自适应调整采样批次与椭球近邻，提升高维路径规划效率与解质量。
APT*: Asymptotically Optimal Motion Planning via Adaptively Prolated Elliptical R-Nearest Neighbors
- 根据环境反馈动态调节采样批次，结合电荷力模型优化近邻选择。
- 在4至16维空间中，收敛速度更快且路径成本更低，优于现有方法。
- 适合高维复杂场景下的机器人路径规划，实测验证效果显著。
最优路径规划旨在从起点到目标点确定状态序列，同时满足规划目标。现有方法常采用固定批量采样，忽略障碍物信息，缺乏问题特异性。本文提出自适应延展树（APT*），基于力向导知情树（FDIT*）改进，引入自适应批量大小与椭球r-近邻模块，根据环境反馈动态调节搜索过程。APT*依据知情集的超体积调整批量大小，并将顶点视为电荷，遵循库仑定律定义虚拟力，从而优化长轴近邻选择。该方法采用非线性延展机制，自适应调整顶点电荷以定义力，显著提升收敛速度并降低解成本。对比实验表明，APT*在ℝ⁴至ℝ¹⁶维度下均优于现有单查询采样规划器，并在真实机器人操作任务中得到验证。实验视频见：https://youtu.be/gCcUr8LiEw4
原文摘要 · Abstract (English)
Optimal path planning aims to determine a sequence of states from a start to a goal while accounting for planning objectives. Popular methods often integrate fixed batch sizes and neglect information on obstacles, which is not problem-specific. This study introduces Adaptively Prolated Trees (APT*), a novel sampling-based motion planner that extends based on Force Direction Informed Trees (FDIT*), integrating adaptive batch-sizing and elliptical $r$-nearest neighbor modules to dynamically modulate the path searching process based on environmental feedback. APT* adjusts batch sizes based on the hypervolume of the informed sets and considers vertices as electric charges that obey Coulomb's law to define virtual forces via neighbor samples, thereby refining the prolate nearest neighbor selection. These modules employ non-linear prolate methods to adaptively adjust the electric charges of vertices for force definition, thereby improving the convergence rate with lower solution costs. Comparative analyses show that APT* outperforms existing single-query sampling-based planners in dimensions from $\mathbb{R}^4$ to $\mathbb{R}^{16}$, and it was further validated through a real-world robot manipulation task. A video showcasing our experimental results is available at: https://youtu.be/gCcUr8LiEw4
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