Deployment of Heterogeneous Multi-Agent Systems via a PDE Approach

Spatial deployment of large-scale heterogeneous multi-agent systems (HMASs) over desired 2D or 3D curves is investigated in this paper. With assumption that HMASs consist of numerous first-order agents (FOAs) and second-order agents (SOAs) that could obtain local information of desired curves and their positions relative to their closest neighbors, the collective dynamics of large-scale HMASs are modeled as heterogeneous partial differential equations (PDEs). In particular, this paper introduces series-dependent topological weights between neighboring agents, which are more versatile and practical than constant topological weights commonly used in previous studies. A novel single-point control scheme is proposed, where an informed agent is situated between the last FOA and first SOA. This operation could not only ensure successful implementation of spatial deployment, but also guarantee well-posedness of the constructed heterogeneous error PDEs. By utilizing inequality techniques, sufficient conditions for exponential convergence of error system are derived. A numerical example is presented to demonstrate effectiveness of the proposed approaches.