Heterogeneous Multi-Agent Multi-Target Tracking using Cellular Sheaves

TL;DR

This paper introduces a novel cellular sheaves framework for multi-agent multi-target tracking, effectively handling heterogeneity and nonlinear dynamics, with proven stability and validated simulation results.

Contribution

It extends cellular sheaves to non-cooperative tracking problems, enabling decentralized control for heterogeneous agents with nonlinear dynamics.

Findings

Effective modeling of heterogeneous agents using cellular sheaves

Decentralized control law guarantees tracking error convergence

Simulation validates stability and tracking performance

Abstract

Multi-agent target tracking in the presence of nonlinear dynamics and agent heterogeneity, where state-space dimensions may differ, is a challenging problem that traditional graph Laplacian methods cannot easily address. This work leverages the framework of cellular sheaves, a mathematical generalization of graph theory, to natively model such heterogeneous systems. While existing coordination sheaf frameworks focus on cooperative problems like consensus, this work extends them to the non-cooperative target-tracking problem. The tracking of multiple, unknown targets is formulated as a harmonic extension problem on a cellular sheaf, accommodating nonlinear dynamics and external disturbances for all agents. A decentralized control law is developed using the sheaf Laplacian, and a corresponding Lyapunov-based stability analysis is provided to guarantee tracking error convergence, with results validated by simulation.