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.

翻译：我们提出保形李群作用预测集（CLAPS），这是一种基于对称感知的保形预测算法，可为给定作用构建一个集合，保证在用户定义的概率下包含最终的系统配置。我们的保证在随机不确定性和认知不确定性下均成立，无需渐近条件，且不依赖于对真实系统动力学、不确定性来源或近似动力学模型质量的强假设。通常，不确定性量化通过强假设误差分布或幅度，或依赖未校准的不确定性估计（即与频率概率无关联）来处理，这些方法对于安全控制而言并不充分。近年来，保形预测作为一种统计框架出现，能够为测试时预测精度提供无分布的概率保证。虽然当前的保形方法将机器人视为欧几里得点，但许多系统具有非欧几里得配置，例如某些移动机器人具有SE(2)。在本工作中，我们使用李群严格分析配置误差，将先前欧几里得空间的理论保证扩展到SE(2)。我们在模拟JetBot和真实MBot上的实验表明，通过考虑配置空间的结构，我们基于对称性的非一致性评分能够生成比现有方法更体积高效的预测区域，更好地表征了底层不确定性。