This paper considers the perception safety problem in distributed vision-based leader-follower formations, where each robot uses onboard perception to estimate relative states, track desired setpoints, and keep the leader within its camera field of view (FOV). Safety is challenging due to heteroscedastic perception errors and the coupling between formation maneuvers and visibility constraints.
We propose a distributed, formation-aware adaptive conformal prediction method based on Risk-Aware Mondrian CP to produce formation-conditioned uncertainty quantiles. The resulting bounds tighten in high-risk configurations (near FOV limits) and relax in safer regions. We integrate these bounds into a Formation-Aware Conformal CBF-QP with a smooth margin to enforce visibility while maintaining feasibility and tracking performance.
Gazebo simulations show improved formation success rates and tracking accuracy over non-adaptive (global) CP baselines that ignore formation-dependent visibility risk, while preserving finite-sample probabilistic safety guarantees.
Our framework integrates perception uncertainty directly into the safety layer of a leader-follower system. Because perception errors are highly heteroscedastic (increasing near FOV boundaries), relying on a single global uncertainty bound is overly conservative. We solve this by leveraging a Risk-Aware Mondrian Conformal Predictor to generate state-dependent uncertainty bounds, which are then used to parameterize a Formation-Aware Conformal CBF-QP.
Standard Conformal Prediction (CP) assumes exchangeability over the entire state space, yielding a global error bound that restricts mobility in safe regions and may under-approximate risk near boundaries. We use a Mondrian taxonomy to partition the state space into distinct risk groups based on proximity to the FOV limits. This allows us to compute formation-conditioned uncertainty quantiles that accurately reflect the heavier error tails present in high-risk zones.
Directly switching between uncertainty bounds across different risk regions introduces discontinuities in the Control Barrier Function constraints. To maintain smooth control inputs while preserving statistical coverage guarantees, we introduce a continuous margin transition that interpolates between adjacent quantiles. This tightened, Lipschitz-continuous barrier ensures strict FOV constraint satisfaction while maximizing optimization feasibility.
This summary video demonstrates the proposed Formation-Aware Adaptive Conformalized Perception framework in a Gazebo simulation. As the leader-follower multi-robot system maneuvers, the Risk-Aware Mondrian CP dynamically adjusts the perception uncertainty bounds. The Conformal CBF-QP safely intervenes when the leader approaches the edge of the follower's Field of View (FOV), successfully maintaining visibility without being overly conservative.
The time-series plots illustrate the dynamic behavior of our proposed Risk-Aware Bound over the course of the simulation. As the robot transitions between safe and risky configurations, the Mondrian CP algorithm dynamically tightens the perception uncertainty margins. This targeted conservatism ensures that the Control Barrier Function cleanly enforces visibility constraints near the FOV boundaries, while permitting smooth control inputs and low tracking errors in nominal regions.
The summary metrics aggregate the performance across the different bounding strategies to highlight the trade-offs between safety and tracking efficiency. Our Risk-Aware Adaptive CP eliminates out-of-view failures (which plague the Low Risk and Nominal baselines) without incurring the excessive tracking error and controller feasibility issues associated with the strictly conservative High Risk Bound.
@inproceedings{anonymous2024formation,
author = {Anonymous Authors},
title = {Formation-Aware Adaptive Conformalized Perception for Safe Leader-Follower Multi-Robot Systems},
booktitle = {Under Double-Blind Review},
year = {2024},
}