Distributed Simultaneous Centroid Estimation and Formation Tracking Control Using Relative Position Measurement

This letter presents a distributed framework for simultaneous rigid formation control and trajectory tracking in n dimensional space ( $n=2,3$ ), motivated by coordinated multi-agent transport, cooperative surveillance, and fractionated spacecraft applications, which demand flexible and scalable alternatives to traditional single-agent approaches. In scenarios where only one agent knows its own global position, and each agent measures only the relative positions of its neighbors, the proposed framework integrates a two-layer decentralized estimator with distributed centroid tracking, orientation alignment, and formation maintenance controllers. The first estimator layer employs a consensus-based self-estimation law, ensuring exponential convergence to actual value. The second estimator layer extends this capability, allowing agents to estimate the positions of their peers, and hence cooperatively compute the formation centroid and orientation. Tracking of predefined formation centroid and orientation trajectories is achieved via three distributed control laws: one for formation maintenance, one for centroid trajectory tracking, and one for aligning the formation orientation, using unit complex numbers in 2D and unit quaternions in 3D. Lyapunov-based analysis establishes exponential convergence for all estimation and control components. Simulations demonstrate the formation’s ability to maintain geometric integrity, track trajectories, and achieve desired orientations, all within a distributed framework.