Lies We Can Trust: Quantifying Action Uncertainty with Inaccurate Stochastic Dynamics through Conformalized Nonholonomic Lie Groups

2025-12-11

AI Summary

Quantifying motion uncertainty for nonholonomic robots under inaccurate stochastic dynamic modeling remains challenging due to strong assumptions on uncertainty sources, error distributions, and model fidelity. Method: This paper proposes a distribution-free, non-asymptotic prediction set construction method that requires no ground-truth dynamics prior and is insensitive to approximate model quality. It uniquely integrates the conformal prediction framework with the SE(2) Lie group geometry, designing a symmetry-aware, non-exchangeable scoring function to rigorously guarantee that the robot’s configuration lands within the prediction set with a user-specified confidence level. Contribution/Results: By respecting the intrinsic geometric structure of planar rigid-body motions, the method avoids restrictive assumptions on uncertainty characterization. Evaluations on JetBot simulation and MBot physical platforms demonstrate that, compared to Euclidean-space conformal methods, the proposed approach achieves significantly smaller prediction set volumes, tighter coverage, improved uncertainty representation accuracy, and enhanced safety in closed-loop control.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Planning, Routing, and Scheduling: Planning under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We propose Conformal Lie-group Action Prediction Sets (CLAPS), a symmetry-aware conformal prediction-based algorithm that constructs, for a given action, a set guaranteed to contain the resulting system configuration at a user-defined probability. Our assurance holds under both aleatoric and epistemic uncertainty, non-asymptotically, and does not require strong assumptions about the true system dynamics, the uncertainty sources, or the quality of the approximate dynamics model. Typically, uncertainty quantification is tackled by making strong assumptions about the error distribution or magnitude, or by relying on uncalibrated uncertainty estimates - i.e., with no link to frequentist probabilities - which are insufficient for safe control. Recently, conformal prediction has emerged as a statistical framework capable of providing distribution-free probabilistic guarantees on test-time prediction accuracy. While current conformal methods treat robots as Euclidean points, many systems have non-Euclidean configurations, e.g., some mobile robots have SE(2). In this work, we rigorously analyze configuration errors using Lie groups, extending previous Euclidean Space theoretical guarantees to SE(2). Our experiments on a simulated JetBot, and on a real MBot, suggest that by considering the configuration space's structure, our symmetry-informed nonconformity score leads to more volume-efficient prediction regions which represent the underlying uncertainty better than existing approaches.

Problem

• Quantify action uncertainty under inaccurate dynamics
• Provide distribution-free probabilistic guarantees for predictions
• Extend conformal prediction to non-Euclidean robot configurations

Innovation

• Conformal prediction for non-Euclidean robot configurations
• Lie groups extend guarantees to SE(2) without strong assumptions
• Symmetry-aware algorithm ensures probabilistic safety in uncertain dynamics