  Formation coordination is a critical aspect of swarm robotics, which involves
coordinating the motion and behavior of a group of robots to achieve a specific
objective. In formation coordination, the robots must maintain a specific
spatial arrangement while in motion. In this paper, we present a
leader-follower column formation coordination problem in an unknown,
two-dimensional nonlinear manifold, where we redefining it as a trajectory
estimation problem. Leveraging Koopman operator theory and Extended Dynamic
Mode Decomposition, we estimate the measurement vectors for the follower agent
and guide its nonlinear trajectories.
