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.

翻译：近期，应用于机器人学的预训练大语言模型（LLMs）的发展已证明其能够在简单机器人任务中通过编排一系列离散技能来实现开放目标。本文研究了LLM针对一组连续参数化技能的规划问题，这些技能的执行必须避免违反一系列运动学、几何和物理约束。我们引导LLM输出一个包含开放参数的函数代码，该函数与环境约束共同构成一个连续约束满足问题（CCSP）。该CCSP可通过采样或优化方法求解，以找到既能实现目标又能避免约束违反的技能序列与连续参数设置。此外，我们考虑了LLM可能提出不可满足CCSP的情况（例如运动学不可行、动态不稳定或导致碰撞的情形），并据此重新提示LLM以形成新的CCSP。在三个不同的模拟3D领域进行的实验表明，我们提出的策略PRoC3S能够比现有基线方法更高效、更有效地解决各类具有连续参数现实约束的复杂操作任务。