Conformalized Non-uniform Sampling Strategies for Accelerated Sampling-based Motion Planning

TL;DR

The paper tackles inefficiency in sampling-based motion planning by introducing a certified non-uniform sampling approach that biases exploration toward regions likely to contain the optimal path. It leverages conformal prediction to quantify uncertainty in generic heuristic path predictors, producing prediction sets that contain the optimal trajectory with probability at least $1-\alpha$ and decomposing these into per-step regions to guide sampling. This CP-driven sampling is integrated into RRT*, yielding CP-RRT* which demonstrates substantial runtime improvements and robust generalization across obstacle densities and unseen environments, while remaining agnostic to the chosen predictor and training-free. The work has practical impact for fast, reliable kinodynamic planning in cluttered or high-dimensional settings and offers a flexible framework that can pair with A*, VLMs, or planning networks.

Abstract

Sampling-based motion planners (SBMPs) are widely used to compute dynamically feasible robot paths. However, their reliance on uniform sampling often leads to poor efficiency and slow planning in complex environments. We introduce a novel non-uniform sampling strategy that integrates into existing SBMPs by biasing sampling toward `certified' regions. These regions are constructed by (i) generating an initial, possibly infeasible, path using any heuristic path predictor (e.g., A* or vision-language models) and (ii) applying conformal prediction to quantify the predictor's uncertainty. This process yields prediction sets around the initial-guess path that are guaranteed, with user-specified probability, to contain the optimal solution. To our knowledge, this is the first non-uniform sampling approach for SBMPs that provides such probabilistically correct guarantees on the sampling regions. Extensive evaluations demonstrate that our method consistently finds feasible paths faster and generalizes better to unseen environments than existing baselines.

Figures (5)

• Figure 1: Illustration of the NCS and the corresponding prediction regions. In (a), the NCS is computed as the maximum distance between each predicted state ${\mathbf p}(k)$ and the portion of the optimal trajectory $\rho$ (blue) within its Voronoi cell ${\mathcal{V}}(k)$. In (b), the resulting point-wise prediction regions ${\mathcal{C}}_k$ (shaded) are shown as the intersections of balls of radius $\hat{q}$ centered at ${\mathbf p}(k)$ with their respective Voronoi regions. The start and goal states are indicated in blue and green, respectively, and obstacles are shown in black.
• Figure 2: Representative environments for 30% and 50% obstacle density classes with overlaid CP-RRT* trees.
• Figure 3: Comparison of CP-RRT* against baselines in different obstacle density scenarios in terms of raw execution times (top) and the percentage of improvement in execution time against RRT* for each set of dynamics (bottom). The first, second, and third column correspond to the holonomic robot, Dubins car, and 5-D car, respectively.
• Figure 4: Example of a maze environment along with a tree constructed by CP-RRT*.
• Figure 5: Evaluation of CP-RRT* across different values of $p_{\text{bias}}$ and $\alpha$ in terms of execution time for the 30% obstacle-density case. The star marker denotes the parameter setting used in Section \ref{['sec:exp-time']}/Fig. \ref{['fig:cs1-time']}.

Theorems & Definitions (3)

• Proposition III.1: Set Decomposition
• proof
• Remark III.2: Calibration Dataset & NCS