LLM-A*: Large Language Model Enhanced Incremental Heuristic Search on Path Planning

TL;DR

The paper addresses the inefficiency of traditional A* in large-scale path planning and the spatial-reasoning gaps of LLMs. It introduces LLM-A*, a hybrid algorithm that generates a target waypoint sequence $T$ from an LLM and integrates it into the A* search via a modified heuristic $f(s)=g(s)+h(s)+cost(t,s)$. Empirical results show substantial reductions in operation and storage needs while maintaining accurate, collision-free paths and near-linear scalability across environment sizes. The work demonstrates the potential of combining global environmental reasoning with deterministic planning to improve robotic navigation, while also noting that optimality is not strictly guaranteed and highlighting avenues for broader model evaluation and advanced prompting in future work.

Abstract

Path planning is a fundamental scientific problem in robotics and autonomous navigation, requiring the derivation of efficient routes from starting to destination points while avoiding obstacles. Traditional algorithms like A* and its variants are capable of ensuring path validity but suffer from significant computational and memory inefficiencies as the state space grows. Conversely, large language models (LLMs) excel in broader environmental analysis through contextual understanding, providing global insights into environments. However, they fall short in detailed spatial and temporal reasoning, often leading to invalid or inefficient routes. In this work, we propose LLM-A*, an new LLM based route planning method that synergistically combines the precise pathfinding capabilities of A* with the global reasoning capability of LLMs. This hybrid approach aims to enhance pathfinding efficiency in terms of time and space complexity while maintaining the integrity of path validity, especially in large-scale scenarios. By integrating the strengths of both methodologies, LLM-A* addresses the computational and memory limitations of conventional algorithms without compromising on the validity required for effective pathfinding.

Figures (5)

• Figure 1: An comparison between LLM-A* and A* in computation and memory efficiency during pathfinding process. LLM-A* leverages target states generated by LLMs as waypoints to guide the searching process, significantly reducing the number of visited states, which leads to fewer operations and storage usage than A*.
• Figure 2: Visual comparison of pathfinding efficiency Between A* and LLM-A*. This figure illustrates the performance differences between the traditional A* algorithm (left and upper images) and the LLM-A* algorithm (right and lower images). Red lines indicate the computed paths, blue dots mark the starting state, green dots indicate the goal state, gray areas represent visited states, and black lines denote obstacles. The LLM-A* algorithm demonstrates more efficient pathfinding by requiring significantly fewer visited states than A*.
• Figure 3: The comparative analysis examines the computational and memory efficiency between A* and LLM-A* (incorporating LLAMA3 with few-shot prompting) across scaled environments ranging from $1$ to $10$ times enlargement, based on the means of $10$ trials of random sampling. A* exhibits exponential growth in both (a) OPERATION and (b) STORAGE with linear increasing, environment scale, in contrast, LLM-A* achieves a near linear scalability.
• Figure 4: Visualization of pathfinding process with LLM-A* algorithms (under chebyshev heuristic setting in $11 \times 11$ grid environment) utilizing each LLM-generated waypoint, as well as comparison with A* in number of explored states. The blue and green rectangles denote the start and goal states, respectively. Grey rectangles indicate the states explored by the LLM-A* algorithms, while pink rectangles represent states explored by A*. Red line illustrate the generated paths. Stars indicate LLM-generated waypoints. (See Section \ref{['sec:qualitative']} for more)
• Figure : LLM-A* Algorithm for Path Planning