Task-Aware Conformal State Estimation for Reliable Robotic Planning

Pretrained perception models are increasingly used to estimate symbolic world states for robotic planning and execution in open-world environments. While these models enable powerful decision-making capabilities, they provide limited reliability guarantees and can lead to brittle behavior when perception errors occur. We address this challenge by introducing $\alpha$-error Conformal Minimal Belief Set (CMBS$\alpha$ ), a conformal prediction framework for state estimation that provides formal coverage guarantees while maintaining compact belief representations for a user-specified acceptable error rate $\alpha$. We present a general calibration procedure applicable to any off-the-shelf state estimator together with an efficient algorithm for constructing minimal-cardinality belief sets. We further introduce Anytime Confidence-maximizing Plan Search (ACPS), a planning framework that leverages CMBS$\alpha$ to generate plans with certified success guarantees under perceptual uncertainty. Our theoretical analysis establishes robustness guarantees for downstream planning and characterizes the anytime behavior of our approach. Experiments in simulated and real robotic manipulation domains demonstrate how our approach achieves the desired guarantees while producing significantly smaller belief sets, enabling robust and efficient task planning.