  While grasp detection is an important part of any robotic manipulation
pipeline, reliable and accurate grasp detection in $SE(3)$ remains a research
challenge. Many robotics applications in unstructured environments such as the
home or warehouse would benefit a lot from better grasp performance. This paper
proposes a novel framework for detecting $SE(3)$ grasp poses based on point
cloud input. Our main contribution is to propose an $SE(3)$-equivariant model
that maps each point in the cloud to a continuous grasp quality function over
the 2-sphere $S^2$ using a spherical harmonic basis. Compared with reasoning
about a finite set of samples, this formulation improves the accuracy and
efficiency of our model when a large number of samples would otherwise be
needed. In order to accomplish this, we propose a novel variation on
EquiFormerV2 that leverages a UNet-style backbone to enlarge the number of
points the model can handle. Our resulting method, which we name
$\textit{OrbitGrasp}$, significantly outperforms baselines in both simulation
and physical experiments.
