Geometry-Aware Edge-State Tracking for Resilient Affine Formation Control

Affine formation control (AFC) is a subset of formation control methods that enables coordinated multiagent movement while preserving affine relationships, and has recently gained increasing popularity due to its broad applicability across diverse applications. AFC is inherently distributed, where each agent's local controller relies on the relative displacements of neighboring agents. The unavailability of these measurements in practice, due to node or communication failures, leads to a change in the underlying graph topology and subsequently causes instability or sub-optimal performance. In this work, each edge in the graph is modeled using a state-space framework, allowing the corresponding edge-states to be estimated with or without up-to-date measurements. We then propose a Kalman-based estimation framework where we fuse both temporal information from agents' dynamics and spatial information, which is derived from the geometry of the affine formations. We give convergence guarantees and optimality analysis on the proposed algorithm, and numerical validations show the enhanced resilience of AFC against these topology changes in several practical scenarios.