Formation Graph Embedding with Consideration of Infeasility

Abstract

This paper studies formation control of single-integrator nodes. Inspired by knowledge graph embedding, we formulate displacement-based formation control within a unified formation graph embedding (FGE) framework and show that existing control laws can be derived using distributed optimization techniques. We define the feasibility of FGEs based on whether the desired formation constraints are realizable and analyze the system's behavior when displacement-based FGE is infeasible. Our theoretical results identify conditions for specific motion patterns under infeasibility, which are validated through numerical simulations. This study provides a unified perspective on formation control and enhances understanding of multi-agent coordination under infeasibility. © 2025 The Authors. This is an open access article under the CC BY-NC-ND license.