Closed-Loop Long-Horizon Robotic Planning via Equilibrium Sequence Modeling

In the endeavor to make autonomous robots take actions, task planning is a major challenge that requires translating high-level task descriptions to long-horizon action sequences. Despite recent advances in language model agents, they remain prone to planning errors and limited in their ability to plan ahead. To address these limitations in robotic planning, we advocate a self-refining scheme that iteratively refines a draft plan until an equilibrium is reached. Remarkably, this process can be optimized end-to-end from an analytical perspective without the need to curate additional verifiers or reward models, allowing us to train self-refining planners in a simple supervised learning fashion. Meanwhile, a nested equilibrium sequence modeling procedure is devised for efficient closed-loop planning that incorporates useful feedback from the environment (or an internal world model). Our method is evaluated on the VirtualHome-Env benchmark, showing advanced performance with improved scaling w.r.t. inference-time computation. Code is available at https://github.com/Singularity0104/equilibrium-planner.