From Prediction Uncertainty to Conformalized Distance Fields for Safe Motion Planning

2026-07-01

AI Summary

This work addresses the challenge of achieving safe and real-time motion planning in dynamic environments by effectively handling uncertainty in obstacle predictions. Existing approaches are limited in spatial consistency and computational scalability. To overcome these limitations, the paper introduces a Functional Conformal Prediction (FCP) framework—the first to apply conformal prediction to full distance fields rather than scalar errors. By modeling residual fields with low-rank and time-invariant structures, FCP generates distribution-free, decomposable, field-level safety lower bounds in coefficient space. The method integrates functional principal component analysis, Gaussian mixture-induced conformal prediction, and a lightweight online adaptive update (AFCP) into a sampling-based MPC formulation (FCP-MPC). Experiments on the ETH–UCY pedestrian datasets and a 3D quadrotor task with 280 dynamic obstacles demonstrate significant improvements in safety, trajectory feasibility, and computational efficiency, with per-step overhead substantially lower than existing online uncertainty-aware planners.

Abstract

Safe motion planning in dynamic environments requires reasoning about the uncertainty in predicted obstacle motion without sacrificing real-time performance. Existing conformal approaches conformalize a scalar score that aggregates per-obstacle prediction errors, losing spatial coherence and scaling poorly with scene density. We instead conformalize the entire predicted distance field at once. This functional conformal prediction (FCP) framework yields a distribution-free, field-level lower bound, from which safety follows uniformly: any trajectory satisfying the resulting constraint is certified safe, independent of how the control space is sampled. The key enabler is that the residual distance field is empirically low-rank and approximately time-invariant, which makes the bound decomposable in coefficient space. An envelope is fitted offline via functional PCA and a Gaussian-mixture inductive conformal procedure, then refined online by a lightweight adaptive functional conformal (AFCP) update on a low-dimensional vector. This keeps the per-step cost largely insensitive to obstacle count and retains long-run field coverage under distribution shift. We embed the envelope as a tightened safety constraint in a sampling-based model predictive controller, FCP-MPC. On the ETH--UCY pedestrian benchmarks and a dense 3D quadrotor task with up to 280 dynamic obstacles, FCP-MPC attains a favorable balance of safety, feasibility, and efficiency, reaching goals where pointwise and egocentric conformal baselines become too conservative or too expensive, while keeping per-step computation far below online uncertainty-reasoning baselines.

Problem

• safe motion planning
• prediction uncertainty
• dynamic environments
• conformal prediction
• distance fields

Innovation

• Functional Conformal Prediction
• Distance Fields
• Safe Motion Planning
• Low-rank Structure
• Adaptive Conformal Prediction