part
in 92% of the cases and successfully grasping the object in 82% of the tasks we
evaluate. Additional videos, experiments, code, and data are available on our
project website: https://shapegrasp.github.io/.
