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Safe Decentralized Multi-Agent Control using Black-Box Predictors, Conformal Decision Policies, and Control Barrier Functions

Sacha Huriot, Hussein Sibai

TL;DR

The paper tackles safe control in decentralized multi-agent systems with uncertain black-box trajectory predictors. It combines control barrier functions (CBFs) with conformal decision theory (CDT) to adapt safety constraints based on observed prediction errors, by introducing a conformal variable $\lambda$ as a slack in the CBF constraints. A formal long-term risk bound is established, ensuring the average loss between the constrained and ground-truth safety specifications remains bounded, with guarantees that can be tightened by adjusting $\lambda$. Experimental validation on the Stanford Drone Dataset demonstrates that the proposed conformal CBF framework reduces safety violations and collisions while maintaining task progress, across various hyperparameters. Overall, the approach provides a robust, theory-grounded mechanism to reconcile accuracy-limited predictions with safety requirements in real-time multi-agent navigation.

Abstract

We address the challenge of safe control in decentralized multi-agent robotic settings, where agents use uncertain black-box models to predict other agents' trajectories. We use the recently proposed conformal decision theory to adapt the restrictiveness of control barrier functions-based safety constraints based on observed prediction errors. We use these constraints to synthesize controllers that balance between the objectives of safety and task accomplishment, despite the prediction errors. We provide an upper bound on the average over time of the value of a monotonic function of the difference between the safety constraint based on the predicted trajectories and the constraint based on the ground truth ones. We validate our theory through experimental results showing the performance of our controllers when navigating a robot in the multi-agent scenes in the Stanford Drone Dataset.

Safe Decentralized Multi-Agent Control using Black-Box Predictors, Conformal Decision Policies, and Control Barrier Functions

TL;DR

The paper tackles safe control in decentralized multi-agent systems with uncertain black-box trajectory predictors. It combines control barrier functions (CBFs) with conformal decision theory (CDT) to adapt safety constraints based on observed prediction errors, by introducing a conformal variable as a slack in the CBF constraints. A formal long-term risk bound is established, ensuring the average loss between the constrained and ground-truth safety specifications remains bounded, with guarantees that can be tightened by adjusting . Experimental validation on the Stanford Drone Dataset demonstrates that the proposed conformal CBF framework reduces safety violations and collisions while maintaining task progress, across various hyperparameters. Overall, the approach provides a robust, theory-grounded mechanism to reconcile accuracy-limited predictions with safety requirements in real-time multi-agent navigation.

Abstract

We address the challenge of safe control in decentralized multi-agent robotic settings, where agents use uncertain black-box models to predict other agents' trajectories. We use the recently proposed conformal decision theory to adapt the restrictiveness of control barrier functions-based safety constraints based on observed prediction errors. We use these constraints to synthesize controllers that balance between the objectives of safety and task accomplishment, despite the prediction errors. We provide an upper bound on the average over time of the value of a monotonic function of the difference between the safety constraint based on the predicted trajectories and the constraint based on the ground truth ones. We validate our theory through experimental results showing the performance of our controllers when navigating a robot in the multi-agent scenes in the Stanford Drone Dataset.
Paper Structure (15 sections, 3 theorems, 11 equations, 1 figure, 2 tables, 1 algorithm)

This paper contains 15 sections, 3 theorems, 11 equations, 1 figure, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Quadratic programming for CBF-based safe control
  5. Conformal decision theory
  6. Problem setup
  7. Pairwise collision avoidance
  8. Sensors and black-box trajectory predictors
  9. Algorithm
  10. CBF-based conformal controller
  11. Conformal CBF-based safe multi-agent control
  12. Feasibility
  13. Conformal CBF guarantees
  14. Experimental Results
  15. Conclusion

Key Result

Theorem 1

(Long-term risk bound lekeufack2024conformal) Fix a user-defined $\epsilon\in [0,1]$, a learning rate$\eta \in {\mathbb{R}}^{>0}$, an eventually safe conformal controller, and consider the following update rule for the conformal control variable: $\forall k\in{\mathbb{N}}^{>0},\ \lambda_{k+1}=\lamb Hence, it results in an $\epsilon+o(1)$ average loss in the long term, where $o(1)$ converges to ze

Figures (1)

  • Figure 1: The reference controller and QP solver run in a feedback loop instantaneously (plain arrows), while the trajectory predictor and conformal update run periodically (dashed arrows). For $t\in I_k=[k\tau,(k+1)\tau)$, the control $u_i(t)$ is the minimal deviation $u$ from $u_{ref}(x_i(t),t)$ that satisfies the conformal safety constraints $\left\{\hat{C}_j(x_i,\xi_j(t),u,\hat{\dot{\xi}}_j(t),\lambda_k)\right\}_j$, where the predicted trajectories $\{\hat{\xi}_j\}_{j\in[N_{k}]}$ and the conformal parameter $\lambda_k$ were obtained at $k\tau$. To update the latter, we use the maximal prediction error between the ground truth trajectories $\{\xi_j\}_{j\in[N_{k-1}]}$ obtained from the sensor over $I_{k-1}$ and the predicted trajectories at $(k-1)\tau$.

Theorems & Definitions (9)

  • Definition 1
  • Definition 2
  • Definition 3
  • Theorem 1
  • Remark 1
  • Theorem 2
  • proof
  • Theorem 3
  • proof