  With large language models, robots can understand language more flexibly and
more capable than ever before. This survey reviews and situates recent
literature into a spectrum with two poles: 1) mapping between language and some
manually defined formal representation of meaning, and 2) mapping between
language and high-dimensional vector spaces that translate directly to
low-level robot policy. Using a formal representation allows the meaning of the
language to be precisely represented, limits the size of the learning problem,
and leads to a framework for interpretability and formal safety guarantees.
Methods that embed language and perceptual data into high-dimensional spaces
avoid this manually specified symbolic structure and thus have the potential to
be more general when fed enough data but require more data and computing to
train. We discuss the benefits and tradeoffs of each approach and finish by
providing directions for future work that achieves the best of both worlds.
