# Safe Policy Synthesis in Multi-Agent POMDPs via Discrete-Time Barrier Functions

## TL;DR

This paper introduces a novel barrier function-based approach for ensuring safety in multi-agent POMDPs without discretizing belief space, enabling online safe policy synthesis for heterogeneous autonomous agents.

## Contribution

It develops a new method using discrete-time barrier functions for safety in MPOMDPs, avoiding belief space discretization and enabling online implementation.

## Key findings

- Method guarantees safety in MPOMDPs.
- Applicable to heterogeneous robot simulations.
- Supports Boolean composition of safe sets.

## Abstract

A multi-agent partially observable Markov decision process (MPOMDP) is a modeling paradigm used for high-level planning of heterogeneous autonomous agents subject to uncertainty and partial observation. Despite their modeling efficiency, MPOMDPs have not received significant attention in safety-critical settings. In this paper, we use barrier functions to design policies for MPOMDPs that ensure safety. Notably, our method does not rely on discretization of the belief space, or finite memory. To this end, we formulate sufficient and necessary conditions for the safety of a given set based on discrete-time barrier functions (DTBFs) and we demonstrate that our formulation also allows for Boolean compositions of DTBFs for representing more complicated safe sets. We show that the proposed method can be implemented online by a sequence of one-step greedy algorithms as a standalone safe controller or as a safety-filter given a nominal planning policy. We illustrate the efficiency of the proposed methodology based on DTBFs using a high-fidelity simulation of heterogeneous robots.