Sampling-based planning algorithm is a powerful tool for solving planning problems in high-dimensional state spaces. In this article, we present a novel approach to sampling in the most promising regions, which significantly reduces planning time-consumption. The RRT# algorithm defines the Relevant Region based on the cost-to-come provided by the optimal forward-searching tree. However, it uses the cumulative cost of a direct connection between the current state and the goal state as the cost-to-go. To improve the path planning efficiency, we propose a batch sampling method that samples in a refined Relevant Region with a direct sampling strategy, which is defined according to the optimal cost-to-come and the adaptive cost-to-go, taking advantage of various sources of heuristic information. The proposed sampling approach allows the algorithm to build the search tree in the direction of the most promising area, resulting in a superior initial solution quality and reducing the overall computation time compared to related work. To validate the effectiveness of our method, we conducted several simulations in both $SE(2)$ and $SE(3)$ state spaces. And the simulation results demonstrate the superiorities of proposed algorithm.

翻译：基于采样的规划算法是解决高维状态空间规划问题的强大工具。本文提出了一种在最有前景区域进行采样的新方法，显著减少了规划时间消耗。RRT#算法基于最优正向搜索树提供的到达成本（cost-to-come）定义相关区域，但采用当前状态与目标状态直接连接的累积成本作为剩余成本（cost-to-go）。为提升路径规划效率，我们提出一种批采样方法，该方法基于最优到达成本与自适应剩余成本，利用多种启发式信息源定义精炼相关区域，并采用直接采样策略进行采样。提出的采样方法使算法能够沿最有前景区域方向构建搜索树，相较于相关工作，不仅获得了更优的初始解质量，还降低了总体计算时间。为验证方法有效性，我们在$SE(2)$和$SE(3)$状态空间中进行了多组仿真实验，结果证明了所提算法的优越性。