  Recent developments in pretrained large language models (LLMs) applied to
robotics have demonstrated their capacity for sequencing a set of discrete
skills to achieve open-ended goals in simple robotic tasks. In this paper, we
examine the topic of LLM planning for a set of continuously parameterized
skills whose execution must avoid violations of a set of kinematic, geometric,
and physical constraints. We prompt the LLM to output code for a function with
open parameters, which, together with environmental constraints, can be viewed
as a Continuous Constraint Satisfaction Problem (CCSP). This CCSP can be solved
through sampling or optimization to find a skill sequence and continuous
parameter settings that achieve the goal while avoiding constraint violations.
Additionally, we consider cases where the LLM proposes unsatisfiable CCSPs,
such as those that are kinematically infeasible, dynamically unstable, or lead
to collisions, and re-prompt the LLM to form a new CCSP accordingly.
Experiments across three different simulated 3D domains demonstrate that our
proposed strategy, PRoC3S, is capable of solving a wide range of complex
manipulation tasks with realistic constraints on continuous parameters much
more efficiently and effectively than existing baselines.
