LiP-LLM: Integrating Linear Programming and dependency graph with Large Language Models for multi-robot task planning

Abstract: This study proposes LiP-LLM: integrating linear programming and dependency graph with LLMs for multi-robot task planning. In order for multiple robots to perform tasks more efficiently, it is necessary to manage the precedence dependencies between tasks. Although multi-robot decentralized and centralized task planners using LLMs have been proposed, none of these studies focus on precedence dependencies from the perspective of task efficiency or leverage traditional optimization methods. It addresses key challenges in managing dependencies between skills and optimizing task allocation. LiP-LLM consists of three steps: skill list generation and dependency graph generation by LLMs, and task allocation using linear programming. The LLMs are utilized to generate a comprehensive list of skills and to construct a dependency graph that maps the relationships and sequential constraints among these skills. To ensure the feasibility and efficiency of skill execution, the skill list is generated by calculated likelihood, and linear programming is used to optimally allocate tasks to each robot. Experimental evaluations in simulated environments demonstrate that this method outperforms existing task planners, achieving higher success rates and efficiency in executing complex, multi-robot tasks. The results indicate the potential of combining LLMs with optimization techniques to enhance the capabilities of multi-robot systems in executing coordinated tasks accurately and efficiently. In an environment with two robots, a maximum success rate difference of 0.82 is observed in the language instruction group with a change in the object name.