  Legged robots have the potential to expand the reach of autonomy beyond paved
roads. In this work, we consider the difficult problem of locomotion on
challenging terrains using a single forward-facing depth camera. Due to the
partial observability of the problem, the robot has to rely on past
observations to infer the terrain currently beneath it. To solve this problem,
we follow the paradigm in computer vision that explicitly models the 3D
geometry of the scene and propose Neural Volumetric Memory (NVM), a geometric
memory architecture that explicitly accounts for the SE(3) equivariance of the
3D world. NVM aggregates feature volumes from multiple camera views by first
bringing them back to the ego-centric frame of the robot. We test the learned
visual-locomotion policy on a physical robot and show that our approach, which
explicitly introduces geometric priors during training, offers superior
performance than more na\"ive methods. We also include ablation studies and
show that the representations stored in the neural volumetric memory capture
sufficient geometric information to reconstruct the scene. Our project page
with videos is https://rchalyang.github.io/NVM .
