  Sampling-based motion planners rely on incremental densification to discover
progressively shorter paths. After computing feasible path $\xi$ 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
$c(\xi)$ and Euclidean heuristic $h$, $IS = \{ x | x \in \mathcal{C}, h(x_s, x)
+ h(x, x_t) \leq c(\xi) \}$.
  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
$\mathbb{R}^7$.
