Particle-Based Conformal Prediction for Contact-Aware Uncertainty Calibration in Stratified Configuration Spaces
Authors: Luís Marques, Kristian Popov, Dmitry Berenson
Organizations: Department of Robotics, University of Michigan, Ann Arbor, MI, 48109, USA · Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109, USA
Reliable uncertainty representation is essential for deploying autonomous systems that interact with their environment, as robots must reason about how uncertainty arising from both stochasticity and model mismatch is impacted by contacts with obstacles (e.g., when navigating through a cluttered environment or inserting a part into an assembly). We propose Calibrated Particle-sets for Trans-dimensional Uncertainty Representation (CaPTURe), a geometry-aware, conformal prediction-based algorithm that generates probabilistically valid prediction regions of the unknown future system configuration using particle-based models of arbitrary fidelity. While calibrated uncertainty predictions are essential for safe and efficient planning, analytical or learned motion models are often inaccurate - due to limited data, simplifying assumptions, unmodeled effects, etc. - which can lead to unsafe executions or task failure. Additionally, when a robot contacts an obstacle, the distribution of its future configurations can become multimodal or disjoint, or lie along manifolds of lower intrinsic dimension than the space of possible robot configurations. Our method uses a calibration dataset of system transitions to locally calibrate motion uncertainty estimates, constructing regions guaranteed to contain the future robot configuration at a user-set probability. Our calibration procedure captures how motion uncertainty varies between contact-rich and contactless motions, leading to sufficient coverage in both cases. We evaluate our method on two simulated planning tasks: controlling a marble around a labyrinth and performing tight-tolerance peg-in-hole insertion with a manipulator. Compared to relevant baselines, CaPTURe achieves the user-specified coverage requirement both in and out of contact and achieves up to a 30% absolute improvement in task success rate over the best baseline.
We introduce Observation-aware Conformal Uncertainty Local-Calibration (OCULAR), a conformal prediction-based algorithm that uses perception information to provide uncertainty quantification guarantees for unseen test-time environments. While previous conformal approaches lack the ability to discriminate between state-action space regions leading to higher or lower model mismatch, and require environment-specific data, our method uses data collected from visually similar environments to provably calibrate a linear Gaussian dynamics model of arbitrary fidelity. The prediction regions generated from OCULAR are guaranteed to contain the future system states with, at least, a user-set likelihood, despite both aleatoric and epistemic uncertainty -- i.e., uncertainty arising from both stochastic disturbances and lack of data. Our guarantees are non-asymptotic and distribution-free, not requiring strong assumptions about the unknown real system dynamics. Our calibration procedure enables distinguishing between observation-velocity-action inputs leading to higher and lower next-state-uncertainty, which is helpful for probabilistically-safe planning. We numerically validate our algorithm on a double-integrator system subject to random perturbations and significant model mismatch, using both a simplified sensor and a more realistic simulated camera. Our approach calibrates approximate uncertainty estimates both when in-distribution and out-of-distribution, producing volume-efficient prediction regions without requiring environment-specific data.
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.
Safe human-robot collaboration (HRC) requires accurate human pose estimation and motion prediction to prevent critical collisions. Existing certifiable safe HRC approaches are highly conservative or rely on marker-based motion tracking, while vision-based pose estimators lack the statistical guarantees required for certification in accordance with ISO 13849-1. Hence, we propose a pipeline that predicts 3D human motion and strong probabilistic bounds on the prediction error using conformal prediction. A gradient-based monitor detects out-of-distribution input poses and replaces them with poses from past predicted motions to maintain smooth operation. The resulting conformal prediction sets directly integrate into the provably safe HRC approach SARA shield. In experiments on the Human3.6M dataset and a real-world HRC setting, our conformal prediction sets have a 7.6 times smaller volume than model-based predictions, and we bound the probability of a dangerous failure per hour by 9.5E-7 with 99.999 % confidence under our test distribution, which is necessary but not sufficient for performance level d. All code and models are available at https://jakob-thumm.com/conformal_human_motion_prediction/.