# Distributed Assignment with Limited Communication for Multi-Robot Multi-Target Tracking

## TL;DR

This paper develops distributed algorithms for multi-robot multi-target tracking under limited communication, providing approximation guarantees and empirical comparisons to optimal solutions.

## Contribution

It introduces two novel distributed algorithms with provable approximation bounds and adjustable trade-offs between solution quality and communication rounds.

## Key findings

- The greedy algorithm guarantees a 2-approximation with worst-case linear communication rounds.
- The local algorithm achieves adjustable approximation with logarithmic communication rounds.
- Empirical results show competitive performance compared to centralized optimal solutions.

## Abstract

We study the problem of tracking multiple moving targets using a team of mobile robots. Each robot has a set of motion primitives to choose from in order to collectively maximize the number of targets tracked or the total quality of tracking. Our focus is on scenarios where communication is limited and the robots have limited time to share information with their neighbors. As a result, we seek distributed algorithms that can find solutions in bounded amount of time. We present two algorithms: (1) a greedy algorithm that is guaranteed finds a $2$-approximation to the optimal (centralized) solution albeit requiring $|R|$ communication rounds in the worst-case, where $|R|$ denotes the number of robots; and (2) a local algorithm that finds a $\mathcal{O}\left((1+\epsilon)(1+1/h)\right)$-approximation algorithm in $\mathcal{O}(h\log 1/\epsilon)$ communication rounds. Here, $h$ and $\epsilon$ are parameters that allow the user to trade-off the solution quality with communication time. In addition to theoretical results, we present empirical evaluation including comparisons with centralized optimal solutions.