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

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.

Quantifying Aleatoric and Epistemic Dynamics Uncertainty via Local Conformal Calibration

Whether learned, simulated, or analytical, approximations of a robot's dynamics can be inaccurate when encountering novel environments. Many approaches have been proposed to quantify the aleatoric uncertainty of such methods, i.e. uncertainty resulting from stochasticity, however these estimates alone are not enough to properly estimate the uncertainty of a model in a novel environment, where the actual dynamics can change. Such changes can induce epistemic uncertainty, i.e. uncertainty due to a lack of information/data. Accounting for both epistemic and aleatoric dynamics uncertainty in a theoretically-grounded way remains an open problem. We introduce Local Uncertainty Conformal Calibration (LUCCa), a conformal prediction-based approach that calibrates the aleatoric uncertainty estimates provided by dynamics models to generate probabilistically-valid prediction regions of the system's state. We account for both epistemic and aleatoric uncertainty non-asymptotically, without strong assumptions about the form of the true dynamics or how it changes. The calibration is performed locally in the state-action space, leading to uncertainty estimates that are useful for planning. We validate our method by constructing probabilistically-safe plans for a double-integrator under significant changes in dynamics.