Formation control of multi-agent systems has been a prominent research topic, spanning both theoretical and practical domains over the past two decades. Our study delves into the leader-follower framework, addressing two critical, previously overlooked aspects. Firstly, we investigate the impact of an unknown nonlinear manifold, introducing added complexity to the formation control challenge. Secondly, we address the practical constraint of limited follower sensing range, posing difficulties in accurately localizing the leader for followers. Our core objective revolves around employing Koopman operator theory and Extended Dynamic Mode Decomposition to craft a reliable prediction algorithm for the follower robot to anticipate the leader's position effectively. Our experimentation on an elliptical paraboloid manifold, utilizing two omni-directional wheeled robots, validates the prediction algorithm's effectiveness.

翻译：多智能体系统编队控制已成为过去二十余年理论与应用领域的重要研究课题。本研究聚焦领导者-跟随者框架，着力解决两个此前被忽视的关键问题：首先，我们探究未知非线性流形对编队控制问题带来的额外复杂性；其次，针对跟随者传感范围有限这一实际约束，解决跟随者难以精确定位领导者位置的难题。核心目标在于运用库普曼算子理论与扩展动态模态分解方法，为跟随机器人构建可靠的位置预测算法，使其能够有效预判领导者的轨迹。通过在椭球抛物面流形上使用两台全向轮式机器人开展实验，验证了该预测算法的有效性。