  Multimodal Large Language Models (MLLMs) have demonstrated a wide range of
capabilities across many domains, including Embodied AI. In this work, we study
how to best ground a MLLM into different embodiments and their associated
action spaces, with the goal of leveraging the multimodal world knowledge of
the MLLM. We first generalize a number of methods through a unified
architecture and the lens of action space adaptors. For continuous actions, we
show that a learned tokenization allows for sufficient modeling precision,
yielding the best performance on downstream tasks. For discrete actions, we
demonstrate that semantically aligning these actions with the native output
token space of the MLLM leads to the strongest performance. We arrive at these
lessons via a thorough study of seven action space adapters on five different
environments, encompassing over 114 embodied tasks.
