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Formation-Aware Adaptive Conformalized Perception for Safe Leader-Follower Multi-Robot Systems

Richie R. Suganda, Bin Hu

TL;DR

A distributed, formation-aware adaptive conformal prediction method based on Risk-Aware Mondrian CP to produce formation-conditioned uncertainty quantiles and integrates these bounds into a Formation-Aware Conformal CBF-QP with a smooth margin to enforce visibility while maintaining feasibility and tracking performance.

Abstract

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. The experimental videos are available on the \href{https://nail-uh.github.io/iros2026.github.io/}{project website}\footnote{Project Website: https://nail-uh.github.io/iros2026.github.io/}.

Formation-Aware Adaptive Conformalized Perception for Safe Leader-Follower Multi-Robot Systems

TL;DR

A distributed, formation-aware adaptive conformal prediction method based on Risk-Aware Mondrian CP to produce formation-conditioned uncertainty quantiles and integrates these bounds into a Formation-Aware Conformal CBF-QP with a smooth margin to enforce visibility while maintaining feasibility and tracking performance.

Abstract

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. The experimental videos are available on the \href{https://nail-uh.github.io/iros2026.github.io/}{project website}\footnote{Project Website: https://nail-uh.github.io/iros2026.github.io/}.
Paper Structure (13 sections, 1 theorem, 20 equations, 8 figures, 1 algorithm)

This paper contains 13 sections, 1 theorem, 20 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Control Barrier Functions
  4. Split Conformal Prediction
  5. System Framework & Problem Formulation
  6. Methodology
  7. Onboard Perception
  8. Risk-Aware Mondrian Conformal Prediction
  9. Conformal Formation-Aware CBFs
  10. Simulation Results
  11. Success rate
  12. Tracking Performance and Bound Size
  13. Conclusion

Key Result

Theorem 1

Consider the leader--follower dynamics eq:generic_dynamics and the safe set $\mathcal{C}_i \triangleq \{x_i\in\mathbb{R}^n \mid h_\ell(x_i)\ge 0,\ \forall \ell\}$. Assume Assumption ass:exchangeable holds, and each $h_\ell$ is locally Lipschitz. Let $\mathcal{V}_i \subseteq \{1,\dots,R\}$ denote the Since $\sum_{r\in\mathcal{V}_i}\delta_r\le \sum_{r=1}^R\delta_r$, we also have the unconditional bo

Figures (8)

  • Figure 1: Formation-Aware Adaptive Conformalized Leader–Follower System. Under heteroscedastic, formation-dependent perception errors, the proposed risk-aware conformal bounds tighten in low-risk configurations to preserve tracking performance and expand near FOV limits to enforce probabilistic safety.
  • Figure 2: Risk-Aware Adaptive Conformal Control for Safe Leader–Follower Formation Architecture. Onboard sensing feeds a risk-aware Mondrian conformal predictor that produces state-dependent uncertainty bounds, which parameterize the formation-aware conformal CBF-QP safety filter to enable safe tracking under perception uncertainty.
  • Figure 3: Empirical nonconformity-score distributions across formation-dependent risk regions. The scores are strongly heteroscedastic: the high-risk near-boundary set $B_1$ exhibits substantially larger variance and heavier tails than the low-risk interior set $B_3$. This pronounced risk-dependent error structure motivates a formation-aware (risk-aware) conformal calibration that assigns region-specific quantiles, rather than a single global bound.
  • Figure 4: Risk-aware Mondrian conformal quantiles projected over the camera FOV: uncertainty increases near the safety boundaries (red) and decreases toward the interior (green).
  • Figure 5: Linear interpolation of the risk-aware conformal quantiles across Mondrian risk partitions, yielding a continuous margin $\tilde{q}_i(h)$ as in \ref{['eq:smooth_margin']}.
  • ...and 3 more figures

Theorems & Definitions (7)

  • Definition 1: Control Barrier Function (CBF) ames2019control
  • Example 1: Vision-based leader--follower kinematics
  • Example 2: camera FOV constraints
  • Example 3: Vision-based leader-follower estimation
  • Theorem 1: Risk-Aware Probabilistic Forward Invariance
  • proof
  • Remark 1: Miscoverage vs. Safety