Allocating Corrective Control to Mitigate Multi-agent Safety Violations Under Private Preferences

TL;DR

This paper introduces a privacy-preserving framework that allocates corrective control efforts to maintain safety in multi-agent systems using high-order control barrier functions and auction-based resource distribution, validated through multi-robot experiments.

Contribution

It presents a novel, privacy-preserving method combining control barrier functions with an auction mechanism for optimal safety correction in multi-agent systems.

Findings

Efficiently distributes corrective efforts without revealing private preferences.

Ensures formal safety guarantees in complex dynamical systems.

Validated through multi-robot hardware experiments.

Abstract

We propose a novel framework that computes the corrective control efforts to ensure joint safety in multi-agent dynamical systems. This framework efficiently distributes the required corrective effort without revealing individual agents' private preferences. Our framework integrates high-order control barrier functions (HOCBFs), which enforce safety constraints with formal guarantees of safety for complex dynamical systems, with a privacy-preserving resource allocation mechanism based on the progressive second price (PSP) auction. When a joint safety constraint is violated, agents iteratively bid on new corrective efforts via 'avoidance credits' rather than explicitly solving for feasible corrective efforts that remove the safety violation. The resulting correction, determined via a second price payment rule, coincides with the socially optimal safe distribution of corrective actions. Critically, the bidding process achieves this optimal allocation efficiently and without revealing private preferences of individual agents. We demonstrate this method through multi-robot hardware experiments on the Robotarium platform.