  Conventional Task and Motion Planning (TAMP) approaches rely on manually
crafted interfaces connecting symbolic task planning with continuous motion
generation. These domain-specific and labor-intensive modules are limited in
addressing emerging tasks in real-world settings. Here, we present LLM^3, a
novel Large Language Model (LLM)-based TAMP framework featuring a
domain-independent interface. Specifically, we leverage the powerful reasoning
and planning capabilities of pre-trained LLMs to propose symbolic action
sequences and select continuous action parameters for motion planning.
Crucially, LLM^3 incorporates motion planning feedback through prompting,
allowing the LLM to iteratively refine its proposals by reasoning about motion
failure. Consequently, LLM^3 interfaces between task planning and motion
planning, alleviating the intricate design process of handling domain-specific
messages between them. Through a series of simulations in a box-packing domain,
we quantitatively demonstrate the effectiveness of LLM^3 in solving TAMP
problems and the efficiency in selecting action parameters. Ablation studies
underscore the significant contribution of motion failure reasoning to the
success of LLM^3. Furthermore, we conduct qualitative experiments on a physical
manipulator, demonstrating the practical applicability of our approach in
real-world settings.
