Learned Critical Probabilistic Roadmaps for Robotic Motion Planning

Robot motion planning computes a collision free, dynamically feasible, and low-cost trajectory from an initial configuration to goal region [1]. Sampling-based motion planning (SBMP) approaches, such as probabilistic roadmaps (PRMs) [2], efficiently solve complex planning problems through a set of probing samples to construct a roadmap, an implicit topological graph of the robot’s configuration space. To connect the inital state and goal region, PRMs search the roadmap and identify a sequence of configurations and local connections which the robot may traverse. Though these algorithms can form arbitrarily accurate representations as the number of samples increases to infinity, in practice, only a few critical states are necessary to parameterize solution trajectories. Often these critical states enjoy significant structure, for example entries to narrow passages, yet are only identified through exhaustive sampling [3]. We present a method that learns to recognize critical configurations and use them to construct a hierarchical PRM. These critical configurations are quantified through betweenness centrality [4], a graph-theoretic measure of centrality based on a sample’s importance to shortest paths through a graph, followed by a smoothing step that retains critical samples that are necessary for planning. Online, given a new planning problem, we construct a Critical Probabilistic Roadmap, which samples a small number of critical configurations and large number of non-critical configurations. The non-critical samples are connected locally, preserving the theoretical guarantees of SBMP, while the critical configurations are connected to all samples, providing critical edges through the graph. We show two orders of magnitude improvement in solving a narrow passage problem. Related Work. Learned sample distributions for robotic motion planning have been studied recently [3], [5], [6], [7]. [3] and [5] use offline solution trajectories to learn a distribution of samples and bias sampling towards regions where an optimal solution might lie. [6] learns a local sampler to bias sampling towards. Finally [7] learns to identify critical regions for sampling based on images of successful solutions and leverages these samples by growing trees from them. In this work, we identify critical regions from graph theoretical techniques in the configuration space and incorporate these samples into a Critical Roadmap, which allows the critical samples to connect throughout the configuration space. Several approaches exist to compute a sample’s “criticality”; the most promising we identified were: label propagation [8] (Fig. 1a), minimum k-cuts [9] (Fig. 1c), and betweenness centrality [4] (Fig. 1d). Label propagation finds reasonable results for very narrow passage problems, but the results are unstable and poorly defined for problems with less constrained bottlenecks (Fig 1b). Minimum k-cuts can identify many critical samples, but require a fixed number of cuts be provided which can result in too few cuts, thus ignoring critical regions, or too many, thus identifying noncritical regions, e.g., corners, Fig. 1c. Furthermore, minimum k-cuts is significantly slower than the other approaches. Ultimately, we selected betweenness centrality, which captures the number of all-pairs shortest paths that pass through a given node, as it is fast to compute, stable, and principled.