APT*：通过自适应扁长椭圆R近邻的渐近最优运动规划
APT*: Asymptotically Optimal Motion Planning via Adaptively Prolated Elliptical R-Nearest Neighbors
AI总结：
APT*在FDIT*基础上引入自适应批量大小和椭圆r近邻模块，通过环境反馈动态调节搜索过程，在R^4至R^16维度上优于现有单查询采样规划器并完成真实机器人操作验证。
摘要：
最优路径规划旨在确定从起点到目标的状态序列，同时考虑规划目标。常用方法通常采用固定批量大小，并忽略障碍物信息，这并非针对具体问题。本研究引入了自适应扁长树（APT*），这是一种新颖的基于采样的运动规划器，它在力方向信息树（FDIT*）的基础上进行扩展，集成了自适应批量大小和椭圆r近邻模块，以根据环境反馈动态调节路径搜索过程。APT*根据信息集的超体积调整批量大小，并将顶点视为遵循库仑定律的电荷，通过邻居样本定义虚拟力，从而细化扁长最近邻选择。这些模块采用非线性扁长方法自适应地调整顶点的电荷以定义力，从而在降低解成本的同时提高收敛速度。对比分析表明，APT*在从R^4到R^16的维度上优于现有的单查询基于采样的规划器，并通过真实世界机器人操作任务进一步验证。展示我们实验结果的视频可在以下链接获取：https://youtu.be/gCcUr8LiEw4
英文摘要：
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
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
