Guided Incremental Local Densification for Accelerated Sampling-based Motion Planning

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 $\mathbb{R}^7$.