  A fundamental task in robotics is to navigate between two locations. In
particular, real-world navigation can require long-horizon planning using
high-dimensional RGB images, which poses a substantial challenge for end-to-end
learning-based approaches. Current semi-parametric methods instead achieve
long-horizon navigation by combining learned modules with a topological memory
of the environment, often represented as a graph over previously collected
images. However, using these graphs in practice requires tuning a number of
pruning heuristics. These heuristics are necessary to avoid spurious edges,
limit runtime memory usage and maintain reasonably fast graph queries in large
environments. In this work, we present One-4-All (O4A), a method leveraging
self-supervised and manifold learning to obtain a graph-free, end-to-end
navigation pipeline in which the goal is specified as an image. Navigation is
achieved by greedily minimizing a potential function defined continuously over
image embeddings. Our system is trained offline on non-expert exploration
sequences of RGB data and controls, and does not require any depth or pose
measurements. We show that O4A can reach long-range goals in 8 simulated Gibson
indoor environments and that resulting embeddings are topologically similar to
ground truth maps, even if no pose is observed. We further demonstrate
successful real-world navigation using a Jackal UGV platform.
