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.

翻译：编队协调是群机器人学中的关键问题，涉及协调一组机器人的运动与行为以实现特定目标。在编队协调过程中，机器人需要在运动时保持特定的空间排列。本文提出了一种在未知二维非线性流形上的领航-跟随纵队编队协调问题，并将其重构为轨迹估计问题。通过利用Koopman算子理论和扩展动态模态分解，我们估算了跟随智能体的测量向量，并引导其非线性轨迹。