This paper presents the FS-Planner, a fast graph-search planner based on a modified Lazy Theta* algorithm that exploits the analytical properties of Euclidean Distance Fields (EDFs). We introduce a new cost function that integrates an EDF-based term proven to satisfy the triangle inequality, enabling efficient parent selection and reducing computation time while generating safe paths with smaller heading variations. We also derive an analytic approximation of the EDF integral along a segment and analyze the influence of the line-of-sight limit on the approximation error, motivating the use of a bounded visibility range. Furthermore, we propose a gradient-based neighbour-selection mechanism that decreases the number of explored nodes and improves computational performance without degrading safety or path quality. The FS-Planner produces safe paths with small heading changes without requiring the use of post-processing methods. Extensive experiments and comparisons in challenging 3D indoor simulation environments, complemented by tests in real-world outdoor environments, are used to evaluate and validate the FS-Planner. The results show consistent improvements in computation time, exploration efficiency, safety, and smoothness in a geometric sense compared with baseline heuristic planners, while maintaining sub-optimality within acceptable bounds. Finally, the proposed EDF-based cost formulation is orthogonal to the underlying search method and can be incorporated into other planning paradigms.

翻译：本文提出FS-Planner——一种基于改进Lazy Theta*算法的快速图搜索规划器，该算法充分利用欧氏距离场（EDF）的解析特性。我们引入了一种新的代价函数，该函数整合了已被证明满足三角不等式的EDF项，从而在生成航向变化较小的安全路径的同时，实现高效的父节点选择并减少计算时间。我们还推导了沿线段EDF积分的解析近似表达式，分析了视线限制对近似误差的影响，这为采用有限可见范围提供了理论依据。此外，我们提出了一种基于梯度的邻域选择机制，该机制在保证安全性和路径质量的前提下，减少了待探索节点数量并提升了计算性能。FS-Planner无需后处理方法即可生成航向变化小的安全路径。通过在具有挑战性的三维室内仿真环境中进行大量实验与对比，并辅以真实室外环境测试，我们对FS-Planner进行了全面评估与验证。结果表明，相较于基准启发式规划器，该算法在计算时间、探索效率、安全性及几何意义上的平滑度方面均取得持续改进，同时将次优性控制在可接受范围内。最后，所提出的基于EDF的代价函数构造与底层搜索方法正交，可被整合到其他规划范式中。