Trajectory Estimation in Unknown Nonlinear Manifold Using Koopman Operator Theory

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.