Staying on Spec: Real-Time Monitoring under Uncertainty with a Maritime Case Study

Robots operating in physical environments make control decisions based on uncertain sensor measurements, which can lead to unsafe or suboptimal actions. Runtime monitors that check their behavior against safety specifications must represent this uncertainty soundly. Zonotopes are a widely used representation, but continuously incorporating new measurements grows their order unboundedly, so monitors must periodically apply an over-approximating reduction. The choice of the reduction method substantially affects the zonotope's precision, yet existing approaches typically utilize a fixed method throughout the run, even though the optimal choice depends on the current state. This paper presents a Predictive Zonotope Reduction (PZR) approach, which frames reducer selection as an optimal control problem and solves it using beam-search model predictive control. Policy distillation into a small neural policy further provides substantially higher execution speed than model predictive control while maintaining improved performance, enabling uncertainty-aware runtime monitoring on resource-constrained real-time systems. We implement our approach in the RLola runtime monitoring framework and evaluate it on a 5-degree-of-freedom robotic arm simulated in MuJoCo, with sensor uncertainty modeled according to ISO 5725. Experiments on a Raspberry Pi 5 show that dynamic reduction significantly lowers false-positive rates in monitoring compared with static reduction strategies.

Safe navigation in dynamic and uncertain environments often relies on accurate estimation of, or assumptions about, the true underlying uncertainty. However, accurately characterizing the true uncertainty distribution is often difficult due to limited data or imperfect information. An incorrect understanding of the uncertainty and its associated risk may lead to dangerous decisions even under high levels of risk aversion. To address this issue, we propose a risk-aware model predictive control (RA-MPC) framework that incorporates prediction sets to guarantee risk control below a user-specified threshold without requiring assumptions about the underlying uncertainty distribution. To generate the prediction sets, we develop a distribution-free risk quantification framework that extends conformal risk control (CRC) to general spectral risk measures. We then show that incorporating the prediction sets into the MPC framework provides statistical safety guarantees in terms of spectral risk constraint satisfaction even under uncertainty misspecification. We validate the proposed framework in simulated vehicle obstacle avoidance scenarios, demonstrating improved safety and reduced solve time compared to a baseline RA-MPC framework.

This paper presents an observation-only autonomy framework for Unmanned Underwater Vehicles (UUVs) navigation in dynamic underwater environments that integrates persistent occupancy mapping, global clearance-aware planning, and risk-aware local control. The proposed pipeline constructs occupancy maps solely from onboard sonar and depth image observations, adapts a clearance-constrained global planner (GP) to provide long-horizon structure, and integrates a reinforcement learning (RL) policy to handle short-range tracking and reactive avoidance. To further support decision-making under partial observability, the system learns a compact latent state representation from onboard sensor data, encoding environmental structure, obstacle dynamics, and uncertainty. Behavior tree (BT) distillation with staged supervision is introduced to improve safety and training stability, while an uncertainty-calibrated distillation mechanism reweights teacher guidance using online latent-model uncertainty, emphasizing uncertain regimes during learning, with time-to-collision (TTC) and clearance cues remaining explicit in planning and local policy features. To demonstrate the efficacy of the framework, a reproducible multi-seed evaluation protocol is established in high-fidelity GPU-accelerated simulation using NVIDIA Isaac Sim, and performance is benchmarked against BT-only and standard RL baselines. The results obtained demonstrate improved robustness and safety under dynamic conditions, thus providing a general pipeline with a unified hybrid planning learning architecture and a reproducible methodology for robust UUV autonomy under partial observability.