基于加速采样的运动规划中的引导增量局部加密
Guided Incremental Local Densification for Accelerated Sampling-based Motion Planning
摘要：
基于采样的运动规划器依赖于增量致密化来发现逐渐更短的路径。在计算开始$x_s$和目标$x_t$之间的可行路径$ξ$之后，通知集（IS）通过保守地消除不能产生较短路径的点来修剪配置空间$\mathcal{C}$。通过从该知情集采样的致密化保持从整个配置空间采样的渐近最优性。对于路径长度$c(ξ)$和欧几里德启发式$h$，$IS = \{ x | x \in \mathcal{C}, h(x_s, x) + h(x, x_t) \leq c(ξ) \}$。依赖于启发式可以使IS在高维或复杂环境中特别保守。此外，IS仅在发现较短路径时缩小。因此，如果加密和规划的每次迭代不能产生更短的路径，则浪费了来自加密和规划的每次迭代的计算工作，尽管改进了搜索树中的顶点的成本。我们的关键见解是，即使在这样的失败，更短的路径到顶点的搜索树（而不仅仅是目标）可以立即改善规划的采样策略。GuILD（Guided Incremental Local Densification）利用这些信息从IS的局部子集中进行采样。我们表明，GuILD显着优于均匀采样的知情集在模拟$\mathbb{R}^2$，$SE(2)$环境和操作任务中的$\mathbb{R}^7$。
英文摘要：
Sampling-based motion planners rely on incremental densification to discover progressively shorter paths. After computing feasible path $ξ$ between start $x_s$ and goal $x_t$, the Informed Set (IS) prunes the configuration space $\mathcal{C}$ by conservatively eliminating points that cannot yield shorter paths. Densification via sampling from this Informed Set retains asymptotic optimality of sampling from the entire configuration space. For path length $c(ξ)$ and Euclidean heuristic $h$, $IS = \{ x | x \in \mathcal{C}, h(x_s, x) + h(x, x_t) \leq c(ξ) \}$. Relying on the heuristic can render the IS especially conservative in high dimensions or complex environments. Furthermore, the IS only shrinks when shorter paths are discovered. Thus, the computational effort from each iteration of densification and planning is wasted if it fails to yield a shorter path, despite improving the cost-to-come for vertices in the search tree. Our key insight is that even in such a failure, shorter paths to vertices in the search tree (rather than just the goal) can immediately improve the planner's sampling strategy. Guided Incremental Local Densification (GuILD) leverages this information to sample from Local Subsets of the IS. We show that GuILD significantly outperforms uniform sampling of the Informed Set in simulated $\mathbb{R}^2$, $SE(2)$ environments and manipulation tasks in $\mathbb{R}^7$.
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。
