{"ID":5551745,"CreatedAt":"2026-07-02T01:54:51.863792489Z","UpdatedAt":"2026-07-04T10:42:23.705510313Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.00776","arxiv_id":"2607.00776","title":"From Prediction Uncertainty to Conformalized Distance Fields for Safe Motion Planning","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.","short_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 d...","url_abs":"https://arxiv.org/abs/2607.00776","url_pdf":"https://arxiv.org/pdf/2607.00776v1","authors":"[\"Jaeuk Shin\",\"Yoonseok Ra\",\"Insoon Yang\"]","published":"2026-07-01T11:02:51Z","proceeding":"cs.RO","tasks":"[\"cs.RO\",\"eess.SY\"]","methods":"[]","has_code":false}