A Framework for Guided Motion Planning

TL;DR

The paper addresses the pervasive reliance on heuristics in sampling-based motion planning by formalizing guided search through a guiding-space framework. It introduces a mapping from task-space to a guiding space via a projection conditioned on the search tree and proposes an information-theoretic evaluation of guidance, enabling principled comparison and combination of guiding sources. The key contributions include a taxonomy of guiding-space categories (robot, environment, and experience-based), a quantitative sampling-efficiency metric SE_Q(P) based on $D_{KL}$ and a softened target $Q_T$, and demonstrations that hybrid guiding spaces can outperform individual methods. This framework supports modular, reusable guidance that can improve planning efficiency in complex C-spaces and offers a principled path to hybrid algorithms with practical significance for robotics motion planning.

Abstract

Randomized sampling based algorithms are widely used in robot motion planning due to the problem's intractability, and are experimentally effective on a wide range of problem instances. Most variants bias their sampling using various heuristics related to the known underlying structure of the search space. In this work, we formalize the intuitive notion of guided search by defining the concept of a guiding space. This new language encapsulates many seemingly distinct prior methods under the same framework, and allows us to reason about guidance, a previously obscured core contribution of different algorithms. We suggest an information theoretic method to evaluate guidance, which experimentally matches intuition when tested on known algorithms in a variety of environments. The language and evaluation of guidance suggests improvements to existing methods, and allows for simple hybrid algorithms that combine guidance from multiple sources.

Figures (7)

• Figure 1: An illustration of guiding spaces and their usage. (a) depicts a 2D workspace with a fixed-base 2-joint manipulator and 2 obstacles, alongside two configurations $s$ and $t$ and two intermediates (in dashed gray) on the $(s,t)$-path found in the guiding space (b). We observe that one intermediate is invalid. In (b) we see the lazy planning guiding space for the environment (a) without obstacle $o_2$. A red curve shows a path between the current and target configurations shown in (a), and a blue wedge shows the resulting sampling bias. In (c) we see another 2D environment with a 3 DoF $(x,y,\theta)$ rectangular robot, and in (d) we see a guiding space, the workspace medial-axis, and the projections of the configurations $s$ and $t$ shown in (c) onto the medial-axis. Again, note that the shortest $(s,t)$ path in (d) is not valid in (c).
• Figure 2: A simple 2D example of the components of sampling efficiency: efficiency and (sub)-optimality. The nodes are colored on a green (best) to red (worst) scale. (a) and (b) show the efficiency score of each node, which corresponds to the work remaining. (c) and (d) show the suboptimality scores of the nodes, which captures the deviation of each node from the optimal path. Notice that the value of a node is relative to the other nodes, e.g., adding a new sample from (a) to (b) changes the value of all others. Notice that suboptimality depends on the tree structure, e.g., the rewiring between (c) and (d) changes the values of the nodes. Finally, despite depicting identical trees, (b) and (c) show how efficiency and suboptimality produce very different distributions over the nodes.
• Figure 3: The environments in which we evaluate the different guiding space algorithms. We draw the robot in its start and goal configurations in red.
• Figure 4: Example guiding spaces of each algorithm. We display the starts and goals of the rectangular robot for (a) RRT, (b) LazyPRM, and (d) PathDatabase to indicate that these guiding spaces are in C-space, whereas (c) MedialAxis is in workspace. (a) For RRT in SimplePassage, we show the Voronoi decomposition. (b) For LazyPRM in Cup, we show the unvalidated roadmap. (c) For MedialAxis in Trap, we show the workspace skeleton. (d) For PathDatabase in RandomSimplePassage, we display the paths from the database that pass near the goal.
• Figure 5: We show examples of each guidance method on the main environment it was tested on. Note that the visualizations are the 2D projections of the 3D C-space of a planar rectangular robot. In all cases, our implementation queries the local planner for valid edges to the goal, thus terminating the search once a configuration has been found that is visible from the goal. The final paths are highlighted in red.

Theorems & Definitions (1)

• definition thmcounterdefinition: Sampling efficiency